WO2005008305A1 - フォトニック結晶導波路、均質媒体導波路、及び光学素子 - Google Patents
フォトニック結晶導波路、均質媒体導波路、及び光学素子 Download PDFInfo
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- WO2005008305A1 WO2005008305A1 PCT/JP2004/010232 JP2004010232W WO2005008305A1 WO 2005008305 A1 WO2005008305 A1 WO 2005008305A1 JP 2004010232 W JP2004010232 W JP 2004010232W WO 2005008305 A1 WO2005008305 A1 WO 2005008305A1
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- G—PHYSICS
- G02—OPTICS
- G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
- G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
- G02F1/29—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the position or the direction of light beams, i.e. deflection
- G02F1/31—Digital deflection, i.e. optical switching
- G02F1/313—Digital deflection, i.e. optical switching in an optical waveguide structure
- G02F1/3136—Digital deflection, i.e. optical switching in an optical waveguide structure of interferometric switch type
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B82—NANOTECHNOLOGY
- B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
- B82Y20/00—Nanooptics, e.g. quantum optics or photonic crystals
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
- G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
- G02B6/122—Basic optical elements, e.g. light-guiding paths
- G02B6/1225—Basic optical elements, e.g. light-guiding paths comprising photonic band-gap structures or photonic lattices
-
- G—PHYSICS
- G02—OPTICS
- G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
- G02F2202/00—Materials and properties
- G02F2202/32—Photonic crystals
Definitions
- Photonic crystal waveguide homogeneous medium waveguide, and optical element
- the present invention relates to a photonic crystal waveguide, and more particularly, to a photonic crystal waveguide using a waveguide-shaped one-dimensional photonic crystal that propagates an electromagnetic wave in a direction without periodicity.
- Optical devices in which a waveguide is arranged on a substrate have already been put into practical use, but recently, a defect waveguide using a two-dimensional photonic crystal (2D-PhC) has attracted attention, and research and development has been carried out. It is being actively conducted. That is, a two-dimensional photonic crystal is formed by arranging regular holes in a high-refractive-index thin film layer (such as Si), and a complete photonic band gap in the planar direction (XZ direction) is obtained in the operating frequency range.
- a linear defect is provided in this 2D_PhC, light entering the defect cannot be emitted to the photonic crystal portion and is confined, so that it can be used as a waveguide (see Patent Document 1).
- a waveguide using 2D_PhC has the following features.
- the waveguide can be bent sharply (60 °, 90 °, etc.), the individual optical elements themselves or the wiring connecting them can be very compact.
- a group velocity anomaly can be caused in the electromagnetic wave propagating in the waveguide, and the nonlinear effect can be increased to improve the characteristics of the element and reduce the size.
- optical elements using a waveguide formed by such a two-dimensional or three-dimensional photonic crystal or a normal waveguide not formed by a photonic crystal are examples of optical elements using a waveguide formed by such a two-dimensional or three-dimensional photonic crystal or a normal waveguide not formed by a photonic crystal.
- Patent Document 1 Japanese Patent Application Laid-Open No. 2001-281480
- Patent Document 2 Japanese Patent Application Laid-Open No. 2001-174652
- Patent Document 3 Japanese Patent Application Laid-Open No. 2002-303836
- Patent Document 4 JP 2001-272555 A
- Patent Document 5 JP 2003-161971 A
- Patent Document 6 JP-A-2002-236206
- Patent Document 7 Japanese Patent Application Laid-Open No. 2002-169022
- Patent Document 8 Japanese Patent Application Laid-Open No. 2002-182026
- Patent Document 9 Japanese Patent Application Laid-Open No. 2002-267845
- Patent Document 10 JP 2003-240934 A
- Patent Document 11 JP 2003-287633 A
- Non-Patent Document 1 "Optronitas", April 2002, p. 132
- Non-Patent Document 2 "Photonic Crystal Technology and Its Application", CMC Publishing, 2002, p. 244.
- the above conventional waveguide has the following problems.
- the structure of the photonic crystal that constitutes the waveguide is a square array, the angle of sharp bending is almost 90 °.
- the force is 60 ° and 120 °. Therefore, it is not possible to arrange the above-described various optical elements formed using the waveguide and the waveguide at an arbitrary angle, which is a limitation in design.
- An object of the present invention is to provide a photonic crystal waveguide, a homogeneous medium waveguide, and an optical element using the same, which can be rapidly bent or arranged at an arbitrary angle and have low propagation loss. There is to be.
- the present invention provides a photonic crystal waveguide including a core formed of a photonic crystal having periodicity in one direction and having a core in which electromagnetic waves propagate in a direction perpendicular to the one direction.
- the electromagnetic wave is propagated by a propagation mode of a photonic band on a boundary of a Brillouin zone in a photonic band structure of the core, and a side surface of the core parallel to the one direction has a uniform refractive index n. In contact with the media cladding, before s
- the wavelength of the electromagnetic wave in a vacuum is I
- the period of the photonic crystal is a
- the electromagnetic wave propagates in the core.
- An optical device that utilizes light propagated by higher-order bands of a photonic crystal (higher-order band propagation light) is very useful. Higher order band propagating light traveling in the photonic crystal in a direction perpendicular to the one direction can be obtained by using a photonic band on the boundary of the Brillouin zone.
- optical elements such as optical delay elements and dispersion control elements are used to reduce the incident light energy. It can be manufactured without reducing the usage efficiency and S / N ratio.
- a checkered electric field pattern is exposed on the side surface (parallel to the one direction) of the photonic crystal waveguide. Assuming that its side is in contact with a homogeneous medium with a refractive index n, its side s
- the side of the core can be confined.
- “direction perpendicular to one direction” refers to any direction parallel to a plane perpendicular to one direction. For example, if one direction is the Y direction, the “direction perpendicular to one direction” means any direction parallel to the XZ plane perpendicular to the Y direction (XZ plane direction).
- a surface of the core perpendicular to the one direction is made of a homogeneous material or a photonic crystal having periodicity in at least one direction, and an electromagnetic wave propagating in the core leaks out of the surface.
- a confinement cladding may be provided to prevent this. According to this configuration, the confinement cladding can prevent electromagnetic waves propagating in the core from leaking outside from the surface perpendicular to one direction of the core.
- the propagation angle ⁇ of the electromagnetic wave that satisfies is within a range of 0 ⁇ ⁇ 90 °, and a value within the range is a maximum value ⁇ of a propagation angle at which the electromagnetic wave is confined on the side surface, and the inside of the core is
- the width 2L of the core in the direction perpendicular to the waveguide length direction is:
- the “propagation angle ⁇ of the electromagnetic wave” as used herein means the direction in which the electromagnetic wave propagating in the core travels in a direction perpendicular to the one direction (for example, the ⁇ plane direction) and the length direction of the waveguide of the core. Angle.
- the side surface of the core corresponds to a plurality of types of periods.
- a wavefront may be generated on the homogeneous medium side, resulting in light leakage.
- the period a ( ⁇ / cos ⁇ ) is the leakage light is generated / ⁇ ( ⁇ / 2cos ⁇ ) 2 + a 2 ⁇ ° - wavefront corresponding to 5
- the photonic crystal waveguide can be configured as an “incompletely confined single mode waveguide”.
- the waveguide width 2L is sufficiently small, a single mode condition is required.
- the photonic crystal waveguide can be a “perfectly confined multimode waveguide”, and the following operational effects can be obtained.
- the resonator can have a free shape.
- the width 2L of the core in a direction perpendicular to the waveguide length direction is:
- the photonic crystal waveguide can be a “fully confined single mode waveguide”.
- the waveguide width 2L is within the range where only the 0th-order mode exists under the phase matching condition regardless of the value of the propagation angle ⁇ . In such a “perfect confinement single mode waveguide”, the following operation and effect can be obtained.
- a functional waveguide which desirably has large characteristics such as abnormal speed.
- the nonlinear action is enhanced, so that the characteristics of the optical element using the nonlinear action can be increased or the optical path length can be shortened.
- a cladding layer for confining the photonic crystal which has a periodicity in at least one direction and is made of the same material as the core, is provided on the surface of the core,
- the photonic band gap caused by the cladding layer in the one direction may confine the propagation mode of the core in the one direction and make a mode close to the propagation mode a radiation mode.
- the effective refractive index power of the light propagating in the waveguide in the direction perpendicular to the one direction (XZ plane direction) is less than ⁇ , it is possible to prevent the leakage of the electromagnetic wave in the one direction even if the medium is air. Disappears.
- the photonic band gap of the photonic crystal provided on the surface of the core causes the above-mentioned effect. It can force S to confine electromagnetic waves in one direction.
- photonic crystal waveguide with low propagation loss and low cost can be realized.
- phase modulation means may be provided on an end face where the periodic structure of the core is exposed, and a wave propagating in the core and an external plane wave may be coupled by the phase modulation means. Good. According to this configuration, it is possible to obtain only propagating light belonging to a specific higher-order band on the boundary of the Brillouin zone. When the optical path is considered in reverse, higher-order band propagation light can be returned to a plane wave.
- the phase modulating means may be arranged such that n is a refractive index of an external medium, and ⁇ is a wavelength of an external plane wave in a vacuum, and the core is parallel to the one direction of the core.
- the end face is defined as a connecting face with the outside, and the following formula is used in the connecting face.
- n 'sin e-(a / ⁇ ) 0.5
- the plane wave having the incident angle ⁇ ⁇ ⁇ ⁇ in the one direction represented by the following formula may be combined with the end face.
- the photonic on the boundary of the Brillouin zone The band can combine the wave propagating in the z direction in the core with the plane wave.
- the phase modulation means is parallel to the one direction of the core.
- the end face is defined as a connecting face with the outside, and the following formula is used in the connecting face.
- n 'sin e-(a / ⁇ ) 0.5
- the two plane waves having the same angle of incidence in the one direction and having the same phase may be caused to interfere with each other and be coupled to the end face. According to this configuration, if an interference wave is created by intersecting plane waves in two directions and the end face is set there, incident light can be transmitted with light propagated by a single photonic band on the boundary of the Brillouin zone. Can be combined.
- the phase modulation means is arranged close to, in contact with, or integrated with an incident surface of the core, which is an end surface parallel to the one direction, and forms the core.
- a phase grating having twice the period in the same direction as the above, and the phase grating may couple the external plane wave with the wave propagating in the core.
