A Safety Optimization Method for Heriot-Treant Solid Multipass Cells Based on Beam Evolution Calculation

Abstract

This invention provides a safety optimization method for a Heriot-Limited Solid-State Multiplexer based on beam evolution calculation, comprising the following steps: 1. Calculating the transmission matrix of each device in the Heriot-Limited Solid-State Multiplexer; 2. Calculating the beam evolution process of the beam in the Heriot-Limited Solid-State Multiplexer; 3. Optimizing system parameters based on the beam evolution to ensure a stable beam size each time the beam passes through a solid within the Heriot-Limited Solid-State Multiplexer. Using this method, by rapidly and accurately calculating the beam evolution process in the Heriot-Limited Solid-State Multiplexer, the beam parameters at different positions within the multiplexer can be effectively predicted and evaluated, ensuring that devices such as concave mirrors and solid materials in the Heriot-Limited Solid-State Multiplexer are not damaged by the focused beam, thus optimizing the safety and stability of the optical system.

Description

Technical Field

[0001] This invention relates to the field of lasers, and in particular to a method for optimizing the safety of Heriot-Trigger solid-state multipass cells based on beam evolution calculations, which is mainly applicable to ultrafast optics, spectroscopy, atomic and molecular physics, and quantum precision measurement. Background Technology

[0002] Heriot-Limiter solid-state multiplexers can effectively increase the optical path length and ensure beam quality during transmission under a given incident laser energy, thus finding wide application in ultrafast optics, spectroscopy, atomic and molecular physics, and quantum precision measurement. A Heriot-Limiter solid-state multiplexer has two coaxial concave mirrors, with the solid material located at the center of the multiplexer. Understanding, predicting, and evaluating the beam evolution process of Heriot-Limiter solid-state multiplexers is crucial for meeting the needs of optical instruments and systems in physics and optics. This has significant research value and practical implications for protecting optical components and systems, improving accuracy in quantum precision measurement, enhancing the degree of nonlinear effects in ultrafast optics, and increasing excitation intensity in spectroscopy.

[0003] In 2018, Killian Fritsch et al. reported on spectral broadening using a solid multipass cell (Anne-Lise Viotti et al. All-solid-state multipass spectral broadening to sub-20 fs, Optics Letters, Vol.43, No.19, pp4643-4646, 2018). The beam passes through the solid medium in the multipass cell multiple times, enhancing the nonlinear effect and effectively broadening the spectrum. The spectral broadening factor reached 22, and the pulse width was successfully compressed to 18 fs in the post-compression process. However, in some reports (Jaismeen Kaur et al. Simultaneous nonlinear spectral broadening and temporal contrast enhancement of ultrashortpulses in a multi-pass cell, Vol. 6, 015001, 2024), the beam waist changes during each propagation of the beam in the Heriot-Limiter solid-state multi-pass cell. The focused beam can cause the beam power to exceed the damage threshold of the optical components, damaging the optical components and hindering the stable propagation of the beam in the Heriot-Limiter solid-state multi-pass cell, thus affecting the safety of the Heriot-Limiter solid-state multi-pass cell optical system. Summary of the Invention

[0004] The purpose of this invention is to provide a safety optimization method for Heriot-Tropsch solid-state multipass cells based on beam evolution calculation. By rapidly and accurately calculating the beam evolution process of a Heriot-Tropsch solid-state multipass cell, the method effectively predicts and evaluates the beam parameters at different positions in the multipass cell, optimizes the safety of the optical system, and ensures the stability of the optical system.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A safety optimization method for a Heriot-Limited solid multiplexer based on beam evolution calculations is proposed. The Heriot-Limited solid multiplexer has two coaxial concave mirrors with the same radius of curvature. The solid is located at the center of the multiplexer. The structure of "concave mirror-solid-concave mirror" is approximated paraxially and abstracted into a series of optical systems with "thin convex lens-solid" structures. The method includes:

[0007] Step 1: Obtain the structure of the multi-pass cell and the parameters of each optical component, including the center wavelength λ, the radius of curvature R of the concave mirror, and the cavity length d. a Solid thickness d b solid refractive index n b and gas refractive index n a For the cavity structure and each optical component therein, calculate the transmission matrix; based on the optical components that the beam passes through when it starts from a known position, travels through the Heriot-Limiter solid multipass cell an arbitrary number of times, and travels through an arbitrary position, calculate the corresponding transmission matrix; through iteration, obtain the transmission matrix of the beam traveling from the incident position to an arbitrary position.

[0008] Step 2: Based on the transmission matrix of the beam from the initial position to any position, calculate the q parameter of the beam at any position. Using the real and imaginary parts of the q parameter, calculate the corresponding beam radius and wavefront curvature radius, i.e., the beam evolution process in the Heriot-Limited multipass cell.

[0009] Step 3: Adjust the parameters of the incident beam according to the beam evolution process, and calculate the beam distribution in the corresponding Heriot-Limiter solid-state multipass cell; select the corresponding incident beam according to the required beam size and laser intensity, so that the beam maintains a stable beam size each time it passes through the solid in the Heriot-Limiter solid-state multipass cell, so that the optical components are not damaged by the small beam waist, ensuring the safety of the optical components and the system, and improving the stability of the system.

[0010] Preferably, step 1, calculating the transmission matrix for the cavity structure and its various optical devices, specifically includes:

[0011] Step 11: Calculate the transmission matrix M of the concave mirror. cm：Given the radius of curvature R of the concave mirror, its focal length f = R / 2. Abstracting the concave mirror as a thin convex lens, the transfer matrix M... cm for

[0012]

[0013] Step 12: Calculate the transfer matrix M of the solid. b : Obtain the solid thickness d b With the refractive index n of the solid b Calculate the time d in the solid b Distance transmission matrix M b

[0014]

[0015] Step 13: Calculate the air transfer matrix M a : Fix the solid at the center of the multi-pass cell and obtain the distance d between the solid and the concave mirror. a Calculate at distance d a The transfer matrix M of the air a

[0016]

[0017] Step 14: Set the beam propagation step size d in the air. air-step Then the beam propagates through the air by d air-step The transmission matrix is

[0018]

[0019] Step 15: Set the beam propagation step size d in the solid. bulk-step Then the beam propagates through the air by d bulk-step The transmission matrix is

[0020]

[0021] Step 16: Obtain the refractive index n of air a ,but:

[0022] The transmission matrix of the light beam refraction at the air-solid surface is:

[0023]

[0024] The transmission matrix of the light beam refraction at the solid-air surface is:

[0025]

[0026] Preferably, the transmission matrix for the beam to travel from the incident position to any other position in step 1 is calculated as follows:

[0027] Step 17: Based on the number of times the beam travels through the Heriot-Limiter solid-state multipass cell from a known position, the order in which the beam travels to any position, and the sequence of optical components it passes through, by combining formulas (1), (2), (3), (4), (5), (6), and (7), we consider each component the beam passes through during this transmission process as an optical system, and obtain the transmission matrix of this optical system as follows:

[0028]

[0029] And there are constraints.

[0030] det M=AD-BC=1 (9)

[0031] Preferably, step 2 specifically includes:

[0032] Step 21: For a wavelength λ and a solid refractive index n b The incident beam size (radius) is ω input The wavefront radius of curvature is R input A Gaussian beam, its q parameter q input for

[0033]

[0034] Where i is the imaginary unit;

[0035] Step 22, let q input The q parameter is the parameter q before the optical system transmission matrix described in step 17. output Let q be the q parameter after passing through the optical system transmission matrix described in step 17. input and q output The relationship is

[0036]

[0037] Step 23: Based on the relationship between beam size, wavefront radius of curvature, and q-parameter, obtain the beam size and wavefront radius of curvature for the beam to propagate to any position in the multipass cell.

