Non-diffraction partially coherent Pearl beam generation method and system

Abstract

The invention belongs to the field of light field regulation and control, and provides a diffraction-free partially coherent Pearl beam generation method and system, and the method comprises the steps: enabling a light beam emitted by a laser to reach a beam expander through a half-wave plate, and enabling the light beam to irradiate a spatial light modulator after the light beam is expanded by the beam expander; the laser beam is modulated by repeatedly refreshing the spatial light modulator, pseudo modes of the laser beam at different position points on a reciprocal plane are obtained based on a cross density spectrum function, and a corresponding holographic picture is generated; after processing of a 4f optical imaging system, first-order diffraction spots corresponding to each pseudo mode are screened out; a CCD camera is used for recording a first-order diffraction light spot of each pseudo mode, and the pseudo modes are superposed to form a partially coherent Pearls beam. The method provided by the invention has robustness in the transmission process of the light beam, namely, the influence of diffraction and other disturbances is resisted in the transmission process.

Description

Technical Field

[0001] The present invention belongs to the technical field of light field control, and in particular relates to a method and system for generating a non-diffraction partially coherent Pierce light beam. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Partially coherent beams have stable statistical properties, i.e., they allow phase and intensity fluctuations within the beam and in time. Their inherent ability to suppress beam interference and reduce optical noise ensures their reliable performance in speckle-free optical imaging, super-resolution optical holography, and high-performance photonic computing applications. In addition, based on the theory of optical coherence, partially coherent beams can be viewed as an incoherent superposition of multiple modes. These beams are known for their inherent adaptability to environmental perturbations, as the perturbation effects on individual modes tend to cancel each other. This property makes partially coherent beams particularly suitable for critical applications such as optical communications, far-field optical imaging, and optical encryption and decryption in harsh environments.

[0004] As exact solutions of the homogeneous Helmholtz equation, non-diffracting beams maintain their shape unchanged while propagating in free space. These beams have attracted great interest since the pioneering work of Dunin et al. All such beams are inherently free from distortions due to the Babinet principle. They have a wide range of applications in volume imaging, ghost imaging, particle trapping, photon correlation holography, and factorization. Partially coherent non-diffracting beams Factorization and partially coherent beams have both inherent advantages and are receiving increasing attention.

[0005] In recent years, coherence, as a unique degree of freedom of partially coherent beams, has triggered extensive research activities from fundamental physics to valuable applications. Notably, coherence has been explored as an information carrier for image encryption, and by introducing randomness, partially coherent beams have achieved high-capacity information encryption. However, partially coherent beams with low coherence are susceptible to optical diffraction, which causes all degrees of freedom, including coherence, to deteriorate during propagation. Therefore, the encrypted information is inevitably compromised. The basic idea to overcome this challenge lies in how to construct a partially coherent non-diffraction beam. Previously constructed partially coherent Pierce beams will deviate during transmission due to the presence of self-accelerating beams, which will have an adverse effect on optical encryption of information transmission. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a method and system for generating a diffraction-free partially coherent Pierce beam. The present invention utilizes the principle of incoherent superposition to construct a partially coherent diffraction-free Pierce beam, and the intensity, coherence and other properties of the beam remain unchanged when transmitted in free space.

[0007] According to some embodiments, a first solution of the present invention provides a non-diffraction partially coherent Pierce beam generation system, which adopts the following technical solution: A non-diffraction partially coherent Pierce beam generating system, comprising: A laser, wherein the light beam emitted by the laser reaches a beam expander through a half-wave plate, and after being expanded by the beam expander, the laser beam is irradiated onto a spatial light modulator; The spatial light modulator modulates the laser beam using a cross-density spectrum function to generate a modulated light beam; A 4f optical imaging system, wherein the 4f optical imaging system selects a first-order diffraction spot from the modulated light beam; A CCD camera is used to record the first-order diffraction spot.

[0008] Furthermore, the 4f optical imaging system includes a first thin lens, an aperture and a second thin lens.

