CN104808272A - Two-dimensional coding phase grating generating perfect vortex array - Google Patents

Abstract

Disclosed is a two-dimensional coding phase grating generating a perfect vortex array. The grating is composed of coding loading vortex phases and pyramid phases in the pure-phase structure raster, different diffraction levels of a generated diffraction light field carry vortex phases of different topological loads and pyramid phases of different divergence. By the two-dimensional coding phase raster on the Fourier transform plane, annular light spot arrays carrying different topological loads are produced at the same time. Further, the sizes of the annular light spot arrays are equal. The two-dimensional coding phase raster with different topological loads and same size of annular perfect vortexes has important application prospect in the multiplexing aspect of orbital angular momentum of optical fiber communications.

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 grating producing perfect vortex array.

Background technology

Optical eddy, as the core research contents of contemporary optics important branch singular optics, has obtained everybody extensive concern.Optical eddy is the proper phase of laser eigenmodes Laguerre Gaussian beam, can be expressed as be wherein l topological charge, for angle coordinate.This each photon with the light field of vortex phase structure carries orbital angular momentum (OAM), and this orbital angular momentum OAM can be delivered on the particulate by radiation.Just because of this vortex phase, there is a phase singularity in optical eddy center, thus cause the central representation of vortex light field to be blackening.At present, optical eddy has been widely used in optical communication OAM multiplexing (comprising free space optical communication and optical fiber communication), the micro-manipulation of optical imagery, optics, and the field such as quantum optics.Wherein, fiber optical communications OAM multiplex technique is the Fibre Optical Communication Technology having practical prospect obtaining optics circle and industry member extensive concern in nearly 2 years.This OAM multiplex technique, then combine ripe at present wavelength-division multiplex, palarization multiplexing, the message capacity of current optical fiber communication can be brought up to Gigabits per second (Gbit/s) 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 makes traditional vortex be difficult to be coupled on a large scale in same optical fiber.2013, the people such as Ostrovsky proposed perfect optical eddy concept first, the ring radius of this perfect vortex and topological charge irrelevant [Opt.Lett.38,534 (2013)].But, people's implementation more complicated such as Ostrovsky, and the poor signal to noise of the perfect vortex produced.Recently, the people such as Canadian Lavel university Rusch proposes the scheme [Opt.Lett.40,597 (2015)] that another kind realizes perfect vortex.The program utilizes vortex phase and another pyramid Phase Stacking, then on Fourier transform face, achieves perfect vortex.But in actual applications, we need a series of perfect vortex carrying different topology lotus.Above-mentioned all schemes are all difficult to produce the perfect vortex carrying different topology lotus in a large number simultaneously.

Summary of the invention

The object of the invention is to propose a kind of two-dimensional encoded phase grating producing perfect vortex array, this two-dimensional encoded phase grating can produce a series of perfect vortex carrying different topology lotus, and this will have very important using value in optical fiber communication orbital angular momentum is multiplexing.

The present invention utilizes two-dimensional encoded phase grating, and coding carries vortex phase and pyramid phase place wherein, thus can produce the ring-shaped light spot array with multiple perfect vortex in far field.This perfect vortex array possesses ring size and topological charge independent property, thus in optical fiber communication orbital angular momentum multiplex technique, has important using value.

Technical solution of the present invention is as follows:

Produce a two-dimensional encoded phase grating for perfect vortex array, its feature is that this two-dimensional encoded phase grating is phase-only modulation, and the transmittance function of this two-dimensional encoded phase grating meets relational expression:

Wherein, arg{} represents and gets phase operation; for the polar coordinates in this grating planar; Normalization position coordinates vector wherein (x, y) is the rectangular coordinate in grating planar, Λ _xand Λ _yfor this grating is along x and the y direction cycle; C _mand C _nbe respectively the fourier coefficient on x and y direction.Vector represent the two-dimentional order of diffraction time of two-dimensional grating, wherein m and n represents the order of diffraction time of two-dimensional grating along x and y direction respectively; Vector the underlying topology lotus of the vortex phase entrained by two-dimensional grating, wherein l _xand l _yrepresent this two-dimensional grating underlying topology lotus in the x and y direction respectively, 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 _ybe the positive integer being greater than 1; Vector pyramid phase basis angle of divergence parameter entrained by two-dimensional grating, wherein β _xand β _yrepresent this two-dimensional grating basic angle of divergence parameter in the x and y direction respectively, for N _x× N _ytwo-dimensional encoded grating, β _xand β _ymeet relation beta _y/ β _x=N _xor 1/N _y; β ₀for extra pyramid phase place angle of divergence parameter.

