Method for improving optical multi-pass cell beam transmission stability of concave-convex mirror structure

Abstract

This invention provides a method for improving beam transmission stability in an optical multipass cell with a concave-convex mirror structure. The method approximates the "concave mirror-convex mirror" structure of the optical multipass cell as a series of "convex lens-concave lens" structures by paraxial approximation. The beam is incident along the optical axis, and its transmission matrix is ​​calculated. Based on the transmission characteristics of beams satisfying intrinsic modes, the method improves beam transmission stability in the optical multipass cell with a concave-convex mirror structure. q The parameters are consistent; the beam size and radius of curvature remain consistent before and after a complete transmission. The beam eigenvalues ​​are calculated and used as the size of the incident beam injected into the optical multipass cell of the concave-convex mirror structure. ω This allows for stable beam transmission. The method of this invention enhances the stable transmission of beams in the optical multipass cell of the concave-convex mirror structure, and improves quantum and nonlinear effects.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of laser, in particular to a method for improving the stability of beam transmission of a concave-convex mirror structure optical multipass cell, which is mainly suitable for atomic and molecular physics, quantum precision measurement, ultrafast optics and spectroscopy. BACKGROUND

[0002] The concave-convex mirror structure optical multipass cell has a concave mirror and a convex mirror which are placed oppositely and coaxially. Such a structure has the structure of a resonant cavity, which can maintain the quality of the beam, has low loss, and effectively increases the optical path by the reciprocating transmission of the beam between the two mirrors. Moreover, in the concave-convex mirror structure optical multipass cell, the theoretical beam waist is outside the concave mirror, so the beam does not have a focal point when it is transmitted in the multipass cell, which can keep the multipass cell small in size, is not easy to ionize the gas, and has low laser energy loss. Therefore, it is widely used in the research fields of atomic and molecular physics, quantum precision measurement, ultrafast optics and spectroscopy. The eigenmode of the multipass cell refers to the mode in which the beam can be stably transmitted in the multipass cell. If the transverse mode of the incident beam is consistent with the eigenmode, the incident beam can be stably transmitted in the multipass cell. When the beam passes through the same position of the concave-convex mirror structure optical multipass cell, the size of the beam does not change, which effectively ensures that the optical device of the multipass cell is not damaged by the small focused beam, and stable quantum effects or nonlinear effects are generated in the experiment.

[0003] In 2023, Alan Omar et al. reported an optical multi-pass cell with a convex-concave mirror 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 is transmitted back and forth 15 times in the multi-pass cell, a total of 30 times through the air between the two mirrors, and finally after dispersion compensation, the initial laser pulse width of 670 fs is spectrally broadened and pulse compressed to 134 fs. By this method, the optical path is increased by using the optical multi-pass cell with a convex-concave mirror structure, the spectrum is broadened, and the pulse is compressed. However, since the optical multi-pass cell with a convex-concave mirror structure is similar to a resonant cavity, it has two mirrors, i.e. the structure of a resonant cavity. From the principle of the resonant cavity, only when the incident beam satisfies the eigenmode condition, the beam can be stably transmitted in the resonant cavity, otherwise the beam size and the curvature radius of the wavefront will change significantly during transmission. Excessive beam size will affect quantum effects and nonlinear effects, and small beam size will cause power to exceed the damage threshold, resulting in damage to optical components and ionization of gas, so the beam cannot continue to transmit. Therefore, how to improve the stability of the beam transmission in the optical multi-pass cell with a convex-concave mirror structure is a problem to be solved at present. SUMMARY

[0004] The purpose of the present application is to provide a method for improving the stability of beam transmission in an optical multi-pass cell with a convex-concave mirror structure. According to the structure parameters of the optical multi-pass cell with a convex-concave mirror structure, a transmission matrix is established, and the eigenvalue of the optical multi-pass cell with a convex-concave mirror structure is quickly and accurately calculated according to the consistency of the q parameter during beam transmission, so as to control the incident beam to work under the condition of satisfying the eigenmode, thereby enabling the beam to be stably transmitted in the multi-pass cell and fully utilizing the performance characteristics of the optical multi-pass cell with a convex-concave mirror structure.