[0009] Furthermore, the spatial light modulator modulates the laser beam using a cross-density spectrum function, specifically: The cross-density spectrum function is used to obtain the pseudo-mode of the laser beam at different positions on the reciprocal plane; Based on the complex amplitude control algorithm, pseudo patterns at different positions on the reciprocal plane are used to generate holographic images.

[0010] Furthermore, the complex amplitude control algorithm is specifically: ; Among them, the B amplitude is obtained by numerical inversion: ,in, represents the first-order Bessel function of the first kind; "Arg" means taking the phase of the function; represents the grating frequency, is any kernel function, represents the position of the sampling point on the inverse plane, and are the vector positions in the source plane and the reciprocal plane, respectively.

[0011] According to some embodiments, a second solution of the present invention provides a method for generating a non-diffraction partially coherent Pierce beam, which adopts the following technical solution: A method for generating a non-diffraction partially coherent Pierce beam, based on a non-diffraction partially coherent Pierce beam generating system as described in the first solution, comprises: The light beam emitted by the laser reaches the beam expander through the half-wave plate. After being expanded by the beam expander, the laser is irradiated onto the spatial light modulator. The laser beam is modulated by repeatedly refreshing the spatial light modulator, and the pseudo-mode of the laser beam at different positions on the reciprocal plane is obtained based on the cross-density spectrum function, and the corresponding holographic image is generated; After being processed by the 4f optical imaging system, the first-order diffraction spot corresponding to each pseudo-pattern is screened out; The first-order diffraction spot of each pseudo-pattern is recorded by a CCD camera, and each pseudo-pattern is superimposed to form a partially coherent Pierce beam.

[0012] Furthermore, the laser beam is modulated by the repeatedly refreshed spatial light modulator, pseudo patterns of the laser beam at different positions on the reciprocal plane are obtained based on the cross-density spectrum function, and corresponding holographic images are generated, specifically: Use Gaussian and cosine functions to construct power spectral density functions and arbitrary kernel functions; Introducing dimensionless and difference coordinates, converting the mathematical form of power spectral density function and arbitrary kernel function; Based on the converted power spectral density function and the arbitrary kernel function, a cross spectral density function of a single position point is determined; Using Gaussian aperture as the cutoff function of the laser beam, the cutoff cross spectral density function of a single position point is determined; Repeatedly refreshing the spatial light modulator to modulate the laser beam, and using the truncated cross spectral density function of a single position point to obtain pseudo-modes of the laser beam at different positions on the reciprocal plane; Based on the complex amplitude control algorithm, pseudo patterns at different positions on the reciprocal plane are used to generate holographic images.

[0013] Furthermore, the truncated cross spectral density function of a single position point is determined as follows: ; in, and represents the width of the truncation function, where and represents the power spectral density function and arbitrary kernel function using dimensionless and difference coordinate transformation, represents a truncated cross spectrum.

[0014] Furthermore, the CCD camera is used to record the first-order diffraction spot of each pseudo-pattern, and each pseudo-pattern is superimposed to form a partially coherent Pierce beam, specifically: ; in, is the discrete power spectral density function, representing the mode weight, is truncation mode, It is a pseudo mode. represents the position of the sampling point on the inverse plane, and are the coordinates on the source plane.

[0015] Furthermore, the truncation mode is specifically: ; in, represents the position of the sampling point on the inverse plane, d represents the sampling space, is any kernel function, and are the vector positions in the source plane and the reciprocal plane, respectively, Indicates the size of the Gaussian cutoff.

[0016] Furthermore, the first-order diffraction spot contains pseudo-pattern information.

