Calculation method for optimal emission aperture and optimal super-Gaussian order of super-Gaussian beam

Abstract

The present invention discloses a method for calculating the optimal emission aperture and optimal super-Gaussian order of a super-Gaussian beam, which relates to the technical field of strong laser transmission characteristic research and high-power laser design. The method comprises determining a super-Gaussian beam model and a super-Gaussian order n, initializing and setting an emission aperture d, calculating the emission plane light field distribution, calculating the far-field light intensity distribution of the super-Gaussian beam model, calculating the surrounding power curve of the far-field light spot, and obtaining the radius corresponding to the reference surrounding power ratio, namely the power radius R. x ; Change the launch aperture d and calculate the power radius R under different launch apertures d x , and get R x The curve of the change of the launch aperture d; the power radius R x The minimum emission aperture that no longer changes with the emission aperture d is taken as the optimal emission aperture d0. By analyzing the transmission process of a super-Gaussian beam in an atmospheric medium, the present invention provides a relationship between the super-Gaussian order and the optimal emission aperture. Furthermore, the optimal emission aperture can be obtained when the beam model is determined, or the optimal super-Gaussian order can be obtained when the emission aperture is determined. This provides a reference for the application of super-Gaussian beams in the atmospheric transmission of high-power lasers and the design of high-power lasers.

Description

Technical Field

[0001] The invention relates to the technical field of strong laser transmission characteristic research and high-power laser design, and proposes a calculation method for an optimal emission aperture and an optimal super-Gaussian order of a super-Gaussian beam. Background Art

[0002] In high-intensity laser applications in atmospheric environments, the energy concentration of the far-field spot is crucial. A flat-top source can be described by a super-Gaussian beam model. To ensure the energy concentration of the far-field spot of a super-Gaussian beam, the laser's emission aperture must be maximized. However, as the emission aperture increases, the laser's volume increases, resulting in a decrease in the laser's fill factor. Therefore, a method is needed to calculate the optimal emission aperture for a super-Gaussian beam. Summary of the Invention

[0003] In order to overcome the above-mentioned defects in the prior art, the present invention provides a method for calculating the optimal emission aperture of a super-Gaussian beam, which can obtain the optimal emission aperture when the beam model and the super-Gaussian order n are determined.

[0004] To achieve the above object, the present invention adopts the following technical solutions, including:

[0005] A method for calculating the optimal emission aperture of a super-Gaussian beam comprises the following steps:

[0006] S11, determining a super-Gaussian beam model and a super-Gaussian order n, and initializing a transmitting aperture d according to a range of transmitting aperture d;

[0007] S12, calculate the light field distribution on the emission plane;

[0008] S13, calculate the far-field light intensity distribution of the super-Gaussian beam model based on the Huygens-Fresnel principle;

[0009] S14, calculate the surrounding power curve of the far-field spot, that is, the relationship curve between the surrounding power ratio and the radius, select a surrounding power ratio as a reference surrounding power ratio, and obtain the radius corresponding to the reference surrounding power ratio, that is, the power radius R x ;

[0010] S15, change the transmission aperture d, repeat steps S12-S14, and calculate the power radius R under different transmission apertures d x , thus obtaining the power radius R x Curve of change with launch aperture d;

[0011] S16, according to the power radius R x As the launch aperture d changes, the power radius R xThe minimum emission aperture that no longer changes with the emission aperture d is taken as the optimal emission aperture d0, and the super-Gaussian beam model and the optimal emission aperture d0 under the super-Gaussian order n are obtained.

[0012] Preferably, the super-Gaussian order n is changed, and the optimal transmission aperture d0 under different super-Gaussian orders n is calculated according to the method of steps S11-S16, and the relationship between the optimal transmission aperture d0 and the super-Gaussian order n is obtained by fitting, that is, d0=f(n);

[0013] When determining the super-Gaussian beam model and the super-Gaussian order n, the optimal emission aperture d0 is calculated according to the relationship d0=f(n).

[0014] Preferably, when determining the emission aperture d, the optimal super-Gaussian order n0 corresponding to the emission aperture d is calculated according to the relationship d0=f(n).

