1. A method for modulating the complex amplitude of vortex light with diffraction zero order is characterized in that: the existing traditional method is based on Fourier analysis to reconstruct the light field information at the diffraction level one, and in order to reconstruct the light field information at the diffraction level zero and reduce the energy loss to the maximum extent, a step modulation method based on Fourier analysis is adopted to design a hologram reconstructing the light field at the diffraction level 0; the amplitude modulation is completed by adding the blazed grating on the phase of the hologram so that the orders of Fourier series and the diffraction orders correspond to each other one by one, only an amplitude item is left at the diffraction 0 order, the amplitude modulation of the 0 order is completed, and then the spiral phase is added on the basis of the amplitude modulation, so that the complex amplitude modulation of the diffraction 0 order is realized.

2. A method according to claim 1, wherein the method comprises the following steps: amplitude of existing light fieldThe phase information is measured by the formulaIn order to separate the 0 order from the orders other than the 0 order, a blazed grating needs to be added on the basis of the formula, the orders of the Fourier order correspond to the diffraction orders one by one, and only the value J of the function J of the independent variable corresponding to the amplitude a in the zero-order component in the Jacobi-Anger formula is left in the diffraction 0 order₀[f(a)]The amplitude modulation at diffraction order 0 is completed.

3. A method of modulating the complex amplitude of vortex light of diffraction order zero according to claims 1 and 2, characterized in that: with the basis of amplitude modulation, only the spiral phase needs to be added on the basis of the amplitude modulation, and the computational expression psi (phi, a) ═ mod (phi + f (a) sin (phi + f) of the phase-only hologram is obtained_xx+f_yy,2 pi)), 2 pi) to achieve complex amplitude modulation of the eddy current rotation in the diffraction 0 order.

Technical Field

The phenomenon of swirling in the optical field was originally discovered by Boivin, Dow and Wolf in 1967 near the focal plane of the lens stack. In 1973, Bryngdahl first conducted an exploration of experimental methods for preparing vortex light. In 1979 Vaughan and Willets successfully produced vortex rotation using a continuous laser. Yu, Bazgenov V in 1990 completed the preparation of vortex rotation for the first time using the grating method. In 1992, L.Allen found a carrier phase factor under paraxial conditionsHas orbital angular momentum, wherein l is the topological charge number of the orbital angular momentum of the vortex light,is the azimuth; each photon carriesThe orbital angular momentum of (a) is,to approximate the planck constant, the angular phase factor indicates that in the process of propagating eddy optical rotation, if a light beam propagates for a period, the wave front rotates around the optical axis exactly once, and the phase changes by 2 pi l correspondingly.

The vortex rotation is used as a novel structural light beam with a spiral wave front, and has important application value in the fields of optical communication, particle micro-control, motion detection, optical micro-measurement and the like. The Laguerre-Gaussian light is a typical vortex light, photons in the light beam not only have Spin Angular Momentum (SAM) but also have Orbital Angular Momentum (OAM), and the topological charge number determines the size of the OAM. A complete singlet laguerre-gaussian beam has a circular intensity distribution and a hollow dark core, and the region where the beam center intensity is zero is defined as the phase singularity. Vortex light beams can be divided into two types according to the type of the phase singularity, one type is that the deflection directions of light fields are the same, and the phase of the singularity is uncertain and is called phase vortex rotation; the other is the uncertainty of the polarization direction of the singularity, called vector vortex rotation, and the Laguerre-Gauss is a phase vortex rotation. The superposition of the vortex light of multiple single modes can obtain the superposed vortex optical rotation which has different intensity and phase distribution with the single vortex light.

The preparation of vortex rotation is the basis for developing vortex light research, and common preparation methods comprise a mode conversion method, a computational holography method, a spatial light modulator method, a Q plate method and a matrix spiral phase plate method. Under laboratory conditions, the spatial light modulator method is a commonly used fabrication method. The spatial light modulator controls the electric field to cause the change of a spatial phase or amplitude image of the liquid crystal display, thereby writing certain information into the light wave and realizing the modulation of the light wave. The vortex rotation holographic pattern is prepared by a complex amplitude regulation and control technology and loaded to a spatial light modulator, and the spatial light modulator is irradiated by a beam of linearly polarized Gaussian light, so that emergent light is a vortex beam.

