Hering solid multi-pass cell adjusting method and device based on beam eigenvalue calculation

Abstract

This invention discloses a method and apparatus for adjusting a Heriot-Treut solid-state multipass cell based on beam intrinsic calculation, belonging to the field of laser technology. The method includes the following steps: S1, calculating the transmission matrix at the corresponding position within the multipass cell based on the thickness and refractive index of the solid, the refractive index of the gas, and the radius of curvature and spacing parameters of the concave mirrors; S2, determining the incident beam. q Parameters, calculated based on the transmission matrix at the corresponding positions in the multi-pass pool. q Parameters; S3, according to q The parameters are calculated to determine the beam size and wavefront radius of curvature at any position within the Heriot-Lieutenant solid-state multiple-pass cell. Iterative calculations yield the intrinsic modes of the beam within the cell. Steps S4 and S3 are repeated to calculate the intrinsic modes of different incident beams within the cell. The incident beam parameters are then optimized to obtain the desired incident beam and its corresponding optical field and intensity. This invention can quickly and accurately calculate the eigenmodes of a Heriot-Lieutenant solid-state multiple-pass cell.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of laser, and particularly relates to a Heriot solid multi-pass cell adjustment method and device based on beam eigenvalue calculation. BACKGROUND

[0002] The Heriot solid multi-pass cell can effectively increase the optical path and ensure the beam quality, and is widely used in the fields of ultrafast optics and spectroscopy. The Heriot solid multi-pass cell has two concave mirrors, and a solid is located at the center of the multi-pass cell. The symmetrical multi-pass cell system is similar to the structure of a resonant cavity. The eigenmode of the resonant cavity refers to a mode that can be stably transmitted in the resonant cavity. The incident beam that meets the eigenmode can ensure the transmission of the beam in the Heriot solid multi-pass cell, pass through the solid multiple times to increase the optical path, and the beam size does not change when the beam passes through the center of the solid each time, which ensures that the beam transmission to the solid does not produce a small focal point, effectively protects the solid material from being damaged, and produces stable nonlinear effects.

[0003] In 2022, Anne-Lise Viotti et.al reported related work on spectral broadening and pulse compression using a multi-pass cell (Anne-Lise Viotti et.al. Multi-pass cells for post-compression of ultrashort laser pulses, Optica, Vol. 9, No. 2, 2022). In the report, the calculation of the eigenmode of the Heriot gas multi-pass cell and the Heriot solid multi-pass cell both use the traditional calculation formula of the eigenmode of the resonant cavity. However, compared with air medium, the refraction of light waves on the surface of the solid and the transmission characteristics in the solid medium are significantly different. Using the calculation formula of the resonant cavity to calculate the eigenmode of the Heriot solid multi-pass cell will have a large error. The mismatch between the incident beam size and the eigenmode leads to unstable transmission of the beam in the Heriot solid multi-pass cell. The position and size of the beam waist change each time the beam is transmitted in the multi-pass cell. A smaller beam waist can easily cause damage to optical devices, which has a negative effect on the stable transmission of the beam in the Heriot solid multi-pass cell and affects the occurrence of nonlinear effects. Therefore, for the Heriot solid multi-pass cell, it is urgent to explore and develop an accurate eigenmode calculation method. SUMMARY

[0004] The present application aims to at least partially solve one of the above-mentioned technical problems in the related art.

[0005] To this end, the present application aims to provide a Heriot solid multi-pass cell adjustment method and device based on beam eigenvalue calculation, which can quickly and accurately calculate the eigenmode of the Heriot solid multi-pass cell.

