CN104808272B - Produce the two-dimensional encoded phase grating of perfect vortex array - Google Patents

Abstract

A kind of two-dimensional encoded phase grating for producing perfect vortex array, the grating is that coding is loaded into vortex phase and pyramid phase place and forms in pure phase bit architecture grating, carries the pyramid phase place of the vortex phase and different divergence of different topology lotus in the different diffraction level time of produced diffractive light field.Multiple ring-shaped light spot arrays for carrying different topology lotus can be produced on its Fourier transform face simultaneously by the two-dimensional encoded phase grating, and these ring-shaped light spots are equal in magnitude.The perfect vortex in terms of fiber optic communication orbital angular momentum multiplexing of this annular with different topology lotus, formed objects has important application prospect.

Description

Produce the two-dimensional encoded phase grating of perfect vortex array

Technical field

The present invention relates to a kind of two-dimensional encoded grating, particularly a kind of two-dimensional encoded phase place light for producing perfect vortex array Grid.

Background technology

Optical eddy has obtained everybody and has extensively closed as the core research contents of contemporary optics important branch singular optics Note.Optical eddy is the proper phase of laser eigen mode Laguerre Gaussian beam, can be expressed asWherein open up for l Flutter lotus,For angular coordinate.Each photon of this light field with vortex phase structure is carriedOrbital angular momentum , and this orbital angular momentum OAM can be for delivery on the particulate for being radiated (OAM).Just because of this vortex phase, optics There is a phase singularity in vortex center, be blackening so as to cause the central representation of vortex light field.At present, optical eddy is wide General be applied to optic communication OAM be multiplexed (including FSO and fiber optic communication), optical imagery, the micro- manipulation of optics, and The fields such as quantum optices.Wherein, fiber optical communications OAM multiplex techniques are to obtain light educational circles and industrial quarters extensive concern in nearly 2 years The Fibre Optical Communication Technology of great practical prospect.This OAM multiplex techniques, in conjunction with current ripe wavelength-division multiplex, palarization multiplexing, The message capacity of current fiber optic communication can be brought up to Gigabits per second (Gbit/s) or even too bits per second (Tbit/s).

At present, the ring radius of traditional optical eddy increases with the increase of topological charge, and this characteristic causes traditional vortex It is difficult to be coupled in same optical fiber on a large scale.2013, Ostrovsky et al. proposed perfect optical eddy concept first, this Plant the perfect ring radius being vortexed unrelated with topological charge【Opt.Lett.38,534(2013)】.But, Ostrovsky et al. is realized Project plan comparison is complicated, and the perfect poor signal to noise being vortexed for producing.Recently, Canadian Lavel universities Rusch et al. is proposed Another kind of scheme for realizing perfect vortex【Opt.Lett.40,597(2015)】.The program is using vortex phase and another angle Cone Phase Stacking, then achieves perfect vortex on Fourier transform face.However, in actual applications, it would be desirable to which one is Row carry the perfect vortex of different topology lotus.Above-mentioned all schemes are all difficult while producing a large amount of perfections for carrying different topology lotus It is vortexed.

Content of the invention

The purpose of the present invention is to propose to a kind of two-dimensional encoded phase grating for producing perfect vortex array, the two-dimensional encoded phase Position grating can produce a series of perfect vortexs for carrying different topology lotus, and this will tool in the multiplexing of fiber optic communication orbital angular momentum There is very important using value.

The present invention is that coding carries vortex phase and pyramid phase place wherein using two-dimensional encoded phase grating, so as to can There are multiple perfect ring-shaped light spot arrays being vortexed to produce in far field.This perfect vortex array possesses ring size and topological charge Independent property, thus have important using value in fiber optic communication orbital angular momentum multiplex technique.

