Method for improving light beam transmission stability of optical multi-pass cell with concave-convex reflector structure

Abstract

The invention provides a method for improving the light beam transmission stability of an optical multi-pass cell with a concave-convex surface reflector structure, and the method comprises the steps: carrying out the paraxial approximation of a concave surface reflector-convex surface reflector structure of the optical multi-pass cell with the concave-convex surface reflector structure, enabling the concave surface reflector-convex surface reflector structure to be equivalent to a series of convex lens-concave lens structures, enabling a light beam to enter along an optical axis, and enabling the light beam to enter the optical multi-pass cell with the concave-convex surface reflector structure; calculating a transmission matrix for the light beam, and calculating to obtain a light beam eigenvalue according to the transmission characteristics of the light beam meeting the eigenmode, the consistency of q parameters of light beam transmission in the concave-convex surface reflector structure optical multi-pass pool and the consistency of the size and curvature radius of the light beam before and after one-time complete transmission; and the size of the incident light beam injected into the optical multi-pass pool with the concave-convex surface reflector structure is omega, so that the light beam is stably transmitted. According to the method, stable transmission of the light beam in the concave-convex reflector structure optical multi-pass cell can be enhanced, and the quantum effect and the nonlinear effect are improved.

Description

Technical Field

[0001] The invention relates to the field of lasers, and in particular to a method for improving the light beam transmission stability of an optical multi-pass cell with a concave-convex reflector structure, and is mainly applicable to atomic and molecular physics, quantum precision measurement, ultrafast optics and spectroscopy. Background Art

[0002] The optical multi-pass cell with a concave-convex reflector structure has a concave reflector and a convex reflector, which are placed oppositely and coaxially. Such a structure has a resonant cavity structure, and the beam quality is maintained through the cavity structure, and the loss is low. The light path is effectively increased by the reciprocating transmission of the light beam between the two reflectors. And because the theoretical beam waist in the optical multi-pass cell with a concave-convex reflector structure is outside the concave mirror, the light beam does not have a focus when it is transmitted in the multi-pass cell, which can keep the multi-pass cell with a small size, and it is not easy to ionize the gas. The laser energy loss is low, so it is widely used in research fields such as atomic and molecular physics, quantum precision measurement, ultrafast optics and spectroscopy. The eigenmode of the multi-pass cell refers to the mode in which the light beam can be stably transmitted in the multi-pass cell. If the transverse mode of the incident light beam is consistent with the eigenmode, the incident light beam can be stably transmitted in the multi-pass cell. When the light beam passes through the same position of the optical multi-pass cell with a concave-convex reflector structure, the light beam size does not change, which effectively ensures that the optical device of the multi-pass cell is not damaged by a smaller focused light beam, and produces a stable quantum effect or nonlinear effect in the experiment.

[0003] In 2023, Alan Omar et al. reported an optical multi-pass cell with a concave-convex reflector structure (Alan Omar et al. Spectral broadening of 2-mJ femtosecond pulses in a compact air-filled convex-concave multi-pass cell, Optics Letter, Vol. 48, No. 2, pp1458-1461). A laser beam with a single pulse energy of 2 mJ was transmitted back and forth 15 times in the multi-pass cell, passing through the air between the two reflectors 30 times in total, and finally, after dispersion compensation, the initial laser pulse width of 670 fs was compressed to 134 fs after spectral broadening and pulse post-compression. In this way, the optical multi-pass cell with a concave-convex reflector structure is used to increase the optical path, broaden the spectrum, and compress the pulse. However, since the optical multi-pass cell with a concave-convex reflector structure is similar to a resonant cavity, it has two reflectors, i.e., the structure of a resonant cavity. From the principle of the resonant cavity, it can be known that only when the incident light beam meets the conditions of the eigenmode can the light beam be stably transmitted in the resonant cavity. Otherwise, during the transmission process, the size of the light beam and the radius of curvature of the wavefront will undergo significant changes. Too large a beam size will affect the quantum effect and nonlinear effect, and too small a beam size will cause the power to exceed the damage threshold, resulting in damage to optical components and ionization of the gas, and the light beam cannot continue to be transmitted. Therefore, how to improve the light beam transmission stability of the optical multi-pass cell with a concave-convex reflector structure is a problem that needs to be solved at present. Summary of the invention

