Diffracted field calculation method and device for bessel-gauss beam, equipment and medium

Abstract

The application discloses a diffraction field calculation method, device and equipment of a Bessel Gaussian beam and a medium, the Bessel Gaussian beam is reflected by a conical surface of an off-axis conical mirror, and a Gaussian beam is reflected at a preset incidence angle; the method comprises the following steps: obtaining a first light field distribution of a reflected beam formed after the Gaussian beam is just reflected on the off-axis conical mirror; based on the first light field distribution, a virtual surface is constructed, and a third light field distribution of the Gaussian beam on the virtual surface is obtained; the discretization spectrum of the third light field distribution is determined; the discrete sampling point coordinate set of the Bessel Gaussian beam on a preset diffraction field is determined; based on the discretization spectrum, the discrete sampling point coordinate set is subjected to non-uniform discrete Fourier transform, and the second light field distribution of the Bessel Gaussian beam on the preset diffraction field is obtained. The application provides a low-complexity and fast calculation algorithm for calculating the diffraction field of the Bessel Gaussian beam generated by the off-axis conical mirror.

Description

Methods, apparatus, equipment and media for calculating the diffraction field of Bessel-Gaussian beams Technical Field

[0001] This application relates to the field of optics, and in particular to a method, apparatus, device and medium for calculating the diffraction field of a Bessel-Gaussian beam. Background Technology

[0002] In related technologies, a Bessel-Gaussian beam can be obtained by reflecting a Gaussian beam incident at a preset incident angle from the conical surface of an off-axis conical mirror. In this case, the diffraction field distribution of the Bessel-Gaussian beam can be calculated using interpolation methods.

[0003] However, for Bessel-Gaussian beams, the computational complexity of the interpolation algorithm is very high. Summary of the Invention

[0004] The main objective of this application is to provide a method, apparatus, device, and medium for calculating the diffraction field of a Bessel-Gaussian beam, aiming to solve the technical problem of high complexity in calculating the diffraction field of a Bessel-Gaussian beam generated by an off-axis conical mirror.

[0005] To achieve the above objectives, this application provides a method for calculating the diffraction field of a Bessel-Gaussian beam, wherein the Bessel-Gaussian beam is obtained by reflecting the Gaussian beam incident at a preset incident angle by the conical surface of an off-axis conical mirror.

[0006] The methods include:

[0007] Obtain the first optical field distribution of the reflected beam formed immediately after the Gaussian beam is reflected on the off-axis conical mirror;

[0008] Based on the first light field distribution, a virtual surface is constructed, and the third light field distribution of the Gaussian beam on the virtual surface is obtained;

[0009] Determine the discretized spectrum of the third light field distribution;

[0010] Determine the set of coordinates of discrete sampling points of the Bessel-Gaussian beam in the preset diffraction field;

[0011] Based on the discretized spectrum, a non-uniform discrete Fourier transform is performed on the coordinate set of discrete sampling points to obtain the second optical field distribution of the Bessel-Gaussian beam in the preset diffraction field.

[0012] In one possible embodiment of this application, determining the discretized spectrum of the third light field distribution includes:

[0013] A two-dimensional fast Fourier transform is performed on the third light field distribution to obtain the discretized spectrum.

[0014] In one possible embodiment of this application, a virtual surface is constructed based on a first light field distribution, and a third light field distribution of a Gaussian beam on the virtual surface is obtained, including:

[0015] The first optical expression for the first light field distribution is rewritten as an intermediate expression; the first optical expression is:

[0016]

[0017] The intermediate expression is:

[0018] E1(x1,y1)=E 01 (x1,y1)*exp(jky1sinθ);

[0019] Virtual surfaces are constructed based on intermediate expressions;

[0020] The third optical expression for the third optical field distribution of the Gaussian beam on the virtual surface is obtained as follows:

[0021]

[0022] Where E1(x1,y1) represents the first light field distribution of the reflected beam on the first light field plane, the vertex of the off-axis cone mirror is located on the first light field plane, and the angle between the normal of the first light field plane and the incident direction of the Gaussian beam is a preset incident angle θ. The first light field plane has an x1y1 coordinate system, E 01 (x1,y1) represents the third light field distribution, ω represents the waist radius of the Gaussian beam, k represents the wavenumber of the Gaussian beam, λ represents the wavelength of the Gaussian beam, and α represents the apex angle of the off-axis cone mirror.

