阅读说明：本技术 基于全息光栅可调单模态涡旋光束轨道角动量探测方法 (Adjustable single-mode vortex light beam orbit angular momentum detection method based on holographic grating ) 是由 王岩坤 白璐 郭雅� 于 2021-05-22 设计创作，主要内容包括：本发明属于光学技术领域,公开了一种基于全息光栅可调单模态涡旋光束轨道角动量探测方法,所述基于Romero和Dickey提出的最佳分束理论,根据理论,得到一维全息光栅的连续相位函数φ(x)；将一维全息光栅的连续相位函数φ(x)推广到二维φ(x,y)；运用软件编程实现一维全息光栅和二维全息光栅的可行性；结合实验,基于SLM对理论模拟的结果进行验证,确定方法的可行性。本发明采用数值模拟与实验演示的方式,将基于SLM的强度与位置分布可调的全息光栅以数学形式具体化,并给出一个简单的演示实验,以达到对单模态涡旋光束轨道角动量的探测。(The invention belongs to the technical field of optics, and discloses a holographic-grating-based adjustable single-mode vortex beam orbit angular momentum detection method, wherein a continuous phase function phi (x) of a one-dimensional holographic grating is obtained according to the theory based on the optimal beam splitting theory proposed by Romero and Dickey; the continuous phase function phi (x) of the one-dimensional holographic grating is popularized to two dimensions phi (x, y); the feasibility of one-dimensional holographic grating and two-dimensional holographic grating is realized by software programming; and (4) verifying the theoretical simulation result based on the SLM in combination with the experiment to determine the feasibility of the method. The invention adopts a numerical simulation and experimental demonstration mode, embodies the holographic grating with adjustable intensity and position distribution based on the SLM in a mathematical form, and provides a simple demonstration experiment to achieve the detection of the orbital angular momentum of the single-mode vortex beam.)

1. The method for detecting the orbital angular momentum of the adjustable single-mode vortex light beam based on the holographic grating is characterized by comprising the following steps of:

based on the optimal beam splitting theory proposed by Romero and Dickey, obtaining a continuous phase function phi (x) of the one-dimensional holographic grating according to the theory;

the continuous phase function phi (x) of the one-dimensional holographic grating is popularized to two dimensions phi (x, y);

the feasibility of one-dimensional holographic grating and two-dimensional holographic grating is realized by software programming;

and (4) verifying the theoretical simulation result based on the SLM in combination with the experiment to determine the feasibility of the method.

2. The method for detecting orbital angular momentum of a tunable single-mode vortex beam based on a holographic grating as claimed in claim 1, wherein the fourier expansion form of the phase function phi (x) of the one-dimensional holographic grating is:

where m is the diffraction order, T is the grating constant, where the Fourier coefficient C_mComprises the following steps:

the complex amplitude of each diffraction order produced by the phase grating can be expressed as:

wherein | c_mI is the amplitude, phi₀Is the initial phase, l is the topological charge,is the azimuth angle.

3. The method for detecting orbital angular momentum of the tunable single-mode vortex beam based on the holographic grating as claimed in claim 1, wherein the continuous phase function phi (x) of the one-dimensional holographic grating is generalized to two-dimensional phi (x, y) in the following specific process:

expanding the one-dimensional holographic grating to two dimensions, wherein the one-dimensional holographic grating in the x direction is as follows:

the one-dimensional holographic grating in the y direction similarly comprises:

by combining the two formulas, the two-dimensional holographic grating can be obtained:

φ(x,y)＝φ(x)+φ(y)；

wherein, control | c_mAnd if the values of the l and the T are different, the intensity and the position of the light beam diffracted after passing through the holographic grating are regulated, and the topological load at any position is regulated.