[0004] The purpose of the present invention is to provide a method for improving the light beam transmission stability of an optical multi-pass cell with a concave-convex reflector structure. According to the structural parameters of the optical multi-pass cell with a concave-convex reflector structure, a transmission matrix is ​​established. According to the consistency of the q parameter during the light beam transmission process, the eigenvalue of the optical multi-pass cell with a concave-convex reflector structure is quickly and accurately calculated, so as to control the incident light beam to work under the condition of satisfying the eigenmode, so that the light beam can be stably transmitted in the multi-pass cell, and the performance characteristics of the optical multi-pass cell with a concave-convex reflector structure are fully exerted.

[0005] In order to achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0006] A method for improving the light beam transmission stability of an optical multi-pass cell with a concave-convex reflector structure, wherein the optical multi-pass cell with a concave-convex reflector structure has a concave reflector and a convex reflector coaxially and placed opposite to each other. In the method, the structure of "concave reflector-convex reflector" is paraxially approximated to be equivalent to a series of "convex lens-concave lens" structures, and the light beam is incident along the optical axis. The method of the invention comprises the following steps:

[0007] Step 1, obtain the structure and optical parameters of the optical multi-pass cell with a concave-convex reflector structure, calculate the transmission matrix of the concave reflector, convex reflector and air devices and materials, and further calculate the transmission matrix of the optical multi-pass cell with a concave-convex reflector structure when the light beam is incident from different reflectors.

[0008] Step 2: According to the input parameters of the light beam, the light beam starts from one of the mirrors in the optical multi-pass cell with a concave and convex reflector structure, transmits once, and returns to the mirror again. The q parameter remains unchanged. Using the consistency of the q parameter, the eigenvalues ​​of the light beam on the surface of the concave reflector and the convex reflector are calculated. The q parameter is a parameter that characterizes the quality of the laser resonant cavity, which is called the quality factor.

[0009] Step 3, using the beam eigenvalue obtained in step 2 as the size ω of the incident beam injected into the optical multi-pass cell with a concave-convex reflector structure, so that the beam can be stably transmitted.

[0010] Preferably, the beam eigenvalues ​​on the surfaces of the concave reflector and the convex reflector in the optical multi-pass cell with a concave-convex reflector structure are

[0011]

[0012] Where A1 = (LR2) / (2n)-(R1(L / n+(L((LR2) / (2n)+1)) / n)) / 2+1

[0013] B1=L / n+(L((LR2) / (2n)+1)) / n

[0014] D1=(LR2) / (2n)+1

[0015] A2=(R2(L / n-(L((LR1) / (2n)-1)) / n)) / 2-(LR1) / (2n)+1

[0016] B2=L / n-(L((LR1) / (2n)-1)) / n

[0017] D2 = 1 - (LR1) / (2n).

[0018] Preferably, in step 1, calculating the transmission matrix of the concave reflector, the convex reflector, and the air device and material specifically includes:

[0019] Step 11, obtain the curvature radius R1 of the concave reflector, then the focal length is f1 = R1 / 2, the concave reflector is equivalent to a convex lens, and the transfer matrix is

[0020]

[0021] Step 12: Get the radius of curvature R2 of the convex reflector, then the focal length is f2 = R2 / 2, the convex reflector is equivalent to a concave lens, and the transfer matrix is

[0022]

[0023] Step 13: Obtain the distance between the concave reflector and the convex reflector, i.e., the cavity length L, and the gas refractive index n. The transmission matrix is:

[0024]

[0025] Preferably, the calculation of the transmission matrix of the optical multi-pass cell with a concave and convex reflector structure when the light beam is incident from different reflectors includes:

[0026] Step 14. Assume that the initial position of the light beam is located on the surface of the concave reflector and it is transmitted toward the convex reflector. After one cycle of transmission in the optical multi-pass pool of the concave and convex reflector structure, the optical components and media it passes through are: air with a distance of L → convex reflector → air with a distance of L → concave reflector. After passing through the optical system composed of these four parts, its transmission matrix is