[0038]

[0039] This refers to the beam evolution process in the Heriot-Lieutenant multipass cell.

[0040] Through the above steps, based on the parameters and position of the incident beam, the parameters of the structure and devices in the Heriot-Limiter solid-state multipass cell, the calculation step size, and the optical components through which the beam passes, the transmission matrix of the beam from the initial position to any position can be obtained through iteration. Thus, the q parameter of the beam at any position can be calculated. Using the real and imaginary parts of the q parameter, the corresponding beam radius and wavefront curvature radius can be calculated, i.e., the beam evolution process in the Heriot-Limiter multipass cell.

[0041] Compared with existing methods, the present invention has the following advantages:

[0042] The method of this invention can quickly and accurately calculate the beam evolution process of a Heriot-Limited Solid Multiplexer, enabling researchers to understand, predict, and evaluate parameters such as beam size and wavefront radius of curvature at any position during beam propagation in the Heriot-Limited Solid Multiplexer. By optimizing system parameters, it can protect optical devices in the Heriot-Limited Solid Multiplexer from damage by small beams, improve system safety, and enhance experimental results and stability. This method has significant research value and practical significance for improving accuracy in quantum precision measurement, enhancing the degree of nonlinear effects in ultrafast optics, and increasing excitation intensity in spectroscopy. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the structure of the Heriot solid multi-pass cell of the present invention;

[0044] Figure 2 This is a schematic diagram of the paraxial approximation;

[0045] Figure 3 This is a schematic diagram of beam transmission after paraxial approximation;

[0046] The propagation process of the light beam is as follows: it travels a distance of d... a air, air-solid surface refraction, distance d b The solid, solid-air surface refraction, distance d a Air, concave mirror focusing, distance d a air, air-solid surface refraction, distance d b The solid, solid-air surface refraction, distance d a1 The air;

[0047] Figure 4 This diagram illustrates the beam evolution of the Heriot-Treut solid-state multipass cell of the present invention. The simulation parameters in the figure include: center wavelength 1030 nm, concave mirror curvature radius 300 mm, cavity length 599 mm, solid thickness 20 mm, solid refractive index 1.45, and gas refractive index 1. Figure 4(a) and (b) show the evolution of beam size and wavefront radius of curvature for an incident laser with a beam size of 0.116 mm and a wavefront radius of curvature of positive infinity as it propagates through a multipass cell from 1 to 50 times. Figure 4 (c) and (d) represent the evolution of beam size and wavefront curvature radius of the incident laser as it propagates from 1 to 50 times in the multipass cell, with a beam size of 0.063 mm and a wavefront curvature radius of positive infinity. Detailed Implementation

[0048] The following description, with reference to the accompanying drawings and preferred embodiments, illustrates the implementation of the technical solution of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for illustrating the present invention and not for limiting the scope of protection of the present invention.

[0049] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0050] The structure of the Heriot solid multi-pass cell involved in this embodiment is shown in the following figure. Figure 1 The Heriot solid multipass cell has two concave mirrors CM1 and CM2 with the same radius of curvature and coaxiality, and the solid BM is located at the center of the multipass cell.

[0051] See Figure 2 We approximate the "concave mirror-solid-concave mirror" structure of this multi-pass filter using a paraxial approach, abstracting it as an optical system of a series of "thin convex lens-solid" structures. See [link / reference]. Figure 3 A schematic diagram of beam propagation after paraxial approximation. The beam propagation process proceeds sequentially through a distance d. a air, air-solid surface refraction, distance d b The solid, solid-air surface refraction, distance d a Air, concave mirror focusing, distance d a air, air-solid surface refraction, distance d b The solid, solid-air surface refraction, distance d a1 The air.

