CN107976733B - All-dielectric polarization-independent angle filter - Google Patents

All-dielectric polarization-independent angle filter Download PDF

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CN107976733B
CN107976733B CN201711200014.8A CN201711200014A CN107976733B CN 107976733 B CN107976733 B CN 107976733B CN 201711200014 A CN201711200014 A CN 201711200014A CN 107976733 B CN107976733 B CN 107976733B
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钱沁宇
王钦华
徐常清
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Suzhou University
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Abstract

The present invention proposes an all-dielectric polarization independent angular filter with a one-dimensional (1D) Photonic Crystal (PC) composed of semiconductor compatible silicon/silicon dioxide pairs. Efficient polarization independent angle filtering for normal incidence is achieved using approximately symmetric band distributions of P and s polarization components and Fabry-Perot (F-P) resonance. The angle filter was prepared over a large area (5 cm x5 cm) using a vacuum magnetron sputtering scouting design and experiments. Experimental measurements showed that the divergence angle of the polarization-independent transmitted beam for the angle-filtered sample at 1550nm was only 2.2 °, with a transmission at normal incidence of up to 0.8. The proposed angular filter presents an efficient way to design and implement semiconductor-compatible all-dielectric and polarization-independent angular filters in a simple structure and easy to manufacture, with a wide range of potential applications in illumination, beam steering, optical coupling and optical communication.

Description

All-dielectric polarization-independent angle filter
Technical Field
The invention relates to the technical field of optics, in particular to an all-dielectric polarization-independent angle filter.
Background
The complete manipulation of light has been an important issue in the field of optics. An electromagnetic wave can be characterized by its phase, amplitude, frequency, polarization and direction of propagation. A great deal of work has been published to manipulate amplitude, phase, frequency and polarization. Directional filters (or angular filters) have also been extensively studied and have hitherto been an important issue. Zero-refraction materials (ZIMs) have been investigated for angular filtering. Due to the wave vector matching between the ZIM and the surrounding material, the ideal ZIM can filter all non-normal incidence waves. Near-zero dielectric constant materials (ENZ) have a dielectric constant near zero, resulting in a refractive index also near zero, and are therefore commonly used to implement ZIM. Nanowires and multilayer metamaterials made of plasmonic metals are the two most common designs for ENZ materials. Alekseyev et al propose silver nanowire arrays grown in an anodized aluminum film to realize an incident angle filter of p-polarization (electric field vibration direction in the incident plane) at a wavelength of 600nm with a filter angle of 20 °, but with very low transmittance (only 0.12) due to impedance mismatch and plasmon metal loss. It is also noted that ENZ can only operate at one of p-or s-polarized incidence (the direction of electric field vibration is perpendicular to the plane of incidence), which greatly limits its application.
Photonic Crystals (PCs) with dirac cone energy bands (DLCDs) can also be used as angular filters for light of a particular polarization, since PCs with DLCDs can be approximated as dual-zero materials (DZM), i.e. the permittivity and permeability approach zero at the frequency of the dirac point at the same time. In 2013, Moitra et al reported a DZM consisting of a bar of 10 alternating silicon/silicon dioxide layers. The DZM shows good high transmission angle filtering properties over an incident angle of 30 °. However, DZM can also be used only for TM polarized light incidence, and it is difficult to prepare the multilayer silicon/silica rod with a high aspect ratio (height/width) of 3 μm/0.26 μm, especially in large area preparation. In 2014, Shen et al proposed 1DPC with different periodicities to transmit plane waves of a particular incident angle (brewster angle) and reflect incident waves of other incident angles. However, such an angle filter must be immersed in a specific liquid having a specific magnetic permeability and dielectric constant in order to improve efficiency. It is also noted that this angular filter can only be used for oblique incidence at brewster angles (as opposed to conventional normal incidence) and, like other angular filters, is only applicable to p-polarized incidence.
Polarization independent angular filters have not been realized since s-and p-polarized incident waves exhibit significant differences at non-normal incidence.