[0027]

[0028] Step 15. Assume that the initial position of the light beam is located on the surface of the convex reflector, and it is transmitted toward the concave reflector. After one cycle of transmission in the optical multi-pass pool of the concave-convex reflector structure, the optical components and media it passes through are: air with a distance of L → concave reflector → air with a distance of L → convex reflector. After passing through the optical system composed of these four parts, its transmission matrix is

[0029]

[0030] And the determinants of formula (4) and formula (5) are related

[0031]

[0032] Preferably, the step 2 specifically includes:

[0033] Step 21. For a wavelength of λ, the size (radius) of the input Gaussian beam is ω in , the wavefront curvature radius is R in , its q parameter q in for

[0034]

[0035] Step 22: After the light beam in step 21 is transmitted through step 14, its q parameter q 1out for

[0036]

[0037] Step 23: After the light beam in step 21 is transmitted through step 15, its q parameter q 2out for

[0038]

[0039] Step 24. According to the transmission characteristics of the light beam satisfying the eigenvalue in the optical multi-pass cell with a concave-convex reflector structure, the size and curvature radius of the light beam remain the same before and after a complete transmission, that is, the q parameter of the light beam transmission remains unchanged, then formula (8) and formula (9) exist

[0040]

[0041] Step 20, by combining formula (4), formula (5), formula (6), formula (7), formula (8), formula (9), and formula (10), the beam eigenvalues ​​on the surfaces of the concave reflector and the convex reflector in the optical multi-pass cell with a concave-convex reflector structure can be obtained as follows:

[0042]

[0043] It can be seen that by inputting the parameters of various optical devices and materials of the optical multi-pass cell with a concave-convex reflector structure into the above formula, the beam eigenvalue of the optical multi-pass cell with a concave-convex reflector structure can be calculated.

[0044] The advantages and effects of the present invention are as follows:

[0045] The method of the present invention can quickly and accurately calculate the eigenvalues ​​of an optical multi-pass cell with a concave-convex reflector structure, so that designers and researchers can accurately determine the optimal size of a light beam injected into the multi-pass cell, and predict and evaluate the light beam sizes on the concave reflector surface and the convex reflector surface in the optical multi-pass cell with a concave-convex reflector structure. This can not only avoid damage to optical components, but also enhance the stable transmission of light beams in the optical multi-pass cell with a concave-convex reflector structure, improve quantum effects and nonlinear effects, and has important research value and significance for atomic and molecular physics, quantum precision measurement, ultrafast optics and spectroscopy. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic structural diagram of an optical multi-pass cell with a concave-convex reflector structure in the present invention;

[0047] Figure 2 This is a paraxial approximate schematic diagram;

[0048] Figure 3It is a comparison diagram of the beam transmission of the multi-pass cell under the conditions that the beam size is the eigenvalue and the extrinsic value respectively, and other parameters are the same; the central wavelength is 1550nm, the multi-pass cell cavity length is 910mm, the concave reflector radius of curvature is 1000mm, the convex reflector radius of curvature is 900mm, the gas refractive index is 1, and the number of transmissions is 50 times. Figure 3 Figure (a) shows the incident light beam incident along the concave mirror surface. The incident light beam sizes are 0.3240 mm (eigenvalue) and 0.3200 mm (non-eigenvalue), and the wavefront curvature radius is 1000 mm. When the multi-pass pool is transmitted 1-50 times, the beam size on the concave mirror surface each time. Figure 3 Figure (b) shows the incident light beam incident along the convex mirror surface. The incident light beam sizes are 1.5314mm (eigenvalue) and 1.4000mm (non-eigenvalue), and the wavefront curvature radius is 900mm. When the multi-pass pool is transmitted 1-50 times, the beam size on the concave mirror surface each time. DETAILED DESCRIPTION

[0049] The following will refer to the accompanying drawings and preferred embodiments to illustrate 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 contents disclosed in this specification. The present invention can also be implemented or applied through other different specific implementations, and the details in this specification can also be modified or changed in various ways 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, not for limiting the scope of protection of the present invention.