[0023] In one possible embodiment of this application, determining the set of discrete sampling point coordinates of the Bessel-Gaussian beam in a preset diffraction field includes:

[0024] Obtain the optical field width of the reflected beam on the first optical field plane, and the diffraction optical field width and discrete sampling point parameters of the Bessel-Gaussian beam in the preset diffraction field;

[0025] Based on the width of the optical field, the number of sampling points of the reflected beam on the first optical field plane is obtained;

[0026] The coordinate set of discrete sampling points is determined based on the light field width, the diffraction light field width, the number of sampling points, and the discrete sampling point parameters.

[0027] In one possible embodiment of this application, the number of sampling points of the reflected beam on the first plane is obtained based on the optical field width, including:

[0028] The number of sampling points of the reflected beam in the x1 direction is obtained based on the first optical field width of the reflected beam in the first optical field plane, the apex angle of the off-axis conical mirror, the wavelength of the Gaussian beam, and Formula 1.

[0029] The second number of sampling points of the reflected beam in the y1 direction is obtained based on the second optical field width of the reflected beam in the first optical field plane, the apex angle of the off-axis conical mirror, the wavelength of the Gaussian beam, and Formula 1.

[0030] Formula 1 is as follows:

[0031]

[0032] Wherein, when L is the first optical field width, N is the first number of sampling points; when L is the second optical field width, N is the second number of sampling points.

[0033] In one possible embodiment of this application, the preset diffraction field has an x2y2 coordinate system, and the discrete sampling point parameters include a first discrete sampling point parameter in the x2 direction and a second discrete sampling point parameter in the y2 direction;

[0034] Based on the light field width, diffracted light field width, number of sampling points, and discrete sampling point parameters, the coordinate set of discrete sampling points is determined, including:

[0035] Based on the first optical field width of the reflected beam in the x1 direction of the first optical field plane, the third optical field width of the Bessel-Gaussian beam in the x2 direction of the preset diffraction field, the first number of sampling points, and the first discrete sampling point sub-parameters, the first discrete sampling point coordinate subset of the Bessel-Gaussian beam in the x2 direction is obtained; wherein, the first discrete sampling point coordinate subset is:

[0036]

[0037] Based on the second optical field width of the reflected beam in the y1 direction of the first optical field plane, the fourth optical field width of the Bessel-Gaussian beam in the y2 direction of the preset diffraction field, the second number of sampling points, and the second discrete sampling point sub-parameters, the second discrete sampling point coordinate subset of the Bessel-Gaussian beam in the y2 direction is obtained; wherein, the second discrete sampling point coordinate subset is:

[0038]

[0039] The discrete sampling point coordinate set is obtained based on the first discrete sampling point coordinate subset and the second discrete sampling point coordinate subset;

[0040] The discrete sampling point coordinate set is (m,n).

[0041]

[0042]

[0043] Among them, L x L is the width of the first optical field. y For the second optical field width, LL x For the third light field intensity, LL y N is the intensity of the fourth light field. x N represents the number of the first sampling points. y N′ is the number of the second sampling points. x Let N′ be the sub-parameter of the first discrete sampling point. y For the second discrete sampling point sub-parameters.

[0044] In one possible embodiment of this application, the optical expression for the second light field distribution is:

[0045]

[0046] Among them, f s2 (p,q) satisfies:

[0047]

[0048] satisfy:

[0049]

[0050] Where d is the diffraction propagation distance of the reflected beam. The frequency interval of the reflected beam in the x1 direction; The frequency interval of the reflected beam in the y1 direction;

[0051] G1(p,q) is the discretized spectrum of the third optical field distribution, where:

[0052] p = {-N x / 2,-N x / 2+1,...,0,1,..,N x / 2-1};

[0053] q={-N y / 2,-N y / 2+1,...,0,1,..,N y / 2-1}.

[0054] Secondly, this application also provides a device for calculating the diffraction field of a Bessel-Gaussian beam, wherein the Bessel-Gaussian beam is obtained by reflecting the Gaussian beam incident at a preset incident angle by the conical surface of an off-axis conical reflector; the device includes:

[0055] The first light field distribution calculation module obtains the first light field distribution of the reflected beam formed by the Gaussian beam just after it is reflected on the off-axis conical mirror.

[0056] The virtual field determination module is used to construct a virtual surface based on the first light field distribution and obtain the third light field distribution of the Gaussian beam on the virtual surface;

[0057] The spectrum determination module is used to determine the discretized spectrum of the third optical field distribution;

[0058] The discrete coordinate determination module is used to determine the set of coordinates of discrete sampling points of the Bessel-Gaussian beam in a preset diffraction field;

[0059] The second optical field distribution calculation module is used to perform a non-uniform discrete Fourier transform on the coordinate set of discrete sampling points based on the discretized spectrum, so as to obtain the second optical field distribution of the Bessel-Gaussian beam in the preset diffraction field.