- the interference between the + 1st-order diffracted light and the -1st-order diffracted light causes the An electric field pattern with the same antinodes (peaks and valleys in the electric field) and nodes as in the case of interference can be created.
- the photonic crystal is arranged such that the electric field peaks and valleys are present in the high refractive index layer of the photonic crystal, which is a periodic multilayer structure constituting the core, and the nodes are present in the low refractive index layer. , Only the light propagated by the first band is obtained. If the photonic crystal is arranged so that the electric field peaks and valleys are in the low-refractive-index layer and the nodes are in the high-refractive-index layer, only the light propagated by the second band is obtained.
- the phase modulating means is disposed close to, in contact with, or integrated with an end face of the core parallel to the one direction, and is arranged in the same direction as the photonic crystal constituting the core.
- n is the index of refraction of the external medium, or n is the wavelength of the external plane wave in vacuum
- the phase modulation means is disposed close to, in contact with, or integrated with an end face of the core parallel to the one direction, and is twice as large in the same direction as the photonic crystal constituting the core.
- ⁇ is the refractive index of the external medium and ⁇ is the wavelength of the external plane wave in vacuum, the phase grating
- Propagation light by a certain band can be obtained.
- the phase modulating means may directly couple the external plane wave to an oblique end face of the core inclined with respect to the one direction. According to this configuration, it is possible to obtain only propagation light belonging to a specific higher-order band on the boundary of the Brillouin zone. When the optical path is considered in reverse, higher-order band propagation light can be returned to a plane wave.
- a prism or a mirror surface that is in contact with or close to the oblique end surface of the core may be provided to change the incident direction or the outgoing direction of the external plane wave. According to this configuration, when an external plane wave is incident on the oblique end surface of the core, the direction of the incident light can be changed by the prism or the mirror surface.
- an incident direction or an outgoing direction of the external plane wave may be made to coincide with a propagation direction in the core constituted by the photonic crystal. According to this configuration, the incident direction or the outgoing direction of the external plane wave is made to coincide with the propagation direction in the core, so that coupling with another waveguide element or an optical fiber becomes easy.
- the incident direction or the outgoing direction of the external plane wave is
- the photonic crystal may be perpendicular to the propagation direction in the core.
- the external plane wave can be made to enter from the direction perpendicular to the upper surface of the substrate on which the photonic crystal is formed, or to be emitted in the direction perpendicular to the direction.
- the prism may have a refractive index of 3 or more. According to this configuration, even if the frequency of the external plane wave deviates from the design frequency, the displacement of the position of the coupling band from the upper boundary line of the Brillouin zone can be reduced, and the frequency band in which propagation at the boundary line occurs can be reduced. Can be widely taken.
- the photonic crystal waveguide may be constituted by an oblique end face of the core inclined with respect to the one direction, and a diffraction grating which is close to, in contact with, or integrated with the oblique end face. According to this configuration, it is possible to widen the frequency band in which propagation at the boundary of the Brillouin zone occurs. It is desirable that the diffraction grating be designed with a blaze shape or the like so that the diffracted light of a specific order becomes stronger.
- the incident direction or the outgoing direction of the external plane wave coupled with the wave propagating in the core via the diffraction grating is adjusted by the photonic crystal. May be made to coincide with the propagation direction within. According to this configuration, the incident direction or the outgoing direction of the external plane wave is made to coincide with the propagation direction in the core, so that coupling with another waveguide element or an optical fiber becomes easy.
- the width of the core in a direction perpendicular to the waveguide length direction may be changed in a tapered shape.
- the width of the core (waveguide width 2L) is set to, for example, a width at which the waveguide width of the incident portion becomes a multimode propagation condition, and the width is tapered in the middle to reduce the width of the single mode. It can be made into a “tapered waveguide” that converts to a wave path.
- the present invention provides a photonic crystal waveguide comprising a photonic crystal having periodicity in one direction and including a core through which an electromagnetic wave propagates in a direction perpendicular to the one direction.
- the electromagnetic wave propagates by a propagation mode of a higher-order photonic band on the center line of the Brillouin zone in the photonic band structure of the core, and a side surface of the core parallel to the one direction has a uniform refractive index n.
- the electromagnetic wave In contact with the cladding, the electromagnetic wave s in vacuum
- the wavelength is I
- the period of the photonic crystal is a
- the one of the waves propagating in the core is
- “higher-order photonic band” means a photonic band other than the lowest-order photonic band.
- a surface of the core perpendicular to the one direction is formed of a homogeneous material or a photonic crystal having periodicity in at least the one direction, and propagates in the core.
- a confinement cladding may be provided for preventing electromagnetic waves from leaking from the surface to the outside. According to this configuration, the confinement cladding can prevent electromagnetic waves propagating in the core from leaking outside from a surface perpendicular to one direction of the core.
- the propagation angle ⁇ of the electromagnetic wave that satisfies is within a range of 0 to ⁇ and 90 °, and a value within the range is a maximum value ⁇ of a propagation angle at which the electromagnetic wave is confined on the side surface, and is transmitted through the core.
- the width 2L of the core in the direction perpendicular to the waveguide length direction is 2L
- the photonic crystal waveguide can be defined as an “incompletely confined single mode waveguide”.
- the maximum value of the propagation angle of the wave propagating in the core is ⁇ , by making the core width 2L sufficiently small,
- a cladding layer for confining the photonic crystal which has a periodicity in at least one direction and is made of the same material as the core, is provided on the surface of the core,
- the photonic band gap by the cladding layer may confine a propagation mode of the core in the one direction, and set a mode close to the propagation mode to a radiation mode. If the effective refractive index power S1 of the light propagating in the waveguide in the direction perpendicular to the one direction is smaller than the effective refractive index power S1, the leakage of the electromagnetic wave in the one direction cannot be prevented even if the medium is air.
- phase modulation means may be provided on an end face where the periodic structure of the core is exposed, and the wave propagating in the core and an external plane wave may be coupled by the phase modulation means.
- phase modulation means may be provided on an end face where the periodic structure of the core is exposed, and the wave propagating in the core and an external plane wave may be coupled by the phase modulation means.
- the phase modulation means may be arranged such that n is a refractive index of an external medium, ⁇ is a wavelength of an external plane wave in a vacuum, and
- the end face is defined as a connecting face with the outside, and the following formula is used in the connecting face.
- the two plane waves having the same angle of incidence in the one direction and having the same phase which are expressed by the following equation, may be caused to interfere with each other and be coupled to the end face. According to this configuration, if an interference wave is created by intersecting plane waves in two directions, and the end face is placed there, most of the incident light can be converted to higher-order band propagation light.
- the phase modulation means may be arranged such that n is a refractive index of an external medium, and ⁇ is a wavelength of an external plane wave in a vacuum, and the core is parallel to the one direction of the core.
- the end face is defined as a connecting face with the outside, and the following formula is used in the connecting face.
- the core is arranged close to, in contact with, or integrated with an incident surface that is an end surface parallel to the one direction of the core, and is arranged in the same direction as the photonic crystal forming the core.
- the phase grating may have the same period, and the phase grating may couple the external plane wave with the wave propagating in the core. According to this configuration, specific higher-order band propagation light can be obtained.
- the core is perpendicular to the waveguide length direction.
- the horizontal width may be changed in a tapered shape.
- the width of the core (waveguide width 2L) is set to, for example, a width at which the waveguide width of the incident portion becomes a multimode propagation condition, and the width is tapered in the middle to reduce the width of the single mode. It can be made into a “tapered waveguide” that converts to a wave path.
- the present invention comprises a homogeneous medium having a finite thickness in one direction and a refractive index n,
- a homogeneous medium waveguide having a core in which an electromagnetic wave propagates in a direction perpendicular to the one direction.
- the electromagnetic wave propagates in a first or higher order propagation mode in one direction of the core.
- a side of the core parallel to the one direction is in contact with a homogeneous medium cladding having a refractive index of n,
- n n
- this is the minimum condition for performing confinement in a direction perpendicular to the one direction.
- a surface of the core perpendicular to the one direction is formed of a homogeneous material or a photonic crystal having periodicity in at least one direction, and an electromagnetic wave propagating in the core is formed on the surface.
- a containment cladding S for preventing leakage from the surface to the outside may be provided.
- the effective refractive index of the higher-order mode propagating light in the direction perpendicular to the one direction becomes less than 1, it becomes impossible to prevent leakage of the electromagnetic waves in the one direction even if the medium is air.
- the effective refractive index in the direction perpendicular to the one direction is less than 1, the confinement of the electromagnetic wave in the one direction by the photonic band gap of the photonic crystal provided on the surface of the core. Can be performed.
- photonic crystal waveguide with low propagation loss and low cost can be realized.
- the propagation angle of the electromagnetic wave satisfying the direction perpendicular to the one direction is within a range of ⁇ force S0 ⁇ ⁇ 90 °, and a value within the range is a maximum value of a propagation angle at which the electromagnetic wave is confined on the side surface.
- the width 2L of the core in the waveguide length direction is:
- the homogeneous medium waveguide can be defined as an “incompletely confined single mode waveguide”. In such an “incompletely confined single-mode waveguide”, the following effects can be obtained.
- a phase change force SS TT when a wave propagating in the core is perpendicularly incident on the side surface in a direction perpendicular to the one direction ( ⁇ plane direction) and is reflected.
- the homogeneous medium waveguide can be made a “perfectly confined multimode waveguide”, and the following operational effects can be obtained.
- the lateral width 2L of the core is:
- the waveguide width 2L is in a range where only the zero-order mode under the phase matching condition exists regardless of the value of the propagation angle ⁇ in the direction perpendicular to the one direction (XZ plane direction). In such a “completely confined single mode waveguide”, the following operation and effect can be obtained.
- ⁇ The element can be extremely small because it can be bent sharply with single mode propagation and the waveguide width is narrow. Can be grouped into types.
- n is the refractive index of the core and n is
- the refractive index on the light emission side, ⁇ is the propagation angle of the higher-order mode light propagating in the core, and the end face of the core parallel to the one direction is:
- An external plane wave having an incident angle ⁇ ⁇ ⁇ ⁇ in the one direction expressed by the following formula may be combined, and the external plane wave may be used as incident light or output light. According to this configuration, it is possible to couple the incident light with the specific higher-order mode propagating light (propagation angle ⁇ ).