[0015] Preferably, in step S14, a ring power ratio of 86.5% and / or 63.2% is selected as a reference ring power ratio, and the radius corresponding to the reference ring power ratio of 86.5% and 63.2% is obtained, that is, the power radius R 86.5 、R 63.2 ;

[0016] Among them, when the ring power ratio is 86.5% and 63.2% as the reference ring power ratio, the power radius R is obtained respectively. 86.5 and R 63.2 The curve of the change of the launch aperture d is based on the power radius R 86.5 and R 63.2 As the launch aperture d changes, the power radius R 86.5 and R 63.2 The minimum launch aperture that no longer changes with the launch aperture d is taken as the optimal launch aperture d0.

[0017] Preferably, in step S12, the emission plane light field distribution of the super-Gaussian beam model is expressed as:

[0018]

[0019] Where A is the relative amplitude, E(ρ) is the complex amplitude of the light field at point ρ on the emission plane, ρ is the light field coordinate on the emission plane; ω0 is the beam waist radius; d is the laser emission aperture; n represents the super-Gaussian order; the light intensity distribution at point ρ on the emission plane is I(ρ) = |E(ρ)| 2 ;

[0020] circ(·) is the cylindrical function, defined as:

[0021]

[0022] Preferably, in step S13, the far-field light intensity distribution of the super-Gaussian beam model is expressed as:

[0023]

[0024] Where λ and k = 2π / λ represent the wavelength and wave number of the light beam, respectively. i is an imaginary number, z is the coordinate along the transmission direction, L is the transmission distance, and E(r,z = L) represents the complex amplitude of the light field transmitted to the receiving plane at point r. r = (r x ,r y ) represents the coordinate of r on the receiving plane, E(ρ,z=0) represents the complex amplitude of the light field at ρ on the transmitting plane, ρ=(ρ x ,ρ y ) represents the coordinate of point ρ on the emitting plane, and the light intensity distribution at point r on the receiving plane is I(r,z=L)=|E(r,z=L)| 2 .

[0025] The present invention also provides a method for calculating the optimal super-Gaussian order of a super-Gaussian beam, which can obtain the optimal super-Gaussian order when the beam model and the emission aperture d are determined.

[0026] A method for calculating the optimal super-Gaussian order of a super-Gaussian beam comprises the following steps:

[0027] S21, determine the transmitting aperture d, and initialize and set a super Gaussian order n according to the value range of the super Gaussian order n;

[0028] S22, calculating the light field distribution in the emission plane according to the super-Gaussian beam model;

[0029] S23, calculate the far-field intensity distribution of the super-Gaussian beam model based on the Huygens-Fresnel principle;

[0030] S24, calculate and draw the surrounding power curve of the far-field spot, that is, the relationship curve between the surrounding power ratio and the radius, select a surrounding power ratio as a reference surrounding power ratio, and obtain the radius corresponding to the reference surrounding power ratio, that is, the power radius R x ;

[0031] S25, change the super-Gaussian order n, repeat steps S22-S24, and calculate the power radius R under different super-Gaussian orders n x , and thus the power radius R is obtained respectively x Curve changing with super-Gaussian order n;

[0032] S26, according to the power radius R x As the super-Gaussian order n changes, the power radius R xThe minimum super-Gaussian order that no longer changes with the super-Gaussian order n is taken as the optimal super-Gaussian order n0, and the optimal super-Gaussian order n0 under the launch aperture d is obtained.

[0033] Preferably, the transmitting aperture d is changed, and the optimal super-Gaussian order n0 under different transmitting apertures d is calculated according to the method of steps S21-S26, and the relationship between the optimal super-Gaussian order n0 and the transmitting aperture d is obtained by fitting, that is, n0=g(d);

[0034] When determining the super-Gaussian beam model and the emission aperture d, the optimal super-Gaussian order n0 is calculated according to the relationship n0=g(d).

[0035] Preferably, when determining the super-Gaussian order n, the optimal emission aperture d0 corresponding to the super-Gaussian order n is calculated according to the relationship n0=g(d).