In view of the above-mentioned drawbacks, the present designer has made active research and innovation to create an all-dielectric polarization-independent angle filter, which has industrial application value.
Disclosure of Invention
The invention aims to provide an all-dielectric polarization-independent angle filter which can realize normal incident angle filtering and has polarization-independent efficient angle filtering characteristics.
In order to achieve the purpose, the invention adopts the following technical scheme:
an all-dielectric polarization-independent angle filter is characterized by comprising a substrate and two optical coating layers with different dielectric constants stacked on the substrate, wherein one optical coating layer is made of an all-dielectric photonic crystal compatible with a semiconductor, and the other optical coating layer is made of a polarization-independent photonic crystal.
Further, two optical coating layers are periodically stacked on the substrate in an alternating mode.
Furthermore, the two optical coating layers are respectively a silicon layer and a silicon dioxide layer.
Further, the substrate is silicon dioxide, and the optical coating layer stacked on the substrate is the silicon layer.
Further, the thickness L of the silicon layer 180 ± 8nm, the thickness L of the silicon dioxide layer2=454±32nm。
Further, the silicon layers and the silicon dioxide layers are alternately deposited on the substrate in a vacuum ion source sputtering coating mode.
The invention has the beneficial effects that: the Polarization Independent Angle Filter (PIAF) employs an approximately symmetric energy band structure of p and s polarization components near the band edges to achieve normal incidence angle filtering. By designing the frequency of the band edge, the divide by k can be obtainedyTotal reflection of light rays other than 0 point (i.e. normal incidence is the only angle at which incident light can propagate) and this angular filter ensures high transmission of light by optimizing fabry-perot (F-P) resonance in the 1D structure. The experimental result shows that under the condition that the design wavelength is 1550nm, the transmission rate of normal incidence is as high as 0.80, the divergence angle of a transmitted light beam is only 2.2 degrees, and the polarization-independent efficient angular filtering characteristic is realized.
Drawings
FIG. 1 is a diagram of a PIAF structure and experimental measurements provided by an embodiment of the present invention, where (a) shows a schematic drawing of a proposed 1D all-dielectric PIAF, and (b) is an electron micrograph of the fabricated PIAF, where the light color is a silicon (Si) layer and the dark color is silicon dioxide (SiO)2) A layer, graph (c) is an experimentally measured optical path graph, and graph (d) is a transmittance at an incident angle of 0 ° to 80 ° when the measured wavelength is 1550 nm;
fig. 2 is an angular divergence measurement of the PIAF, fig. 2(a) is a schematic of the light path, fig. 2(b) - (g) are six photographs taken at different distances from the PIAF sample, from 20 to 41mm, and the corresponding gaussian fit results, fig. 2(h) is a linear fit of r at different positions;
FIG. 3 shows theoretical design and analysis of PIAF, and FIG. 3(a) shows band structures of p-and s-polarized waves, black oblique lines represent optical axes, and black waterThe flat solid line indicates a wavelength of 1550nm, and the black horizontal broken line indicates kyBand-edge frequency at 0 (ω 0.33(2 π c/a), a wavelength of 1618nm), fig. 3(b) is the electric field distribution when a point source is placed under a PIAF; FIG. 3(c) shows a case where a point light source is placed on SiO2Electric field distribution in the lower process, wherein an external medium is set to be air, and the wavelength is 1550 nm;
FIG. 4 is a transmittance spectrum of a PIAF, FIG. 4(a) is a transmittance spectrum with a different number of units at normal incidence, and FIG. 4(b) is a transmittance spectrum with different Si and SiO in each cell2The transmission spectrum of the thickness, the number of the units is fixed to 10, and the total thickness of each unit is fixed to L1+L2=534nm;
Fig. 5 is a comparison of simulated and experimental transmittance spectra of the PIAF, fig. 5(a) is the transmittance spectrum at normal incidence, fig. 5(b) is the transmittance spectrum at 1550nm incident at angles of incidence varying from 0 ° to 30 ° with 10 layers.