[0060] Thirdly, this application also provides a device for calculating the diffraction field of a Bessel-Gaussian beam, including: a processor, a memory, and a Bessel-Gaussian beam diffraction field calculation program stored in the memory. The Bessel-Gaussian beam diffraction field calculation program is executed by the processor to implement the steps of the above-mentioned Bessel-Gaussian beam diffraction field calculation method.

[0061] Fourthly, this application also provides a computer-readable storage medium storing a program for calculating the diffraction field of a Bessel-Gaussian beam. When the program for calculating the diffraction field of a Bessel-Gaussian beam is executed by a processor, it implements the above-described method for calculating the diffraction field of a Bessel-Gaussian beam.

[0062] This application proposes a method for calculating the diffraction field of a Bessel-Gaussian beam. The method includes obtaining a first optical field distribution of the reflected beam formed after the Gaussian beam is just reflected on an off-axis conical mirror; constructing a virtual surface based on the first optical field distribution and obtaining a third optical field distribution of the Gaussian beam on the virtual surface; determining the discretized spectrum of the third optical field distribution; determining the coordinate set of discrete sampling points of the Bessel-Gaussian beam in a preset diffraction field; and performing a non-uniform discrete Fourier transform on the coordinate set of discrete sampling points based on the discretized spectrum to obtain a second optical field distribution of the Bessel-Gaussian beam in the preset diffraction field.

[0063] Therefore, this application solves the problem of complex interpolation algorithms required when calculating the diffraction field of a Bessel-Gaussian beam using traditional angular spectrum algorithms by cleverly utilizing non-uniform discrete Fourier transform in a reflective optical path. This provides a low-complexity and fast calculation algorithm for calculating the diffraction field of a Bessel-Gaussian beam generated by an off-axis conical mirror. Attached Figure Description

[0064] Figure 1 is the optical path diagram of the Bessel-Gaussian beam generated using an off-axis cone mirror in this application;

[0065] Figure 2 is a schematic diagram of the structure of the diffraction field calculation device of the Bessel-Gaussian beam involved in the embodiment of this application;

[0066] Figure 3 is a flowchart illustrating the first embodiment of the method for calculating the diffraction field of the Bessel-Gaussian beam in this application;

[0067] Figure 4 is a schematic diagram of the discretized spectrum in an example of this application;

[0068] Figure 5 is a schematic diagram of the light field distribution of a Bessel-Gaussian beam on the x2y2 plane in an example of this application;

[0069] Figure 6 is a schematic diagram of the functional modules of the Bessel-Gaussian beam diffraction field calculation device of this application.

[0070] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0071] It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit this application.

[0072] The optical path system used in the technical implementation of this application will be described below according to the embodiments of this application:

[0073] Referring to Figure 1, which is the optical path diagram of the Bessel-Gaussian beam 20 generated using the off-axis conical mirror 30 in this application, the incident beam is a Gaussian beam 10 incident perpendicular to the x0y0 plane. In Figure 1, the x0y0 plane is a vertical plane, therefore the Gaussian beam 10 is incident in a horizontal direction. The Gaussian beam 10 propagates to the conical surface of the off-axis conical mirror 30, and after reflection, diffraction occurs, generating the Bessel-Gaussian beam 20.

[0074] It is worth mentioning that the angle between the normal of the off-axis conical mirror 30 and the horizontal plane is θ, which is also the incident angle of the Gaussian beam 10 relative to the off-axis conical mirror 30 is θ. In other words, the central axis of the off-axis conical mirror 30 is tilted at an angle relative to the horizontal direction, and this tilt angle is the incident angle θ.

[0075] The optical expression for the light field distribution of Gaussian beam 10 in the x0y0 plane is:

[0076]

[0077] Where ω is the waist radius of the Gaussian beam 10, k is the wave number of the Gaussian beam 10, k = 2π / λ, and λ is the wavelength of the Gaussian beam 10.

[0078] The optical expression for the light field distribution in the x1y1 plane of the reflected beam formed immediately after the Gaussian beam 10 is reflected by the off-axis conical mirror 30 is:

[0079]

[0080] Where α is the apex angle of the off-axis conical mirror 30. It can be understood that the first light field plane described below is the x1y1 plane in Figure 1. Referring to Figure 1, the vertex of the cone surface of the off-axis conical mirror 30 is located on the x1y1 plane, and the angle between the normal of the x1y1 plane and the incident direction of the Gaussian beam 10 is the incident angle θ. The x1y1 plane has an x1y1 coordinate system.

[0081] Along the propagation direction of the Bessel-Gaussian beam 10, there is a preset diffraction field plane x2y2. In this embodiment, the problem addressed is the calculation of the light field distribution as the beam propagates from the x1y1 plane to the x2y2 plane. The specific location of the preset diffraction field plane x2y2 is determined by the diffraction propagation distance d.