[0005] To achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0006] A method for improving the stability of beam transmission in an optical multi-pass cell with a convex-concave mirror structure, the optical multi-pass cell with a convex-concave mirror structure having a concave mirror and a convex mirror coaxially and oppositely placed. In this method, the structure of "concave mirror-convex mirror" is paraxial approximated and equivalent to a series of "convex lens-concave lens" structure, and the beam is incident along the optical axis. The method of the present application comprises the following steps:

[0007] Step 1, obtaining the structure and optical parameters of the concave-convex mirror structured optical multipass cell, calculating the transmission matrix of the concave mirror, the convex mirror and the air device and material, and further calculating the transmission matrix of the concave-convex mirror structured optical multipass cell under the condition that the light beam is incident from different mirrors.

[0008] Step 2, according to the input parameters of the light beam, the light beam is transmitted once in the concave-convex mirror structured optical multipass cell from one of the mirrors, and then returns to the mirror again, and the q parameter is unchanged, and the light beam eigenvalue of the concave mirror and the convex mirror surface is calculated by using the consistency of the q parameter. The q parameter is a parameter for characterizing the quality of the laser resonant cavity, which is called quality factor.

[0009] Step 3, taking the light beam eigenvalue obtained in step 2 as the size ω of the incident light beam injected into the concave-convex mirror structured optical multipass cell, so that the light beam obtains stable transmission.

[0010] Preferably, the light beam eigenvalue of the concave mirror and the convex mirror surface in the concave-convex mirror structured optical multipass cell is

[0011]

[0012] 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, the calculation of the transmission matrix of the concave mirror, the convex mirror and the air device and material specifically includes:

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

[0020]

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

[0022]

[0023] Step 13, get the distance between the concave mirror and the convex mirror, i.e. the cavity length L, and the gas refractive index n, the transfer matrix is

[0024]

[0025] Preferably, the calculation of the transfer matrix of the concave-convex mirror structure optical multipass cell under the condition that the light beam is incident from different mirrors includes:

[0026] Step 14, assuming that the initial position of the light beam is on the surface of the concave mirror and the light beam is transmitted towards the convex mirror, after one cycle of transmission in the concave-convex mirror structure optical multipass cell, the optical components and media passed are: air with a distance of L→convex mirror→air with a distance of L→concave mirror. The transfer matrix of the optical system composed of the four parts is

[0027]

[0028] Step 15, assuming that the initial position of the light beam is on the surface of the convex mirror and the light beam is transmitted towards the concave mirror, after one cycle of transmission in the concave-convex mirror structure optical multipass cell, the optical components and media passed are: air with a distance of L→concave mirror→air with a distance of L→convex mirror. The transfer matrix of the optical system composed of the four parts is

[0029]

[0030] And the determinant of formula (4) and formula (5) has a relationship

[0031]

[0032] Preferably, the step 2 specifically includes:

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

[0034]

[0035] Step 22, after the light beam of step 21 is transmitted according to step 14, the q parameter q 1out is

[0036]

[0037] Step 23, when the light beam of step 21 passes through the transmission of step 15, the q parameter q of the light beam is 2out For

[0038]

[0039] Step 24, according to the transmission characteristics of the light beam satisfying the eigenvalue in the concave-convex mirror structure optical multipass cell, the size and the curvature radius of the light beam remain unchanged before and after passing through a complete transmission, that is, the q parameter of the light beam transmission is unchanged, then formula (8) and formula (9) exist

[0040]

[0041] Step 20, by simultaneously solving formula (4), formula (5), formula (6), formula (7), formula (8), formula (9), formula (10), the light beam eigenvalue of the concave-convex mirror structure optical multipass cell can be obtained as

[0042]

[0043] It can be seen that by inputting the parameters of each optical device and material of the concave-convex mirror structure optical multipass cell into the above formula, the light beam eigenvalue of the concave-convex mirror structure optical multipass cell can be calculated.

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

[0045] The method of the present application can quickly and accurately calculate the eigenvalue of the concave-convex mirror structure optical multipass cell, so that the designers and researchers can accurately determine the optimal size of the light beam injected into the multipass cell, and predict and evaluate the light beam size of the concave mirror surface and the convex mirror surface in the concave-convex mirror structure optical multipass cell, which not only avoids damage to optical components, but also enhances the stable transmission of the light beam in the concave-convex mirror structure optical multipass cell, improves 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 DRAWINGS

[0046] Figure 1 It is a structure schematic diagram of the concave-convex mirror structure optical multipass cell in the present application;

[0047] Figure 2 It is a paraxial approximation schematic diagram;