The fourier coefficient C of described two-dimensional encoded phase grating _mand C _nmeet relational expression:

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

Wherein, Φ (x) or Φ (y) in the two-dimensional phase grating monocycle along the PHASE DISTRIBUTION in x and y direction, it can be write as wherein, j represents x or y; Parameter Q and P can be write as $Q(j,\mathrm{\α},\mathrm{\μ})=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_n\cos (q_{n}j+{\mathrm{\α}}_n),P(j,\mathrm{\α},\mathrm{\μ})=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_n\sin (q_{n}j+{\mathrm{\α}}_n),$ Wherein, { μ _nand { α _nbe respectively amplitude corresponding to harmonic component and phase place; { q _nbe n-th order of diffraction time of the correspondence on x or y direction, and n=1,2 ... N, wherein N represents the order of diffraction time number total in an x or y direction, and the order of diffraction time number on note x and y direction 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 optimized as required _x× N _ydot matrix number, determines the order of diffraction time { q of the needs on x or y direction _n, wherein N _xand N _yrepresent along time number of the order of diffraction on x and y direction;

2. { μ is set _nbe 1, get fixed { α at random _na class value, optimize { α _nmake to be diffracted into the N on x or y direction _xor N _yenergy on the individual order of diffraction is secondary is maximum;

If be 3. diffracted into the N on x or y direction _xor N _yenergy on the individual order of diffraction is secondary is maximum, gets now { α _nvalue be { α _nvalue; If be diffracted into the N on x or y direction _xor N _yenergy on the individual order of diffraction is secondary does not reach maximum, returns 2.;

4. { α is got _nbe { the α at the end of previous step optimization _nvalue, get fixed { μ at random _na class value, optimize { μ _nmake to be diffracted into the N on x or y direction _xor N _ybetween the individual order of diffraction is secondary, energy uniformity is best;

If be 5. diffracted into the N on x or y direction _xor N _yenergy uniformity between the individual order of diffraction is secondary is best, gets now { μ _nvalue be { μ _nvalue; If be diffracted into the N on x or y direction _xor N _yenergy uniformity between the individual order of diffraction is secondary does not reach best, returns 4.;

7. according to { μ _nand { α _nvalue, according to formula with $C_n={\∫}_{-\mathrm{\π}}^{\mathrm{\π}}\exp \left[\mathrm{i\Φ}\left(y\right)\right]\exp (-\mathrm{iny})$ Calculate fourier coefficient C _mand C _n.

Technique effect of the present invention:

The present invention brings vortex phase and pyramid phase place in by coding in two-dimensional phase grating, and the far field that can be implemented in this two-dimensional encoded phase grating produces the ring-shaped light spot array with multiple perfect vortex.These perfect vortexs are arranged according to rectangular array, and the ring size of each ring-shaped light spot and entrained topological charge have nothing to do.Can be produced by an incident field simultaneously and carry different topology lotus, perfect vortex array that ring radius is identical, thus in optical fiber communication orbital angular momentum multiplex technique, there is very important application prospect.

Accompanying drawing explanation

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

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

Fig. 3 is the distribution of light intensity theoretical modeling figures (left side) of 5 × 5 two-dimensional encoded phase gratings on NA=0.025 lens focal plane, and the order of diffraction of correspondence time distributes with each order of diffraction time corresponding topological charge.

Fig. 4 is along the one dimension distribution of light intensity distribution in the left figure of Fig. 3 shown in dotted line.

Embodiment

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

Wherein, arg{} represents and gets phase operation; for the polar coordinates in this grating planar, (x, y) is the rectangular coordinate in grating planar, Λ _xand Λ _yfor this grating is along x and the y direction cycle; represent the order of diffraction time of two-dimensional grating, wherein m and n represents the order of diffraction time of two-dimensional grating along x and y direction respectively; the underlying topology lotus of the vortex phase entrained by two-dimensional grating, wherein l _xand l _yrepresent this two-dimensional grating underlying topology lotus in the x and y direction respectively; pyramid phase basis parameter entrained by two-dimensional grating, wherein β _xand β _yrepresent this two-dimensional grating underlying parameter in the x and y direction respectively.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 _yrepresent respectively along time number of the total order of diffraction on x and y direction.β ₀for extra pyramid phase place angle of divergence parameter.Coefficient C _mand C _nmeet relational expression

$\begin{array}{c}{C}_m={\∫}_{-\mathrm{\π}}^{\mathrm{\π}}\exp \left[\mathrm{i\Φ}\left(x\right)\right]\exp (-\mathrm{imx})\\ C_n={\∫}_{-\mathrm{\π}}^{\mathrm{\π}}\exp \left[\mathrm{i\Φ}\left(y\right)\right]\exp (-\mathrm{iny})\end{array},---\left(2\right)$