In the existing optical devices, there is only a device capable of adjusting the Phase of the vortex light, for example, a Spiral Phase Plate (SPP), which is a Phase filter capable of realizing the Spiral wave surface transformation. As a new pure phase diffraction optical component, the optical thickness is in direct proportion to the rotation azimuth angle phi, the phase delay function is exp (il phi), wherein l is the topological charge of SPP, phi is the rotation azimuth angle, and the phase change of one circle of rotation around the center is 2l pi. The outgoing beam of the incident plane wave through the SPP has a helical phase front. SPP has been practically used as a new type of diffractive optical element in a variety of fields such as optical information processing, optical micromanipulation, biomedicine, topography measurement, astronomical observation, and the like. By the manufacturing algorithm of the optical diffraction element (DOE) in the vortex light preparation, an optical element without a Spatial Light Modulator (SLM) can be manufactured, and the amplitude and the phase of vortex light are directly modulated, namely complex amplitude modulation of vortex rotation is completed.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: aiming at the problem that the existing known method reconstructs light field information in diffraction 1 order on the basis of Fourier analysis, a vortex light complex amplitude modulation method of diffraction zero order is provided, in order to reduce energy loss to the maximum extent, a hologram reconstructing a light field in diffraction 0 order is required to be designed, and compared with the traditional algorithm, the algorithm has good effects on reconstruction of the light field information and modulation of the amplitude and phase of the vortex light.

The technical solution of the invention is as follows:

the invention relates to a complex amplitude modulation method of diffraction zero order, which mainly comprises the following steps:

(1) the method comprises the steps of presetting the phase of vortex rotation, transforming the phase distribution of vortex light according to a Jacobi-Anger equation, setting the component of the Jacobi-Anger equation at the 0 level as the amplitude of an original light field, adding a blazed grating on the basis of the equation, corresponding the Fourier series level and the diffraction level one by one, and completing amplitude modulation of the 0 level of diffraction.

(2) With the basis of amplitude modulation, theoretically, only the spiral phase needs to be added to the amplitude modulation, and the computational expression ψ ″ (Φ, a) ═ mod (Φ + f (a)) sin (mod (Φ + f) of the phase-only hologram is obtained_xx+f_yy,2 pi)), 2 pi) and loading the resulting hologram onto a Spatial Light Modulator (SLM) to achieve complex amplitude modulation of eddy current rotation in the diffraction 0 order.

The principle of the invention is as follows:

assuming that the complex amplitude of a certain light field can be expressed as:

s(x,y)＝a(x,y)exp[iφ(x,y)] (1)

wherein a (x, y) is amplitude and is located at [0,1 ]; phi (x, y) denotes a phase, located at-pi, pi. The purpose of complex amplitude modulation is to encode s (x, y) to obtain a phase-only hologram, whose expression is:

h(x,y)＝exp[iψ(a,φ)] (2)

where ψ (a, φ) is the hologram phase containing the initial light field amplitude and phase. The Fourier series expansion of the formula (2) comprises the following steps:

wherein the content of the first and second substances,

if the equation exists:

the information of the original formula s (x, y) can be represented by the first order Fourier series h in formula (3)₁(x, y) reduction, wherein A is a constant greater than 0. Equation (5) is a condition for achieving complex amplitude modulation. If equation (5) exists, then the relationship exists:

after expansion by the Euler formula, the sum of the relational expressions can be obtained, and the sum of the relational expressions is taken as an essential condition of the formula (7).

The summation of equations (8) and (9) provides a reference for the determination of the hologram. Equation (9) limits ψ (φ, a) to have to be an odd symmetric function with respect to φ; and since the maximum value of equation (7) is 2 pi, the maximum value of a is limited to 1.

In order to prepare an optical diffraction element (DOE) and minimize energy loss, a step modulation method based on fourier analysis is used to realize a hologram that reconstructs a light field at diffraction order 0.

Assuming the existence of an odd function

ψ(φ,a)＝f(a)sin(φ) (10)

According to the Jacobi-Anger equation, one can obtain:

in order to realize complex amplitude modulation of eddy rotation at level 0, amplitude modulation is first performed at level 0. If order

J₀[f(a)]＝a (12)

The term of 0-n in equation (12) can restore the amplitude term in s (x, y). In order to separate the 0 th order from the orders other than the 0 th order, it is necessary to add a blazed grating to the formula (11) and to correspond the fourier series orders to the diffraction orders one by one, and there are:

thus, only the amplitude term J remains in the diffraction order 0₀[f(a)]Amplitude modulation at diffraction order 0 can be achieved.

At the same time, [0,1]]May be in [0, x ] value₀]Take the corresponding value of f (a), where x₀R 2.4048, the first positive root of the 0 th order bessel function. By numerical inversion, we can obtain the corresponding value of f (a) at each pixel point.

Finally, the calculation for the phase-only hologram is:

ψ′(φ,a)＝f(a)sin(mod(φ+f_xx+f_yy,2π)) (14)

in summary, if the formula is selected as the hologram phase expression, the amplitude modulation of the diffraction 0 can be realized by only performing numerical inversion through the formula to obtain f (a) and superimposing blazed gratings on the basis of phi.

Above, we have completed the first step: and (4) amplitude modulation. Based on the amplitude modulation, theoretically, complex amplitude modulation of eddy rotation at level 0 can be realized by adding a spiral phase on the basis of the amplitude modulation. The calculation formula of the phase-only hologram is:

ψ″(φ,a)＝mod(φ+f(a)sin(mod(φ+f_xx+f_yy,2π)),2π) (15)

the required complex amplitude hologram is derived from this equation.