[0006] To solve the above technical problems, the present application is implemented as follows:

[0007] The embodiment of the present application provides a Herriott solid multi-pass cell adjustment method based on beam eigenvalue calculation, wherein the Herriott solid multi-pass cell is internally provided with alternately arranged solid and concave mirrors, and the adjacent solid and concave mirrors are filled with gas; the calculation method comprises the following steps:

[0008] S1, according to the thickness, refractive index of the solid, refractive index of the gas, and the curvature radius and spacing parameters of the concave mirror, the transmission matrix of the corresponding position in the Herriott solid multi-pass cell is calculated;

[0009] The transmission matrix is represented as follows:

[0010] Wherein, A, B, C, D represent the elements in the transmission matrix; the determinant value of the transmission matrix is 1;

[0011] S2, the q parameter of the incident light beam is determined, and the q parameter of the corresponding position in the Herriott solid multi-pass cell is calculated according to the transmission matrix of step S1;

[0012] S3, according to the q parameter calculated in step S2, the beam size and the wavefront curvature radius of the light beam transmitted to any position in the Herriott solid multi-pass cell are calculated, and the eigenvalue distribution of the light beam in the Herriott solid multi-pass cell is obtained through iterative calculation;

[0013] S4, the method of steps S2 and S3 is repeated, the eigenvalue distribution of the incident light beam with different parameters when transmitting in the Herriott solid multi-pass cell is calculated, and the incident light beam parameters are optimized and adjusted according to the calculation results to obtain the required incident light beam and the corresponding light field and light intensity.

[0014] In addition, the Herriott solid multi-pass cell adjustment method based on beam eigenvalue calculation according to the present application can also have the following additional technical features:

[0015] In some embodiments, the transmission matrix M is obtained by multiplying one or more of the transmission matrix of the light beam in the solid, the transmission matrix of the light beam at the interface between the solid and the gas, the transmission matrix of the light beam in the gas, the transmission matrix of the light beam in the concave mirror, the transmission matrix of the light beam in the gas, the transmission matrix of the light beam at the interface between the gas and the solid, and the transmission matrix of the light beam in the solid.

[0016] In some embodiments, the transmission matrix of the light beam in the concave mirror is calculated according to the curvature radius of the concave mirror.

[0017] In some of the embodiments, the transmission matrix of the light beam in the solid is a transmission matrix of the light beam at a middle position of the solid, which is calculated according to the thickness of the solid and the refractive index of the solid.

[0018] In some of the embodiments, the transmission matrix of the light beam in the gas is a transmission matrix of the light beam at a middle position of the gas segment, which is calculated according to the length of the gas.

[0019] In some of the embodiments, the transmission matrix of the light beam at the interface between the solid and the gas and the transmission matrix of the light beam at the interface between the gas and the solid are calculated according to the refractive index of the gas and the refractive index of the solid.

[0020] In some of the embodiments, the q parameter before the corresponding optical system of the Heriot solid multipass cell is denoted as q1, and the q parameter after the corresponding optical system of the Heriot solid multipass cell is denoted as q2; the relationship between q1 and q2 is:

[0021]

[0022] In some of the embodiments, the solid is arranged at the center of the Heriot solid multipass cell, and the distance between the solid and the concave mirror arranged on the two sides is equal; the wavefront of the solid is a plane; and ω c denotes the size of the light beam, n B denotes the refractive index of the solid, i is an imaginary unit, and the relationship between q1 and q2 satisfies:

[0023]

[0024] In some of the embodiments, the eigen distribution of the light beam is:

[0025]

[0026] ω c denotes the size of the light beam, n B denotes the refractive index of the solid.

[0027] The embodiment of the present application also provides a calculation device for the eigen mode of the light beam of the Heriot solid multipass cell, which comprises a memory and a processor, the memory stores a program, and the processor can realize the calculation process of the adjustment method of the Heriot solid multipass cell based on the eigen calculation of the light beam according to the program stored in the memory.

[0028] Compared with the prior art, the present application has at least the following beneficial effects:

[0029] The Herriott solid multi-pass cell adjustment method based on the eigen calculation of a light beam provided in the embodiment of the present application can quickly and accurately calculate the eigen mode of the Herriott solid multi-pass cell, so that the size of the light beam does not change when the light beam passes through the center of the solid each time, the optical device can be protected from being damaged by a small focused light beam, and the nonlinear effect is effectively improved.