Wherein, Φ (x) or Φ (y) in the two-dimensional phase grating monocycle along the PHASE DISTRIBUTION in x and y direction, it can be write as

$\mathrm{\Φ}\left(j\right)=\arctan \left[\frac{Q(j,\mathrm{\α},\mathrm{\μ})}{P(j,\mathrm{\α},\mathrm{\μ})}\right],---\left(3\right)$

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

$\begin{array}{c}Q(j,\mathrm{\α},\mathrm{\μ})=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_n\cos (q_{n}j+{\mathrm{\α}}_n)\\ P(j,\mathrm{\α},\mathrm{\μ})=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_n\sin (q_{n}j+{\mathrm{\α}}_n)\end{array},---\left(4\right)$

Wherein, { q _nbe n-th order of diffraction time of the correspondence on x or y direction, and n=1,2 ... N, wherein N represents the order of diffraction time number total in an x or y direction, and the order of diffraction time number on note x and y direction is respectively N _xand N _y; { μ _nand { α _nbe respectively amplitude corresponding to harmonic component and phase place.By regulating { α _nand { μ _n, we mainly can be distributed in the energy of optical grating diffraction field in several orders of diffraction of wanting time.Fig. 2 gives the specific design flow process of this two-dimensional encoded phase grating that the present invention proposes.First, the N optimized as required _x× N _ydot matrix, setting { μ _nbe 1, optimize { α _ndiffraction efficiency is made to concentrate on N substantially _x× N _yon the order of diffraction is secondary.Then, { μ is optimized _n, make the energy uniformity of diffractive light field be distributed in N best _x× N _yon individual level is secondary.Once obtain { μ _nand { α _noccurrence, we substitute into formula (2), (3) and (4), just can obtain the fourier coefficient in formula (1).Then based on the actual application requirements, the periods lambda on x and y direction is determined _xand Λ _y, the vortex phase underlying topology lotus of carrying the pyramid phase basis angle of divergence parameter of carrying and the angle of divergence parameter beta of extra pyramid phase place ₀.Then, the transmittance function of designed two-dimensional encoded phase grating is obtained according to formula (1).The two-dimensional grating of this continuous phase distribution can be realized by spatial light modulator in practice, or is directly processed on optical base-substrate by gray scale photoetching or multiple stage rank alignment.

Embodiment

Below for 5 × 5 two-dimensional encoded phase gratings, for its operation wavelength (1550nm), provide a kind of two-dimensional encoded phase grating producing perfect vortex array.If the following l of 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 beta ₀=3 × 10 ^-2.The number of cycles along x and y direction in aperture is 30.According to the specific design flow process provided in Fig. 2, once obtain fourier coefficient, according to formula (1), namely we can obtain the transmitance distribution of this 5 × 5 two-dimensional encoded phase grating.Fig. 1 gives the PHASE DISTRIBUTION of this 5 × 5 two-dimensional encoded phase grating, and in figure, black part divides expression 0 phase place, and white portion represents 2 π phase places.The two-dimensional encoded grating of this continuous phase distribution can be realized by the spatial light modulator of a phase-only modulation.For the PLUTO-TELCO-013-C model spatial light modulator of German HoloEye company, its operation wavelength covers 400 ~ 1700 nanometer range.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 utilize wherein 8.5mm × 8.5mm active area, be then about 35 pixels in each cycle, and this is enough to realize PHASE DISTRIBUTION required in the monocycle.

Shown in figure as left in Fig. 3, the distribution of light intensity distribution of this 5 × 5 two-dimensional encoded phase gratings of our theoretical modeling on the lens focal plane of NA=0.025 numerical aperture.As can be seen from the figure, we obtain the equal-sized ring-shaped light spot array of 5 × 5.Shown in the order of diffraction time figure as right in Fig. 3 that these ring-shaped light spots are corresponding, time { q of the order of diffraction in the x-direction _n}={ 0,1,2,3,4}; Time { the q of the order of diffraction in the y-direction _n}={-2 ,-1,0,1,2}.The topological charge that the perfect wraps correction of these correspondences 5 × 5 is answered 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 gives along dotted line one dimension intensity distributions in Fig. 3, therefrom can find out, the diameter of the ring-shaped light spot produced is about 490 λ, and corresponding 1550 wavelength are 760 microns.Our theoretical modeling result shows, by this two-dimensional encoded phase grating that the present invention proposes, the perfect vortex array carrying different topology lotus can be produced simultaneously, these perfect vortexs show as a series of equal-sized ring-shaped light spot, and this will provide solid foundation for optical fiber communication orbital angular momentum multiplex technique is practical.