[0036] Preferably, in step S24, a ring power ratio of 86.5% and / or 63.2% is selected as a reference ring power ratio, and the radius corresponding to the reference ring power ratio of 86.5% and 63.2% is obtained, that is, the power radius R 86.5 、R 63.2 ;

[0037] Among them, when the ring power ratio is 63.2% and 86.5% as the reference ring power ratio, the power radius R is obtained respectively. 63.2 and R 86.5 The curve of the change of super Gaussian order n, according to the power radius R 63.2 and R 86.5 As the super-Gaussian order n changes, the power radius R 63.2 and R 86.5 The minimum super-Gaussian order that no longer changes with the super-Gaussian order n is taken as the optimal super-Gaussian order n0.

[0038] The advantages of the present invention are:

[0039] (1) This paper proposes a method for calculating the optimal emission aperture of a super-Gaussian beam. By analyzing the transmission process of a super-Gaussian beam in an atmospheric medium, the relationship between the super-Gaussian order and the optimal emission aperture is presented. Furthermore, the optimal emission aperture can be obtained when the beam model is determined, or the optimal super-Gaussian order can be obtained when the emission aperture is determined. This provides a reference for the application of super-Gaussian beams in the atmospheric transmission of high-power lasers and the design of high-power lasers.

[0040] (2) Super-Gaussian beams have the advantage of a simple field distribution function, but their transmission laws are difficult to describe using analytical formulas. The calculation method proposed in this invention can quickly calculate the optimal emission aperture for super-Gaussian beam transmission while ensuring accuracy.

[0041] (3) There are many methods for analyzing the far-field beam quality of super-Gaussian beams. The calculation method proposed in this invention has good versatility. For different beam quality evaluation methods, the corresponding optimal emission aperture can be obtained after a simple modification of the algorithm.

[0042] (4) The calculation method proposed in this invention and the empirical formula obtained by fitting can provide a certain reference for the design of high-power lasers. While ensuring the far-field beam quality, the emission aperture can be reduced as much as possible and the filling factor can be increased, thereby reducing the laser volume and improving the near-field beam quality.

[0043] (5) The present invention also proposes a method for calculating the optimal super-Gaussian order of a super-Gaussian beam. By analyzing the transmission process of a super-Gaussian beam in an atmospheric medium, the relationship between the super-Gaussian order and the optimal emission aperture is presented. Furthermore, the optimal super-Gaussian order can be obtained by determining the emission aperture, or the optimal emission aperture can be obtained by determining the beam model. This provides a reference for the application of super-Gaussian beams in the atmospheric transmission of high-power lasers and the design of high-power lasers. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Intensity distribution diagram of super-Gaussian beams of different orders.

[0045] Figure 2 The on-axis intensity distribution diagram of super-Gaussian beams of different orders.

[0046] Figure 3 It is the light intensity distribution diagram on the far-field spot axis.

[0047] Figure 4 This is a graph showing how the far-field spot power ratio changes with radius.

[0048] Figure 5 The graph shows the change of two kinds of ring power radius with relative emission aperture of different order super-Gaussian beams.

[0049] Figure 6 This is a graph showing how the optimal launch aperture changes with the super-Gaussian order.

[0050] Figure 7 This is a schematic flow chart of the calculation process of the optimal emission aperture of a super-Gaussian beam in the present invention.

[0051] Figure 8 This is a graph showing how the optimal transmitting aperture changes with the super-Gaussian order under different ring power radii. DETAILED DESCRIPTION

[0052] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0053] Example 1

[0054] Depend on Figure 7 As shown, the calculation process of the optimal emission aperture of a super-Gaussian beam of the present invention is specifically as follows:

[0055] S11, determine the super-Gaussian beam model and the super-Gaussian order n. The actual laser emission aperture d is limited. According to the value range of the emission aperture d, an emission aperture d is initialized and set.

[0056] S12, calculating the light field distribution on the emission plane.

[0057] The light field distribution of the emission plane based on the super-Gaussian beam model can be expressed as:

[0058]

[0059] Where A is the relative amplitude, E(ρ) is the complex amplitude of the light field at point ρ on the emission plane, ρ is the light field coordinate on the emission plane; ω0 is the beam waist radius; d is the laser emission aperture; n represents the super-Gaussian order; the light intensity distribution at point ρ on the emission plane is I(ρ) = |E(ρ)| 2 .