[0050] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0051] The optical multi-pass cell structure of the concave-convex reflector structure involved in this embodiment can be found in Figure 1, the optical multi-pass cell has a concave reflector and a convex reflector which are coaxial and placed opposite to each other. When the structural parameters of the optical multi-pass cell and the optical parameters of each component are determined, in order to make the incident light beam obtain stable transmission in the multi-pass cell, it is necessary to accurately calculate the eigenvalue of the light beam in the optical multi-pass cell with the concave and convex reflector structure, so that the incident light beam is injected into the multi-pass cell with the eigenvalue of the light beam. The method is to approximate the structure of "concave reflector-convex reflector" paraxially, and make it equivalent to a series of "convex lens-concave lens" structures. The light beam is incident along the optical axis, and the transmission matrix is ​​calculated for it. According to the q parameter of the light beam transmission in the optical multi-pass cell with the concave and convex reflector structure, according to the transmission characteristics of the light beam that meets the eigenvalue in the optical multi-pass cell with the concave and convex reflector structure, before and after a complete transmission, the size of the light beam and the radius of curvature are kept consistent, and the eigenvalue of the light beam is calculated.

[0052] The specific steps include:

[0053] Step 1. Obtain the structure and optical parameters of the optical multi-pass cell with a concave-convex reflector structure, calculate the transmission matrix of the concave reflector, convex reflector and air devices and materials, and further calculate the transmission matrix of the optical multi-pass cell with a concave-convex reflector structure when the light beam is incident from different reflectors.

[0054] Step 11, determine the radius of curvature R1 of the concave reflector, then the focal length is f1 = R1 / 2, the concave reflector is equivalent to a convex lens, and the transfer matrix is

[0055]

[0056] Step 12: Determine the radius of curvature R2 of the convex reflector, then the focal length is f2 = R2 / 2, the convex reflector is equivalent to a concave lens, and the transfer matrix is

[0057]

[0058] Step 13, determine the cavity length L (the distance between the concave reflector and the convex reflector), the gas refractive index n, and the transmission matrix is

[0059]

[0060] Step 14. Assume that the initial position of the light beam is located on the surface of the concave mirror and it is transmitted toward the convex mirror. After one cycle of transmission in the optical multi-pass pool of the concave and convex reflector structure, the optical components and media it passes through are: air with a distance of L → convex reflector → air with a distance of L → concave reflector. After passing through the optical system composed of these four parts, its transmission matrix is

[0061]

[0062] Step 15. Assume that the initial position of the light beam is located on the surface of the convex mirror and it is transmitted toward the concave mirror. After one cycle of transmission in the optical multi-pass pool of the concave-convex reflector structure, the optical components and media it passes through are: air with a distance of L → concave reflector → air with a distance of L → convex reflector. After passing through the optical system composed of these four parts, its transmission matrix is

[0063]

[0064] And the determinants of formula (4) and formula (5) are related

[0065]

[0066] Step 2, according to the q parameter of the beam transmission in the optical multi-pass cell with concave and convex reflector structure:

[0067] Step 21. For a wavelength of λ, the size (radius) of the input Gaussian beam is ω in , the wavefront curvature radius is R in , its q parameter q in for

[0068]

[0069] Step 22: After the light beam in step 21 is transmitted through step 14, its q parameter q 1out for

[0070]

[0071] Step 23: After the light beam in step 21 is transmitted through step 15, its q parameter q 2out for

[0072]

[0073] Step 24. According to the transmission characteristics of the light beam satisfying the eigenvalue in the optical multi-pass cell with a concave-convex reflector structure, before and after a complete transmission, the size of the light beam and the radius of curvature remain consistent, then formula (8) and formula (9) exist

[0074]

[0075] Step 25. By combining formula (4), formula (5), formula (6), formula (7), formula (8), formula (9), and formula (10), the beam eigenvalues ​​on the surfaces of the concave reflector and the convex reflector in the optical multi-pass cell with a concave-convex reflector structure can be obtained as follows:

[0076]

[0077] Where A1 = (LR2) / (2n)-(R1(L / n+(L((LR2) / (2n)+1)) / n)) / 2+1

[0078] B1=L / n+(L((LR2) / (2n)+1)) / n

[0079] D1=(LR2) / (2n)+1

[0080] A2=(R2(L / n-(L((LR1) / (2n)-1)) / n)) / 2-(LR1) / (2n)+1

[0081] B2=L / n-(L((LR1) / (2n)-1)) / n

[0082] D2 = 1 - (LR1) / (2n).