In sum, the present invention proposes a kind of the specific design method and the embodiment that produce the two-dimensional encoded phase grating of perfect vortex array, and for NA=0.025 condenser lens, 5 × 5 two-dimensional encoded phase gratings, for its operation wavelength 1550nm, a kind of two-dimensional encoded phase grating specific design flow process and feasible technology implementation route are proposed.

The above two-dimensional encoded phase grating producing perfect vortex array only have expressed a kind of embodiment of the present invention, therefore can not be interpreted as limiting the scope of the invention.It should be pointed out that for the person of ordinary skill of the art, under the prerequisite not departing from basic thought of the present invention, can also make some distortion and improvement to the concrete implementation detail that this patent proposes, these all belong to protection scope of the present invention.

Claims (3)

1. produce a two-dimensional encoded phase grating for perfect vortex array, it is characterized in that this two-dimensional encoded phase grating is phase-only modulation, and the transmittance function of this two-dimensional encoded phase grating meet relational expression:

Wherein, arg{} represents and gets phase operation; for the polar coordinates in this grating planar; Normalization position coordinates vector wherein (x, y) is the rectangular coordinate in grating planar, Λ _xand Λ _yfor this grating is along x and the y direction cycle; C _mand C _nbe respectively the fourier coefficient on x and y direction, vector represent the two-dimentional order of diffraction time of two-dimensional grating, wherein m and n represents the order of diffraction time of two-dimensional grating along x and y direction respectively; Vector the underlying topology lotus of the vortex phase entrained by two-dimensional grating, wherein l _xand l _yrepresent this two-dimensional grating underlying topology lotus in the x and y direction respectively, 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 _ybe the positive integer being greater than 1; Vector pyramid phase basis angle of divergence parameter entrained by two-dimensional grating, wherein β _xand β _yrepresent this two-dimensional grating basic angle of divergence parameter in the x and y direction respectively, for N _x× N _ytwo-dimensional encoded grating, β _xand β _ymeet relation beta _y/ β _x=N _xor 1/N _y; β ₀for extra pyramid phase place angle of divergence parameter.

2. the two-dimensional encoded phase grating of generation according to claim 1 perfect vortex array, is characterized in that the fourier coefficient C of described two-dimensional encoded phase grating _mand C _nmeet relational expression:

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

Wherein, Φ (x) and Φ (y) in the two-dimensional phase grating monocycle along the PHASE DISTRIBUTION in x and y direction, it can be write as wherein, j represents x or y; Parameter Q and P can be write as:

$Q(j,\mathrm{\α},\mathrm{\μ})=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_n\cos (q_{n}j+{\mathrm{\α}}_n)$ With

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

Wherein, { μ _nand { α _nbe respectively amplitude corresponding to harmonic component and phase place; { q _nbe n-th order of diffraction time of the correspondence on x or y direction, and n=1,2 ... N, wherein N represents the order of diffraction time number total in an x or y direction, and time number of the order of diffraction on x and y direction is respectively N _xand N _y.

3. the two-dimensional encoded phase grating of generation according to claim 1 perfect vortex array, is characterized in that the fourier coefficient C of described two-dimensional encoded phase grating _mand C _nobtained by following Optimization Steps:

1. the N optimized as required _x× N _ydot matrix number, determines the order of diffraction time { q of the needs on x or y direction _n, wherein N _xand N _yrepresent along time number of the order of diffraction on x and y direction;

2. { μ is established _nbe 1, get fixed { α at random _na class value, optimize { α _nmake to be diffracted into the N on x or y direction _xor N _yenergy on the individual order of diffraction is secondary is maximum;

If be 3. diffracted into the N on x or y direction _xor N _yenergy on the individual order of diffraction is secondary is maximum, gets now { α _nvalue be { α _nvalue; If be diffracted into the N on x or y direction _xor N _yenergy on the individual order of diffraction is secondary does not reach maximum, returns step 2.;

4. { α is got _nbe { the α at the end of previous step optimization _nvalue, get fixed { μ at random _na class value, optimize { μ _nmake to be diffracted into the N on x or y direction _xor N _ybetween the individual order of diffraction is secondary, energy uniformity is best;

If be 5. diffracted into the N on x or y direction _xor N _yenergy uniformity between the individual order of diffraction is secondary is best, gets now { μ _nvalue be { μ _nvalue; If be diffracted into the N on x or y direction _xor N _yenergy uniformity between the individual order of diffraction is secondary does not reach best, returns step 4.;

6. according to { μ _nand { α _nvalue, substitute into formula with $C_n={\∫}_{-\mathrm{\π}}^{\mathrm{\π}}\exp \left[\mathrm{i\Φ}\left(y\right)\right]\exp (-\mathrm{iny})$ Calculate fourier coefficient C _mand C _n.