[0030] The computing device for the eigen mode of the light beam of the Herriott solid multi-pass cell of the present application is used to implement the Herriott solid multi-pass cell adjustment method based on the eigen calculation of a light beam, and thus has all the features and advantages of the Herriott solid multi-pass cell adjustment method based on the eigen calculation of a light beam, which will not be described here again. Additional aspects and advantages of the present application will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 The structural schematic diagram of the Herriott solid multi-pass cell disclosed for an embodiment of the present application is shown in the figure;

[0032] Figure 2 The structural schematic diagram after the paraxial approximation disclosed for an embodiment of the present application is shown in the figure;

[0033] Figure 3 The figure shows the comparison of the light beam size each time passing through the center of the solid for the Herriott solid multi-pass cell disclosed for an embodiment of the present application, with the laser center wavelength being 1064 nm, the cavity length L = 580 mm, the curvature radius of the concave mirror R = 300 mm, the solid length d = 18 mm, and the solid refractive index n = 1.45. B B DETAILED DESCRIPTION

[0034] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0035] The embodiments of the present application will be described in detail below with reference to the drawings and specific embodiments and application scenarios.

[0036] The present application provides a Herriott solid multi-pass cell adjustment method based on the eigen calculation of a light beam, the Herriott solid multi-pass cell is provided with solids and concave mirrors arranged alternately, and the adjacent solid and concave mirror are filled with gas; the steps of the calculation method include:

[0037] ​​S1, according to the thickness of the solid in the Heriot solid multi-pass cell, the refractive index of the solid, the refractive index of the gas, and the curvature radius and spacing parameters of the concave mirror, the transmission matrix of the corresponding position in the Heriot solid multi-pass cell is calculated;

[0038] The transmission matrix is represented as:

[0039] Wherein A, B, C, D represent elements in the transmission matrix; the determinant value of the transmission matrix is 1;

[0040] S2, determine the q parameter of the incident light beam, and calculate the q parameter of the corresponding position in the Heriot solid multi-pass cell according to the transmission matrix of step S1;

[0041] S3, according to the q parameter calculated in step S2, the beam size and the wavefront curvature radius of the light beam transmitted to any position in the Heriot solid multi-pass cell are calculated, and the eigen distribution of the light beam in the Heriot solid multi-pass cell is obtained by iterative calculation;

[0042] S4, repeat the method of steps S2 and S3, calculate the eigen distribution of the incident light beam with different parameters in the Heriot solid multi-pass cell, and optimize and adjust the parameters of the incident light beam according to the calculation results to obtain the required incident light beam and the corresponding light field and light intensity.

[0043] The transmission matrix M is obtained by multiplying one or more of the transmission matrix of the light beam in the solid, the transmission matrix of the light beam at the interface between the solid and the gas, the transmission matrix of the light beam in the gas, the transmission matrix of the light beam in the concave mirror, the transmission matrix of the light beam in the gas, the transmission matrix of the light beam at the interface between the gas and the solid, and the transmission matrix of the light beam in the solid.

[0044] The transmission matrix of the light beam in the concave mirror is calculated according to the curvature radius of the concave mirror. The transmission matrix of the light beam in the solid is the transmission matrix of the light beam at the middle position of the solid, which is calculated according to the thickness of the solid and the refractive index of the solid. The transmission matrix of the light beam in the gas is the transmission matrix of the light beam at the middle position of the gas, which is calculated according to the length of the gas. The transmission matrix of the light beam at the interface between the solid and the gas and the transmission matrix of the light beam at the interface between the gas and the solid are calculated according to the refractive index of the gas and the refractive index of the solid.

[0045] Please refer to Figures 1-2 In some embodiments of the present application, a Heriot solid multi-pass cell adjustment method based on eigen calculation of light beam is provided, and the steps of the calculation method include:

[0046] Step 1: The Heriot solid multi-pass cell has two concave mirrors with the same radius of curvature, and the solid is located in the center of the multi-pass cell. The structure of "concave mirror-solid-concave mirror" of the Heriot solid multi-pass cell is approximated as a series of optical systems of "thin convex lens-solid" structure by paraxial approximation, and the transfer matrix is calculated for the cavity structure and each optical device therein, including the following steps:

[0047] Step 11, determine the radius of curvature R of the two concave mirrors, the focal length f = R / 2, and the transfer matrix of each concave mirror (thin convex lens) is:

[0048]

[0049] Step 12, determine the thickness d of the solid B and the refractive index n of the solid B , and the transfer matrix of the solid through a distance of d B / 2 in the solid is

[0050]

[0051] Step 13, determine the cavity length (the distance between the two concave mirrors) L, and the solid is located in the center of the cavity, so the distance from the surface of the solid to the concave mirror is (L-d B ) / 2, and the transfer matrix of the air is:

[0052]

[0053] In the above formula, (L-d B ) / 2 can be replaced by d A to represent the distance from the surface of the solid to the concave mirror on both sides, as described in detail in Figure 1 .

[0054] Step 14, determine the refractive index n A of the air, and the transfer matrix of the air-solid surface refraction is

[0055]

[0056] The transfer matrix of the solid-air surface refraction is

[0057]

[0058] Step 15, according to the transfer matrices of formula (1), formula (2), formula (3), formula (4) and formula (5), calculate the light beam from the center of the solid, through a distance of d B / 2 in the solid, solid-air surface refraction, transmission of (L-d B ) / 2 in the air, thin convex lens, transmission of (L-d B) / 2 distance, air-solid surface refraction, d in solid B After transmitting a distance of / 2, the system returned to its initial position. The transmission matrix of the optical system consisting of these seven parts is:

[0059]

[0060] And there exists a constraint relationship with a determinant value of 1, specifically:

[0061] detM=AD-BC=1 (7)

[0062] Step 2: Based on the beam propagation characteristics in a Heriot-Treut solid-state multipass cell, calculate the eigenmodes of the beam passing through the center of the solid:

[0063] Step 21: For a wavelength λ and a solid refractive index n B A Gaussian beam with beam size (radius) ω and wavefront radius of curvature R has the following q-parameters:

[0064]

[0065] Step 22: q1 is the q parameter before passing through the optical system transmission matrix described in step 15, and q2 is the q parameter after passing through the optical system transmission matrix described in step 15. The relationship between q1 and q2 is as follows:

[0066]

[0067] Step 23: Since the solid is located at the center of the Heriot-Treut solid multipass cell, the wavefront at this location is planar, therefore the radius of curvature is R = ∞. Let the beam size be ω. c The q parameter in step 22 is:

[0068]

[0069] i is the imaginary unit;

[0070] Step 24: Substitute equations (6), (7), and (10) into equation (9), and after rearranging and simplifying, obtain the eigenmode of the beam passing through the center of the solid in the Heriot-Treut solid multipass cell as follows:

[0071]

[0072] After determining parameters such as the center wavelength, cavity length of the Heriot-Limiter solid-state multiplexer, radius of curvature of the concave mirror, solid length, and solid refractive index, the eigenmode of the beam passing through the center of the solid in the Heriot-Limiter solid-state multiplexer can be calculated. By adjusting the size of the incident beam to match the eigenmode of the Heriot-Limiter solid-state multiplexer, the beam can be continuously transmitted within the multiplexer, stably performing nonlinear effects while protecting the optical components. Figure 3 As shown, the intrinsic mode calculated using the method of this application was transmitted 50 times in a Heriot-Trent solid-state multipass cell. The beam size remained stable at the center of the solid each time, proving the effectiveness and accuracy of the calculation method of this invention.

[0073] The parts of this invention not described in detail are techniques known to those skilled in the art.

[0074] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of the present invention.

