A Design Method of Mask for Generating High-Order Optical Vortex Beams by an Interference Method

Abstract

A design method of a mask for generating a high-order optical vortex beam by an interference method, which superimposes partial multiple Laguerre-Gaussian beams to obtain an electric field expression of their spatial overlapping field; combines the phases, amplitudes of multiple Laguerre-Gaussian beams and a blazed grating to obtain a complex transmittance function of the mask. The mask for generating a high-order optical vortex beam designed by the interference method of the present invention generates a high-order optical vortex beam with a controllable topological charge value in the far field. The high-order optical vortex beam is determined by the superimposed Laguerre-Gaussian beams, including that the topological charge value of the superimposed beams determines the topological charge value of the high-order optical vortex beam, the weight factor between the superimposed beams determines the intensity distribution of the high-order optical vortex, and the initial phase factor of the superimposed beams j determines the structure of the dark core of the high-order optical vortex. The present invention has the characteristics of contactless generation and miniaturization development, and thus has important value in the fields of optical micro-manipulation, optical communication, quantum entanglement, etc.

Description

Technical Field

[0001] The present invention relates to the fields of optical micro - manipulation and quantum information encoding, and specifically relates to a mask design method for generating high - order optical vortex beams by an interference method. Background Art

[0002] In the past ten - plus years, optical vortices have important applications in the fields of optical micro - manipulation, optical communication, chiral microstructure formation, etc. After more than 30 years of development, the basic problems and application boundaries of optical vortices are still continuously expanding, especially for high - order optical vortices. High - order optical vortex beams carry more orbital angular momentum and have important research significance in the fields of optical micro - manipulation [Nanophotonics, 10:2487(2021)], optical communication [Nat. Commun., 11:3875(2020)], and quantum entanglement [Light:Sci.Appl., 5:e16157(2016)]. The traditional methods for generating high - order optical vortex beams are to utilize the interaction between light and matter, including spiral phase plates [J.Opt.Soc.Am.A, 22:849(2005)] and spatial light modulators [Opt.Lett., 38:534(2013)]. However, currently, the generation of high - order optical vortex beams cannot avoid the limitations brought by the material defects and resolution of the related generating devices. Fortunately, multi - wave interference, as a technique for generating optical vortices by an interference method, has the potential of non - contact generation and miniaturized modulation, which can alleviate the impending crisis. However, the optical vortices generated by the beam interference method can only be low - order optical vortex beams, which limits the development of related applications. The reason is that the phase modulation depth of high - order optical vortex beams is greater than 2π in three - dimensional space, while the phase modulation depth generated by the interference method is less than 2π, which brings great difficulties to the generation of high - order optical vortex beams. Therefore, to break through the modulation depth limitation in the process of generating high - order optical vortex beams, there is an urgent need for a method of generating high - order optical vortex beams by an interference method.

[0003] In summary, in the fields of optical micro - manipulation and quantum information encoding, there is still a lack of a method for generating high - order optical vortex beams by an interference method to cope with the modulation depth limitation in the process of generating high - order optical vortex beams. Summary of the Invention

[0004] To solve the above deficiencies, the object of the present invention is to provide a mask design method for generating high - order optical vortex beams by an interference method. By using this mask, high - order optical vortex beams with controllable topological charge values can be generated, which have very important application values in the fields of optical micro - manipulation, optical communication, quantum entanglement, etc.

[0005] The invention utilizes the principle of computer-generated holography. Through the partial spatial superposition of the optical field, the phase period of the original optical field is used as an additional phase to supplement the deficiency of the modulation depth. The partial spatial superposition interference is carried out using a Laguerre-Gaussian beam that provides an angular phase spectrum, thereby generating the high-order optical vortex beam in the far field. This high-order optical vortex beam has the characteristics of non-contact generation and miniaturization development, and thus has important value in the fields of optical micro-manipulation, optical communication, quantum entanglement, etc.