[0017] Compared with the prior art, the present invention has the following beneficial effects: The present invention utilizes the principle of incoherent superposition to construct a partially coherent non-diffraction Pierce beam, the intensity, coherence and other properties of which remain unchanged when transmitted in free space, and are robust during transmission, that is, they resist the influence of diffraction and other disturbances during transmission. The intensity and coherence of such beams remain unchanged during propagation. Even in practical scenarios, the truncated version still retains significant resistance to optical diffraction. These beams naturally have two significant advantages: low coherence and non-diffraction propagation. Low coherence ensures the robustness of the beam in harsh environments, while the non-diffraction characteristics allow the use of certain degrees of freedom, such as coherence and intensity, as information carriers for long-distance information transmission. Therefore, non-diffraction partially coherent Pierce beams have great application potential in the fields of optical communications, information transmission, optical imaging, etc., especially in harsh environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0019] Figure 1 It is a structural diagram of a non-diffraction partially coherent Pierce beam generating system in Embodiment 1 of the present invention; Figure 2 This is a flow chart of a method for generating a non-diffraction partially coherent Pierce beam in Embodiment 2 of the present invention; Figure 3 is the normalized intensity of the truncated non-diffracting partially coherent Pierce beam in the second embodiment of the present invention when propagating in free space; Figure 4 is the sum coherence of the truncated non-diffracting partially coherent Pierce beam propagating in free space in the second embodiment of the present invention; Figure 5 are the intensity similarity (upper coordinate axis) and coherence (lower coordinate axis) of the truncated non-diffracting partially coherent Pierce beam propagating in free space in the second embodiment of the present invention; Figure 6 These are the theoretical and experimental results of the intensity distribution of the non-diffracting partially coherent Pierce beam in the second embodiment of the present invention when it is transmitted in free space. DETAILED DESCRIPTION

[0020] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0021] It should be noted that the following detailed descriptions are all illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0022] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0023] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0024] Embodiment 1 like Figure 1 As shown, this embodiment provides a non-diffraction partially coherent Pierce beam generation system, comprising: A laser, wherein the light beam emitted by the laser reaches a beam expander through a half-wave plate, and after being expanded by the beam expander, the laser beam is irradiated onto a spatial light modulator; The spatial light modulator modulates the laser beam using a cross-density spectrum function to generate a modulated light beam; A 4f optical imaging system, wherein the 4f optical imaging system selects a first-order diffraction spot from the modulated light beam; A CCD camera is used to record the first-order diffraction spot.

[0025] The 4f optical imaging system includes a first thin lens, an aperture and a second thin lens.

[0026] The spatial light modulator modulates the laser beam using a cross-density spectrum function, specifically: The cross-density spectrum function is used to obtain the pseudo-mode of the laser beam at different positions on the reciprocal plane; Based on the complex amplitude control algorithm, pseudo patterns at different positions on the reciprocal plane are used to generate holographic images.

[0027] Optical devices such as Figure 1 The wavelength is The light beam is emitted from a helium-neon laser, and is expanded by a beam expander after passing through a half-wave plate. We adjust the direction of the half-wave plate so that the polarization direction of the outgoing light beam is horizontally aligned to achieve the best response of the SLM. After passing through the beam expander, the light beam is irradiated onto a pure phase liquid crystal spatial light modulator (SLM), and each pseudo-mode is designed as a holographic image and loaded onto the SLM using a complex amplitude modulation encoding algorithm. After being reflected by the SLM, the light beam passes through an improved 4f optical imaging system consisting of two identical lenses and an aperture. The function of the 4f optical imaging system is to select and filter out the first-order diffraction spot. The first-order diffraction spot contains information and is required by this embodiment. The remaining diffraction orders are not required. The aperture located on the frequency plane is used to select a positive or negative first-order diffraction spot. The selected first-order diffraction spot contains the information of each pseudo-mode. Each pseudo-mode is recorded by a CCD camera. Later, we will superimpose each pseudo-mode recorded by the CCD to form a partially coherent Pierce beam.

[0028] The spatial light modulator uses a complex amplitude modulation algorithm (SLM) to program each pattern into a form that the SLM can use to control the light beam, that is, the holographic image loaded on the SLM.