Detailed Description
The technical scheme of the invention is further explained by the specific implementation mode in combination with the attached drawings.
The invention provides an all-dielectric polarization-independent angle filter (PIAF), which comprises a substrate and two optical coating layers with different dielectric constants, wherein the two optical coating layers are periodically stacked on the substrate in an alternating mode, one optical coating layer is made of all-dielectric photonic crystals compatible with semiconductors, and the other optical coating layer is made of polarization-independent photonic crystals. Specifically, the substrate is silicon dioxide, the two optical coating layers are respectively a silicon layer and a silicon dioxide layer, and the optical coating layer stacked on the substrate is the silicon layer.
Experiments prove that the semiconductor compatible all-dielectric and polarization-independent one-dimensional photonic crystal can realize normal incidence angle filtering.
Figure 1 shows the operating performance of 1D PIAF at 1550nm wavelength. Each unit is respectively composed of L180nm and L2454nm silicon (Si) and silicon dioxide (SiO)2) The layers are formed. As shown in FIG. 1(a), electromagnetic waves are emitted from the Substrate (SiO)2) The direction is incident. Sputtering Si and SiO by vacuum ion source2Alternate deposition of layersSiO at 5cm by 5cm2On a substrate. Fig. 1(b) shows an electron micrograph of the 1D all-dielectric PIAF. The transmission was measured using a near infrared laser (Agilent Technologies, 81960A, wavelength tuning range 1503nm to 1632nm) and a detector (Thorlabs, PAX5710IR1-T) (FIG. 1 (c)). Polarizers and half-wave plates are used to adjust the polarization direction. As shown in fig. 1(c), the transmittance of the incident beam at a design wavelength of 1550nm was measured when the PIAF was tilted at different angles. Fig. 1(d) illustrates the angular filtering performance of the PIAF, and it can be seen that the transmission is 0.8 at normal incidence, and rapidly drops to 0.17 as the angle of incidence increases to 2 °, respectively, and the transmission drops to zero as the angle of incidence increases to 5 °. It can also be seen that the PIAF exhibits the same angular filtering performance for both p-and s-polarized light incidence, which clearly demonstrates its polarization independent performance.
To further demonstrate the angular filtering effect, the experimental setup shown in fig. 2(a) was used to measure the divergence angle of the laser beam of the transmitted light transmitted through the PIAF. The laser was first expanded with a microscope objective (20 x) and then passed through a PIAF. The light intensity at different positions of the transmitted PIAF beam is recorded by an infrared camera (XENICS, XEVA-1.7-320, 320X 256 pixels). Fig. 2(b) shows a photograph of a transmission through the PIAF and a corresponding light intensity profile fitted by MATLAB. It can be observed that the PIAF has good angular filtering properties for the beam. A three-dimensional fit of these intensity distributions can be made to obtain a quantitative estimate of the transmitted beam size at different positions:
Figure BDA0001480679140000061
where I is the intensity (grey value in the photograph) and x and y represent the coordinates of the light points in the photograph. A, B, C and D are fitting parameters, where A is the maximum value of the gray values in all pixels, and B and D are the x-coordinate of the column where the sum of the gray values is maximum and the y-coordinate of the row where the sum of the gray values is maximum, respectively. Fig. 2(b) - (g) are fitted gaussian distributions of experimental beam spots at distances of 20mm to 41mm from the PIAF, with step sizes of 1mm (only six of which are shown). FIG. 2(h) shows the fitted beam size r (defined as r) at different positionsThe central light point with the maximum intensity and the intensity reduced to 1/e of the central light intensity2The distance between (d) and (d). The slope of the line in fig. 2(h) represents the divergence angle of the transmitted beam. FIG. 2(h) uses a linear fit and yields the following relationship: r-0.0379 d +5.6240 where d is the distance from the PIAF to the CCD camera (as shown in fig. 2 (a)). The divergence angle of the transmitted beam can be calculated as θ ═ arctan0.0379 ≈ 2.2 °, which is consistent with the previous results (fig. 1 (d)).