[0083] Using the above method, for an optical multi-pass cell structure with a concave-convex reflector structure, after determining parameters such as the central wavelength of the incident light beam of 1550nm, the multi-pass cell cavity length of 910mm, the curvature radius of the concave reflector of 1000mm, the curvature radius of the convex reflector of 900mm, and the gas refractive index of 1, the beam eigenvalues ​​on the surfaces of the concave reflector and the convex reflector in the optical multi-pass cell with a concave-convex reflector structure can be calculated, which are 1.5314mm and 0.3240mm respectively, and their wavefront curvature radii are the curvature radii of the concave reflector and the convex reflector respectively.

[0084] As a verification, two incident beams, one with a beam size of 1.5314 mm and a wavefront curvature radius of 1000 mm and one with a beam size of 0.3240 mm and a wavefront curvature radius of 900 mm, were injected into the multi-pass cell of the above structure from the surface of the concave reflector and the other with the convex reflector, respectively. The beams were transmitted back and forth 50 times in the multi-pass cell. The beam sizes irradiated on the concave reflector and the convex reflector each time were as follows: Figure 3 As shown by the grey solid lines in (a) and (b), the beam sizes of 50 times are consistent and very stable, which is consistent with the theory of the resonant cavity and also verifies the correctness of the calculation method of the eigenvalue of the optical multi-pass cell with a concave-convex mirror structure proposed in the present invention.

[0085] For comparison, the two injected beams are not the eigenvalues ​​of the multi-pass cell. The beam size incident from the concave reflector surface is 1.400 mm, and the beam size incident from the convex reflector surface is 0.3200 mm. The initial curvature radius is the curvature radius of the corresponding reflector. The beam size incident on the two reflector surfaces each time is as follows: Figure 3As shown in the black solid lines in (a) and (b), although the difference between the injected beam size and the eigenvalue is only ~100μm and ~10μm, after dozens of transmissions through the concave-convex mirror structure optical multi-pass cell, the fluctuation is very large. While a larger beam reduces quantum effects and nonlinear effects, a smaller beam brings huge optical power per unit area, which can easily damage optical devices. Therefore, providing an accurate calculation of the eigenvalue of the concave-convex mirror structure optical multi-pass cell can provide guidance for the evaluation of the multi-pass cell structure and the prediction of beam transmission, which also verifies the importance and feasibility of the present invention.

[0086] The above shows and describes 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 above embodiments and descriptions only describe the principles of the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention. These changes and improvements fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for improving the light beam transmission stability of an optical multi-pass cell with a concave-convex reflector structure, characterized in that: The optical multi-pass cell of the concave-convex reflector structure has a concave reflector and a convex reflector coaxially and placed opposite to each other, and the "concave reflector-convex reflector" structure is paraxially approximated to be equivalent to a series of "convex lens-concave lens" structures, and the light beam is incident along the optical axis; the method comprises the following steps: Step 1, obtaining the structure and optical parameters of the optical multi-pass cell with a concave-convex reflector structure, including the incident laser center wavelength λ, the curvature radius R1 of the concave reflector, the curvature radius R2 of the convex reflector, the air with a distance L between the concave reflector and the convex reflector, and the gas refractive index n, respectively calculating the transmission matrices of the concave reflector, the convex reflector and the air, and further calculating the transmission matrix of the optical multi-pass cell with a concave-convex reflector structure when the light beam is incident from different reflectors; Step 2, according to the input parameters of the light beam, the light beam starts from one of the mirrors in the optical multi-pass cell of the concave and convex reflector structure, transmits once, and returns to the mirror again, and the q parameter remains unchanged. The eigenvalues ​​of the light beam on the surfaces of the concave reflector and the convex reflector are calculated using the consistency of the q parameter; Step 3, using the beam eigenvalue obtained in step 2 as the size ω of the incident beam injected into the optical multi-pass cell with a concave-convex reflector structure, so that the beam can be stably transmitted.