- an oblique end face of the core inclined with respect to the one direction has an incident angle coupled to a propagation angle ⁇ of the higher-order mode light in the one direction propagating in the core.
- An external plane wave may be coupled to make the external plane wave incident light or output light. According to this configuration, the incident light can be coupled with the specific higher-order mode propagation light having a large propagation angle ⁇ .
- a prism or a mirror surface that is in contact with or close to an oblique end surface of the core that is inclined with respect to the one direction is installed, and high-order mode light propagating in the one direction propagates in the core.
- an external plane wave, and the external plane wave may be used as incident light or outgoing light. According to this configuration, when an external plane wave is incident on the oblique end face of the core, the direction of the incident light can be changed by the prism or the mirror surface.
- the incident direction or the outgoing direction of the external plane wave may be made to coincide with the propagation direction in the waveguide. According to this configuration, the incident direction or the outgoing direction of the external plane wave is made to coincide with the propagation direction in the core, so that coupling with another waveguide element or optical fiber becomes easy.
- the incident direction or the outgoing direction of the external plane wave may be perpendicular to the propagation direction in the waveguide.
- the external plane wave can be made to enter or exit in a direction perpendicular to the upper surface of the substrate on which the homogeneous medium waveguide is formed.
- the refractive index of the prism may be 3 or more. According to this configuration, even if the frequency of the external plane wave departs from the design frequency, the position of the coupling band does not change. The deviation from the upper boundary of the Lilian zone can be reduced, and the frequency band where propagation at the boundary occurs can be widened.
- a diffraction grating that is close to, in contact with, or integrated with the core may be provided on an oblique end surface of the core that is inclined with respect to the one direction. According to this configuration, it is possible to widen the frequency band in which propagation occurs at the boundary of the Brillouin zone. It is desirable that the diffraction grating be designed with a blaze shape or the like so that diffracted light of a specific order becomes strong.
- the incident direction or the outgoing direction of the external plane wave may be made to coincide with the propagation direction in the waveguide.
- the incident direction or the outgoing direction of the external plane wave is made to coincide with the propagation direction in the core, so that coupling with another waveguide element or an optical fiber becomes easy.
- a phase grating that is close to, in contact with, or integrated with, the end face of the core parallel to the one direction is provided, and an external plane wave and light diffracted by the phase grating propagate in the core.
- the plane wave may be used as incident light or outgoing light by being combined with higher-order mode light in the one direction. According to this configuration, the incident light perpendicularly incident on the end face can be coupled with the specific higher-order mode propagation light.
- the width of the core in a direction perpendicular to the waveguide length direction may be changed in a tapered shape.
- the width of the core (waveguide width 2L) is set to, for example, a width such that the waveguide width of the incident portion becomes a multi-mode propagation condition, and the width is tapered in the middle to reduce the single mode. It can be a “tapered waveguide” that can be converted into a waveguide.
- the present invention provides an optical element used as a directional coupler having two waveguides bent so as to be close to each other in a coupling region having a predetermined coupling length.
- Each of the two waveguides is composed of either the photonic crystal waveguide or the homogeneous medium waveguide. According to this configuration, the following operation and effect can be obtained.
- each waveguide can be bent sharply, and The degree of freedom in the arrangement of each waveguide on the plate is increased. This makes it possible to reduce the size of the directional coupler itself and facilitate integration.
- each waveguide so as to satisfy the above-mentioned single mode condition, it becomes possible to efficiently couple with an external single mode optical fiber.
- the coupling length of the coupling region of the two waveguides can be made much shorter than that of the conventional directional coupler waveguide, and the size can be reduced and the function of the directional coupler can be enhanced. Can be done.
- each waveguide is a photonic crystal waveguide
- the basic structure is a one-dimensional photonic crystal that is a simple periodic multilayer structure, and the difference in the refractive index of the photonic crystal may be small.
- the directional coupler can be manufactured at low cost.
- the present invention relates to a Mach-Zehnder type having one linear waveguide, two waveguides branched from the waveguide, and one linear waveguide in which these two waveguides are merged.
- An optical element used as an optical switch is provided.
- Each waveguide is composed of either the photonic crystal waveguide or the homogeneous medium waveguide. According to this configuration, the following operation and effect can be obtained.
- each waveguide of the Mach-Zehnder type optical switch is composed of the photonic crystal waveguide or the homogeneous medium waveguide, each waveguide can be bent sharply, and each waveguide on the substrate can be bent rapidly.
- the degree of freedom of arrangement increases. For this reason, compared to an optical switch having a two-dimensional photonic crystal as described in Patent Document 3, the optical switch itself can be reduced in size, and an optical module can be manufactured by integrating with other elements on a substrate. Integration becomes easier.
- the photonic crystal waveguide or the homogeneous medium waveguide constituting each waveguide is manufactured so as to satisfy the above-mentioned single mode condition, so that it can be efficiently coupled to an external single mode optical fiber. It is possible to realize an optical system using a single mode optical fiber.
- each waveguide is a photonic crystal waveguide
- a one-dimensional photonic crystal having a periodic laminated structure is used as a basic structure, and the difference in the refractive index of the photonic crystal may be small.
- the optical switch can be manufactured at low cost.
- the present invention provides an optical element used as an optical delay line having a linear waveguide and one waveguide including a delay portion.
- the waveguide and the delay portion are constituted by either the photonic crystal waveguide or the homogeneous medium waveguide. According to this configuration, the following operation and effect can be obtained.
- the waveguide should have a free shape. Power S can. Therefore, it is possible to improve bending loss by giving a small radius of curvature instead of steep bending, and it is possible to design an optical delay line realizing both miniaturization and low loss at the same time.
- the optical delay line can be realized at low cost by using a photonic crystal waveguide made of a one-dimensional photonic crystal or a homogeneous medium waveguide.
- the delay part can be bent sharply, increasing the degree of freedom in arranging optical delay lines on the board. This makes it possible to reduce the size of the optical delay line itself, and to combine other elements on the substrate. Integrating them together to make an optical module facilitates integration.
- the photonic crystal waveguide or the homogeneous medium waveguide constituting the one waveguide is manufactured so as to satisfy the above-described single mode condition, so that it can efficiently communicate with an external single mode optical fiber. Coupling becomes possible, and it is possible to realize an optical system using a single-mode optical fiber.
- the basic structure is a one-dimensional photonic crystal, which is a simple periodic multilayer structure, and even if the difference in the refractive index of the photonic crystal is small. As a result, the optical delay line can be manufactured at low cost.
- the delay portion of the long path can be arranged with a small area on the substrate, and the size and integration can be further improved.
- the present invention provides a dispersion control device having a waveguide.
- the waveguide is composed of either the photonic crystal waveguide or the homogeneous medium waveguide, and propagation light having a large dispersion condition is used as propagation light propagating through the waveguide. According to this configuration, by using the propagating light under the condition of large dispersion, it is possible to give reverse dispersion to a signal in which dispersion has occurred in an optical communication system, and to compensate for chromatic dispersion caused by a long-distance optical fiber. Power S can.
- the present invention provides an optical element including a waveguide.
- the waveguide is comprised of either a photonic crystal waveguide or the homogeneous medium waveguide.
- the core of the waveguide includes a material having nonlinear characteristics.
- Two electrodes are provided on both surfaces in the one direction of the waveguide. According to this configuration, by controlling the voltage and the current applied to the electrode, the nonlinear material contained in the core of the waveguide formed of either the photonic crystal waveguide or the homogeneous medium waveguide can be controlled. The effect can be controlled. As a result, the nonlinear effect due to the abnormal group velocity can be varied, and the nonlinear effect and the nonlinear element can be realized.
- the present invention provides an optical element including a waveguide.
- the waveguide is composed of the photonic crystal waveguide or the homogeneous medium waveguide.
- the core of the waveguide includes a material having a non-linear characteristic.
- Two electrodes are provided on both surfaces in the one direction of the waveguide.
- the optics are driven by a voltage applied to the two electrodes, A modulator for changing a current is provided.
- a modulator for changing a current is provided.
- the phase, amplitude, polarization plane, and frequency of the incident light are changed. It is possible to emit a modulated signal light to which modulation such as is applied.
- the present invention provides an optical element provided with either the photonic crystal waveguide or the homogeneous medium waveguide.
- the optical element generates refracted light from the core by imperfectly confining the cladding.
- a part of the propagating light becomes refracted light toward the air side or the substrate side.
- the direction of the refracted light is constant with respect to the wavelength of the external plane wave in a vacuum, and becomes a light beam with very good directivity.
- the effective refractive index changes greatly with the frequency change of the external plane wave, so that it can be used as a high-resolution demultiplexer.
- the present invention provides an optical element used as a symmetric Mach-Zehnder optical switch.
- the optical element includes one linear waveguide, two waveguides branched from the waveguide, two linear waveguides branched from a junction of the two waveguides, and a control light guide. And a wave path.
- Each waveguide is composed of either a photonic crystal waveguide or a homogeneous medium waveguide, and each of the two waveguides is provided with a nonlinear portion including a component having nonlinear optical activity. According to this configuration, the following advantages can be obtained.
- a symmetric Mach-Zehnder type optical switch similar to that of Non-Patent Document 1 using a two-dimensional photonic crystal defect waveguide is provided by using a one-dimensional photonic crystal photonic crystal waveguide or a homogeneous medium waveguide. And can be realized at low cost. Since each waveguide (371-377) is composed of a photonic crystal waveguide or a homogeneous medium waveguide, each waveguide can be bent sharply, and the degree of freedom of arrangement of each waveguide on the substrate increases. . Therefore, the size of the optical switch itself can be reduced as compared with Non-Patent Document 1, and the integration when manufacturing an optical module by integrating the optical switch with other elements on the substrate becomes easier.
- each waveguide is a photonic crystal waveguide
- a one-dimensional photonic crystal which is a simple periodic multilayer structure, is used as the basic structure, and the difference in the refractive index of the photonic crystal may be small.
- a symmetric Mach-Zehnder optical switch including each waveguide can be manufactured at low cost.
- the present invention provides an optical element used as a point defect resonator (wavelength filter).
- the optical element includes a linear waveguide and at least one point defect provided near the linear waveguide.
- the linear waveguide is composed of either the photonic crystal waveguide or the homogeneous medium waveguide. According to this configuration, the following advantages can be obtained.