4. A program storage medium for receiving user input, the stored computer program causing an electronic device to execute the method for detecting orbital angular momentum of a tunable single-mode vortex beam based on a holographic grating according to any one of claims 1 to 3, comprising the steps of:

step one, based on an optimal beam splitting theory provided by Romero and Dickey, obtaining a continuous phase function phi (x) of the one-dimensional holographic grating according to the theory;

step two, the continuous phase function phi (x) of the one-dimensional holographic grating is popularized to two dimensions phi (x, y);

thirdly, the feasibility of the one-dimensional holographic grating and the feasibility of the two-dimensional holographic grating are realized by software programming;

and step four, verifying theoretical simulation results based on the SLM in combination with experiments to determine feasibility of the method.

5. A computer program product stored on a computer readable medium, comprising a computer readable program for providing a user input interface for implementing the holographic grating based tunable single-mode vortex beam orbital angular momentum detection method of any of claims 1 to 3 when executed on an electronic device.

Technical Field

The invention belongs to the technical field of optics, and particularly relates to a holographic grating-based adjustable single-mode vortex beam orbit angular momentum detection method.

Background

At present, the vortex beam carries orbital angular momentum, and the detection and determination of the orbital angular momentum has become an important issue. The traditional method for determining the orbital angular momentum of the vortex beam comprises an interference method, a diffraction method and the like, however, the two methods have the defects of high requirement on light path collimation, difficulty in obtaining a diffraction element and the like. Due to the wide application of Spatial Light Modulators (SLM), SLM-based holographic grating methods have been reported and proposed; however, due to the diffraction effect of the SLM, the diffraction efficiency cannot reach 100% either, and the diffraction intensity and position distribution is not adjustable. Therefore, a detection method of vortex beam orbital angular momentum with adjustable intensity and position distribution is urgently needed, so that the topological load of the vortex beam is determined.

Through the above analysis, the problems and defects of the prior art are as follows: the prior art is limited by the diffraction effect of the SLM, the diffraction efficiency of the SLM can not reach 100%, and the diffraction intensity and position distribution of the SLM are not adjustable.

The difficulty in solving the above problems and defects is: since the diffraction efficiency cannot reach 100%, there is a problem of insufficient diffraction; in addition, because the diffraction intensity and the position distribution are not adjustable, errors exist in screening and measuring of the corresponding channels at the rear end, and the alignment and the construction of an optical system are difficult.

The significance of solving the problems and the defects is as follows: after the distribution of the diffraction positions and the corresponding intensity distribution are adjustable, a more accurate scheme is provided for OAM detection, the adjustment and control of the diffraction positions are realized by adjusting the grating constants, convenience is provided for the alignment and the construction of a rear-end optical system, so that the corresponding channels can be modulated and demodulated, and the measurement is more accurate.

Disclosure of Invention

Aiming at the problems in the prior art, the invention provides a holographic grating-based adjustable single-mode vortex beam orbit angular momentum detection method. The invention provides a detection method by applying the intensity and position adjustable holographic grating to a detection system of orbital angular momentum of a vortex beam.

The invention is realized in such a way that a method for detecting orbital angular momentum of a tunable single-mode vortex light beam based on a holographic grating comprises the following steps:

step one, based on an optimal beam splitting theory provided by Romero and Dickey, obtaining a continuous phase function phi (x) of the one-dimensional holographic grating according to the theory; based on the optimal beam splitting theory, reference is provided for the design of the phase function of the one-dimensional holographic grating, a basis is provided for the popularization of the two-dimensional holographic grating, and theoretical guidance is provided for the design and the proof of the following experiment.

Step two, the continuous phase function phi (x) of the one-dimensional holographic grating is popularized to two dimensions phi (x, y); the diffraction angle of the one-dimensional holographic grating is limited, if the two-dimensional holographic grating is popularized to two dimensions, the diffraction order of the two-dimensional holographic grating can be more selected, the two-dimensional holographic grating can fully utilize the diffraction surface of the SLM, the light can be fully modulated, and the number of channels is greatly increased;

thirdly, the feasibility of the one-dimensional holographic grating and the feasibility of the two-dimensional holographic grating are realized by software programming; the feasibility of the scheme is theoretically verified, and theoretical guidance is provided for the following experiments;

and step four, verifying theoretical simulation results based on the SLM in combination with experiments to determine feasibility of the method. The feasibility of the method is determined by combining simple experimental cases, the matching is good from the comparison of theory and experiment, and a guideline is provided for the design of the whole holographic grating and the detection of OAM.