[0029] Based on the complex amplitude control algorithm, the SLM phase corresponding to the electric field to be encoded is expressed as: (1); Among them, the B amplitude is obtained by numerical inversion: ,in, Represents the first-order Bessel function of the first kind; "Arg" represents the phase of the function. Represents the grating frequency.

[0030] Embodiment 2 like Figure 2 As shown, this embodiment provides a method for generating a non-diffraction partially coherent Pierce beam, based on a non-diffraction partially coherent Pierce beam generating system as described in Embodiment 1, comprising: The light beam emitted by the laser reaches the beam expander through the half-wave plate. After being expanded by the beam expander, the laser is irradiated onto the spatial light modulator. The laser beam is modulated by repeatedly refreshing the spatial light modulator, and the pseudo-mode of the laser beam at different positions on the reciprocal plane is obtained based on the cross-density spectrum function, and the corresponding holographic image is generated; After being processed by the 4f optical imaging system, the first-order diffraction spot corresponding to each pseudo-pattern is screened out; The first-order diffraction spot of each pseudo-pattern is recorded by a CCD camera, and each pseudo-pattern is superimposed to form a partially coherent Pierce beam.

[0031] The laser beam is modulated by the repeatedly refreshed spatial light modulator, pseudo-modes of the laser beam at different positions on the reciprocal plane are obtained based on the cross-density spectrum function, and corresponding holographic images are generated, specifically: Use Gaussian and cosine functions to construct power spectral density functions and arbitrary kernel functions; Introducing dimensionless and difference coordinates, converting the mathematical form of power spectral density function and arbitrary kernel function; Based on the converted power spectral density function and the arbitrary kernel function, a cross spectral density function of a single position point is determined; Using Gaussian aperture as the beam cutoff function, determine the cutoff cross spectral density function at a single position point; Repeatedly refreshing the spatial light modulator to modulate the laser beam, and using the truncated cross spectral density function of a single position point to obtain pseudo-modes of the laser beam at different positions on the reciprocal plane; Based on the complex amplitude control algorithm, pseudo patterns at different positions on the reciprocal plane are used to generate holographic images.

[0032] In the spatial frequency domain, the statistical properties of partially coherent light are characterized by the cross-spectral density function, which is as follows: (2); in, represents the power spectral density function, is any kernel function. and are the vector positions in the source plane and the reciprocal plane, respectively. To construct a non-diffracting partially coherent Pierce beam, we use the following form: (3); (4); in and Represent the coherence width and beam width respectively. Here we introduce dimensionless and difference coordinates as (5); Substituting equations (3)-(5) into equation (2), the cross spectral density function of a single position point of the desired beam can be rewritten as follows: (6); here: (7); (8); in is the Pierce function, defined as , Determines the global coherence of the source beam. The cross spectral density function depends on only one parameter . is the bump function on the background, which is characterized by The propagation behavior of partially coherent light can be studied with the help of the Fresnel diffraction integral, as shown below: (9); Substituting equations (6)-(8) into equation (9) and converting them into dimensionless and difference coordinates, we can prove through direct integration that the cross-spectral function of the non-diffracting partially coherent Pierce beam is independent of the propagation distance z, that is, This clearly demonstrates that this beam is not affected by optical diffraction.

[0033] However, this beam presents an infinite profile, symbolizing infinite energy, which is physically impossible. To solve this problem, a Gaussian aperture is introduced as the beam truncation function. The truncated version of the cross-spectral density function is then rewritten as the truncated cross-spectral density function at a single location, specifically: (10); in and Indicates the width of the truncation function.

[0034] Its evolutionary behavior is Figure 3 and Figure 4 As shown, the width of the truncated Gaussian profile is set to The total propagation distance is 100m, spanning from the left plane to the right plane. The results vividly show that the intensity (such as Figure 3 ) and coherence (as shown in Figure 4 Each figure shows three planes corresponding to the propagation distances at z = 0, 50 m and 100 m.