- the present invention provides an optical element used as a point defect resonator.
- the optical element includes one linear waveguide, two waveguides branched from the waveguide, two linear waveguides branched from a junction of the two waveguides, and the two waveguides. At least one point defect provided in the vicinity of at least one of the two.
- Each waveguide is constituted by the photonic crystal waveguide or the homogeneous medium waveguide. According to this configuration, the following advantages are obtained.
- the present invention provides an optical element including a waveguide.
- the waveguide is composed of either the photonic crystal waveguide or the homogeneous medium waveguide.
- the core of the waveguide includes a light-emitting substance, and the light-emitting substance is an optical amplifying element excited by pump light. According to this configuration, the following advantages can be obtained.
- the amplified signal light can be extracted as signal light.
- the light-emitting substance is, for example, enolevium, bismuth, or the like.
- the present invention provides an optical element having a waveguide.
- the waveguide is the photonic crystal It is composed of either a waveguide or the homogeneous medium waveguide.
- the core of the waveguide includes a material having nonlinear characteristics.
- Two electrodes are provided on both surfaces in the one direction of the waveguide.
- the optical element is placed in a high-temperature state, and is subjected to a process of returning to normal temperature while two electrode DC voltages are applied.
- the processing (polling) has the effect of increasing the characteristics of the nonlinear material contained in the core of the waveguide formed of either the photonic crystal waveguide or the homogeneous medium waveguide.
- incident light such as laser light is made incident on the waveguide of the poled waveguide device with electrodes, for example, strong second harmonic (SHG) and third harmonic (THG) emission light can be generated. Therefore, wavelength conversion of laser light can be performed.
- the present invention provides an optical element provided with a waveguide.
- the waveguide is composed of the photonic crystal waveguide or the homogeneous medium waveguide.
- the core of the waveguide contains a luminescent material.
- Two electrodes, at least one of which is a transparent electrode, are provided on both side surfaces in the one direction of the waveguide. According to this configuration, while the incident light is made incident on the photonic crystal waveguide, by applying a voltage or flowing a current to both electrodes, the light whose incident light is amplified by the luminescent material is converted into two electrodes. The light can be emitted upward through the transparent electrode. Therefore, the waveguide device with electrodes can be configured as a light emitting device.
- FIG. 1 is a schematic view showing light propagation in a photonic crystal.
- FIG. 2 is a diagram showing an example of a photonic band structure of a photonic crystal.
- FIG. 3 is an explanatory diagram showing, by a photonic band, coupling between a photonic crystal and light incident perpendicularly to an end face of the photonic crystal.
- FIG. 4 is a diagram showing the coupling between the photonic crystal and the incident light perpendicularly incident on the end face of the photonic crystal limited to only the Z direction of the prillian zone.
- FIG. 5 is an explanatory diagram showing, as a photonic band, coupling between incident light obliquely incident on an end face of a photonic crystal and the photonic crystal.
- FIG. 6 is an explanatory diagram showing, by a photonic band, the coupling between incident light obliquely incident so as to propagate on a Brillouin zone boundary and a photonic crystal.
- FIG. 7 is a diagram showing the coupling between the incident light and the photonic crystal obliquely incident so that propagation on the Brillouin zone boundary occurs only in the Z direction of the Brillouin zone.
- FIG. 8 is a diagram showing phase-modulated incident light due to plane waves in two intersecting directions.
- FIG. 9 is a diagram showing phase-modulated incident light due to plane waves in three intersecting directions.
- FIG. 10 is a schematic diagram showing phase modulation by a phase grating having a period a and set on the incident side and the exit side of a photonic crystal.
- FIG. 11 is a diagram schematically showing light propagated by first and second bands on a Brillouin zone boundary.
- FIG. 12 is a diagram schematically showing an electric field pattern on the boundary line of the Brillouin zone by combining propagating lights by the first and second bands.
- FIG. 13 is an explanatory diagram showing, by a photonic band, coupling between incident light obliquely incident on an end face of the photonic crystal and the photonic crystal.
- FIG. 14 is a view showing phase modulation of incident light due to interference of plane waves in two directions intersecting with each other.
- FIG. 15 is a schematic diagram showing phase modulation by a phase grating having a period of 2a provided on the incident side and the emission side of the photonic crystal.
- FIG. 16 is a diagram showing diffracted light of a phase grating in a calculation example in the case of using a phase grating having a period 2a and an interference wave caused by oblique incidence.
- FIG. 17 is a view showing an electric field pattern in a calculation example in the case of using a phase grating having a period 2a and an interference wave caused by oblique incidence.
- FIG. 18 is a diagram showing an electric field pattern in a calculation example in a case where a phase grating having a period 2a and an interference wave caused by oblique incidence are used and the phase grating is installed under specific conditions.
- FIG. 19 (a) Diagram showing the incidence of a plane wave on the oblique end face to obtain light propagating on the boundary of the Brillouin zone.
- Fig. 19 (b) shows the incident angle ⁇ on the oblique end face. Incident light
- FIG. 4 is an explanatory diagram showing a bond with an otonic crystal by a photonic band.
- FIG. 20 is a perspective view showing an optical element using the photonic crystal waveguide according to the first embodiment of the present invention.
- FIG. 21 is a schematic diagram showing light propagation in the photonic crystal waveguide according to the first embodiment.
- FIG. 22 is a perspective view showing a core of the photonic crystal waveguide of FIG. 21.
- FIG. 24 is an explanatory view of a core thickness 2A of a photonic crystal.
- FIG. 25 is an explanatory diagram of propagating light satisfying a phase matching condition, that is, a mode.
- FIG. 26 is an explanatory view showing a mode using a second band.
- FIG. 27 is a band diagram when a core having a period a is provided with a cladding having a period b (a ⁇ b).
- FIG. 28 is an explanatory diagram showing the m-th mode band in the Y direction in the XZ direction of the inverse space.
- FIG. 29 is a view showing an electric field pattern exposed on the side surface of the photonic crystal waveguide in the case of normal incidence at the Brillouin zone boundary propagation.
- FIG. 30 is a diagram showing an electric field pattern exposed on the side surface of the photonic crystal waveguide in the case of oblique incidence at the Brillouin zone boundary propagation.
- FIG. 31 is an explanatory diagram of a phase matching condition in a case where propagation light at the Brillouin zone boundary propagation travels with a propagation angle ⁇ in the XZ plane with respect to the Z direction.
- FIG. 32 A graph schematically showing the range of 2L satisfying the single mode condition with respect to the propagation angle ⁇ at the Brillouin zone boundary propagation.
- Figure 33 A graph schematically showing the 2L range that satisfies the confinement condition and single-mode condition in Brillouin zone boundary propagation.
- FIG. 34 is a graph similar to FIG. 33 under conditions different from those in FIG. 33.
- FIG. 35 is a graph similar to FIG. 33 under conditions different from those in FIG. 33.
- FIG. 37 is a view showing an electric field pattern exposed on the side surface of the photonic crystal waveguide in the case of oblique incidence at the center of the Brillouin zone according to the second embodiment of the present invention.
- FIG. 38 A graph schematically showing the 2L range satisfying the single mode condition with respect to the confinement condition and propagation angle ⁇ in the central Brillouin zone propagation.
- FIG. 39 A graph similar to FIG. 38 under conditions different from those in FIG.
- FIG. 40 is a schematic view showing light propagation in a waveguide according to a third embodiment of the present invention.
- FIG. 411 is an explanatory diagram showing modes in the band diagram of the core shown in FIG. 40.
- FIG. 42] An explanatory view showing an electric field pattern exposed on the side of the core when higher-order mode propagating light in the core shown in FIG. 40 travels at a propagation angle ⁇ in the XZ plane.
- FIG. 43 A graph schematically showing the confinement condition of the core shown in Fig. 40 and the range of 2L satisfying the single mode condition with respect to the propagation angle ⁇ .
- FIG. 44 A graph similar to FIG. 43 under conditions different from those in FIG.
- FIG. 45 A graph similar to FIG. 43 under conditions different from those in FIG.
- FIG. 46 is a schematic diagram showing light propagation in a photonic crystal waveguide according to a fourth embodiment of the present invention.
- FIG. 47 is a plan view showing a photonic crystal waveguide according to a fifth embodiment of the present invention.
- FIG. 48 is a perspective view showing the photonic crystal waveguide of FIG. 47.
- FIG. 49 is a plan view showing the incident side of the photonic crystal waveguide of FIG. 47.
- FIG. 50 is an explanatory view showing simulation results of the photonic crystal waveguide of FIG. 47.
- FIG. 51 is a plan view showing a photonic crystal waveguide according to a sixth embodiment of the present invention.
- FIG. 52 is an explanatory diagram showing a simulation result of the photonic crystal waveguide of FIG. 51.
- FIG. 53 is a plan view showing a photonic crystal waveguide according to a seventh embodiment of the present invention.
- FIG. 54 is an explanatory view showing simulation results of the photonic crystal waveguide of FIG. 53.
- FIG. 55 is a perspective view showing a directional coupler as an optical element according to an eighth embodiment of the present invention.
- FIG. 56 is a plan view showing an optical switch as an optical element according to a ninth embodiment of the present invention.
- FIG. 57 is a plan view showing a symmetric Mach-Zehnder all-optical switch as an optical element according to a tenth embodiment of the present invention.
- FIG. 58 A plan view showing a conventional example of an optical delay line using a two-dimensional photonic crystal defect waveguide.
- FIG. 59 is a plan view showing an optical delay line as an optical element according to an eleventh embodiment of the present invention.
- FIG. 60 is a plan view showing an optical delay line as an optical element according to a twelfth embodiment of the present invention.
- FIG. 61 A plan view showing a point defect resonator as an optical element according to a thirteenth embodiment of the present invention.
- FIG. 62 A plan view showing a point defect resonator as an optical element according to a fourteenth embodiment of the present invention.
- a description will be given of a dispersion control element as an optical element according to a fifteenth embodiment of the present invention. Band diagram.
- FIG. 64 is a graph showing the relationship between the wavelength and the dispersion of incident light obtained by calculation for the propagating light (a) in FIG. 63.
- FIG. 65 is a graph showing the relationship between the wavelength of incident light and the dispersion obtained by calculation for the propagating light (mouth) in FIG. 63.