The technical solution of the present invention is as follows：

A kind of two-dimensional encoded phase grating for producing perfect vortex array, its feature are that the two-dimensional encoded phase grating is Phase-only modulation, and the transmittance function of the two-dimensional encoded phase grating meets relational expression：

Wherein, arg { } is represented and is taken phase operation；For the polar coordinates in the grating planar；Normalization position coordinates arrow AmountWherein (x, y) is the rectangular co-ordinate in grating planar, Λ_xAnd Λ_yFor The grating is along x the and y directions cycle；C_mAnd C_nFourier coefficient respectively on x and y directions.VectorRepresent two dimension The two-dimentional diffraction time of grating, wherein m and n represent diffraction time of the two-dimensional grating along x and y directions respectively；Vector The underlying topology lotus of the vortex phase entrained by two-dimensional grating, wherein l_xAnd l_yRepresent the two-dimensional grating in x and y directions respectively Upper underlying topology lotus, for N_x×N_yTwo-dimensional encoded grating, l_xAnd l_yMeet relational expression l_y/l_x=N_xOr 1/N_y；, N_xAnd N_y? It is the positive integer more than 1；VectorPyramid phase basis diverging angular dimensions entrained by two-dimensional grating, wherein β_x And β_yThe two-dimensional grating in the x and y direction basis diverging angular dimensions is represented respectively, for N_x×N_yTwo-dimensional encoded grating, β_xWith β_yMeet relation beta_y/β_x=N_xOr 1/N_y；β₀Angular dimensions is dissipated for extra pyramid phase place.

The fourier coefficient C of described two-dimensional encoded phase grating_mAnd C_nMeet relational expression：

Wherein, Φ (x) or Φ (y) is the phase distribution in the two-dimensional phase grating monocycle along x and y directions, It can be write asWherein, j represents x or y；Parameter Q and P can be write asWherein, { μ_nAnd { α_nIt is respectively harmonic component Corresponding amplitude and phase place；{q_nFor corresponding n-th diffraction time on x or y directions, n=1, wherein 2 ... N, N are represented Total diffraction time number on x or y directions, remembers that the diffraction time number on x and y directions is respectively N_xAnd N_y.

The fourier coefficient C of described two-dimensional encoded phase grating_mAnd C_nObtained by following Optimization Steps：

1. the N for optimizing as needed_x×N_yDot matrix number, determines the diffraction time { q of the needs on x or y directions_n, wherein N_xAnd N_yRepresent the diffraction time number on x and y directions；

2. { μ is set_n1 is, take fixed { α at random_nA class value, optimize { α_nSo that being diffracted into the N on x or y directions_x Or N_yEnergy in individual diffraction time is maximum；

If the N being 3. diffracted on x or y directions_xOr N_yEnergy in individual diffraction time is maximum, takes now { α_nValue be {α_nValue；If the N being diffracted on x or y directions_xOr N_yEnergy in individual diffraction time is not reaching to maximum, returns 2.；

4. { α is taken_nFor previous step optimize at the end of { α_nValue, take fixed { μ at random_nA class value, optimize { μ_nMake diffraction N on x or y directions_xOr N_yBetween individual diffraction time, energy uniformity is best；

If the N being 5. diffracted on x or y directions_xOr N_yEnergy uniformity between individual diffraction time preferably, takes now { μ_n} Value be { μ_nValue；If the N being diffracted on x or y directions_xOr N_yEnergy uniformity between individual diffraction time be not reaching to best, Return 4.；

7. according to { μ_nAnd { α_nValue, according to formulaWith Calculate fourier coefficient C_mAnd C_n.

The technique effect of the present invention：

The present invention passes through coding in two-dimensional phase grating and brings vortex phase and pyramid phase place in, it is possible to achieve in the two dimension The far field of encoding phase grating produces has multiple perfect ring-shaped light spot arrays being vortexed.These perfections are vortexed according to rectangular array Arrangement, and the ring size of each ring-shaped light spot is unrelated with entrained topological charge.Can be produced simultaneously by an incident field Raw carrying different topology lotus, ring radius identical perfection vortex array, thus in fiber optic communication orbital angular momentum multiplex technique There is very important application prospect.