[0035] In order to quantitatively describe the ability of a beam to resist optical diffraction, we introduce the similarity measure to evaluate the similarity of the intensity (or coherence) distributions at the receiving plane and the source plane. The similarity measure is defined as follows: (11); in, is the coherence or intensity distribution at the propagation distance z, is the coherence or intensity distribution at the source plane. Its value is in the range [0, 1]. The larger the value, the stronger the immunity to light diffraction.

[0036] like Figure 5 As shown, the similarity curves of intensity (upper coordinate axis) and coherence (lower coordinate axis) are plotted. It can be observed that although the curve decreases slightly with the increase of propagation distance, the similarity remains at about 0.98 at the propagation distance z=100m, proving that the beam has strong resistance to optical diffraction. In addition, the effect of the only parameter that changes, global coherence, on the similarity of intensity and coherence is studied. The results show that, except for a slight change in coherence, both are basically unaffected by this parameter. This shows that even with lower coherence, the constructed beam still has significant anti-diffraction capabilities. This effectively solves the traditional dilemma that lower beam coherence usually leads to greater diffraction and more obvious light field distortion.

[0037] In order to further explore the beam characteristics of truncated non-diffraction partially coherent Pearcey beams and facilitate experimental construction, the pseudo-mode superposition principle is used to represent such beams.

[0038] The first-order diffraction spot of each pseudo-pattern is recorded by a CCD camera, and each pseudo-pattern is superimposed to form a partially coherent Pierce beam, specifically: (12); in, is the discrete power spectral density function, representing the mode weight. is truncation mode (or pseudo-mode), defined as: (13); here represents the position of the sampling point on the inverse plane, d represents the sampling space, and N represents the total number of sampling points along the horizontal or vertical direction. Since free space is a linear system, the propagation behavior of the truncated non-diffractive partially coherent Pearcey beam can be evaluated by the incoherent superposition of all pseudo-modes propagated to the receiving plane with the help of the light wave propagation theory.

[0039] The experimental results are in good agreement with the theoretical results, proving the feasibility of the scheme. In addition, we further experimentally studied the transmission behavior of light beams in free space. Figure 6As shown in the figure, the intensity of the beam does not change with the transmission of the beam. The experimental results are consistent with the theoretical predictions, proving that the partially coherent beam we constructed has a strong ability to resist optical diffraction. The relevant parameters are set to =1, from left to right, transmission distance z=0.5m, 1m, 1.5m.

[0040] In this paper, the customization of diffraction-free partially coherent Pierce beams is theoretically proposed and experimentally advanced. The intensity and coherence of such beams remain unchanged during propagation. Even in practical scenarios, the truncated versions still retain significant resistance to optical diffraction. These beams naturally have two significant advantages: low coherence and diffraction-free propagation. The low coherence guarantees the robustness of the beams in harsh environments, while the diffraction-free properties allow the use of certain degrees of freedom, such as coherence and intensity, as information carriers for long-distance information transmission. Therefore, diffraction-free partially coherent Pierce beams have great application potential in the fields of optical communications, information transmission, optical imaging, etc., especially in harsh environments.

[0041] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A non-diffraction partially coherent Pierce beam generation system, characterized in that: include: A laser, wherein the light beam emitted by the laser reaches a beam expander through a half-wave plate, and after being expanded by the beam expander, the laser beam is irradiated onto a spatial light modulator; The spatial light modulator modulates the laser beam using a cross-density spectrum function to generate a modulated light beam; A 4f optical imaging system, wherein the 4f optical imaging system selects a first-order diffraction spot from the modulated light beam; A CCD camera is used to record the first-order diffraction spot.

2. A non-diffraction partially coherent Pierce beam generating system as claimed in claim 1, characterized in that: The 4f optical imaging system includes a first thin lens, an aperture and a second thin lens.