- FIG. 66 is a graph showing the relationship between the wavelength and dispersion of incident light obtained by calculation for the propagating light (c) in FIG. 63.
- FIG. 67 is a graph showing the relationship between the wavelength of incident light and the dispersion obtained by calculation for the propagating light (2) in FIG. 63.
- FIG. 68 is a perspective view showing an optical amplifying element as an optical element according to a sixteenth embodiment of the present invention.
- FIG. 69 is a perspective view showing a waveguide device with electrodes as an optical device according to a seventeenth embodiment of the present invention.
- FIG. 70 is a perspective view showing a waveguide device with electrodes as an optical device according to an eighteenth embodiment of the present invention.
- FIG. 71 is a perspective view showing a waveguide device with electrodes as an optical device according to a nineteenth embodiment of the present invention.
- FIG. 72 is a perspective view showing a waveguide device with electrodes as an optical device according to a twentieth embodiment of the present invention.
- FIG. 73 (a) is a schematic diagram showing oblique end surface incidence, and FIG. 73 (b) is an explanatory diagram showing positions of coupling bands.
- FIG. 74 (a)-(f) is a schematic diagram showing a configuration example in which a prism and a mirror surface are combined on an oblique end surface.
- FIG. 75 (a) is a schematic diagram showing a configuration example in which a high refractive index prism is combined on an oblique end face
- FIG. 75 (b) is an explanatory view of the band.
- FIG. 76 (a) is a schematic diagram showing a configuration example in which a diffraction grating is combined on an oblique end face
- FIG. 76 (b) is an explanatory diagram showing positions of coupling bands.
- FIG. 77 (a)-(h) is a schematic view showing various configuration examples in which a diffraction grating is combined with an oblique end face.
- FIG. 78 (a) is a schematic view illustrating the principle of an optical element according to a twenty-first embodiment of the present invention.
- FIG. 78 (b) is an explanatory view showing the position of a binding band.
- FIG. 79 (a) is a perspective view showing an optical element according to prototype example 1 of the twenty-first embodiment, and FIG. 79 (b) is a side view thereof.
- FIG. 81 (a) is a perspective view showing an optical element according to a prototype example 2 of the twenty-first embodiment, and FIG. 81 (b) is a side view thereof.
- FIG. 82 is a graph showing the angular dispersion of the optical elements according to Prototype Example 2 and Prototype Example 3.
- FIG. 1 schematically shows propagation of an electromagnetic wave in a non-periodic direction (Z direction) of a one-dimensional photonic crystal 50 having periodicity only in one direction (Y direction).
- FIG. 1 a plane having a wavelength ⁇ in a vacuum from one end face 50a of the one-dimensional photonic crystal 50 is shown.
- the incident light 51 which is a zero wave (electromagnetic wave)
- the incident light 51 becomes a propagating light 52, propagates in the photonic crystal 50, and is emitted from the other end face 50b as an emission light 53.
- How the incident light 51 propagates in the one-dimensional photonic crystal 50 can be known by calculating a photonic band and creating a band diagram.
- one end face 50a and the other end face 50b each of which is a “coupling plane” with the outside, are end faces where the periodicity is exposed and correspond to the Y direction as the periodic direction (one direction).
- the end faces are parallel, and serve as an entrance surface and an exit surface, respectively.
- the one-dimensional photonic crystal 50 shown in Fig. 1 has an infinite periodic structure in the Y direction (stacking direction), and the X and Z directions (periodic multilayer) perpendicular to the paper surface. It is assumed that it extends infinitely in the direction parallel to each layer plane of the film).
- FIG. 1 [0121]
- the results of the band calculations in the Y and Z directions for the multilayer structure with a period a (one-dimensional photonic crystal 50) with alternating layers of TE are shown as the first, second, and third bands of TE polarized light.
- the three bands are shown within the range of the first Brillouin zone.
- the band diagram shown in FIG. 2 is contoured by connecting points at which the normalized frequency ⁇ a / 2 ⁇ c has the same value, and the subscript in the figure means the value of ⁇ a / 271c.
- ⁇ is the angular frequency of the incident light 51
- a is the period of the multilayer structure (one-dimensional photonic crystal 50)
- c is the speed of light in a vacuum.
- the normalized frequency ⁇ a / 2 TIC is also expressed as a / ⁇ using the wavelength of incident light in vacuum.
- the normalized frequency is simply described as a / ⁇ in the following.
- the width of the Brillouin zone in the ⁇ direction shown in Fig. 2 is 2 ⁇ / a. Since the photonic crystal 50 has no periodicity in the Z direction, the X direction (the direction perpendicular to the paper) and the Z direction in FIG. There is no boundary of the Brillouin zone in the lateral direction, and the Brillouin zone extends as far as possible.
- TE polarized light indicates polarized light whose electric field is in the X direction.
- the band diagram (not shown) for TM polarized light (polarized light whose magnetic field is in the X direction) has a somewhat different shape with a force similar to that of TE polarized light.
- the incident light 51 which is a plane wave incident on the one end face 50a of the one-dimensional photonic crystal 50 shown in Fig. 1, a propagating light 52 in the photonic crystal 50 is considered.
- Figure 3 shows a plane wave (TE polarization) with a specific normalized frequency aZ
- the coupling band on the photonic crystal 50 side can be obtained by drawing.
- FIG. 3 since there are corresponding points 91 1 and 912 on the first band and the second band, the waves corresponding to the first band and the second band respectively propagate in the photonic crystal 50.
- the wave number vectors of each propagating light are indicated by reference numerals 913 and 914.
- the traveling directions of the wave energy in the photonic crystal 50 are represented by the normal directions 915 and 916 of the contour lines, and the light propagated by any band travels in the ⁇ direction.
- Fig. 4 shows the band diagram limited to the ⁇ direction.
- the incident light (plane wave) 51 at the normalized frequency a / ⁇ is incident light (plane wave) 51 at the normalized frequency a / ⁇ .
- the wavelength in vacuum is converted to the wavelength ( ⁇ , ⁇ in the corresponding photonic crystal 50).
- the refractive index is almost invariant to the change in the wavelength of the incident light 51.
- the second band is almost invariant to the change in the wavelength of the incident light 51.
- the effective refractive index greatly changes with the change of I
- the effective refractive index power may be less than si.
- the value obtained by differentiating the band curve as shown in FIG. 4 with kz is the group velocity of the propagating light.
- the group velocity anomaly in a photonic crystal is extremely large and opposite to the dispersion of a normal homogeneous substance (waves of incident light). Since the group velocity decreases as the length increases), an optical element such as an optical delay element or a dispersion control element can be manufactured using the group velocity anomaly of higher-order band propagating light.
- an optical element using light propagated by a higher-order band (light transmitted by a higher-order band) is very useful.
- the first band propagating light (propagating light due to the first band) must also be generated at the normalized frequency a / ⁇ at which the higher band propagating light of the second band or higher propagates.
- the first band propagating light has the above-described "extremely large chromatic dispersion" (a change in the wavelength of the propagating light (2 ⁇ / kz) with respect to a change in frequency increases), and a "group velocity anomaly". Has almost no effect. Therefore, when the higher-order band propagating light and the first-band propagating light exist, the first-band propagating light is simply a loss when using the higher-order band propagating light. Not only does this significantly reduce the light intensity, but also as stray light that reduces the S / N ratio of the optical element.
- FIG. 5 shows a coupling band (photonic band) on the photonic crystal 50 side when the incident light 51 is obliquely incident at an angle ⁇ on one end face 50a of the photonic crystal 50 shown in FIG. .
- the waves corresponding to the first band and the second band respectively propagate in the photonic crystal 50.
- the wave number vector of each propagating light is indicated by reference numerals 533 and 534.
- the traveling direction of the wave propagating in the photonic crystal 50 is the normal direction 535, 536 of the contour line, and there are two types.
- n-sin ⁇ ⁇ (a / ⁇ ) 0.5
- n- sin ⁇ -(a / ⁇ ) 1.0, 1.5, 2.0,
- Fig. 7 shows the band diagram on the boundary line of the Brillouin zone limited to the Z direction.
- all the bands including the first band change similarly to the higher-order bands shown in FIG. Therefore, “significant changes in effective refractive index due to wavelength” and “group velocity anomaly” occur in all bands.
- optical elements such as optical delay elements and dispersion control elements can be used to reduce incident light energy. Power without reducing the usage efficiency and S / N ratio.
- a plane wave outside the photonic crystal for example, a plane wave (incident light 51) incident on the photonic crystal 50 (see FIG. 1) and the inside of the photonic crystal 50 in the Z direction.
- the “band on the center line of the Brillouin zone” refers to a photonic band existing on the center line of the Brillouin zone in the photonic band structure.
- the first band on the center line 60 of the Brillouin zone ⁇ the second band force on the center line 61 of the Brillouin zone corresponds to the photonic band existing on the center line .
- two plane waves 62a and 62b intersect to create an interference wave having a period a in the Y direction.
- the end face 50a By installing the end face 50a, most of the incident light energy can be converted to higher-order band propagation light.
- an “electric field pattern” is exposed on the left and right surfaces (a cross section perpendicular to the X direction) of the waveguide formed by the photonic crystal 50 through which the higher-order band propagation light propagates.
- the electric field peak 98 indicated by the thick solid line has a larger amplitude than the electric field peak 99 indicated by the thin solid line.
- FIG. 8 shows that, of the periodic multilayer films constituting the photonic crystal 50, the electric field peak 98 and the electric field peak 99 are shifted from each other by “half a wavelength” in each adjacent layer having a different refractive index. Show that
- phase grating 64 having a period a is provided immediately before one end face 50a of the photonic crystal 50, and the incident light 5 ⁇ of the plane wave is phase-modulated by the phase grating 64 to perform phase modulation having a period a.
- a wave 65 is formed, and the phase modulated wave 65 is made incident.
- 64 can also be formed by a simple method of forming a groove near one end face 50a of the photonic crystal 50, for example.
- the end face of the photonic crystal for example, one end face 50a of the photonic crystal 50 shown in FIG.
- n 'sin e-(a / ⁇ ) 0.5
- the first band propagating light has a high refractive index layer as an antinode and a low refractive index layer as a node. That is, an electric field peak 106 and an electric field valley 107 exist in the high refractive index layer 104 of the photonic crystal 50, and an electric field node exists in the low refractive index layer 105.