Theoretical design and analysis of the PIAF can be based on Si and SiO2The layer formation is carried out in units of respective thicknesses L10.15a and L20.85a, where a is the lattice constant (a 534 nm). Incident electromagnetic wave
Figure BDA0001480679140000071
It may be a p-polarized wave or an s-polarized wave. For s-polarized waves, the electric field is perpendicular to the x-y plane, and for p-polarized waves the magnetic field is oriented perpendicular to the x-y plane, as shown in FIG. 3 (a). The band structures of p-and s-polarized waves are shown in fig. 3 (a). The light and dark grey areas represent the propagation states of the p and s polarized wave incident, respectively. The white areas represent regions of directional bandgap. These states in the bandgap can propagate in a homogeneous medium but can decay in the PIAF. The black diagonal lines represent the optical axis. Above the optical axis, incident waves from the substrate can propagate freely in the PIAF. Below the optical axis, there is an evanescent wave that cannot propagate for a long distance. It is noted that there is an omnidirectional reflection region in the first bandgap, which is defined between the band edge and the optical axis. At a frequency above and near the band edge (black horizontal dotted line, band edge frequency ω 0.33(2 π c/a), wavelength 1618nm) in FIG. 3(a) (i.e., black horizontal solid line, corresponding to wavelength 1550nm), the eigenstates in the PIAF are distributed at kyNear 0, this indicates that light waves near normal incidence can pass through the PIAF sample. For kyNot equal to 0, the transmittance will decrease rapidly due to the presence of the directional bandgap. Thus, such a 1DPC structure can be applied to achieve angular filtering, i.e. only the positive incident wave will be transmitted through the PC structure, while all other incident waves will be reflected due to the presence of the directional bandgap. Also note that p and s above the optical axis in fig. 3(a)The energy band diagram of the polarized wave is almost symmetrical, which provides a physical theoretical basis for the polarization independent angular filtering of the proposed PIAF. The effect of angular filtering by the PIAF can also be visualized from the numerical simulation shown in fig. 3 (b). In fig. 3(b), the point light source is placed directly below the PIAF. It can be seen that the PIAF structure effectively filters out large k as expectedyWhile near-normal incidence electromagnetic waves can pass through the PIAF with a small divergence angle. In contrast, when the PIAF is pure SiO2Instead (fig. 3(c)), it can be seen that the transmitted wave of the point source propagates in all directions (spherical wave).
However, the transmittance at normal incidence through the PIAF is typically very low due to the impedance mismatch of the 1DPC structure and the surrounding medium. To improve energy efficiency, the F-P effect can be exploited to achieve high transmission and sharp resonance peaks in the transmission spectrum. The F-P formants can be designed using the scaling characteristics of maxwell's equations. If the linear dimensions of the structures in a given PC are scaled uniformly by a factor a, the frequency ω and the wave vector k should also be scaled according to a relationship, which satisfies the relationships ω '═ ω/α and k' ═ k/α. The transmission spectra (8-12 layers) of the PIAF structures with different number of layers of cells are plotted in FIG. 4 (a). Simulations were performed using a finite difference time domain method (logical FDTD Solutions, Canada). In the simulation, L is used180nm and L2454 nm. As can be seen from fig. 4(a), the F-P formants vary with the number of layers. Only the rightmost peak can be used to design the corner filter because it is closest to the band edge. This behavior can be used to tune the operating wavelength, as shown in FIG. 4(a), by L180nm and L2A 10-layer PIAF structure of 454 yields an operating wavelength of 1550nm (black vertical line) nanometers. The rightmost peak can be adjusted to be in the range of 1535nm to 1558nm (indicated by the dashed circle in fig. 4 (a)).