[0082] Referring to Figure 2, which is a schematic diagram of the structure of the diffraction field calculation device of the Bessel-Gauss beam involved in the embodiment of this application.

[0083] As shown in Figure 2, the diffraction field calculation device for the Bessel-Gaussian beam may include: a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. The communication bus 1002 is used to enable communication between these components. The user interface 1003 may include a display screen and an input unit such as a keyboard; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface). The memory 1005 may be a high-speed random access memory (RAM) or a stable non-volatile memory (NVM), such as a disk drive. The memory 1005 may also optionally be a storage device independent of the aforementioned processor 1001.

[0084] Those skilled in the art will understand that the structure shown in Figure 2 does not constitute a limitation on the diffraction field calculation device for the Bessel-Gaussian beam 20, and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0085] As shown in Figure 2, the memory 1005, which serves as a storage medium, may include an operating system, a data storage module, a network communication module, a user interface module, and a diffraction field calculation program for the Bessel-Gauss beam 20.

[0086] In the diffraction field calculation device of the Bessel-Gaussian beam 20 shown in Figure 2, the network interface 1004 is mainly used for data communication with the network server; the user interface 1003 is mainly used for data interaction with the user; the processor 1001 and the memory 1005 in the diffraction field calculation device of the Bessel-Gaussian beam 20 of this application can be set in the diffraction field calculation device of the Bessel-Gaussian beam 20. The diffraction field calculation device of the Bessel-Gaussian beam 20 calls the diffraction field calculation program of the Bessel-Gaussian beam 20 stored in the memory 1005 through the processor 1001 and executes the diffraction field calculation method of the Bessel-Gaussian beam 20 provided in the embodiment of this application.

[0087] Based on the above optical path structure and hardware structure, this application provides a first embodiment of a method for calculating the diffraction field of a Bessel-Gaussian beam. Referring to Figure 3, Figure 3 shows a schematic flowchart of the first embodiment of the method for calculating the diffraction field of a Bessel-Gaussian beam.

[0088] It should be noted that although the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than that shown here.

[0089] In this embodiment, the method for calculating the diffraction field of the Bessel-Gaussian beam includes:

[0090] Step S100: Obtain the first light field distribution of the reflected beam formed after the Gaussian beam is just reflected on the off-axis conical mirror.

[0091] Understandably, the first light field distribution is the light field distribution of the reflected beam formed by the Gaussian beam 10 after it has just been reflected by the off-axis conical mirror 30, in the x1y1 plane, and its optical expression is:

[0092]

[0093] Step S200: Based on the first light field distribution, construct a virtual surface and obtain the third light field distribution of the Gaussian beam on the virtual surface.

[0094] Specifically, as shown in Figure 1, the Gaussian beam 10 incident on the off-axis conical mirror 30 is given a phase that is related to the tilt angle of the conical mirror. Therefore, in the diffraction calculation, the number of sampling points used to describe the incident light field needs to increase with the tilt angle, which results in the high computational complexity of the existing diffraction field calculation algorithm.

[0095] Therefore, this embodiment utilizes the frequency shift characteristic of Fourier transform. By performing a simple spectrum shift in the frequency domain, the calculation method provided in this embodiment can be applied to any tilt angle without changing the number of sampling points.

[0096] As one embodiment, step S200 specifically includes:

[0097] Step S201: Rewrite the first optical expression of the first light field distribution into an intermediate expression. The first optical expression is:

[0098]

[0099] The intermediate expression is:

[0100] E1(x1,y1)=E 01 (x1,y1)*exp(jky1sinθ);

[0101] Step S202: Construct a virtual surface based on the intermediate expression;

[0102] Step S203: Obtain the third optical expression for the third light field distribution of the Gaussian beam on the virtual surface:

[0103]

[0104] Specifically, for the first optical expression:

[0105]

[0106] It can be rewritten as an intermediate expression:

[0107] E1(x1,y1)=E 01 (x1,y1)*exp(jky1sinθ);

[0108] At this time, E 01 (x1, y1) represents the third light field distribution, which is the Gaussian beam 10 on the virtual surface (x1y1). 01 The third optical expression for the third light field distribution on the surface is:

[0109]

[0110] Where E1(x1,y1) represents the first light field distribution of the Gaussian beam 10 on the first light field plane, the vertex of the off-axis cone reflector 30 is located on the first light field plane, and the angle between the normal of the first light field plane and the incident direction of the Gaussian beam 10 is a preset incident angle θ. The first light field plane has an x1y1 coordinate system, E 01 (x1,y1) represents the third light field distribution, ω represents the waist radius of the Gaussian beam 10, k represents the wavenumber of the Gaussian beam 10, λ represents the wavelength of the Gaussian beam 10, and α represents the apex angle of the off-axis cone reflector.