[0048] Figure 3Figure (a) in the figure is the light beam transmission contrast diagram of the multi-pass cell under the condition that the beam size is the eigenvalue and the non-eigenvalue respectively, and other parameters are the same; wherein the central wavelength is 1550nm, the multi-pass cell cavity length is 910mm, the concave mirror curvature radius is 1000mm, the convex mirror curvature radius is 900mm, the gas refractive index is 1, and the transmission number is 50 times. Figure 3 Figure (a) in the figure is the light beam transmission contrast diagram of the multi-pass cell under the condition that the beam size is the eigenvalue and the non-eigenvalue respectively, and other parameters are the same; wherein the central wavelength is 1550nm, the multi-pass cell cavity length is 910mm, the concave mirror curvature radius is 1000mm, the convex mirror curvature radius is 900mm, the gas refractive index is 1, and the transmission number is 50 times. Figure 3 Figure (a) in the figure is the light beam transmission contrast diagram of the multi-pass cell under the condition that the beam size is the eigenvalue and the non-eigenvalue respectively, and other parameters are the same; wherein the central wavelength is 1550nm, the multi-pass cell cavity length is 910mm, the concave mirror curvature radius is 1000mm, the convex mirror curvature radius is 900mm, the gas refractive index is 1, and the transmission number is 50 times. DETAILED DESCRIPTION

[0049] The other advantages and effects of the present application can be easily understood by those skilled in the art from the content disclosed in the specification. The present application can also be implemented or applied by other different specific embodiments, and the details in the specification can be modified or changed based on different views and applications without departing from the spirit of the present application. It should be understood that the preferred embodiments are only for illustrating the present application, but not for limiting the protection scope of the present application.

[0050] It should be noted that the figures provided in the following embodiments only illustrate the basic concept of the present application in a schematic manner, and only the components related to the present application are shown in the figures, but not the number, shape and size of the components when actually implemented. The type, number and proportion of each component when actually implemented can be arbitrarily changed, and the component layout type can also be more complex.

[0051] The concave-convex mirror structure optical multi-pass cell structure involved in the present embodiment is shown in Figure 1The optical multipass cell has a concave mirror and a convex mirror coaxially and oppositely arranged. In the case that the structural parameters of the optical multipass cell and the optical parameters of the components are determined, in order to make the incident light beam obtain stable transmission in the multipass cell, the eigenvalue of the concave-convex mirror structure optical multipass cell is accurately calculated, and the incident light beam is injected into the multipass cell with the eigenvalue. The method is to make a paraxial approximation to the "concave mirror-convex mirror" structure, and equivalently to a series of "convex lens-concave lens" structure, and the light beam is incident along the optical axis, and the transmission matrix is calculated, and according to the q parameter of the light beam transmission in the concave-convex mirror structure optical multipass cell, and according to the transmission characteristics of the eigenvalue of the light beam in the concave-convex mirror structure optical multipass cell, the size and the curvature radius of the light beam remain consistent before and after a complete transmission, and the eigenvalue of the light beam is calculated.

[0052] Specifically comprising the following steps:

[0053] Step 1, obtaining the structure and optical parameters of the concave-convex mirror structure optical multipass cell, calculating the transmission matrix of the concave mirror, the convex mirror and the air device and material, and further calculating the transmission matrix of the concave-convex mirror structure optical multipass cell under the condition that the light beam is incident from different mirrors.

[0054] Step 11, determining the curvature radius R1 of the concave mirror, and the focal length f1=R1 / 2, equivalently taking the concave mirror as a convex lens, and the transmission matrix is

[0055]

[0056] Step 12, determining the curvature radius R2 of the convex mirror, and the focal length f2=R2 / 2, equivalently taking the convex mirror as a concave lens, and the transmission matrix is

[0057]

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

[0059]

[0060] Step 14, assuming that the initial position of the light beam is located on the surface of the concave mirror and is transmitted towards the convex mirror, and after one cycle of transmission in the concave-convex mirror structure optical multipass cell, the optical components and media passed are: air with a distance of L→convex mirror→air with a distance of L→concave mirror. The transmission matrix of the optical system composed of the four parts is

[0061]

[0062] Step 15, assuming the initial position of the light beam is on the convex mirror surface, and the transmission is in the direction of the concave mirror, after one cycle of transmission in the concave-convex mirror structure optical multipass cell, the optical components and media passed are: air with a distance of L → concave mirror → air with a distance of L → convex mirror. After the transmission of the optical system composed of the four parts, its transmission matrix is