By varying the Si and SiO in each unit2(L1And L2) The F-P resonance peak can also be adjusted in a wider range because of the change of L1And L2The band-edge frequency varies (conversely, the band-edge frequency does not vary when the number of layers is varied), where L1And L2(fixed a ═ L)1+L2534nm) will result in a change in the dielectric constant distribution. When the dielectric constant of the unit is changed from epsilon (r) to epsilon (r)
Figure BDA0001480679140000081
The eigenfrequency will vary from ω according to the formulankTo
Figure BDA0001480679140000082
Figure BDA0001480679140000091
Wherein Enk(r) represents the field distribution of the unperturbed mode. Under the guidance of equation (2), we can adjust the thickness of silicon (the total thickness of silicon and silicon dioxide is fixed) to adjust the eigenfrequency (operating wavelength). Fig. 4(b) shows the ability to adjust the transmittance peak of a normal-incidence wave around 1550nm having a 10-layer PIAF structure. When silicon (L)1) The wavelength of the peak closest to the band edge can be tuned from 1530nm to 1575nm (indicated by the dashed circle in FIG. 4 (b)) as the thickness of the layer varies from 60nm to 100nm, and can be at L1A peak at wavelength 1550nm is obtained at 80nm (vertical line in fig. 4 (b)). It should be noted that Si and SiO may be used2And the number of unit cells to achieve similar performance of the PIAF.
In FIG. 5, a PIAF (L) is given180. + -.8 nm and L2454 ± 32nm) and theory (L)180nm and L2454nm) results. Fig. 5(a) and 5(b) show experimental and simulated transmittance comparisons at normal incidence and different incidence angles of 0 ° to 30 ° at a wavelength of 1550nm, respectively. It can be seen that the experimental results agree well with the theoretical simulation, but the transmittance is slightly less (0.80 in the experiment, 0.92 in the normal incidence simulation). These deviations may be due to errors in fabrication, such as the thickness of each layer, which may weaken the F-P resonance. The transmittance spectra of the p-and s-polarized incident waves almost coincide, which demonstrates excellently polarization independent angular filtering of the manufactured PIAFAnd (4) wave property.
The technical principle of the present invention is described above in connection with specific embodiments. The description is made for the purpose of illustrating the principles of the invention and should not be construed in any way as limiting the scope of the invention. Based on the explanations herein, those skilled in the art will be able to conceive of other embodiments of the present invention without inventive effort, which would fall within the scope of the present invention.

Claims (5)

1. An all-dielectric polarization-independent angle filter is characterized by comprising a substrate and two optical coating layers with different dielectric constants stacked on the substrate, wherein one optical coating layer is made of an all-dielectric photonic crystal compatible with a semiconductor, and the other optical coating layer is made of a polarization-independent photonic crystal;
the two optical coating layers are respectively a silicon layer and a silicon dioxide layer;
at fixed a ═ L1+L2In the case of 534nm, adjust L1And L2The frequency of the time band edge changes, and when the dielectric constant of the unit changes from epsilon (r) to epsilon (r)
Figure FDA0002453005750000011
The eigenfrequency will vary from ω according to the formulankTo
Figure FDA0002453005750000012
Figure FDA0002453005750000013
Wherein E isnk(r) field distribution of unperturbed modes, L1Represents the thickness of the silicon layer, L2Represents the thickness of the silicon dioxide layer.
2. The all-dielectric polarization-independent angular filter of claim 1, wherein two of said optical coatings are periodically stacked on said substrate in an alternating manner.
3. The all-dielectric polarization-independent angle filter of claim 1, wherein the substrate is silicon dioxide and the optical coating layer stacked on the substrate is the silicon layer.
4. The all-dielectric polarization-independent angular filter of claim 1, wherein the thickness L of the silicon layer180 ± 8nm, the thickness L of the silicon dioxide layer2=454±32nm。
5. The all-dielectric polarization independent angle filter of claim 1, wherein the silicon layers and the silicon dioxide layers are alternately deposited on the substrate by vacuum ion source sputter coating.
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