[0052] In this Heriot-Limited Solid-State Multiplexer structure, the beam waist changes during each propagation process within the multiplexer. The focused beam can cause its power to exceed the damage threshold of the optical components, damaging them and hindering stable beam propagation within the Heriot-Limited Solid-State Multiplexer, thus impacting the safety of the optical system. To optimize system safety, this implementation employs the following optimization method, specifically including the following steps:

[0053] Step 1: Obtain the structure of the multi-pass cell and the parameters of each optical component, mainly including the center wavelength λ, the radius of curvature R of the concave mirror, and the cavity length d. a Solid thickness d b solid refractive index n b and gas refractive index n a Parameters such as these are determined. Furthermore, the transmission matrix is ​​calculated for the cavity structure and each optical component within it. Further, based on the beam's trajectory from a known position through the Heriot-Limiter solid multipass cell an arbitrary number of times, and the optical components it passes through to reach any position, the corresponding transmission matrix is ​​calculated. Through iteration, the transmission matrix for the beam's journey from the initial position to any other position is obtained.

[0054] Step 1 specifically includes:

[0055] Step 11: Determine the radius of curvature R of the concave mirror and the focal length f = R / 2. Abstract the concave mirror as a thin convex lens. The transfer matrix is:

[0056]

[0057] Step 12: Determine the solid thickness d b With the refractive index n of the solid b Calculate the time d in the solid b The distance transmission matrix is

[0058]

[0059] Step 13: Fix the solid at the center of the multi-channel cell, with the distance between the solid and the concave mirror being d. a At a distance of d a The air transport matrix is

[0060]

[0061] Step 14: Set the transmission step size d in the air. air-step Then the beam propagates through the air by d air-step The transmission matrix is

[0062]

[0063] Step 15: Set the transmission step size d in the solid state. bulk-step Then the beam propagates through the air by d bulk-step The transmission matrix is

[0064]

[0065] Step 16: Determine the refractive index n of air. a The transfer matrix for refraction at the air-solid surface is:

[0066]

[0067] The transfer matrix for refraction at the solid-air surface is:

[0068]

[0069] Step 17: Taking the beam being introduced from behind the concave mirror as an example, the center wavelength of the incident beam is λ, and the refractive index of the solid is n. b The refractive index of air is n a The incident beam size (radius) is ω input The wavefront radius of curvature is R input A Gaussian beam, for example: the propagation process of a beam is as follows: it travels through a distance d... a air, air-solid surface refraction, distance d b The solid, solid-air surface refraction, distance d a Air, concave mirror focusing, distance d a air, air-solid surface refraction, distance d b The solid, solid-air surface refraction, distance d a1 After the air, the transfer matrix is

[0070]

[0071] And there are constraints.

[0072] det M=AD-BC=1 (9)

[0073] Similar to step 17, through iteration, the corresponding transmission matrix can be calculated based on the optical components that the beam passes through when it starts from a known incident position, travels through the Heriot-Treut solid multipass cell an arbitrary number of times, and reaches an arbitrary position in the multipass cell.

[0074] Step 2: Based on the transmission matrix of the beam from the initial position to any position, calculate the q parameter of the beam at any position. Using the real and imaginary parts of the q parameter, calculate the corresponding beam radius and wavefront curvature radius, i.e., the beam evolution process in the Heriot-Limited multipass cell.

[0075] Step 2 specifically includes:

[0076] Step 21: For a wavelength λ and a solid refractive index n b The incident beam size (radius) is ω input The wavefront radius of curvature is R input A Gaussian beam, its q parameter q input for

[0077]

[0078] Step 22, q input The q parameter is the parameter q before the optical system transmission matrix described in step 17. output Let q be the q parameter after passing through the optical system transmission matrix described in step 17. input and q output The relationship is

[0079]

[0080] Step 23: Based on the relationship between beam size, wavefront radius of curvature, and q-parameter, obtain the beam size and wavefront radius of curvature for the beam to propagate to any position in the multipass cell.