- the second band propagation light has a low refractive index layer as an antinode and a high refractive index layer as a node, and its period is longer than that of the first band propagating light. That is, the electric field peak 106 and the electric field valley 107 exist in the low refractive index layer 105 of the photonic crystal 50, the electric field node exists in the high refractive index layer 104, and the period of the electric field peak 106 and the valley 107 is It is longer than the light propagated by the first band.
- the method of obtaining a wave in which the propagation of the first band and the propagation of the second band are superposed as described above is the simplest method because it only tilts the incident light (plane wave). Furthermore, increase the value of aZ
- the end face of the photonic crystal for example, the photonic crystal shown in FIG.
- the incident angle ⁇ of the light obliquely incident on one end surface 50a of 50 is
- n-sin 0-(a / ⁇ ) 0.5
- reference numeral 131 denotes a corresponding point on the first band
- reference numeral 133 denotes a traveling direction of a wave in the first band. There is no corresponding point on the second band, so there is no propagation.
- the photonic crystal 50 When the photonic crystal 50 is arranged so that the electric field peak 106 and the electric field valley 107 are present in the low refractive index layer 105 and the nodes are present in the high refractive index layer 104, the second band shown in FIG. As in the case of propagation by, only light propagated by the second band is generated.
- n-sin ⁇ ⁇ (a / ⁇ ) 0.5
- ⁇ is the refractive index on the incident light side.
- phase grating 70 has a shape optimized so that the ⁇ 1st-order diffracted light is as strong as possible.
- phase grating 70 When the phase grating 70 is optimized at a specific wavelength, the efficiency of the first-order diffracted light does not drop sharply and stays at a high level even if the wavelength slightly changes.
- the wave number band can be wider than other methods.
- phase modulation wave by the phase grating 70 is indicated by reference numeral 65. Also, by installing a phase grating 71 having a period 2a just like the phase grating 70 immediately after the other end face 50b of the photonic crystal 50, the outgoing light 68 'can be returned by the plane wave 69.
- the propagation light in the photonic crystal 50 where the first band propagation light and the second band propagation light coexist (overlap) with each other is generated at the end face (the other end face 50b) on the emission side of the phase grating.
- the intensity of the diffracted light emitted can be changed depending on the position. That is, as shown by positions H and J in FIG. 16, when the output side end face of the phase grating is on the slope of the peak-and-valley pattern, the diffracted light on one side becomes strong. Further, as shown by a position I in FIG. 16, when the end face on the emission side of the phase grating is at the top or bottom of the peak-valley pattern, the intensity of the two-sided diffracted light is substantially equal.
- the interference pattern due to the emitted light at which the intensities of the diffracted light on both sides are almost equal is obtained by the method (2d) above.
- a photonic crystal with the same period a as the phase grating is placed immediately after the end face on the emission side of the phase grating because the interference wave is similar to the interference wave created by the phase grating. Can be obtained.
- phase grating and the photonic crystal a periodic multilayer film having the same structure (of course, the same period a) can be used, but antinodes (peaks and valleys) of the electric field due to the interference wave can be used. It is necessary to adjust the position of the node and the node to match the photonic crystal side. Also,
- n-sin ⁇ ⁇ (a / ⁇ ) 0.5
- phase grating made of a low-refractive-index substance such as gas. If the phase grating is made of silicon or other high-refractive index material, the intensity of the first-order diffracted light can be increased. .
- the period of the phase grating is set to 2a, which is twice that of the photonic crystal, and
- a pair of diffracted lights that generate an interference wave as shown in FIG. 17 can be strengthened.
- the period in the Y direction of the phase grating 110 is 2a
- the thickness of the phase grating 110 in the Z direction is 1.5642a.
- phase grating was optimized so that specific diffracted light became strong.
- FIG. 17 shows an interference wave generated by the phase grating 110. Since the interference wave that propagates on both sides and is perpendicular to the phase grating 110 where the interference wave is strong is weak, it can be seen that the interference pattern has a staggered interference pattern.
- the photonic crystal 50 is used instead of the medium N, and the phase grating 110 and the photonic crystal 50 are arranged at an interval of 0.990909a.
- the position of the phase grating 110 in the Y direction was adjusted so that the antinode of the interference wave (the peak and the valley of the electromagnetic wave) was located at the center of the high refractive index layer of the photonic crystal 50.
- the width of the incident portion on one end face of the photonic crystal 50 was about 24 periods.
- FIG. 18 shows a simulation result of such a configuration example.
- Propagating light on the boundary of the Brillouin zone can also be obtained by making the end face on the incident side of the photonic crystal an oblique end face and making a plane wave incident on the oblique end face.
- the position P of the coupling band (see FIG. 19B) can be obtained by drawing. If ⁇ and ⁇ are adjusted so that the position P is on the boundary of the Brillouin zone, a higher-order propagating light 81 traveling in the Z direction can be obtained.
- FIG. 73 (a) shows incident light (plane wave) at an incident angle ⁇ on the oblique end face (angle ⁇ ) 50c of the photonic crystal 50, similarly to the photonic crystal waveguide described in FIG. 19 (a). Make 80 incident
- FIG. 73 (b) is a band diagram obtained by plotting the positions of the binding bands in the configuration example shown in FIG. 73 (a).
- the solid line 83 shows the coupling state with the photonic band when the incident light 80 incident on the oblique end face 50c is the incident light at the design frequency, and the incident light 80 has a frequency lower than the design frequency.
- the dashed line 84 shows the same coupling state when the incident light is small.
- a broken line 85 is a line connecting the center of the band diagram of the photonic crystal and the center of the circle representing the incident light, and is orthogonal to the boundary line 89 having the same inclination angle as the oblique end face 50c.
- the position of the coupling band indicated by a black circle (the coupling point on the band) 87 corresponds to the Brillouin zone.
- ⁇ and ⁇ are adjusted to be on the boundary line 86.
- the configuration in which the incident light 80 is incident the frequency range in which propagation at the Brillouin zone boundary 86 on the photonic crystal 50 side is limited. Therefore, the configuration as shown in FIG. 19 (a) and FIG. 73 (a) is suitable for applications where the frequency range is limited.
- the angle of the incident light 80 is also determined by the inclination angle ⁇ of the oblique end face 50c.
- the direction (angle of the incident light 80) is not always a practically convenient direction. Therefore, when a prism or a mirror is combined with the oblique end face 50c, the force S for adjusting the direction of the incident light can be obtained.
- a pentagonal prism 120A is provided so as to be in contact with the oblique end face 50c of the photonic crystal 50.
- This prism 120A allows the incident light 80, which is an external plane wave, to enter the prism at an arbitrary angle (incident angle ⁇ ).
- the “incident direction” here refers to the angle at which the incident light 80 enters
- the “outgoing direction” refers to the angle at which the incident light propagates through the photonic crystal 50 and exits from the exit-side prism or mirror.
- the direction of the incident light 80 can be changed by the prism 120A.
- a square prism 120B is provided so as to be in contact with the oblique end face 50c of the photonic crystal 50.
- the incident direction (or outgoing direction) of the incident light 80 incident on the prism 120B coincides with the propagation direction (Z direction) of the incident light 80 in the photonic crystal 50.
- the incident direction (or the outgoing direction) of the incident light 80 is set in the Z direction, coupling with another waveguide element or an optical fiber becomes easy.
- a rectangular prism 120C is provided so as to be in contact with the oblique end face 50c of the photonic crystal 50.
- the incident direction (or outgoing direction) of the incident light 80 is perpendicular to the propagation direction (Z direction) of the incident light 80 in the photonic crystal 50.
- the incident light 80 can be incident from a direction perpendicular to the upper surface of the substrate on which the photonic crystal 50 is formed.
- a triangular shape is set so as to be in contact with the oblique end face 50c.
- the prism 120D is installed.
- the incident direction (or the outgoing direction) of the incident light 80 incident on the prism 120D is changed in the same manner as the photonic crystal waveguide shown in FIG. 74 (b). Matches the direction of propagation. According to this configuration example, coupling with another waveguide element or an optical fiber becomes easy.
- a pentagonal prism 120E is provided so as to be in contact with the oblique end face 50c. Utilizing the total reflection of the prism 120E, the incident direction (or the exit direction) of the incident light 80 incident on the prism 120E is changed within the photonic crystal 50 similarly to the photonic crystal waveguide shown in FIG. Coincides with the propagation direction of the incident light 80 at. According to this configuration example, coupling with another waveguide element or optical fiber becomes easy.
- the mirror 121 is provided so as to be close to the oblique end face 50c of the photonic crystal 50.
- the incident direction (or the outgoing direction) of the incident light 80 incident on the mirror 121 matches the propagation direction of the incident light 80 in the photonic crystal 50.
- the mirror surface 121a of the mirror 121 is a mirror surface made of a metal surface or a multilayer film. According to this configuration example, coupling with another waveguide element or one optical fiber becomes easy.
- FIG. 75 (a) shows an example of the configuration of the photonic crystal waveguide described with reference to FIG. 74 (d) using a prism 122 having a particularly high refractive index instead of the triangular prism 120D.
- FIG. 75 (b) is a band diagram similar to FIG. 73 (b) in the configuration example shown in FIG. 75 (a).
- the solid line 123 shows the coupling state with the photonic band when the incident light 80 incident on the oblique end face 50c is the incident light at the design frequency, and the incident light 80 has a frequency lower than the design frequency.
- the same coupling state when the incident light is small is indicated by a broken line 124.
- the position 126 of the coupling band indicated by the black circle is the upper boundary line 125 of the Brillouin zone.
- ⁇ and ⁇ have been adjusted so that they are at the top. In this case, proceed in the Z direction in the photonic crystal 50
- the position 127 of the coupling band indicated by the white circle is on the upper boundary line 125 of the prinorean zone.
- a material having a refractive index of 3 or more, for example, silicon (having a refractive index of 3.47) can be used as the material of the prism 122.
- the refractive index of the prism 122 is increased so that the position 126 of the coupling band is coupled to the band on the upper boundary 125 of the Brillouin zone.
- FIG. 76 (a) shows a configuration example of a photonic crystal waveguide in which a diffraction grating 130 is interposed between the oblique end face 50c and the incident light 80 near the oblique end face 50c of the photonic crystal 50.