2. The method for improving the light beam transmission stability of an optical multi-pass cell with a concave-convex reflector structure according to claim 1, characterized in that: The eigenvalues ​​of the beams on the concave and convex reflectors in the optical multipass cell are Where A1 = (LR2) / (2n)-(R1(L / n+(L((LR2) / (2n)+1)) / n)) / 2+1 B1=L / n+(L((LR2) / (2n)+1)) / n D1=(LR2) / (2n)+1 A2=(R2(L / n-(L((LR1) / (2n)-1)) / n)) / 2-(LR1) / (2n)+1 B2=L / n-(L((LR1) / (2n)-1)) / n D2 = 1 - (LR1) / (2n).

3. The method for improving the light beam transmission stability of an optical multi-pass cell with a concave-convex reflector structure according to claim 1, characterized in that: In step 1, calculating the transmission matrix of the concave reflector, the convex reflector and the air includes: Step 11, calculate the transfer matrix M1 of the concave reflector: obtain the curvature radius R1 of the concave reflector, then the focal length is f1=R1 / 2, and the concave reflector is equivalent to a convex lens, then the transfer matrix M1 of the concave reflector is Step 12, calculate the transfer matrix M2 of the convex reflector: obtain the curvature radius R2 of the convex reflector, then the focal length is f2=R2 / 2, and the convex reflector is equivalent to a concave lens, then the transfer matrix M2 of the convex reflector is Step 13: Calculate the air transmission matrix M air :Get the distance between the concave reflector and the convex reflector, that is, the cavity length L, and the gas refractive index n, then the transmission matrix of the air at a distance of L is 4. The method for improving the light beam transmission stability of an optical multi-pass cell with a concave-convex reflector structure according to claim 3, characterized in that: In the step 1, the transmission matrix of the optical multi-pass cell with a concave and convex reflector structure is calculated when the light beam is incident from different reflectors, including: Step 14: Calculate the transmission matrix M of the optical system a a :Assume that the initial position of the light beam is located on the surface of the concave reflector and is transmitted toward the convex reflector, which is optical system a. The light beam undergoes a cycle of transmission in the optical multi-pass pool of the concave and convex reflector structure. Then the transmission matrix M of the optical system a is a for Step 15: Calculate the transfer matrix M of the optical system b b :Assume that the initial position of the light beam is located on the surface of the convex reflector and is transmitted toward the concave reflector, which is the optical system b. After one cycle of transmission in the optical multi-pass pool of the concave and convex reflector structure, the transmission matrix M of the optical system b is b for And the determinants of formula (4) and formula (5) are related 5. The method for improving the light beam transmission stability of an optical multi-pass cell with a concave-convex reflector structure according to claim 4, characterized in that: The step 2 comprises: Step 21. For a wavelength of λ, the size (radius) of the input Gaussian beam is ω in , the wavefront curvature radius is R in , the q parameter q of the light beam propagating in the optical multi-pass cell with concave and convex reflectors in for Step 22: After the light beam in step 21 is transmitted through step 14, its q parameter q 1out for Step 23: After the light beam in step 21 is transmitted through step 15, its q parameter q 2out for Step 24. According to the transmission characteristics of the light beam satisfying the eigenvalue in the optical multi-pass cell with a concave-convex reflector structure, before and after a complete transmission, the size of the light beam and the radius of curvature remain consistent, then formula (8) and formula (9) exist Step 25, by combining formula (4), formula (5), formula (6), formula (7), formula (8), formula (9), and formula (10), the beam eigenvalues ​​on the surfaces of the concave reflector and the convex reflector in the optical multi-pass cell with a concave-convex reflector structure are obtained as follows:

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