Compared with the prior art, the scheme of the invention has the main advantages that:

(1) the reconstruction of the existing optical field information through Fourier analysis is concentrated on the diffraction level one at present, and the reconstruction is moved to the position of the diffraction level 0 by the method, so that the excessive attenuation of light intensity is avoided, most energy is reserved, and the detection is convenient;

(2) the method has the advantages of reducing cost and saving space, and can realize complex amplitude regulation and control of vortex light by using a preparation light path of common vortex optical rotation.

(3) The flexibility is strong, can be according to the phase place of nimble regulation hologram of demand, realizes the complex amplitude regulation and control of vortex rotation at diffraction 0 level. By ψ' (φ, a) ═ mod (φ + f (a)) sin (mod (φ + f)_xx+f_yy,2 pi)), 2 pi), under the condition that the initial phase is known, the phase of the hologram is changed by adjusting the coefficient of the blazed grating, and then the amplitude and the phase of the vortex rotation are simultaneously changed.

FIG. 1 is a flowchart of an algorithm and application of a Diffractive Optical Element (DOE);

FIG. 2 is a schematic diagram of amplitude modulation;

FIG. 3 is a schematic diagram of complex amplitude modulation;

FIG. 4 is a diagram of an experimental setup for preparing optical field information of diffracted 0-order vortex light;

detailed description of the preferred embodiments

The invention takes a hologram generated by a manufacturing algorithm of an optical diffraction element (DOE) in vortex light preparation as an experimental object, and an implementation object is a spatial light modulator, and the specific implementation steps are as follows:

firstly, the amplitude and phase of a known light field are measured, and a hologram for carrying out complex amplitude modulation on diffracted 0-order vortex light is encoded and loaded on a pure-phase spatial light modulator. The laser (NEWPORT N-LHP-151) emits a collimated Gaussian beam with a wavelength of 632.8nm after collimation using a Linear Polarizer (LP), a half-wave plate (HWP) and a telescope consisting of two lenses (L1, L2). The combination of the LP and HWP is used to adjust the power of the light incident on the SLM. The SLM (UPOLABS HDSLM80R) accurately modulates the incident light by loading the hologram as described above. The 0 th order diffraction of the beam is then selected by means of an Aperture (AP) to avoid further stray light. The CCD camera (NEWPORT LBP2) recorded the intensity distribution after L4 as shown in fig. 4.

For example, fourier analysis is performed on the phase of the hologram reconstructed light field, so that the value of the component of the Jacobi-Anger equation at the zero order is the amplitude of the original light field, in order to separate the 0 order from the orders other than the 0 order, we obtain f (a) by numerical inversion on the basis of the known equation, a blazed grating is added on the basis of phi, the orders of the fourier series correspond to the diffraction orders one by one, and the amplitude modulation of the diffraction 0 order can be realized, as shown in fig. 2, by using LG₀₂For example, plotting ψ (a, φ) as a hologram is shown in FIG. 2 (a). After loading the hologram, the phase distribution at the simulated spectral plane is shown on fig. 2(b), and it can be seen that there is a uniform ring phase distribution at the level 0 position, with a corresponding amplitude distribution as in fig. 2 (b). After the filtering process of the frequency spectrum surface signal is performed, the inverse fourier transform is performed on the signal after the filtering process of the simulated diaphragm, and the light field distribution obtained by the simulation preparation can be obtained from fig. 2(c), wherein the amplitude distribution of the light beam is similar to the vortex light amplitude distribution, but the light field does not have the actual vortex light phase, as shown in fig. 2 (c).

On the basis of amplitude modulation, IComplex amplitude modulation of eddy rotation at level 0 can be realized by adding spiral phase on the basis of amplitude modulation. Obtaining the hologram expression after adding the spiral phase, as shown in FIG. 3, with LG₀₂For example, a complex amplitude hologram obtained by calculation is shown in fig. 3(a), and the spectral distribution of the phase and amplitude is shown in fig. 3 (b). The light field intensity and phase distribution after reconstruction is shown in fig. 3 (c). The reconstructed LG can be seen₀₂Not only the intensity distribution is uniform, but also the phase position is in 2-order spiral distribution.

The complex amplitude modulation method can be obtained by deducing an algorithm, the algorithm can realize complex amplitude modulation on vortex light with any topological charge number, for example, a Laguerre-Gaussian beam with the topological charge number of 2 is selected to carry out simulation verification, and perfect complex amplitude modulation is realized on the vortex light through the algorithm.

In addition, the spatial light modulator limits the incident angle and power of the light beam, so the specific light path design is performed according to the actual conditions of a laboratory.

Those skilled in the art will appreciate that the details of the present invention not described in detail herein are well within the skill of those in the art.