[0060] circ(·) is the cylindrical function, defined as:

[0061]

[0062] For example, when the laser's emission aperture d = 2 cm, the beam that exceeds the beam waist radius ω0 will be cut off, and the resulting two-dimensional light intensity distribution and on-axis light intensity distribution are as follows: Figure 1 and Figure 2 As shown, Figure 1 Indicates the intensity distribution of super-Gaussian beams of different orders (3rd, 5th, and 7th orders), Figure 2 It shows the on-axis intensity distribution of super-Gaussian beams of different orders (3rd, 5th, and 7th order).

[0063] S13, based on the Huygens-Fresnel principle, calculate the far-field light intensity distribution of the super-Gaussian beam model to obtain the light intensity distribution of the wave source in the far field.

[0064] The Huygens-Fresnel principle is a method for studying light wave propagation. This method can obtain the light intensity distribution of the wave source in the far field. Its mathematical expression is:

[0065]

[0066] Where λ and k = 2π / λ represent the wavelength and wave number of the light beam, respectively. i is an imaginary number, z is the coordinate along the transmission direction, L is the transmission distance, and E(r,z = L) represents the complex amplitude distribution of the light field transmitted to point r on the receiving plane. r = (r x ,r y ) represents the coordinate of r on the receiving plane, E(ρ,z=0) represents the complex amplitude distribution of the light field at ρ on the transmitting plane, ρ=(ρ x ,ρ y ) represents the coordinate of point ρ on the emission plane, and the light intensity distribution at point ρ on the emission plane is I(ρ,z=0)=|E(ρ,z=0)| 2 , the light intensity distribution at point r on the receiving plane is I(r,z=L)=|E(r,z=L)| 2 .

[0067] The far-field light spot is obtained by transmitting in free space, and its on-axis light intensity distribution is as follows Figure 3 As shown, Figure 3 It shows the intensity distribution of the far-field spot on the axis when the laser emission aperture d = 2 cm and the super-Gaussian order n = 3. Figure 3 It can be seen that after 1000m of free-space transmission, the super-Gaussian beam has degenerated into a quasi-Gaussian beam.

[0068] S14, calculate the surrounding power curve of the far-field spot, that is, the relationship curve between the surrounding power ratio and the radius, select a surrounding power ratio as a reference surrounding power ratio, and obtain the radius corresponding to the reference surrounding power ratio, that is, the power radius R x .

[0069] The ring power ratio of 86.5% and / or 63.2% can be selected as the reference ring power ratio, and the radius corresponding to the reference ring power ratio of 86.5% and 63.2% is obtained, that is, the power radius R 86.5 、R 63.2 In this embodiment, when the ring power ratio is 86.5% and 63.2% as the reference ring power ratio, the power radius R is obtained respectively. 86.5 and R 63.2 .

[0070] The ring power ratio refers to the ratio of the power of the light beam within a certain radius to the total power.

[0071] In order to analyze its energy distribution, the ring power curve is calculated, that is, the curve of the ring power ratio changing with the radius. The results are as follows: Figure 4 As shown, Figure 4 The figure shows the variation of the far-field spot power ratio with the radius when the laser emission aperture d = 2 cm and the super-Gaussian order n = 3, and then the radius corresponding to the power ratio of 63.2% is obtained, that is, the power radius R 63.2 The radius corresponding to the ring power ratio of 86.5% is the power radius R 86.5 Obviously, R 63.2 and R 86.5 The smaller it is, the more concentrated the beam energy is, and thus the better the beam quality is.

[0072] S15, change the transmission aperture d, repeat steps S12-S14, and calculate the power radius R under different transmission apertures d x , thus obtaining the power radius R x Curve showing the change with the launch aperture d.

[0073] In this embodiment, the ring power ratios of 86.5% and 63.2% are selected as reference ring power ratios, and the power radius R is obtained respectively. 86.5 and R 63.2 Curve showing the change with the launch aperture d.

[0074] As the laser emission aperture d decreases, the diffraction effect of the beam in the far field will intensify. It is not difficult to infer that R 63.2 and R 86.5 The radius (R) corresponding to the two ring power ratios (63.2% and 86.5%) of super-Gaussian beams of different orders (1-8) is 63.2 and R 86.5 ) changes with the relative emission aperture of the light beam (i.e. d / 2 / ω0) as shown in the following example: Figure 5 As shown in the figure, there is a clear conversion relationship between the launch aperture d and the relative launch aperture d / 2 / ω0, and the changing relationship can be equivalently applied.