Description of the drawings

Fig. 1 is the two-dimensional phase distribution of the two-dimensional encoded phase grating that the present invention produces perfect vortex array.

Fig. 2 is the specific design flow process of the two-dimensional encoded phase grating that the present invention produces perfect vortex array.

Fig. 3 is distribution of light intensity theory mould of 5 × 5 two-dimensional encoded phase gratings on NA=0.025 lens focal planes Intend figure (left side), and corresponding diffraction time and the corresponding topological charge distribution of each diffraction time.

Fig. 4 is the one-dimensional distribution of light intensity distribution along Fig. 3 left figures shown in dotted line.

Specific embodiment

Fig. 1 is the two-dimensional phase distribution of the two-dimensional encoded phase grating embodiment that the present invention produces perfect vortex array, Its transmittance function can be expressed as：

Wherein, arg { } is represented and is taken phase operation；For the polar coordinates in the grating planar, (x, y) is grating planar Interior rectangular co-ordinate, Λ_xAnd Λ_yIt is the grating along x the and y directions cycle； Represent that the diffraction time of two-dimensional grating, wherein m and n represent diffraction time of the two-dimensional grating along x and y directions respectively；The underlying topology lotus of the vortex phase entrained by two-dimensional grating, wherein l_xAnd l_yRepresent the two-dimensional grating in x respectively With underlying topology lotus on y directions；Pyramid phase basis parameter entrained by two-dimensional grating, wherein β_xAnd β_yPoint The two-dimensional grating in the x and y direction underlying parameter is not represented.For N_x×N_yTwo-dimensional encoded grating, l_xAnd l_yMeet relational expression l_y/l_x=N_xOr 1/N_y；β_xAnd β_yMeet relation beta_y/β_x=N_xOr 1/N_y, wherein, N_xAnd N_yRepresented along x and y directions respectively Total diffraction time number.β₀Angular dimensions is dissipated for extra pyramid phase place.Coefficient C_mAnd C_nMeet relational expression

Wherein, Φ (x) or Φ (y) is the phase distribution in the two-dimensional phase grating monocycle along x and y directions, and it can be write as

Wherein, j represents x or y；Parameter Q and P can be write as：

Wherein, { q_nFor corresponding n-th diffraction time on x or y directions, n=1, wherein 2 ... N, N are represented in x or y Total diffraction time number on direction, remembers that the diffraction time number on x and y directions is respectively N_xAnd N_y；{μ_nAnd { α_nBe respectively The corresponding amplitude of harmonic component and phase place.By adjusting { α_nAnd { μ_n, we can mainly be distributed the energy of optical grating diffraction field In the several diffraction times that wants.Fig. 2 gives the specific design stream of this two-dimensional encoded phase grating proposed by the present invention Journey.First, the N for optimizing as needed_x×N_yDot matrix, sets { μ_n1 is, optimize { α_nDiffraction efficiency is made substantially to concentrate In N_x×N_yIn diffraction time.Then, optimize { μ_nSo that the energy uniformity of diffractive light field is best distributed in N_x×N_yIndividual level On secondary.Once obtain { μ_nAnd { α_nOccurrence, we substitute into formula (2), (3) and (4), it is possible to obtain in formula (1) Fourier coefficient.Then based on the actual application requirements, determine the periods lambda on x and y directions_xAnd Λ_y, carry vortex phase base Plinth topological chargeThe pyramid phase basis diverging angular dimensions of carryingAnd the diverging of extra pyramid phase place Angular dimensions β₀.Then, the transmittance function of designed two-dimensional encoded phase grating is obtained according to formula (1).This continuous phase The two-dimensional grating of bit distribution can be realized by spatial light modulator in practice, or passes through grayscale lithography or multi-step set Carve and directly process on optical base-substrate.