[0063]

[0064] And the determinant of formula (4) and formula (5) has a relationship

[0065]

[0066] Step 2, according to the q parameter of the light beam transmission in the concave-convex mirror structure optical multipass cell:

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

[0068]

[0069] Step 22, after the light beam of step 21 undergoes the transmission of step 14, its q parameter q 1out is

[0070]

[0071] Step 23, after the light beam of step 21 undergoes the transmission of step 15, its q parameter q 2out is

[0072]

[0073] Step 24, according to the transmission characteristics of the light beam satisfying the eigenvalue in the concave-convex mirror structure optical multipass cell, the size and curvature radius of the light beam remain consistent before and after one complete transmission, then formula (8) and formula (9) have

[0074]

[0075] Step 25, by simultaneously solving formula (4), formula (5), formula (6), formula (7), formula (8), formula (9), and formula (10), the eigenvalue of the light beam on the surface of the concave mirror and the convex mirror in the concave-convex mirror structure optical multipass cell is

[0076]

[0077] 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 a concave-convex mirror structure optical multipass cell structure, in the case of determining the center wavelength of the incident light beam 1550 nm, the multipass cell cavity length 910 mm, the concave mirror radius of curvature 1000 mm, the convex mirror radius of curvature 900 mm, the gas refractive index 1, etc. Parameters, the eigenvalue of the light beam on the surface of the concave-convex mirror in the concave-convex mirror structure optical multipass cell can be calculated as 1.5314 mm and 0.3240 mm respectively, and the wavefront curvature radius of them is the radius of curvature of the concave mirror and the convex mirror respectively.

[0084] As a verification, two incident light beams with a beam size of 1.5314 mm and a wavefront curvature radius of 1000 mm and a beam size of 0.3240 mm and a wavefront curvature radius of 900 mm are injected into the above-mentioned structure multipass cell from the surfaces of the concave mirror and the convex mirror respectively, and the beam size on the surface of the concave mirror and the convex mirror is transmitted in the multipass cell for 50 times. As shown by the gray solid lines in (a) and (b), the beam size is consistent and very stable after 50 times, which accords with the theory of the resonant cavity and also verifies the correctness of the calculation method of the eigenvalue of the concave-convex mirror structure optical multipass cell proposed in the present application. Figure 3

[0085] As a comparison, two light beams with a beam size that is not the eigenvalue of the multipass cell are injected, the beam size incident from the surface of the concave mirror is 1.400 mm, and the beam size incident from the surface of the convex mirror is 0.3200 mm, and the initial curvature radius is the curvature radius of the corresponding mirror, and the beam size on the surface of the two mirrors is irradiated every time. As shown by the gray solid lines in (a) and (b), the beam size is not consistent and very unstable after 50 times, which does not accord with the theory of the resonant cavity. Figure 3 ​As shown by the black solid line in (a) and (b) in the figure, although the difference between the injected beam size and the eigenvalue is only at the level of about 100 μm and about 10 μm, the fluctuation is very large after the transmission of the concave-convex mirror structure optical multipass cell for dozens of times. The larger beam reduces the quantum effect and the nonlinear effect, and the smaller beam brings huge light power per unit area, which is easy to damage the optical device. Therefore, the calculation of the eigenvalue of the concave-convex mirror structure optical multipass cell provides guidance for the evaluation of the multipass cell structure and the prediction of the beam transmission, which also verifies the importance and feasibility of the present application.

[0086] The above shows and describes the basic principles, main features and advantages of the present application. Those skilled in the art should understand that the present application is not limited to the above-mentioned embodiments, and the above-mentioned embodiments and descriptions in the specification are only the principles of the present application. Various changes and improvements can be made without departing from the spirit and scope of the present application, and these changes and improvements all fall within the scope of the claimed present application. The scope of protection required by the present application is defined by the appended claims and their equivalents.