Further, in the first step, the fourier expansion form of the phase function Φ (x) of the one-dimensional holographic grating is:

where m is the diffraction order, T is the grating constant, where the Fourier coefficient C_mComprises the following steps:

the complex amplitude of each diffraction order produced by the phase grating can be expressed as:

wherein | c_mI is the amplitude, phi₀Is the initial phase, l is the topological charge,is the azimuth angle.

Further, in the second step, the continuous phase function Φ (x) of the one-dimensional holographic grating is generalized to two dimensions Φ (x, y), and the specific process is as follows:

expanding the one-dimensional holographic grating to two dimensions, wherein the one-dimensional holographic grating in the x direction is as follows:

the one-dimensional holographic grating in the y direction similarly comprises:

by combining the two formulas, the two-dimensional holographic grating can be obtained:

φ(x,y)＝φ(x)+φ(y)；

wherein, control | c_mAnd if the values of the l and the T are different, the intensity and the position of the light beam diffracted after passing through the holographic grating are regulated, and the topological load at any position is regulated.

Another object of the present invention is to provide a program storage medium for receiving user input, the stored computer program enabling an electronic device to execute the method for detecting orbital angular momentum of a holographic-grating-based tunable single-mode vortex beam, comprising the steps of:

step one, based on an optimal beam splitting theory provided by Romero and Dickey, obtaining a continuous phase function phi (x) of the one-dimensional holographic grating according to the theory;

step two, the continuous phase function phi (x) of the one-dimensional holographic grating is popularized to two dimensions phi (x, y);

thirdly, the feasibility of the one-dimensional holographic grating and the feasibility of the two-dimensional holographic grating are realized by software programming;

and step four, verifying theoretical simulation results based on the SLM in combination with experiments to determine feasibility of the method.

It is another object of the present invention to provide a computer program product stored on a computer readable medium, comprising a computer readable program for providing a user input interface to implement the method for detecting orbital angular momentum of a holographic grating based tunable single-mode vortex beam when executed on an electronic device.

By combining all the technical schemes, the invention has the advantages and positive effects that: the invention adopts a numerical simulation and experimental demonstration mode, embodies the holographic grating with adjustable intensity and position distribution based on the SLM in a mathematical form, and provides a simple demonstration experiment to achieve the detection of the orbital angular momentum of the single-mode vortex beam.

Drawings

Fig. 1 is a flowchart of a method for detecting orbital angular momentum of a tunable single-mode vortex beam based on a holographic grating according to an embodiment of the present invention.

Fig. 2 is a theoretical simulation and experimental diagram of a gaussian beam incident on a one-dimensional holographic grating according to an embodiment of the present invention.

Fig. 3 is an experimental optical path diagram provided by an embodiment of the present invention.

Fig. 4 is a theoretical simulation and experimental diagram of a gaussian beam incident on a two-dimensional holographic grating according to an embodiment of the present invention.

Fig. 5 is an experimental diagram of a vortex beam of different modes incident on a two-dimensional holographic grating according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

Aiming at the problems in the prior art, the invention provides a holographic grating-based adjustable single-mode vortex beam orbit angular momentum detection method, which is described in detail below with reference to the accompanying drawings.

A person skilled in the art can also perform other steps to implement the method for detecting orbital angular momentum of a single mode vortex light beam based on a tunable holographic grating, and the method for detecting orbital angular momentum of a single mode vortex light beam based on a tunable holographic grating provided by the present invention shown in fig. 1 is only one specific example.

As shown in fig. 1, a method for detecting orbital angular momentum of a tunable single-mode vortex beam based on a holographic grating according to an embodiment of the present invention includes:

s101: based on the optimal beam splitting theory proposed by Romero and Dickey, a continuous phase function phi (x) of the one-dimensional holographic grating is obtained according to the theory.

S102: the continuous phase function phi (x) of a one-dimensional holographic grating is generalized to two dimensions phi (x, y).