Embodiment

Below by taking 5 × 5 two-dimensional encoded phase gratings as an example, for its operation wavelength (1550nm), providing one kind can produce The two-dimensional encoded phase grating of perfect vortex array.If the following l of the underlying topology lotus value of coding vortex phase_x=5, l_y=1； The following β of underlying parameter value of coding pyramid phase place_x=1 × 10^-3And β_y=5 × 10^-3；Extra pyramid phase beta₀=3 × 10^-2. The number of cycles along x and y directions in aperture is 30.According to the specific design flow process be given in Fig. 2, once obtain Fourier Coefficient, according to formula (1), we can obtain the transmitance distribution of 5 × 5 two-dimensional encoded phase grating.Fig. 1 give this 5 The phase distribution of × 5 two-dimensional encoded phase gratings, in figure, black portions represent that 0 phase place, white portion represent 2 π phase places.This company The two-dimensional encoded grating of continuous phase distribution can be realized by the spatial light modulator of a phase-only modulation.With Germany As a example by the PLUTO-TELCO-013-C model spatial light modulators of HoloEye companies, its operation wavelength covers 400～1700 and receives Rice scope.Whole spatial light modulator pixel number 1920 × 1080, single pixel size is 8 microns, and effective active area is about 15.36mm×8.64mm.We are then about 35 pixels in each cycle using wherein 8.5mm × 8.5mm active areas, this Phase distribution needed for being enough to realize in the monocycle.

As shown in Fig. 3 left figures, this 5 × 5 two-dimensional encoded phase gratings of our theoretical modelings are in NA=0.025 numerical apertures Distribution of light intensity distribution on the lens focal plane in footpath.It can be seen that we have obtained 5 × 5 equal-sized annular Spot array.The corresponding diffraction time of these ring-shaped light spots as shown in Fig. 3 right figures, diffraction time { q in the x-direction_n}={ 0,1, 2,3,4 }；Diffraction time { q in the y-direction_n}={ -2, -1,0,1,2 }.These corresponding topologys of corresponding 5 × 5 perfections vortex Lotus is respectively -2, -1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22.Fig. 4 Give dotted line along Fig. 3 one-dimensional intensity distribution, there it can be seen that the diameter of produced ring-shaped light spot is about 490 λ, right It is 760 microns to answer 1550 wavelength.Our theoretical modeling result shows, by this two-dimensional encoded phase place light proposed by the present invention Grid, can produce the perfect vortex array for carrying different topology lotus simultaneously, and these perfection vortexs show as a series of equal in magnitude Ring-shaped light spot, this will be the practical offer solid foundation of fiber optic communication orbital angular momentum multiplex technique.

In sum, the present invention proposes a kind of specifically setting for two-dimensional encoded phase grating for producing perfect vortex array Meter method and embodiment, and by taking NA=0.025 condenser lenses, 5 × 5 two-dimensional encoded phase gratings as an example, for its work Wavelength 1550nm, proposes a kind of two-dimensional encoded phase grating specific design flow process and feasible technology implementation route.

The two-dimensional encoded phase grating of the perfect vortex array of the above generation only expresses a kind of concrete reality of the present invention Mode is applied, therefore limiting the scope of the invention can not be interpreted as.It should be pointed out that common for this area For technical staff, on the premise of without departing from basic thought of the present invention, being embodied as that this patent can also be proposed is thin Section makes some deformations and improvement, and these belong to protection scope of the present invention.

Claims (3)

1. a kind of two-dimensional encoded phase grating for producing perfect vortex array, it is characterised in that the two-dimensional encoded phase grating is pure Phase-modulation, and the transmittance function of the two-dimensional encoded phase grating meets relational expression：