3. A non-diffraction partially coherent Pierce beam generating system as claimed in claim 1, characterized in that: The spatial light modulator modulates the laser beam using a cross-density spectrum function, specifically: The cross-density spectrum function is used to obtain the pseudo-mode of the laser beam at different positions on the reciprocal plane; Based on the complex amplitude control algorithm, pseudo patterns at different positions on the reciprocal plane are used to generate holographic images.

4. A non-diffraction partially coherent Pierce beam generating system as claimed in claim 1, characterized in that: The complex amplitude control algorithm is specifically: ； Among them, the B amplitude is obtained by numerical inversion: ,in, represents the first-order Bessel function of the first kind; "Arg" means taking the phase of the function; represents the grating frequency, is any kernel function, represents the position of the sampling point on the inverse plane, and are the vector positions in the source plane and the reciprocal plane, respectively.

5. A method for generating a non-diffraction partially coherent Pierce beam, based on a non-diffraction partially coherent Pierce beam generating system as claimed in any one of claims 1 to 4, characterized in that: include: The light beam emitted by the laser reaches the beam expander through the half-wave plate. After being expanded by the beam expander, the laser is irradiated onto the spatial light modulator. The laser beam is modulated by repeatedly refreshing the spatial light modulator, and the pseudo-mode of the laser beam at different positions on the reciprocal plane is obtained based on the cross-density spectrum function, and the corresponding holographic image is generated; After being processed by the 4f optical imaging system, the first-order diffraction spot corresponding to each pseudo-pattern is screened out; The first-order diffraction spot of each pseudo-pattern is recorded by a CCD camera, and each pseudo-pattern is superimposed to form a partially coherent Pierce beam.

6. A method for generating a non-diffraction partially coherent Pierce beam as claimed in claim 5, characterized in that: The laser beam is modulated by the repeatedly refreshed spatial light modulator, pseudo-modes of the laser beam at different positions on the reciprocal plane are obtained based on the cross-density spectrum function, and corresponding holographic images are generated, specifically: Use Gaussian and cosine functions to construct power spectral density functions and arbitrary kernel functions; Introducing dimensionless and difference coordinates, converting the mathematical form of power spectral density function and arbitrary kernel function; Based on the converted power spectral density function and the arbitrary kernel function, a cross spectral density function of a single position point is determined; Using Gaussian aperture as the cutoff function of the laser beam, the cutoff cross spectral density function of a single position point is determined; Repeatedly refreshing the spatial light modulator to modulate the laser beam, and using the truncated cross spectral density function of a single position point to obtain pseudo-modes of the laser beam at different positions on the reciprocal plane; Based on the complex amplitude control algorithm, pseudo patterns at different positions on the reciprocal plane are used to generate holographic images.

7. A method for generating a non-diffraction partially coherent Pierce beam as claimed in claim 6, characterized in that: The truncated cross spectral density function of a single position point is determined as follows: ； in, and represents the width of the truncation function, where and represents the power spectral density function and arbitrary kernel function using dimensionless and difference coordinate transformation, represents a truncated cross spectrum.

8. A method for generating a non-diffraction partially coherent Pierce beam as claimed in claim 6, characterized in that: The first-order diffraction spot of each pseudo-pattern is recorded by a CCD camera, and each pseudo-pattern is superimposed to form a partially coherent Pierce beam, specifically: ； in, is the discrete power spectral density function, representing the mode weight, is truncation mode, It is a pseudo mode. represents the position of the sampling point on the inverse plane, and are the coordinates on the source plane.

9. A method for generating a non-diffraction partially coherent Pierce beam as claimed in claim 8, characterized in that: The truncation mode is specifically: ； in, represents the position of the sampling point on the inverse plane, d represents the sampling space, is any kernel function, and are the vector positions in the source plane and the reciprocal plane, respectively, Indicates the size of the Gaussian cutoff.

10. A method for generating a non-diffraction partially coherent Pierce beam as claimed in claim 5, characterized in that: The first-order diffraction spot contains information of the pseudo-pattern.

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