S103: and the feasibility of the one-dimensional holographic grating and the two-dimensional holographic grating is realized by software programming.

S104: and (4) verifying the theoretical simulation result based on the SLM in combination with the experiment to determine the feasibility of the method.

In S101 provided by the embodiment of the present invention, a fourier expansion form of a phase function Φ (x) of a one-dimensional holographic grating is:

where m is the diffraction order and T is the grating constant. Wherein the Fourier coefficient C_mComprises the following steps:

the complex amplitude of each diffraction order produced by the phase grating can be expressed as:

wherein | c_mI is the amplitude, phi₀Is an initial phase, l is an extensionThe lotus is put in a pot to be covered,is the azimuth angle.

In S102 provided by the embodiment of the present invention, the continuous phase function Φ (x) of the one-dimensional holographic grating is generalized to two dimensions Φ (x, y), and the specific process is as follows:

expanding the one-dimensional holographic grating to two dimensions, wherein the one-dimensional holographic grating in the x direction is as follows:

the one-dimensional holographic grating in the y direction similarly comprises:

by combining the two formulas, the two-dimensional holographic grating can be obtained:

φ(x,y)＝φ(x)+φ(y)；

as can be seen, control | c_mThe values of | and T are different, the intensity and the position of the light beam diffracted after passing through the holographic grating are regulated, and the topological load at any position can also be regulated.

The feasibility of the one-dimensional holographic grating and the two-dimensional holographic grating is realized theoretically by using software programming; the results of the theoretical simulation were validated in conjunction with experiments to determine the feasibility of this approach. The invention theoretically expands the one-dimensional holographic grating phase function to two dimensions, and achieves the detection of orbital angular momentum of vortex beams by regulating and controlling the intensities and positions of different diffraction orders. In addition, the feasibility of the method is proved theoretically and experimentally, and a detection method for the orbital angular momentum of the single-mode vortex light beam is provided.

The technical solution of the present invention is further described with reference to the following specific examples.

1. Theoretically used calculation software and basic parameters

The theoretical software used was Mathematica software under Wolfram.

C of one-dimensional grating_m1＝1，C_m2＝1，l₁＝+1，l₂＝+2，T＝10μm；

| c of two-dimensional grating_(-1,1)|＝0.01279，|c_(1,1)|＝0.25894，|c_(-1,-1)|＝0.58262，|c_(1,-1)|＝0.14565，φ₀＝0，l_(-1,1)＝-3，l_(1,1)＝-1，l_(-1,-1)＝1，l_(1,-1)＝3，T_x＝T_y＝10μm。

2. Theory and experimental result of one-dimensional holographic grating

The results of the intensity distribution theory and experiment of the gaussian beam after passing through the one-dimensional holographic grating are shown in fig. 2.

3. Theory and experimental result of experimental light path and two-dimensional holographic grating

The experimental light path is shown in fig. 3. The theoretical and experimental results of a gaussian beam passing through a two-dimensional holographic grating are shown in fig. 4. The experimental results of the single mode vortex beam passing through the two-dimensional holographic grating are shown in fig. 5.

In summary, the invention provides a detection method for a single-mode vortex beam based on adjustable intensity and position of a holographic grating. Theoretically, the phase function of the one-dimensional holographic grating is popularized to be two-dimensional, and a far-field intensity distribution pattern of the Gaussian beam after the Gaussian beam enters the holographic grating is obtained by software programming. And further combining the experimental result, the feasibility of the method is verified, a far-field intensity distribution pattern of the single-mode vortex light beam after the single-mode vortex light beam is incident on the holographic grating is obtained, and the orbital angular momentum of the single-mode vortex light beam is successfully detected. The encoding basis of the holographic grating with adjustable strength and position is provided by regulating and controlling the grating constant, the topological charge and the strength distribution.

It should be noted that the embodiments of the present invention can be realized by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. Those skilled in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such code being provided on a carrier medium such as a disk, CD-or DVD-ROM, programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier, for example. The apparatus and its modules of the present invention may be implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of hardware circuits and software, e.g., firmware.

The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.