[0081]

[0082] Step 3: Adjust the parameters of the incident beam according to the beam evolution process, and calculate the beam distribution in the corresponding Heriot-Limiter solid-state multipass cell; select the corresponding incident beam according to the required beam size and laser intensity, so that the beam maintains a stable beam size each time it passes through the solid in the Heriot-Limiter solid-state multipass cell, so that the optical components are not damaged by the small beam waist, ensuring the safety of the optical components and the system, and improving the stability of the system.

[0083] The following simulation experiment further demonstrates the effectiveness of the invention:

[0084] Beam evolution of a Heriot solid-state multipass cell as follows Figure 4 As shown, Figure 4 The simulation parameters include: center wavelength 1030nm, concave mirror curvature radius 300mm, cavity length 599mm, solid thickness 20mm, solid refractive index 1.45, and gas refractive index 1. Figure 4 In the figures (a) and (b), the beam size is 0.063 mm and the wavefront curvature radius is positive infinity. These figures represent the evolution of the beam size and wavefront curvature radius as the incident laser propagates through the multipass cell from 1 to 50 times. Figure 4(c) and (d) represent the evolution of beam size and wavefront curvature radius of the incident laser as it travels from 1 to 50 times in the multipass cell, with a beam size of 0.116 mm and a wavefront curvature radius of positive infinity.

[0085] Using the above method, after determining parameters such as the center wavelength of the incident beam, beam size, wavefront radius of curvature, cavity length of the Heriot-Limiter solid multiplexer, radius of curvature of the concave mirror, solid length, solid refractive index, and air refractive index, the parameters of the beam at any position after passing through the Heriot-Limiter solid multiplexer can be calculated, such as... Figure 4 The diagram illustrates the evolution of a beam in a Heriot solid multipass cell, including the beam size and the radius of curvature of the wavefront. Figure 4 In Figures (a) and (b), the parameters of the incident laser in the multipass cell are a beam size of 0.063 mm and a wavefront radius of curvature of positive infinity. The laser propagates 50 times in a Heriot-Limiter solid multipass cell, and the evolution of the beam size and wavefront radius of curvature during each propagation between two concave mirrors in the cell. Figure 4 In (a), the black portion represents the beam waist, which is smaller than 0.4 mm. The laser energy is highly concentrated, exhibiting significant variations with each transmission. The beam waist distribution is very dispersed, easily damaging optical components in the system. Through traversal, a more stable beam distribution is obtained. The parameters of the incident beam are adjusted to a beam size of 0.116 mm and a wavefront radius of curvature of positive infinity, as shown... Figure 4 As shown in (c) and (d), the beam has its largest size each time it passes the surface of the concave mirror, and the radius of curvature of its wavefront is the same as that of the concave mirror. When the beam passes the center of the multipass cell, i.e., the center of the solid, it has its smallest size, and the wavefront is a plane. Through safety optimization, a stable beam distribution ensures system safety and improves experimental performance. This fully demonstrates the correctness of the calculation method for beam evolution in a Heriot-Limited Solid Multipass Cell and the reliability of the system safety optimization method. This method can fully predict and evaluate the evolution of the beam size and wavefront radius of curvature of a beam with known parameters, after several transmissions in a Heriot-Limited Solid Multipass Cell with a known structure, and optimize the system safety. This is of great significance for the research of Heriot-Limited Solid Multipass Cells in ultrafast optics, spectroscopy, atomic and molecular physics, and quantum precision measurement.