Claims

1. A method for improving the stability of the light beam transmission of a multi-pass cell with a concave-convex mirror structure, characterized in that, The concave-convex mirror structure optical multipass cell has a concave mirror and a convex mirror coaxially and oppositely arranged, the structure of "concave mirror-convex mirror" is paraxial approximated and equivalent to a series of "convex lens-concave lens" structures, and a light beam is incident along an optical axis; the method comprises the following steps: Step 1, obtaining the structure and optical parameters of the concave-convex mirror structured optical multipass cell, including the central wavelength of the incident laser λ , the curvature radius of the concave mirror R 1, the curvature radius of the convex mirror R 2, the distance between the concave mirror and the convex mirror is L air, the refractive index of the gas n , respectively calculating the transmission matrix of the concave mirror, the convex mirror and the air, and further calculating the transmission matrix of the concave-convex mirror structured optical multipass cell under the condition that the light beam is incident from different mirrors; Step 2, according to the input parameters of the light beam, the light beam is transmitted from one of the face mirrors in the concave-convex mirror structure optical multi-pass cell, and then returned to the face mirror again, q The parameters are consistent, and the eigenvalues of the light beams on the surfaces of the concave mirror and the convex mirror are calculated. q The parameters are consistent, and the eigenvalues of the light beams on the surfaces of the concave mirror and the convex mirror are calculated. Step 3, using the beam eigenvalue obtained in Step 2 as the size of the incident beam of the injection concave-convex mirror structure optical multipass cell ω so that the light beam is stably transmitted.

2. The method for improving the stability of the light beam transmission of a multi-pass cell with a structured optical surface according to claim 1, characterized in that, Eigenvalues of a light beam on surfaces of the concave mirror and the convex mirror in the concave-convex mirror structure optical multipass cell are as follows: ， wherein , , , , , 。 3. The method for improving the stability of the light beam transmission of a multi-pass cell with a structured optical surface according to claim 1, characterized in that, In the step 1, the calculation of the transmission matrix of the concave mirror, the convex mirror and air comprises: Step 11, calculating the transmission matrix M1 of the concave mirror: obtaining the curvature radius of the concave mirror R 1, then the focal length is f 1= R 1 / 2, the concave mirror is equivalent to a convex lens, and the transmission matrix M1 of the concave mirror is: (1), Step 12, calculating the transmission matrix M2 of the convex mirror: obtaining the curvature radius of the convex mirror R 2, the focal length is f 2= R 2 / 2, the convex mirror is equivalent to a concave lens, and the transmission matrix M2 of the convex mirror is: (2), Step 13, Calculate the transmission matrix M of air air : Obtain the distance between the concave mirror and the convex mirror, i.e. the cavity length L , the gas refractive index n , then the distance is L The transmission matrix of air is: (3)。 4. The method for improving the stability of the light beam transmission of a multi-pass cell with a structured optical surface according to claim 3, characterized in that, In the step 1, the calculation of the transmission matrix of the concave-convex mirror structure optical multipass cell under the condition that a light beam is incident from different mirrors comprises: Step 14, calculate the transfer matrix M of optical system a a : Assuming that the initial position of the light beam is on the surface of the concave mirror, and the transmission direction is towards the convex mirror, for the optical system a, the light beam passes through a period of transmission in the concave-convex mirror structure optical multi-pass cell, then the transfer matrix M of the optical system a is: a : (4), Step 15, calculate the transfer matrix M of optical system b b : Assuming that the initial position of the light beam is on the surface of the convex mirror and is transmitted towards the concave mirror, the transfer matrix M of optical system b for one period of transmission in the concave-convex mirror structure optical multipass cell is: b : (5), And the determinants of the formula (4) and the formula (5) have a relationship (6)。 5. The method for improving the stability of the light beam transmission of a multi-pass cell with a structured optical surface according to claim 4, characterized in that, The step 2 comprises: Step 21, for a wavelength of λ , the radius of the input Gaussian beam is ω in , the radius of curvature of the wavefront is R in , the transmission of the beam in the concave-convex mirror structure optical multipass cell is q parameters q in : (7), Step 22, after the light beam of step 21 has passed through the transport of step 14, it is q parameters q 1out for (8), Step 23, after the light beam of step 21 has passed through the transport of step 15, it is q parameters q 2out for (9), In the step 24, according to the transmission characteristics of a light beam satisfying the eigenvalues in the concave-convex mirror structure optical multipass cell, the size and the curvature radius of the light beam remain consistent before and after one complete transmission, and the formula (8) and the formula (9) have (10), In the step 25, by simultaneously solving the formula (4), the formula (5), the formula (6), the formula (7), the formula (8), the formula (9) and the formula (10), the eigenvalues of the light beam on the surfaces of the concave mirror and the convex mirror in the concave-convex mirror structure optical multipass cell are as follows: (11)。

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