[0075] S16, when the laser emission aperture d increases to a certain extent (d>>ω0), further increasing the emission aperture d will not have any effect on the beam. 63.2 and R 86.5 ), there is a minimum transmission aperture d0, which is called the optimal transmission aperture. Therefore, according to the power radius R x As the launch aperture d changes, the power radius R x The minimum emission aperture that no longer changes with the emission aperture d is taken as the optimal emission aperture d0, and the super-Gaussian beam model and the optimal emission aperture d0 under the super-Gaussian order n are obtained.

[0076] In this embodiment, the ring power ratios of 86.5% and 63.2% are selected as reference ring power ratios to obtain the power radius R respectively. 86.5 and R 63.2 As the launch aperture d changes, the power radius R 86.5 and R 63.2 The minimum emission aperture that no longer changes with the emission aperture d is taken as the optimal emission aperture d0, thereby obtaining the super-Gaussian beam model and the optimal emission aperture d0 under the super-Gaussian order n.

[0077] S17, change the super-Gaussian order n, and calculate the optimal transmission aperture d0 under different super-Gaussian orders n according to the method of steps S11-S16, and fit the relationship between the optimal transmission aperture d0 and the super-Gaussian order n, that is, d0=f(n).

[0078] When determining the super-Gaussian beam model and the super-Gaussian order n, the optimal emission aperture d0 is calculated according to the relationship d0=f(n).

[0079] Figure 6 It shows the change of the optimal launch aperture d0 with the super-Gaussian order n, from Figure 6 It can be seen that as the super-Gaussian order n increases, the optimal emission aperture d0 gradually decreases. Simulation results show that when the super-Gaussian order n exceeds 4, the impact on the optimal emission aperture d0 is minimal. This shows that by utilizing high-order super-Gaussian beams, a smaller laser emission aperture can be used while maintaining far-field beam energy concentration.

[0080] In addition, when determining the transmission aperture d, the optimal super-Gaussian order n0 corresponding to the transmission aperture d is also calculated according to the relationship d0=f(n).

[0081] Example 2

[0082] Based on the above embodiment 1, when the super Gaussian order n∈[1,4] and the super Gaussian order n takes a value interval of 0.1, the relationship curve between the optimal emission aperture d0 and the super Gaussian order n is fitted, and the fitting result is as follows: Figure 8 As shown, Figure 8 Indicates different ring power radius (R 63.2 and R 86.5 ) under the condition of optimal launch aperture d0 changing with super-Gaussian order n and the fitting results.

[0083] For a ring power ratio of 63.2%, the optimal transmitting aperture d0 = 1.55·n -0.43 , n∈[1,4]; for the ring power ratio of 86.5%, the optimal transmission aperture d0=1.74·n -0.44, n∈[1,4]. According to these two formulas, the minimum emission aperture can be obtained when the beam model is determined, and the minimum super-Gaussian order can also be obtained when the emission aperture is determined.

[0084] Example 3

[0085] The calculation process of the optimal super-Gaussian order of a super-Gaussian beam of the present invention is specifically as follows:

[0086] S21, determine the transmitting aperture d, and initialize and set a super Gaussian order n according to the value range of the super Gaussian order n.

[0087] S22, calculating the light field distribution in the emission plane according to the super-Gaussian beam model.

[0088] S23, based on the Huygens-Fresnel principle, calculate the far-field light intensity distribution of the super-Gaussian beam model to obtain the light intensity distribution of the wave source in the far field.

[0089] S24, calculate and draw the surrounding power curve of the far-field spot, that is, the relationship curve between the surrounding power ratio and the radius, select a surrounding power ratio as a reference surrounding power ratio, and obtain the radius corresponding to the reference surrounding power ratio, that is, the power radius R x .

[0090] In this embodiment, when the ring power ratio is 86.5% and 63.2% as the reference ring power ratio, the radius corresponding to the reference ring power ratio of 86.5% and 63.2% is obtained respectively, that is, the power radius R 86.5 、R 63.2 .