- FIG. 76 (b) is a band diagram similar to FIG. 73 (a) in the configuration example shown in FIG. 76 (a).
- the solid line 161 shows the coupling state with the photonic band when the incident light 80 incident on the oblique end face 50c of the photonic crystal 50 via the diffraction grating 130 is the incident light at the design frequency.
- the dashed line 162 shows the same coupling state when the incident light 80 is incident light having a frequency lower than the design frequency.
- the diffraction grating 130 is desirably designed with a blaze shape or the like so that diffracted light of a specific order becomes strong.
- An example of the configuration of a photonic crystal waveguide combined with a diffraction grating will be described with reference to FIG. 77 (a)-(h).
- FIG. 77 (a) schematically shows a configuration example of a photonic crystal waveguide in which the oblique end face 50c of the photonic crystal 50 and the diffraction grating 130 are arranged in parallel.
- a parallel plane substrate 136 having a diffraction grating 130 engraved on one surface is installed such that the diffraction grating 130 is close to and parallel to the oblique end face 50c. It is acceptable to install the parallel plane substrate 136 so that one surface thereof is in close contact with the oblique end surface 50c.
- the parallel plane substrate 136 is installed such that the other surface of the parallel plane substrate 136, on which the diffraction grating 130 is not cut, is in close contact with the oblique end surface 50c.
- One surface of the parallel plane substrate 136 on which the diffraction grating 130 is cut may be brought into close contact with the oblique end surface 50c.
- the diffraction grating 130 is directly carved on the oblique end face 50c of the photonic crystal 50.
- FIGS. 77 (e)-(h) show configuration examples in which the diffraction grating 130 is not parallel to the oblique end face 50c.
- a triangular prism 137 in which a diffraction grating 130 is carved on one surface is placed on one side of the surface so that the diffraction grating 130 is not parallel to the oblique end surface 50c. It is installed close to the oblique end face 50c.
- a triangular prism 138 having a diffraction grating 130 engraved on one surface is connected to the other surface so that one surface is not parallel to the oblique end surface 50c. Adhered to the oblique end face 50c.
- a thin film having a certain thickness may be formed on the surface of the oblique end face 50c, the thin film may be processed into a prism shape, and then the diffraction grating 130 may be formed on the surface.
- the parallel plane substrate 136 engraved with the diffraction grating 130 is placed in a vertical posture, and one surface is set so as to be non-parallel to the oblique end surface 50c. .
- the diffraction surface of the diffraction grating 130 is perpendicular to the Z-axis, and the arrangement and adjustment of the diffraction grating 130 are easy.
- a right-angled triangular prism 139 having a diffraction grating 130 engraved on one surface is placed on the other surface side so that the diffraction grating 130 is not parallel to the oblique end surface 50c. Is installed in close contact with the oblique end face 50c.
- a thin film having a certain thickness may be formed on the surface of the oblique end face 50c, and the thin film may be processed into a prism shape, and then the diffraction grating 130 may be formed on the surface.
- phase grating on the incident side used in the above-mentioned method (2d)-(2g) may be installed on the end face on the output side with the opposite direction, or the end face on the output side may be opposite to the oblique end face on the incident side. By setting the oblique end face to the angle S, it is possible to return the output light to a plane wave. This facilitates coupling with an optical fiber or the like.
- the waveguide shape may be determined by the connection with the optical fiber or the above characteristics (“very large size, This is preferable because it facilitates installation of electrodes for controlling “wavelength dispersion” and “group velocity anomaly”).
- the optical element shown in FIG. 20 is configured using the photonic crystal waveguide 200 according to the first embodiment shown in FIG.
- the photonic crystal waveguide 200 is formed in a waveguide shape on a suitable substrate 90 using a one-dimensional photonic crystal as a core.
- the same reference numerals as those of the photonic crystal 50 shown in FIG. 1 are used for the photonic crystals that constitute the core of the photonic crystal waveguide 200, and duplicate descriptions are omitted.
- a plane wave incident light 94 is made to enter the end face of the phase grating 92 by a lens member such as a rod lens 95 as a parallel light flux, and is coupled to a core made of the photonic crystal 50.
- This light propagates through the photonic crystal 50 of the photonic crystal waveguide 200 and becomes outgoing light 97 via a lens member such as the phase grating 93 and the rod lens 96.
- the phase gratings 92 and 93 are similar to the phase gratings 64 and 67 shown in FIG.
- photonic crystal 50 is simply referred to as “photonic crystal 50”.
- the photonic crystal waveguide 200 is composed of a one-dimensional photonic crystal 50 having periodicity only in one direction (Y direction, which is the periodic direction), and a direction perpendicular to one direction (in this example, " It has a core 201 through which an electromagnetic wave (propagating light 52) propagates in the XZ plane direction perpendicular to the Y direction, and a cladding 202 as a cladding layer. Any direction parallel to the XZ plane perpendicular to the Y direction (XZ plane direction).
- the one-dimensional photonic crystal 50 constituting the core 201 has a medium A (refractive index n) having a thickness and a medium B (refractive index n) having a thickness t alternately. Stacked cycle a
- the cladding 202 is formed of a photonic crystal having periodicity in the same direction as the photonic crystal 50 on both surfaces perpendicular to the periodic direction (one direction) of the core 201, and propagates inside the core 201. This is a confinement cladding that prevents electromagnetic waves from leaking outside from surfaces perpendicular to the periodic direction (upper and lower surfaces).
- the wavefront formed in the photonic crystal 50 is perpendicular to k, and its wavelength ⁇ and propagation angle ⁇ are
- the period of the photonic crystal 50 as the core 201 is a, and the number of high refractive index layers is (m + 1) (see FIG. 24).
- ⁇ is a force that is the amount of phase change at the interface between the core 201 and the clad 202.
- the electric field becomes antinode at the center of the high refractive index layer.
- Equation (4) Is sufficient.
- the upper and lower claddings 202 are also used as photonic crystals and confined by PBG (photonic band gap: hereinafter, referred to as “PBG”) as in this example shown in FIG.
- the period of the clad 202 may be made slightly shorter than that of the core 201 and the PBG may be shifted to the left.
- the periods of the core 201 and the clad 202 are the same, and the thickness ratio of the two types of media constituting the multilayer film is different.
- a clad 202 of a combination of media different from the core 201
- Photonic crystal 50 composed of ⁇ layers or more with one periodic force
- the determination of confinement based on the band diagram presupposes an infinite periodic structure. Therefore, if the number of periods of the photonic crystal for confinement of the cladding 202 is, for example, about three, confinement is insufficient. And the propagating light may leak to the outside. Of course, it is not preferable to increase the number of periods unnecessarily in terms of cost, durability and accuracy of the multilayer film. It is desirable that the minimum number of periods actually required be determined by experiment or electromagnetic wave simulation.
- Fig. 28 shows the band of the m-th mode in the Y direction in the XZ direction of the inverse space. Since there is no structure in the XZ direction, the photonic band is a circle.
- the wave vector is
- FIG. 30 shows a case where the propagating light travels more generally with a propagation angle ⁇ with respect to the Z direction. In this case as well,
- phase change ⁇ is between 0 ⁇
- the 2L range (single mode area) satisfying the single mode condition is schematically shown in FIG. From Fig. 32, the necessary conditions for the waveguide width 2L to satisfy the single mode condition are:
- ⁇ ( ⁇ ) ⁇ ( ⁇ / cos ⁇ ) / ⁇ ( ⁇ / 2 cos ⁇ ) 2 + a 2 ⁇ 0 ' 5
- the propagation angle ⁇ is the horizontal axis
- 2L is larger than the range of the single mode condition, the number of propagation modes increases, but no light leaks from the side.
- the value of ⁇ which is the limit of the single mode condition is
- the photonic crystal waveguide 200 can produce the following types of waveguides depending on the confinement strength in the ⁇ direction.
- the photonic crystal waveguide 200 can be made into a “fully confined single mode waveguide”.
- the wave power propagating in the core 201 is confined at the side surface of the core 201.
- the phase when the maximum value of the propagation angle ⁇ is ⁇ 90 ° and reflected at the side surface
- the variation is, which is in the range of 0 ⁇ s ⁇ l.
- ⁇ Complete confinement corresponds to a small value of a / ⁇ less than 0.5, and n
- the photonic crystal waveguide 200 can be made into a “fully confined multimode waveguide”.
- the phase change when the light is reflected from the side surface is s ⁇ , which is in the range of 0 ⁇ s ⁇ 1.
- s ⁇ which is in the range of 0 ⁇ s ⁇ 1.
- the following operation and effect can be obtained.
- the waveguide width does not need to be constant and there is no upper limit, a resonator with a free shape can be used.
- the photonic crystal waveguide 200 can be defined as an “incompletely confined single mode waveguide”.
- f ( ⁇ ) a ( ⁇ / cos ⁇ ) / ⁇ ( ⁇ / 2 cos ⁇ ) 2 + a 2 ⁇ 0 ' 5
- the wave propagating in the core 201 is the maximum value of the propagation angle ⁇ (0 ° ⁇ ⁇ 90 °)
- the phase change amount when the light is reflected by the side surface of the core 201 with 0 0 is S 7T, which is in the range of 0 ⁇ s ⁇ l.
- the photonic crystal waveguide 200 can be made into an “incompletely confined multimode waveguide”.
- ⁇ ( ⁇ ) ⁇ ( ⁇ / cos ⁇ ) / ⁇ ( ⁇ / 2cos ⁇ ) 2 + a 2 ⁇ . ' 5
- the wave propagating in the core 201 is the maximum value of the propagation angle ⁇ (0 ⁇ ⁇ 90 °)
- the phase change amount when the light is reflected by the side surface of the core 201 with 0 0 is S 7T, and the range of 0 ⁇ s ⁇ l It is.
- the wide waveguide width facilitates coupling with an external plane wave. It can be used for a waveguide that does not particularly require single mode propagation, for example, for guiding light to a detector.
- the “0th-order mode of the first band” shown in FIG. 25 is not used because its characteristics are close to those of a normal plane wave.
- the photonic crystal shown in FIG. Like the waveguide 200, the cladding 202 also needs to be confined by PBG as a photonic crystal (see FIG. 36).
- the specific conditions are the same as in the case of “propagation on the boundary of the Prillian zone”.
- the second band and the third band have a relationship as shown in FIG. 36.
- the second band and the third band may overlap and the PBG may not exist.