[0111] Step S300: Determine the discretized spectrum of the third light field distribution.

[0112] Specifically, step S300 involves performing a two-dimensional fast Fourier transform on the third light field distribution to obtain the discretized spectrum.

[0113] As can be clearly seen from the intermediate expression, based on the frequency shifting characteristics of the Fourier transform, the spectrum of the first optical field distribution E1(x1,y1) can be shifted by the third optical field distribution E 01 The spectrum of (x1, y1) is obtained, and the shift is F = sin / λ. Therefore, for E 01 The discretized spectrum G1(p,q) obtained by performing a two-dimensional fast Fourier transform on (x1,y1) can be used to equivalently obtain the discretized spectrum of E1(x1,y1) by shifting the discretized spectrum G1(p,q) obtained by performing a two-dimensional fast Fourier transform on (x1,y1).

[0114] Step S400: Determine the coordinate set of discrete sampling points of the Bessel-Gaussian beam in the preset diffraction field.

[0115] Specifically, since most other regions in the diffraction field have very small light intensity values, only the central diffraction field of the Bessel-Gaussian beam 20 can be calculated, while most other regions in the diffraction field are ignored, in order to further reduce the computational complexity.

[0116] Specifically, step S400 includes:

[0117] Step S401: Obtain the optical field width of the reflected beam on the first optical field plane, and the diffraction optical field width and discrete sampling point parameters of the Bessel-Gaussian beam 20 in the preset diffraction field.

[0118] Specifically, this embodiment uses sampling points to simulate and calculate the light field distribution of the Bessel-Gaussian beam 20 in a preset diffraction field. To ensure the simulation effect, the light field width of the reflected beam in the first light field plane, the diffraction light field width of the Bessel-Gaussian beam 20 in the preset diffraction field, and the discrete sampling point parameters can all be configured before the simulation.

[0119] Specifically, the x1y1 plane has an x1y1 coordinate system, the preset diffraction field has an x2y2 coordinate system, and the optical field width of the reflected beam on the first optical field plane includes the first optical field width L of the reflected beam in the x1 direction of the x1 plane. x The second optical field width L in the y1 direction y And the intensity LL of the third optical field in the x2 direction of the Bessel-Gaussian beam 20 in the preset diffraction field. x The intensity of the fourth light field LL in the y2 direction y The discrete sampling point parameters include the first discrete sampling point parameter N′ in the x2 direction. x and the parameter N′ of the second discrete sampling point in the y2 direction y .

[0120] Understandably, the parameter N′ of the first discrete sampling point x Second discrete sampling point parameter N′ y These are all parameters that control the number of discrete sampling points. Therefore, the parameter N′ of the first discrete sampling point can be adjusted according to the required accuracy of the diffraction field simulation calculation. x Second discrete sampling point parameter N′ y The specific configuration needs to be carried out.

[0121] It is worth mentioning that the parameters of the Gaussian beam 10 and the off-axis conical mirror 30 can be pre-configured in the diffraction field calculation device of the Bessel-Gaussian beam 20, such as the diffraction propagation distance d of the reflected beam and the frequency interval of the reflected beam in the x1 direction. Frequency interval of the reflected beam in the y1 direction The incident angle θ of the Gaussian beam 10 relative to the off-axis conical mirror 30; the beam waist radius ω of the Gaussian beam 10; the wave number k of the Gaussian beam 10, k = 2π / λ; the wavelength λ of the Gaussian beam 10; and the apex angle α of the off-axis conical mirror 30, etc.

[0122] Step S402: Based on the optical field width, obtain the number of sampling points of the reflected beam on the first optical field plane.

[0123] Once the width of the light field is obtained, the total number of sampling points within the width of the light field can be calculated.

[0124] Specifically, step S402 includes:

[0125] (1) Based on the first optical field width of the reflected beam in the x1 direction of the first optical field plane, the apex angle of the off-axis conical reflector 30, the wavelength of the Gaussian beam 10 and Formula 1, the first sampling point of the reflected beam in the x1 direction is obtained.

[0126] (2) Based on the second optical field width of the reflected beam in the y1 direction of the first optical field plane, the apex angle of the off-axis conical reflector 30, the wavelength of the Gaussian beam 10 and Formula 1, the number of second sampling points of the reflected beam in the y1 direction is obtained.

[0127] Formula 1 is as follows:

[0128]

[0129] Wherein, when L is the first optical field width, N is the first number of sampling points; when L is the second optical field width, N is the second number of sampling points.