[0091] S25, change the super-Gaussian order n, repeat steps S22-S24, and calculate the power radius R under different super-Gaussian orders n x , and thus the power radius R is obtained respectively x Curve changing with super-Gaussian order n.

[0092] In this embodiment, the ring power ratios of 86.5% and 63.2% are selected as reference ring power ratios, and the power radius R is obtained respectively. 86.5 and R 63.2 Curve changing with super-Gaussian order n.

[0093] S26, according to the power radius R x As the super-Gaussian order n changes, the power radius R x The minimum super-Gaussian order that no longer changes with the super-Gaussian order n is taken as the optimal super-Gaussian order n0, and the optimal super-Gaussian order n0 under the launch aperture d is obtained.

[0094] In this embodiment, the ring power ratios of 86.5% and 63.2% are selected as reference ring power ratios to obtain the power radius R respectively. 86.5 and R 63.2 As the super-Gaussian order n changes, the power radius R 86.5 and R 63.2 The minimum super-Gaussian order that no longer changes with the super-Gaussian order n is taken as the optimal super-Gaussian order n0, thereby obtaining the optimal super-Gaussian order n0 under the launch aperture d.

[0095] S27, change the transmission aperture d, and calculate the optimal super-Gaussian order n0 under different transmission apertures d according to the method of steps S21-S26, and fit the relationship between the optimal super-Gaussian order n0 and the transmission aperture d, that is, n0=g(d).

[0096] When determining the super-Gaussian beam model and the emission aperture d, the optimal super-Gaussian order n0 is calculated according to the relationship n0=g(d).

[0097] When determining the super-Gaussian order n, the optimal emission aperture d0 corresponding to the super-Gaussian order n is calculated according to the relationship n0=g(d).

[0098] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the optimal emission aperture of a super-Gaussian beam, characterized in that: The following steps are involved: S11, determining a super-Gaussian beam model and a super-Gaussian order n, and initializing a transmitting aperture d according to a range of transmitting aperture d; S12, calculate the light field distribution on the emission plane; S13, calculate the far-field light intensity distribution of the super-Gaussian beam model based on the Huygens-Fresnel principle; S14, calculate the surrounding power curve of the far-field spot, that is, the relationship curve between the surrounding power ratio and the radius, select a surrounding power ratio as a reference surrounding power ratio, and obtain the radius corresponding to the reference surrounding power ratio, that is, the power radius R x ; S15, change the transmission aperture d, repeat steps S12-S14, and calculate the power radius R under different transmission apertures d x , thus obtaining the power radius R x Curve of change with launch aperture d; S16, according to the power radius R x As the launch aperture d changes, the power radius R x The minimum emission aperture that no longer changes with the emission aperture d is taken as the optimal emission aperture d0, and the super-Gaussian beam model and the optimal emission aperture d0 under the super-Gaussian order n are obtained.

2. The method for calculating the optimal emission aperture of a super-Gaussian beam according to claim 1, characterized in that: Changing the super-Gaussian order n, following steps S11-S16, calculate the optimal transmit aperture d0 under different super-Gaussian orders n, and fitting the relationship between the optimal transmit aperture d0 and the super-Gaussian order n, i.e., d0 = f(n); When determining the super-Gaussian beam model and the super-Gaussian order n, the optimal emission aperture d0 is calculated according to the relationship d0=f(n).

3. The method for calculating the optimal emission aperture of a super-Gaussian beam according to claim 2, characterized in that: When determining the transmitting aperture d, the optimal super-Gaussian order n0 corresponding to the transmitting aperture d is calculated according to the relationship d0=f(n).

4. The method for calculating the optimal emission aperture of a super-Gaussian beam according to claim 1, characterized in that: Step S14: Select the ring power ratio of 86.5% and / or 63.2% as the reference ring power ratio, and obtain the radius corresponding to the reference ring power ratio of 86.5% and 63.2%, namely the power radius R. 86.5 、R 63.2 ; Among them, when the ring power ratio is selected as 86.5% and 63.2% as the reference ring power ratio, the power radius R is obtained respectively. 86.5 and R 63.2 The curve of the change of the launch aperture d is based on the power radius R 86.5 and R 63.2 As the launch aperture d changes, the power radius R 86.5 and R 63.2 The minimum launch aperture that no longer changes with the launch aperture d is taken as the optimal launch aperture d0.