[0086] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for optimizing the safety of a Heriot-Treut solid multipass cell based on beam evolution calculation, characterized in that, The Heriot-Treut solid multipass cell has two coaxial concave mirrors with the same radius of curvature. The solid is located at the center of the multipass cell. The "concave mirror-solid-concave mirror" structure is approximated paraxially and abstracted into a series of "thin convex lens-solid" optical systems. The method includes: Step 1: Obtain the structure of the multi-pass cell and the parameters of each optical component, including the center wavelength. λ Concave mirror radius of curvature R The distance between concave mirrors, i.e., the cavity length d a Solid thickness d b solid refractive index n b and air refractive index n a For the cavity structure and each optical component therein, the transmission matrix is ​​calculated; based on the optical components that the beam passes through when it starts from a known position and travels through the Heriot-Limiter solid multipass cell an arbitrary number of times, the corresponding transmission matrix is ​​calculated; through iteration, the transmission matrix of the incident beam from the initial position to any position is obtained. Step 2: Based on the transmission matrix of the beam from its initial position to any other position, calculate the transmission distance of the beam to that other position. q Parameters, using q The real and imaginary parts of the parameters are used to calculate the corresponding beam radius and wavefront radius of curvature, i.e., the beam evolution process in the Heriot-Limited multipass cell; including: Step 21, for a wavelength of λ The refractive index of solids is n b The radius of the incident beam is ω input The wavefront radius of curvature is R input Gaussian beam, parameters q input for: (10)， in, i The imaginary unit; Step 22, set q input For the transmission matrix of the optical system q parameter, q output For the transmission matrix of the optical system q parameter, q input and q output The relationship is: (11) ， Step 23: Based on the beam size, wavefront radius of curvature, and q The relationship between the parameters yields the beam size and wavefront radius of curvature at any position in the multipass cell: (12) ， This refers to the beam evolution process in the Heriot-Limited multiplexer. Step 3: Adjust the parameters of the incident beam according to the beam evolution process, and calculate the beam distribution in the corresponding Heriot-Limiter solid-state multipass cell; select the corresponding incident beam according to the required beam size and laser intensity, so that the beam maintains a stable beam size each time it passes through the solid in the Heriot-Limiter solid-state multipass cell, so that the optical components are not damaged by the small beam waist, ensuring the safety of the optical components and the system, and improving the stability of the system.

2. The method for optimizing the safety of a Heriot-Treut solid-state multipass cell based on beam evolution calculation as described in claim 1, characterized in that, Step 1, which calculates the transmission matrix for the cavity structure and its various optical components, specifically includes: Step 11: Calculate the transmission matrix of the concave mirror. M cm： Obtain the radius of curvature of the concave mirror R Then its focal length f = R / 2, abstracting the concave mirror as a thin convex lens, transmission matrix M cm for: (1) ， Step 12: Calculate the transfer matrix of the solid. M b Obtaining solid thickness d b With solid refractive index n b Calculate the time in the solid d b Distance transmission matrix M b： (2) ， Step 13: Calculate the air transport matrix Ma : Fix the solid at the center of the multi-channel cell to obtain the cavity length. d a Calculate the distance d a Transmission matrix of medium air Ma : (3) ， Step 14: Set the beam propagation step size in the air. d air-step Then the light beam travels through the air. d air-step The transfer matrix is: (4) ， Step 15: Set the beam propagation step size in the solid. d bulk-step Then the light beam travels through the air. d bulk-step The transfer matrix is: (5) ， Step 16: Obtain the refractive index of air n a ,but: The transmission matrix for the refraction of a light beam at an air-solid surface is: (6) ， The transmission matrix for the refraction of a light beam at a solid-air surface is: (7) 。 3. The method for optimizing the safety of a Heriot-Treut solid-state multipass cell based on beam evolution calculation according to claim 2, characterized in that, In step 1, the transmission matrix for the light beam to travel from its initial position to any other position is calculated as follows: Step 17: Based on the number of times the beam travels through the Heriot-Limiter solid multipass cell from a known position, the order in which the beam travels to any position, and the sequence of optical components it passes through, by combining formulas (1), (2), (3), (4), (5), (6), and (7), the various components the beam passes through during this transmission process are considered as an optical system, and the transmission matrix of this optical system is obtained as follows: (8)， And there are constraints: (9)。

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