- the side surface of the core 201 of the photonic crystal waveguide 200 (parallel to the YZ plane) Has an exposed electric field pattern of a pine pattern, similar to the propagation on the boundary of the Brillouin zone, but the period in the Y direction is a, and the electric field of the high refractive index layer and the electric field of the low refractive index layer are They differ in strength and are asymmetric.
- the side is in contact with a homogeneous medium with a refractive index n, and the propagating light s
- g ( ⁇ ) is negative, the wave is confined in the core 201 of the photonic crystal waveguide 200, and if it is positive, the side force of the core 201 is leaked light.
- the function g ( ⁇ ) always becomes positive (diverges to + ⁇ ) as it approaches the propagation angle ⁇ force, it can be seen that perfect confinement independent of ⁇ is impossible.
- the mode in the XZ plane can be defined as in the case of "propagation on the Brillouin zone boundary".
- the region that satisfies the single mode condition is the range where the propagation angle ⁇ is 34 ° or less. Note that the value of the propagation angle ⁇ , which is the limit of the single mode condition, can be adjusted by moving the value of n.
- the photonic crystal waveguide 200 can produce the following types of waveguides depending on the confinement strength in the XZ direction.
- the photonic crystal waveguide 200 can be defined as an “incompletely confined single mode waveguide”.
- the wave propagating in the core 201 is the maximum value of the propagation angle ⁇ (0 ⁇ ⁇ 90 °)
- the phase change amount when the light is reflected by the side surface of the core 201 with 0 0 is 3 ⁇ , and is in the range of 0 ⁇ s ⁇ l.
- the photonic crystal waveguide 200 can be made into an “incompletely confined multimode waveguide”.
- the propagating wave has a maximum value of the propagation angle ⁇ (0 ⁇ ⁇ 90 °)
- the phase change when reflected by is 3 ⁇ , which is in the range of 0 ⁇ s ⁇ l.
- the waveguide width 2L is the size where the first or higher mode exists.
- the wide waveguide width facilitates coupling with an external plane wave. It can be used for a waveguide that does not particularly require single mode propagation, for example, for guiding light to a detector.
- the homogeneous medium waveguide 300 is made of a homogeneous material having a finite thickness in one direction (Y direction) and a refractive index ⁇ , and a direction perpendicular to the one direction (Y direction).
- a core 301 through which electromagnetic waves propagate in the XZ plane direction) and a clad 342 are provided.
- the cladding 342 is formed of a one-dimensional photonic crystal having periodicity in the Y direction on both surfaces perpendicular to the Y direction (one direction) of the core 301, and an electromagnetic wave propagating in the core 301 is irradiated in the Y direction. Use a confinement cladding to prevent leakage from surfaces perpendicular to the surface (upper and lower surfaces).
- the thickness in the Y direction of the core 301 made of a homogeneous material having a refractive index of n is 2B.
- Cladding 342 is provided on both surfaces. Let ⁇ be the propagation angle of the wavefront in core 301 (see Figure 40). The phase matching condition of the wave propagating through the core 301 is
- the mode propagation angle ⁇ is
- FIG. 41 shows a case where there are four modes. As the core thickness 2B increases, the number of modes increases.
- the clad 342 is made of a homogeneous material having a refractive index lower than n, only the lower-order mode is confined.
- phase matching condition is as follows.
- phase change amount ⁇ is between 0 and ⁇
- the propagation angle ⁇ is the horizontal axis
- the maximum value of the limit propagation angle ⁇ can be adjusted by moving the value of n.
- the homogeneous medium waveguide 300 shown in FIG. 40 can produce the following types of waveguides depending on the confinement strength in the XZ direction.
- the photonic crystal waveguide 200 can be made into a “fully confined single mode waveguide”.
- the amount of phase change when reflected by the side surface of the core 301 is s ⁇
- the range is 0 ⁇ s ⁇ l.
- the amount of phase change when the light is reflected from the side surface of the core 301 is S7T, and is determined in the range of 0 ⁇ s ⁇ l.
- the wave propagating in the core 301 is the maximum value of the propagation angle ⁇ (0 ⁇ ⁇ 90 °)
- the amount of phase change is 3 ⁇ , which is in the range of 0 ⁇ s ⁇ l.
- the wave propagating in the core 301 is the maximum value of the propagation angle ⁇ (0 ⁇ ⁇ 90 °)
- the phase change amount when the light is reflected by the side surface of the core 301 with 0 0 is S 7T, which is in the range of 0 ⁇ s ⁇ l.
- the wide waveguide width facilitates coupling with an external plane wave. It can be used for a waveguide that does not particularly require single mode propagation, for example, for guiding light to a detector.
- FIG. 46 shows a photonic crystal waveguide 200A according to the fourth embodiment.
- the photonic crystal waveguide 200A is composed of a one-dimensional photonic crystal 50 having periodicity only in one direction (Y direction which is a periodic direction), and an electromagnetic wave (XZ plane direction) perpendicular to the one direction (XZ plane direction). It has a core 201A through which the propagation light 52) propagates, and a cladding 202A.
- the core 201A has the same configuration as the core 201 of the photonic crystal waveguide 200 shown in FIG.
- the cladding 202A is a reflective layer, such as a metal film, formed on both surfaces perpendicular to the periodic direction (one direction) of the core 201A. Electromagnetic waves propagating in the core 201 are applied to both surfaces (upper and lower surfaces) in the periodic direction. ) Is a confinement cladding that prevents leakage to the outside.
- the photonic crystal waveguide 200A having such a configuration also includes the "completely confined multimode waveguide” and the “incompletely confined multimode waveguide” described in the first embodiment, and the second and third embodiments.
- the “incompletely confined multimode waveguide” described in the embodiment can be realized. However, since the reflectance of a metal film or the like is low, it is difficult to form a waveguide that is too long.
- the photonic crystal waveguide 200B is formed of a one-dimensional photonic crystal (periodic multilayer film) similar to the photonic crystal 50 shown in FIG. It comprises a waveguide structure core 230 bent at a right angle.
- a phase grating 240 similar to the phase grating 70 shown in FIG. 15 is disposed on the incident end surface 230a of the core 230.
- an electromagnetic wave simulation by FDTD, time-domain finite difference method
- the boundary condition in the multilayer stacking direction (Y direction) of the photonic crystal constituting the core 230 was set as a periodic boundary, and only four periods of the periodic multilayer structure were extracted for calculation.
- the next medium A and B are alternately stacked for two periods.
- the period a was set to 430 nm.
- the core 230 has a straight waveguide portion 231 having a length of 2 xm in the Z direction from the incident end surface 230a, and an isosceles triangular right-angled bent portion in which the inner side wall is bent at a right angle and the outer side wall is bent at 45 °. 232 and a straight waveguide section 233 having a length in the X direction of 30 ⁇ .
- the outside of the core 230 is a homogeneous medium having a refractive index of 1, and the width of each of the linear waveguide portions 231 and 233 of the core 230 is 3 ⁇ .
- FIG. 49 shows an arrangement of the phase grating 240 and the linear waveguide portion 231 of the core 230.
- the incident light is made incident on the linear waveguide portion 231 from free space (medium C) having a refractive index of 3.48, and a rectangular periodic groove 241 is formed in the medium C at the boundary portion.
- a phase lattice 240 To form a phase lattice 240.
- the shape of the phase grating 240 is optimized so that ⁇ 1st-order diffracted light becomes strong.
- the phase grating 240 is arranged in contact with the core 230 such that the center of the medium C layer, which is the convex portion, coincides with the center of the high refractive index layer of the core 230 (periodic multilayer film).
- FIG. 50 shows the intensity distribution of the electric field at the center of the high refractive index layer of the core 230.
- the propagating light is a mode based on the first band on the boundary of the Brillouin zone, and the wavelength ⁇ in the propagation direction is 4400 nm.
- the photonic crystal waveguide 200B can be bent sharply with single mode propagation, Since the waveguide width is small, the elements can be extremely small. Also, n is 0.348
- FIG. 51 shows a photonic crystal waveguide 200C according to the sixth embodiment.
- This photonic crystal waveguide 200C is the same as the photonic crystal waveguide 200B except that the waveguide width (3 ⁇ m) of the photonic crystal waveguide 200B in FIG. 47 is 5 ⁇ m. Therefore, the same reference numerals are given except for the core 230 '.
- the perfect confinement condition is the same as that of the photonic crystal waveguide 200B, so that the condition is satisfied.
- FIG. 52 shows the electric field intensity distribution at the center of the high refractive index layer of the one-dimensional photonic crystal (periodic multilayer film) constituting the core 23CT.
- the electric field pattern after the right-angle bending is more complicated than that of the photonic crystal waveguide 200 in FIG. 47, and the 0th and 1st modes are mixed. There is almost no light leakage to the air layer.
- FIG. 53 shows a photonic crystal waveguide 200D according to the seventh embodiment.
- the waveguide width at the incident part of the core 230 ⁇ made of a one-dimensional photonic crystal is set to be wide so as to satisfy the multi-mode propagation condition, and the waveguide width is narrowed in a tapered shape in the middle to simplify the waveguide.
- This is a “tapered waveguide” that converts into a one-mode waveguide.
- Waveguide structure after the incident end face of the core 230B was a linear waveguide 231B, a tapered waveguide 232 B of Daunte path type, a down taper structure composed of a linear waveguide 233B.
- the width of the straight waveguide 231B in the X direction is 5 ⁇ m, and the length in the Z direction is 5 ⁇ m.
- the width in the X direction of the tapered waveguide 232B changes from 5 ⁇ m to 3 ⁇ m, and the length in the Z direction is 6 ⁇ m.
- the width in the X direction of the linear waveguide 233B is 3 ⁇ m, and the length in the Z direction is 10 ⁇ m.
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Abstract
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US10/565,012 US7310468B2 (en) | 2003-07-18 | 2004-07-16 | Photonic crystal waveguide, homogeneous medium waveguide, and optical device |
EP04747696A EP1653260A1 (en) | 2003-07-18 | 2004-07-16 | Photonic crystal waveguide, homogeneous medium waveguide, and optical device |
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Also Published As
Publication number | Publication date |
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US7310468B2 (en) | 2007-12-18 |
US20060251368A1 (en) | 2006-11-09 |
EP1653260A1 (en) | 2006-05-03 |
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