Claims

1. A method for adjusting a Heriot-Treutz solid-state multipass cell based on beam intrinsic calculation, characterized in that, The Heriot solid multipass cell contains alternating solid and concave mirrors, with gas filling the spaces between adjacent solid and concave mirrors; the two concave mirrors have the same radius of curvature, and the solid is located at the center of the multipass cell; the concave mirror-solid-concave mirror structure of the Heriot solid multipass cell is approximated paraxially and abstracted as an optical system of a series of thin convex lens-solid structures. The steps of the method include: S1. Based on the solid thickness, solid refractive index, gas refractive index, radius of curvature of the concave mirror, and distance between the two concave mirrors in the Heriot-Treut solid multipass cell, the beam starts from the center of the solid and the transmission matrix at the corresponding position in the Heriot-Treut solid multipass cell is calculated. The transmission matrix is ​​represented as follows: ,in, A , B , C , D This represents an element in the transmission matrix; the determinant of the transmission matrix is ​​1. S2, Determine the incident beam q Based on the transfer matrix in step S1, calculate the parameters at the corresponding positions in the Heriot-Treut solid multipass cell. q parameter; S3, calculated based on step S2 q The parameters are used to calculate the beam size and wavefront radius of curvature at any position in the Heriot-Lieutenant solid multipass cell. The intrinsic distribution of the beam in the Heriot-Lieutenant solid multipass cell is obtained by iterative calculation. S4. Repeat steps S2 and S3 to calculate the intrinsic beam distribution of incident beams with different parameters when propagating in a Heriot-Limited solid multipass cell. Optimize and adjust the incident beam parameters based on the calculation results to obtain the required incident beam and its corresponding optical field and intensity.

2. The method for adjusting a Heriot-Treutz solid-state multipass cell based on beam intrinsic calculation according to claim 1, characterized in that, The transmission matrix M It is obtained by multiplying one or more of the following transmission matrices: the transmission matrix of the beam in the solid, the transmission matrix of the beam at the interface between the solid and the gas, the transmission matrix of the beam in the gas, the transmission matrix of the beam in the concave mirror, the transmission matrix of the beam in the gas, the transmission matrix of the beam at the interface between the gas and the solid, and the transmission matrix of the beam in the solid.

3. The method for adjusting a Heriot-Treutz solid-state multipass cell based on beam intrinsic calculation according to claim 2, characterized in that, The transmission matrix of the light beam within the concave mirror is calculated based on the radius of curvature of the concave mirror.

4. The method for adjusting a Heriot-Treutz solid-state multipass cell based on beam intrinsic calculation according to claim 2, characterized in that, The transmission matrix of the light beam in the solid is the transmission matrix of the light beam at the middle position of the solid, which is calculated based on the solid thickness and the solid refractive index.

5. The method for adjusting a Heriot-Treutz solid-state multipass cell based on beam intrinsic calculation according to claim 2, characterized in that, The transmission matrix of the light beam in the gas is the transmission matrix of the light beam at the middle position of the gas, which is calculated based on the length of the gas.

6. The method for adjusting a Heriot-Treutz solid-state multipass cell based on beam intrinsic calculation according to claim 2, characterized in that, The transmission matrix of the light beam at the solid-gas interface and the transmission matrix of the light beam at the gas-solid interface are calculated based on the refractive index of the gas and the refractive index of the solid.

7. The Heriot-Treutz solid-state multipass cell adjustment method based on beam intrinsic calculation according to any one of claims 1-6, characterized in that, Before the corresponding optical system of the Heriot solid multi-pass cell q The parameter is denoted as After passing through the corresponding optical system of the Heriot-Treut solid-state multi-pass cell q The parameter is denoted as ; and The relationship is: .

8. The method for adjusting a Heriot-Treutz solid-state multipass cell based on beam intrinsic calculation according to claim 7, characterized in that, The solid is positioned at the center of the Heriot-Treut solid multi-pass cell, equidistant from the concave mirrors on either side; the wavefront of the solid is planar; ω c Refers to the size of the beam. Refers to the refractive index of a solid. If it is the imaginary unit, then and The relationship satisfies: .

9. The method for adjusting a Heriot-Treutz solid-state multipass cell based on beam intrinsic calculation according to claim 7, characterized in that, The intrinsic distribution of the beam is: , ω c Refers to the size of the beam. Refers to the refractive index of a solid.

10. A computing device for calculating the eigenmodes of a Heriot-Treut solid-state multipass cell beam, comprising a memory and a processor, wherein the memory stores a program, characterized in that... When the processor runs the program on the memory, it can implement the calculation process of the Heriot-Treut solid multipass cell adjustment method based on beam intrinsic calculation as described in any one of claims 1 to 9.

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