[0006] The technical solution adopted by the present invention is as follows: A design method for a mask for generating a high-order optical vortex beam by an interference method, and the steps are as follows:

[0007] S1. Superpose a part of multiple Laguerre-Gaussian beams, and the electric field expression of the spatial overlapping field can be expressed as:

[0008]

[0009] where (r, φ) represents the coordinate system; ω0 is the waist radius of the Gaussian beam; N represents the number of superposed optical fields; represents the phase difference factor of the nth superposed optical field, which is used to adjust the angular position of the generated unit optical vortex; P n represents the weight factor of the nth superposed optical field, which is used to adjust the superposition rate between adjacent superposed optical fields; m n represents the topological charge value of the nth superposed optical field, which is used to determine the topological charge value of the generated high-order optical vortex beam, that is, l0 = (m N - m1) / d, where d represents the difference in topological charge values between adjacent superposed optical fields d = m n - m n-1 ; i represents the imaginary unit;

[0010] S2. Combine the phases, amplitudes of multiple Laguerre-Gaussian beams and a blazed grating to obtain the complex transmittance function of the mask for generating the high-order optical vortex beam by the interference method, and its specific expression of the complex transmittance function is:

[0011] HOV = |t|exp{i[angle(t)+D]}

[0012] where |·| represents taking the modulus of the complex amplitude, angle(·) is the angular function, and i represents the imaginary unit;

[0013] S3. The mask described based on this complex transmittance function is the mask for generating the high-order optical vortex beam by the interference method.

[0014] As a preferred solution, the expression of the blazed grating is: D = 2πx / T, where T is the period of the blazed grating, and its function is to generate the electric field expression of the high-order optical vortex beam designed above in the experiment.

[0015] Technical effects of the present invention:

[0016] The interference method designed in the present invention generates a high-order optical vortex beam mask plate that generates a high-order optical vortex beam with a controllable topological charge value in the far field. The high-order optical vortex beam generated by interference is determined by the superposed Laguerre-Gaussian beams, including that the topological charge value of the superposed beams determines the topological charge value of the high-order optical vortex beam, the weight factor between the superposed beams determines the intensity distribution of the high-order optical vortex, and the initial phase factor of the superposed beams determines the structure of the dark core of the high-order optical vortex. The present invention has the characteristics of non-contact generation and miniaturization development, and thus has important value in the fields of optical micro-manipulation, optical communication, quantum entanglement, etc. Description of the drawings

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0018] Figure 1 is a mask plate of a high-order optical vortex beam based on interference generated by the present invention. In the embodiment, the period d of the blazed grating is set to d = 0.26 mm. Among them, (a) shows the topological charge value l0 = 2, N = 3, m1 = 3, m2 = 7, m3 = 11, (b) shows the topological charge value l0 = 3, N = 4, m1 = 3, m2 = 7, m3 = 11, m4 = 15, (c) shows the topological charge value l0 = 4, N = 5, m1 = 3, m2 = 7, m3 = 11, m4 = 15, m5 = 19,

[0019] Figure 2 is Figure 1 high-order optical vortex beams with different topological charge values generated by the mask plate shown in. The unobstructed area is the generated high-order optical vortex beam. (a) High-order optical vortex beam with topological charge value l0 = 2; (b) High-order optical vortex beam with topological charge value l0 = 3; (c) High-order optical vortex beam with topological charge value l0 = 4. Detailed implementation manners

[0020] In order to make the technical means, creative features, achieved purposes and beneficial effects of the present invention easy to understand, the present invention will be further described below in conjunction with specific implementation manners.

[0021] First, consider the partial superposition of multiple Laguerre-Gaussian beams. The electric field expression of their spatially overlapping field can be expressed as:

[0022]

[0023] where (r, φ) represents the coordinate system; ω0 is the waist radius of the Gaussian beam, ω0 = 0.5; N represents the number of superposed light fields; represents the phase difference factor of the nth superposed light field, which is used to adjust the angular position of the generated unit optical vortex. Let P n represents the weight factor of the nth superposed light field, which is used to adjust the superposition rate between adjacent superposed light fields. Let m n represents the topological charge value of the nth superposed light field, which is used to determine the topological charge value of the generated high-order optical vortex beam, that is, l0 = (m N - m1) / d, where d represents the difference in topological charge values between adjacent superposed light fields, d = 4; i represents the imaginary unit;

[0024] The expression of the blazed grating is: D = 2πx / T, where T is the period of the blazed grating, T = 0.26 mm, and its function is to generate the electric field expression of the high-order optical vortex beam designed above in the experiment.

[0025] A mask for generating a high-order optical vortex beam by an interference method is characterized in that it combines the phases and amplitudes of a series of Laguerre-Gaussian beams and a blazed grating. The specific expression of its complex transmittance function is:

[0026] HOV = |t|exp{i[angle(t) + D]}

[0027] where |·| represents taking the modulus of the complex amplitude, angle(·) is the angular function, and i represents the imaginary unit; by technical means, the mask for generating a high-order optical vortex beam by the interference method described in this scheme can be obtained using the complex transmittance function designed above.