[0130] That is to say,

[0131] It is understood that step S302 can also be performed before step S200, and this embodiment does not limit this.

[0132] Step S403: Determine the coordinate set of discrete sampling points based on the light field width, diffraction light field width, number of sampling points, and discrete sampling point parameters.

[0133] Specifically, after calculating the number of sampling points on the x1y1 plane, since the diffraction field on the x2y2 plane is obtained by the diffraction of the reflected beam passing through the x1y1 plane, the set of discrete sampling point coordinates required for simulating the diffraction field on the x2y2 plane can be further calculated.

[0134] Specifically, step S403 includes:

[0135] 1) Based on the first optical field width of the reflected beam in the x1 direction of the first optical field plane, the third optical field width of the Bessel-Gaussian beam 20 in the x2 direction of the preset diffraction field, the first number of sampling points of the reflected beam in the x1 direction, and the first discrete sampling point sub-parameters, the first discrete sampling point coordinate subset of the Bessel-Gaussian beam 20 in the preset diffraction field is obtained; wherein, the first discrete sampling point coordinate subset is:

[0136]

[0137] 2) Based on the second optical field width of the reflected beam in the y1 direction of the first optical field plane, the fourth optical field width of the Bessel-Gaussian beam 20 in the y2 direction, the second number of sampling points and the second discrete sampling point sub-parameter of the reflected beam in the x1 direction, the second discrete sampling point coordinate subset of the Bessel-Gaussian beam 20 in the preset diffraction field is obtained; wherein, the second discrete sampling point coordinate subset is:

[0138]

[0139] 3) Obtain the set of discrete sampling point coordinates based on the first subset of discrete sampling point coordinates and the second subset of discrete sampling point coordinates;

[0140] The discrete sampling point coordinate set is (m,n).

[0141]

[0142]

[0143] It can be seen that the spacing between adjacent sampling points in the x2 direction is 1. The total number of discrete sampling points is determined by and The ratio between them is determined. The spacing between adjacent sampling points in the y2 direction is... The total number of discrete sampling points is determined by and The ratio between them is determined.

[0144] Step S500: Based on the discretized spectrum, perform a non-uniform discrete Fourier transform on the coordinate set of discrete sampling points to obtain the second optical field distribution of the Bessel-Gaussian beam in the preset diffraction field.

[0145] Specifically, the optical expression for the second light field distribution is:

[0146]

[0147] Among them, fs2 (p,q) satisfies:

[0148]

[0149] satisfy: d is the diffraction propagation distance of the reflected beam. The frequency interval of the reflected beam in the x1 direction; The frequency interval of the reflected beam in the y1 direction is denoted as y1.

[0150] Wherein, G1(p,q) is the discretized spectrum of the third optical field distribution, wherein:

[0151] p = {-N x / 2,-N x / 2+1,...,0,1,..,N x / 2-1};

[0152] q={-N y / 2,-N y / 2+1,...,0,1,..,N y / 2-1}.

[0153] Therefore, this application provides a low-complexity, fast diffraction calculation method for calculating the light field distribution of a Bessel-Gaussian beam generated by an off-axis conical mirror. This embodiment uses a non-uniform discrete Fourier transform to solve the diffraction calculation problem between tilted planes.

[0154] Furthermore, to address the issue of the increasing number of sampling points with increasing tilt angle, this embodiment utilizes the frequency shift characteristic of Fourier transform. By performing a simple spectral shift in the frequency domain, the proposed method can be applied to any tilt angle without increasing the number of sampling points. This solves the problem that traditional angular spectrum diffraction algorithms require a large number of sampling points when calculating the diffraction field of a Bessel-Gaussian beam 20.

[0155] Furthermore, this embodiment only calculates the central diffraction field of the Bessel-Gaussian beam 20, while most other areas in the diffraction field are ignored in the calculation because their light intensity values ​​are very small, in order to reduce the computational complexity of this embodiment.

[0156] To enable those skilled in the art to better understand the scope of protection of the claims of this application, specific implementation examples in specific application scenarios are used to explain and illustrate the technical solutions described in the claims of this application. It should be understood that the following examples are only used to explain this application and are not intended to limit the scope of protection of the claims of this application.

[0157] Referring to Figure 1, in one example, the laser generating the Gaussian beam 10 has a center wavelength λ of 532 nm, a beam waist radius λ of 1 mm, and a first optical field width L. x Second optical field width L y All are 5mm in diameter. The incident angle θ of the off-axis cone mirror is 10°, and the apex angle α is 2°. The third optical field width LL x =80μm, fourth optical field width LL y =80μm. Parameter N′ of the first discrete sampling point. x =8000 and the second discrete sampling point parameter N′ y =8000. Diffraction propagation distance d = 7mm.