5. The method for calculating the optimal emission aperture of a super-Gaussian beam according to claim 1, characterized in that: In step S12, the emission plane light field distribution of the super-Gaussian beam model is expressed as: Where A is the relative amplitude, E(ρ) is the complex amplitude of the light field at point ρ on the emission plane, ρ is the light field coordinate on the emission plane; ω0 is the beam waist radius; d is the laser emission aperture; n represents the super-Gaussian order; the light intensity distribution at point ρ on the emission plane is I(ρ) = |E(ρ)| 2 ; circ(·) is the cylindrical function, defined as:

6. The method for calculating the optimal emission aperture of a super-Gaussian beam according to claim 1, characterized in that: In step S13, the far-field light intensity distribution of the super-Gaussian beam model is expressed as: Where λ and k = 2π / λ represent the wavelength and wave number of the light beam, respectively. i is an imaginary number, z is the coordinate along the transmission direction, L is the transmission distance, and E(r,z = L) represents the complex amplitude of the light field transmitted to the receiving plane at point r. r = (r x ,r y ) represents the coordinate of r on the receiving plane, E(ρ,z=0) represents the complex amplitude of the light field at ρ on the transmitting plane, ρ=(ρ x ,ρ y ) represents the coordinate of point ρ on the emitting plane, and the light intensity distribution at point r on the receiving plane is I(r,z=L)=|E(r,z=L)| 2 .

7. A method for calculating the optimal super-Gaussian order of a super-Gaussian beam, characterized in that: The following steps are involved: S21, determine the transmitting aperture d, and initialize and set a super Gaussian order n according to the value range of the super Gaussian order n; S22, calculating the light field distribution in the emission plane according to the super-Gaussian beam model; S23, calculate the far-field intensity distribution of the super-Gaussian beam model based on the Huygens-Fresnel principle; S24, calculate and draw the surrounding power curve of the far-field spot, that is, the relationship curve between the surrounding power ratio and the radius, select a surrounding power ratio as a reference surrounding power ratio, and obtain the radius corresponding to the reference surrounding power ratio, that is, the power radius R x ; S25, change the super-Gaussian order n, repeat steps S22-S24, and calculate the power radius R under different super-Gaussian orders n x , and thus the power radius R is obtained respectively x Curve changing with super-Gaussian order n; S26, according to the power radius R x As the super-Gaussian order n changes, the power radius R x The minimum super-Gaussian order that no longer changes with the super-Gaussian order n is taken as the optimal super-Gaussian order n0, and the optimal super-Gaussian order n0 under the launch aperture d is obtained.

8. The method for calculating the optimal super-Gaussian order of a super-Gaussian beam according to claim 7, wherein: Changing the transmit aperture d, following steps S21-S26, calculate the optimal super-Gaussian order n0 for different transmit apertures d, and fitting the relationship between the optimal super-Gaussian order n0 and the transmit aperture d, i.e., n0 = g(d); When determining the super-Gaussian beam model and the emission aperture d, the optimal super-Gaussian order n0 is calculated according to the relationship n0=g(d).

9. The method for calculating the optimal super-Gaussian order of a super-Gaussian beam according to claim 8, wherein: When determining the super-Gaussian order n, the optimal emission aperture d0 corresponding to the super-Gaussian order n is calculated according to the relationship n0=g(d).

10. The method for calculating the optimal super-Gaussian order of a super-Gaussian beam according to claim 7, wherein: Step S24: Select the ring power ratio of 86.5% and / or 63.2% as the reference ring power ratio, and obtain the radius corresponding to the reference ring power ratio of 86.5% and 63.2%, namely the power radius R. 86.5 、R 63.2 ; Among them, when the ring power ratio is 63.2% and 86.5% as the reference ring power ratio, the power radius R is obtained respectively. 63.2 and R 86.5 The curve of the change of super Gaussian order n, according to the power radius R 63.2 and R 86.5 As the super-Gaussian order n changes, the power radius R 63.2 and R 86.5 The minimum super-Gaussian order that no longer changes with the super-Gaussian order n is taken as the optimal super-Gaussian order n0.

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