[0028] It should be noted that: the technical means of generating the corresponding mask using the complex transmittance function described above is prior art, such as using the global hybrid mask generation technology, etc.

[0029] In the experiment, first determine the values of some parameters according to the design requirements, including the blazed grating period (to determine the center position of the high-order optical vortex beam) and the waist radius (to unify the ring size of the superposed beams). Subsequently, encode the invented mask under these parameter values and observe the high-order optical vortex beam generated in the far field. In subsequent experiments, according to the blazed grating period and waist radius obtained in the first experiment, design high-order optical vortex beams with corresponding topological charge values and encode them as masks under these parameters.

[0030] Embodiment

[0031] Taking a mask with a size of 512×512 as an example, for a laser with a working wavelength of 532 nm, according to the mask complex transmittance function and parameter selection in the specific implementation manner, a high-order optical vortex beam mask is finally obtained as shown below. Figure 1 The high-order optical vortex beam mask generated by this interference method can be realized in the far field of the spatial light modulator. Taking the PLUTO-VIS-016 model spatial light modulator of German Holoeye company as an example, the high-order optical vortex beam mask generated by the proposed interference method is experimentally verified.

[0032] Figure 2 As shown below, the experimental light intensity distribution of the high-order optical vortex beam mask generated by this interference method on the rear focal plane of a lens with a focal length of 200 mm is obtained. It can be seen from (a), (b), and (c) that by selecting Laguerre-Gaussian beams with appropriate topological charge values for interference, high-order optical vortex beams with different topological charge values can be generated. The topological charge value is equal to the topological charge value of the outermost superimposed beam minus the topological charge value of the innermost superimposed beam, and the result is then divided by the difference in topological charge values between adjacent superimposed beams. Moreover, the greater the difference in topological charge values between adjacent superimposed beams, the more high-order optical vortex beams are generated in the same interference field. In summary, this experiment shows that the high-order optical vortex beam mask generated by the interference method proposed in the present invention can realize the generation of high-order optical vortex beams with different topological charge values. This will provide a richer way to generate high-order optical vortex beams for fields such as optical micro-manipulation, optical communication, and quantum entanglement.

[0033] In summary, the present invention proposes a specific design scheme and technical implementation scheme for a high-order optical vortex beam mask generated by an interference method. And for a laser with a working wavelength of 532 nm, a technical implementation route for a high-order optical vortex beam mask with different topological charge values is proposed.

[0034] As described above, the design scheme of a high-order optical vortex beam mask generated by an interference method only represents a specific implementation manner of the present invention, and should not be construed as a limitation on the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the basic idea of the present invention, several deformations and improvements can be made to the specific implementation details proposed in this patent, and these all belong to the protection scope of the present invention.

Claims

1. A method for designing a mask for generating a high-order optical vortex beam by an interference method, characterized in that: The steps are as follows: S1. Partially superpose multiple Laguerre-Gaussian beams, and the electric field expression of the spatially overlapping field can be expressed as: Among them, (r, φ) represents the coordinate system; ω0 is the waist radius of the Gaussian beam; N represents the number of superposed optical fields; represents the phase difference factor of the nth superposed optical field, which is used to adjust the angular position of the generated unit optical vortex; P n represents the weight factor of the nth superposed optical field, which is used to adjust the superposition rate between adjacent superposed optical fields; m n represents the topological charge value of the nth superposed optical field, which is used to determine the topological charge value of the generated high-order optical vortex beam, that is, l0 = (m N - m1) / d, where d represents the difference in topological charge values between adjacent superposed optical fields, d = m n - m n-1 ; i represents the imaginary unit; S2. Combine the phases, amplitudes of multiple Laguerre-Gaussian beams and a blazed grating to obtain the complex transmittance function of the mask for generating a high-order optical vortex beam by the interference method. The specific expression of the complex transmittance function is: HOV = |t|exp{i[angle(t)+D]} where, |·| represents taking the modulus of the complex amplitude, angle(·) is the angular function, and i represents the imaginary unit; S3. The mask described by this complex transmittance function is the mask for generating a high-order optical vortex beam by the interference method.

2. The mask design method for generating a high-order optical vortex beam by an interference method according to claim 1, wherein: The expression of the blazed grating is: D = 2πx / T, where T is the period of the blazed grating.

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