[0158] Based on this, it can be calculated that

[0159] In obtaining N x and N y Then, the third optical expression for the third light field distribution can be derived:

[0160] E was calculated 01 (x1, y1). For the third light field distribution E 01 The discretized spectrum G1(p,q) of E1(x1,y1) can be obtained by performing a two-dimensional fast Fourier transform on (x1,y1), as shown in Figure 4.

[0161] The number of discrete sampling points can be calculated to be 167. Then, the coordinate set (m, n) of the discrete sampling points is calculated.

[0162] Finally, substitute the above parameters into...

[0163]

[0164] Please refer to Figure 5 to calculate the light field distribution of the Bessel-Gaussian beam 20 on the x2y2 plane.

[0165] Based on the same inventive concept, in a second aspect, referring to Figure 6, this application also provides a diffraction field calculation device for a Bessel-Gaussian beam, wherein the Bessel-Gaussian beam 20 is obtained by reflecting the Gaussian beam 10 incident at a preset incident angle by the conical surface of an off-axis conical reflector; the device includes:

[0166] The first light field distribution calculation module 100 obtains the first light field distribution of the reflected beam formed after the Gaussian beam is just reflected on the off-axis conical mirror.

[0167] The virtual field determination module 200 is used to construct a virtual surface based on the first light field distribution and obtain the third light field distribution of the Gaussian beam on the virtual surface;

[0168] The spectrum determination module 300 is used to determine the discretized spectrum of the third optical field distribution;

[0169] Discrete coordinate determination module 400 is used to determine the set of coordinates of discrete sampling points of the Bessel-Gaussian beam in a preset diffraction field;

[0170] The second light field distribution calculation module 500 is used to perform a non-uniform discrete Fourier transform on the coordinate set of discrete sampling points based on the discretized spectrum, so as to obtain the second light field distribution of the Bessel-Gaussian beam in the preset diffraction field.

[0171] It should be noted that the various implementations of the diffraction field calculation device for the Bessel-Gaussian beam in this embodiment and the technical effects they achieve can be referred to the various implementations of the diffraction field calculation method for the Bessel-Gaussian beam in the foregoing embodiments, and will not be repeated here.

[0172] Furthermore, embodiments of this application also propose a computer storage medium storing a program for calculating the diffraction field of a Bessel-Gaussian beam. When executed by a processor, the program implements the steps of the Bessel-Gaussian beam diffraction field calculation method described above. Therefore, it will not be repeated here. Additionally, the beneficial effects of using the same method will not be repeated. For technical details not disclosed in the computer-readable storage medium embodiments of this application, please refer to the description of the method embodiments of this application. As an example, program instructions can be deployed to execute on a single computing device, or on multiple computing devices located at one location, or on multiple computing devices distributed across multiple locations and interconnected via a communication network.

[0173] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0174] It should also be noted that the device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided in this application, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0175] Through the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary general-purpose hardware, or it can be implemented by special-purpose hardware including application-specific integrated circuits, special-purpose CPUs, special-purpose memory, special-purpose components, etc. Generally, any function performed by a computer program can be easily implemented by corresponding hardware, and the specific hardware structure used to implement the same function can also be diverse, such as analog circuits, digital circuits, or special-purpose circuits. However, for this application, software program implementation is more often the preferred implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a readable storage medium, such as a computer floppy disk, USB flash drive, mobile hard disk, read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of this application.

[0176] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for calculating the diffraction field of a Bessel-Gaussian beam, characterized in that, The Bessel-Gaussian beam is obtained by reflecting a Gaussian beam incident at a preset incident angle by the conical surface of an off-axis conical mirror; the method includes: obtaining a first optical field distribution of the reflected beam formed immediately after the Gaussian beam is reflected on the off-axis conical mirror; constructing a virtual surface based on the first optical field distribution and obtaining a third optical field distribution of the Gaussian beam on the virtual surface; determining the discretized spectrum of the third optical field distribution; determining the coordinate set of discrete sampling points of the Bessel-Gaussian beam in a preset diffraction field; performing a non-uniform discrete Fourier transform on the coordinate set of discrete sampling points based on the discretized spectrum to obtain a second optical field distribution of the Bessel-Gaussian beam in the preset diffraction field; the step of constructing a virtual surface based on the first optical field distribution and obtaining the third optical field distribution of the Gaussian beam on the virtual surface includes: rewriting a first optical expression of the first optical field distribution into an intermediate expression; the first optical expression is: The intermediate expression is: Based on the intermediate expression, the virtual surface is constructed; a third optical expression for the third light field distribution of the Gaussian beam on the virtual surface is obtained, and the third optical expression is: ;in, The first light field distribution of the reflected beam on the first light field plane is given, the vertex of the off-axis conical mirror is located on the first light field plane, and the angle between the normal of the first light field plane and the incident direction of the Gaussian beam is the preset incident angle. The first light field plane has coordinate system The third light field distribution, Let be the beam waist radius of the Gaussian beam. Let be the wavenumber of the Gaussian beam. The wavelength of the Gaussian beam is given. The apex angle of the off-axis cone mirror is given.