Wherein, arg { } is represented and is taken phase operation；For the polar coordinates in the grating planar；Normalization position coordinates vectorWherein (x, y) is the rectangular co-ordinate in grating planar, Λ_xAnd Λ_yFor this Grating is along x the and y directions cycle；C_mAnd C_nFourier coefficient respectively on x and y directions, vectorRepresent two-dimensional encoded The two-dimentional diffraction time of phase grating, wherein m and n represent diffraction time of the two-dimensional encoded phase grating along x and y directions respectively； VectorThe underlying topology lotus of the vortex phase entrained by two-dimensional encoded phase grating, wherein l_xAnd l_yRepresent respectively Two-dimensional encoded phase grating underlying topology lotus in the x and y direction, for N_x×N_yTwo-dimensional encoded phase grating, l_xAnd l_yFull Sufficient relational expression l_y/l_x=N_xOr 1/N_y, N_xAnd N_yIt is the positive integer more than 1；VectorFor two-dimensional encoded phase place light Pyramid phase basis diverging angular dimensions entrained by grid, wherein β_xAnd β_yRepresent the two-dimensional encoded phase grating in x and y side respectively Basis dissipates angular dimensions upwards, for N_x×N_yTwo-dimensional encoded phase grating, β_xAnd β_yMeet relation beta_y/β_x=N_xOr 1/N_y； β₀Angular dimensions is dissipated for extra pyramid phase place.

2. the two-dimensional encoded phase grating for producing perfect vortex array according to claim 1, it is characterised in that described The fourier coefficient C of two-dimensional encoded phase grating_mAnd C_nMeet relational expression：

$\begin{array}{c}{C}_m={\∫}_{-\mathrm{\π}}^{\mathrm{\π}}\exp \[i\mathrm{\Φ}\left(x\right)\]\exp (-imx)\\ C_n={\∫}_{-\mathrm{\π}}^{\mathrm{\π}}\exp \[i\mathrm{\Φ}\left(y\right)\]\exp (-iny)\end{array},$

Wherein, Φ (x) and Φ (y) are the phase distribution in the two-dimensional encoded phase grating monocycle along x and y directions, and it can be write asWherein, j represents x or y；Parameter Q and P can be write as：

With

$P(j,\mathrm{\α},\mathrm{\μ})=\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\μ}}_{n}sin(q_{n}j+{\mathrm{\α}}_n),$

Wherein, { μ_nAnd { α_nIt is respectively the corresponding amplitude of harmonic component and phase place；{q_nFor corresponding n-th on x or y directions Individual diffraction time, n=1, wherein 2 ... N, N represent diffraction time number total in an x or y direction, the diffraction on x and y directions Level time number is respectively N_xAnd N_y.

3. the two-dimensional encoded phase grating for producing perfect vortex array according to claim 1, it is characterised in that described The fourier coefficient C of two-dimensional encoded phase grating_mAnd C_nObtained by following Optimization Steps：

1. the N for optimizing as needed_x×N_yDot matrix number, determines the diffraction time { q of the needs on x or y directions_n, wherein N_xWith N_yRepresent the diffraction time number on x and y directions；

2. { μ is set_n1 is, take fixed { α at random_nA class value, optimize { α_nSo that being diffracted into the N on x or y directions_xOr N_yIndividual spread out The energy that penetrates in level time is maximum；

If the N being 3. diffracted on x or y directions_xOr N_yEnergy in individual diffraction time is maximum, takes now { α_nValue be { α_nValue； If the N being diffracted on x or y directions_xOr N_yEnergy in individual diffraction time is not reaching to maximum, and return to step is 2.；

4. { α is taken_nFor previous step optimize at the end of { α_nValue, take fixed { μ at random_nA class value, optimize { μ_nMake to be diffracted into x or N on y directions_xOr N_yBetween individual diffraction time, energy uniformity is best；

If the N being 5. diffracted on x or y directions_xOr N_yEnergy uniformity between individual diffraction time preferably, takes now { μ_nValue For { μ_nValue；If the N being diffracted on x or y directions_xOr N_yEnergy uniformity between individual diffraction time is not reaching to best, return Step is 4.；

6. according to { μ_nAnd { α_nValue, substitute into formulaWith Calculate fourier coefficient C_mAnd C_n.