2. The method for calculating the diffraction field of a Bessel-Gaussian beam according to claim 1, characterized in that, Determining the discretized spectrum of the third light field distribution includes: performing a two-dimensional fast Fourier transform on the third light field distribution to obtain the discretized spectrum.

3. The method for calculating the diffraction field of a Bessel-Gaussian beam according to claim 1, characterized in that, Determining the discrete sampling point coordinate set of the Bessel-Gaussian beam in the preset diffraction field includes: obtaining the optical field width of the reflected beam in the first optical field plane, and the diffraction optical field width and discrete sampling point parameters of the Bessel-Gaussian beam in the preset diffraction field; obtaining the number of sampling points of the reflected beam in the first optical field plane based on the optical field width; and determining the discrete sampling point coordinate set based on the optical field width, the diffraction optical field width, the number of sampling points, and the discrete sampling point parameters.

4. The method for calculating the diffraction field of a Bessel-Gaussian beam according to claim 3, characterized in that, The step of obtaining the number of sampling points of the reflected beam on the first light field plane based on the light field width includes: based on the number of sampling points of the reflected beam on the first light field plane... Using the first optical field width in the direction, the apex angle of the off-axis cone mirror, the wavelength of the Gaussian beam, and Formula 1, the reflected beam is obtained in the direction of the reflection. The number of first sampling points in the direction; based on the reflected beam in the first optical field plane. Using the second optical field width in the direction, the apex angle of the off-axis cone mirror, the wavelength of the Gaussian beam, and Formula 1, the reflected beam is obtained in the direction of the second optical field width, the apex angle of the off-axis cone mirror, the wavelength of the Gaussian beam, and Formula 1. The number of second sampling points in the direction; wherein, Formula 1 is: Wherein, when L is the width of the first light field, N is the number of the first sampling points; when L is the width of the second light field, N is the number of the second sampling points.

5. A device for calculating the diffraction field of a Bessel-Gaussian beam, characterized in that, The Bessel-Gaussian beam is obtained by reflecting a Gaussian beam incident at a preset incident angle from the conical surface of an off-axis conical mirror. The device includes: a first light field distribution calculation module for obtaining the first light field distribution of the reflected beam formed immediately after the Gaussian beam is reflected from the off-axis conical mirror; a virtual field determination module for constructing a virtual surface based on the first light field distribution and obtaining the third light field distribution of the Gaussian beam on the virtual surface; a spectrum determination module for determining the discretized spectrum of the third light field distribution; a discrete coordinate determination module for determining the set of discrete sampling points of the Bessel-Gaussian beam in a preset diffraction field; and a second light field distribution calculation module for performing a non-uniform discrete Fourier transform on the set of discrete sampling points based on the discretized spectrum to obtain the second light field distribution of the Bessel-Gaussian beam in the preset diffraction field. The virtual field determination module is specifically used to rewrite the first optical expression of the first light field distribution into an intermediate expression. The first optical expression is: The intermediate expression is: Based on the intermediate expression, the virtual surface is constructed; a third optical expression for the third light field distribution of the Gaussian beam on the virtual surface is obtained, and the third optical expression is: ;in, The first light field distribution of the reflected beam on the first light field plane is given, the vertex of the off-axis conical mirror is located on the first light field plane, and the angle between the normal of the first light field plane and the incident direction of the Gaussian beam is the preset incident angle. The first light field plane has coordinate system The third light field distribution, Let be the beam waist radius of the Gaussian beam. Let be the wavenumber of the Gaussian beam. The wavelength of the Gaussian beam is given. The apex angle of the off-axis cone mirror is given.

6. A device for calculating the diffraction field of a Bessel-Gaussian beam, characterized in that, include: A processor, a memory, and a program for calculating the diffraction field of a Bessel-Gaussian beam stored in the memory, wherein the program for calculating the diffraction field of a Bessel-Gaussian beam is executed by the processor to implement the steps of the method for calculating the diffraction field of a Bessel-Gaussian beam as described in any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program for calculating the diffraction field of a Bessel-Gaussian beam, which, when executed by a processor, implements the method for calculating the diffraction field of a Bessel-Gaussian beam as described in any one of claims 1 to 4.

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