Mode programmable laser generator based on degenerate cavity
By using a degenerate cavity-based mode-programmable laser generator, combined with components such as a 4-f self-imaging system and a liquid crystal spatial light modulator, efficient control of laser modes is achieved, solving the problems of low mode purity and poor beam quality in traditional lasers, and enabling flexible control of multiple transverse modes and polarization modes.
Patent Information
- Application Number
- CN202423242661.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Utility models(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-27
- Publication Date
- 2026-01-02
- Estimated Expiration
- 2034-12-27
AI Technical Summary
Traditional lasers, due to limitations in the geometric aperture of optical components and end-pumping methods, cannot effectively control high-order cavity modes, resulting in low mode purity and poor beam quality. Furthermore, existing methods for controlling the external optical field are inefficient and lack flexibility.
A degenerate cavity-based mode-programmable laser generator is employed. By combining a 4-f self-imaging system, a liquid crystal spatial light modulator, a gain medium, a pinhole aperture, an FP etalon, and a waveplate, the transverse, longitudinal, and polarization modes of the resonant cavity are controlled. The laser mode is controlled by loading and calculating a hologram using the liquid crystal spatial light modulator.
It achieves efficient real-time control of laser modes, improves mode purity and beam quality, supports multi-transverse mode resonance, flexibly controls longitudinal and polarization modes, and enhances the laser's optical field control capability.
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Figure CN223757844U_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of laser technology, in particular to a mode programmable laser generator based on a degenerate cavity. BACKGROUND
[0002] Optical field regulation refers to regulating the spatial, frequency, polarization and other parameters of the optical field through various optical elements or technical means, which has great application prospects in the fields of optical imaging, laser processing, optical communication, optical sensing and the like. However, due to the limitation of the geometric aperture of the optical element and the end-pumping mode, the traditional laser can only generate low-order cavity eigenmodes, and has the disadvantages of low mode purity and poor beam quality.
[0003] For the regulation of the optical field outside the cavity, the conversion efficiency is low and the regulation cannot be flexibly controlled by using anastigmatic elements, spiral phase plates, liquid crystal spatial light modulators and the like. In addition, although methods for regulating the degrees of freedom have been proposed in the field of lasers, most of them are limited to the regulation of a single degree of freedom.
[0004] Therefore, in view of the application fields of optical manipulation, laser communication, material processing and the like, it is urgent to develop a mode programmable laser generator based on a degenerate cavity. SUMMARY
[0005] The present application aims to solve the above problems and deficiencies, and provides a mode programmable laser generator based on a degenerate cavity, which can effectively regulate the transverse mode, longitudinal mode and polarization mode of the resonant cavity, and further realize the effect of programming the laser mode.
[0006] To achieve the above-mentioned purpose, the technical solution adopted is:
[0007] The present application provides a mode programmable laser generator based on a degenerate cavity, comprising:
[0008] a resonant cavity comprising a liquid crystal surface of a liquid crystal spatial light modulator and an output coupling mirror arranged in parallel;
[0009] a 4-f self-imaging system arranged in the resonant cavity, the 4-f self-imaging system comprising a first thin lens and a second thin lens arranged coaxially;
[0010] a gain medium arranged between the liquid crystal spatial light modulator and the first thin lens;
[0011] a pinhole diaphragm arranged between the first thin lens and the second thin lens, the resonant cavity, the 4-f self-imaging system, the gain medium and the pinhole diaphragm being coaxial;
[0012] a linear polarizer arranged between the gain medium and the pinhole diaphragm;
[0013] a F-P etalon, which is obliquely arranged between the pinhole diaphragm and the second thin lens;
[0014] a wave plate set, which is arranged outside the resonant cavity close to one end of the output coupling mirror, and is used for controlling the polarization mode of the output light field of the resonant cavity;
[0015] and a pump source, which is arranged at the side of the gain medium, and is used for providing energy for the generation of laser.
[0016] According to the mode programmable laser generator based on the degenerate cavity, further, the first thin lens and the second thin lens are both circular and convex.
[0017] According to the mode programmable laser generator based on the degenerate cavity, further, the back focal plane of the first thin lens and the front focal plane of the second thin lens are coincident to form a common focal plane.
[0018] According to the mode programmable laser generator based on the degenerate cavity, further, the pinhole diaphragm is arranged at the common focal plane.
[0019] According to the mode programmable laser generator based on the degenerate cavity, further, the liquid crystal spatial light modulator is located at the front focal plane of the thin lens.
[0020] According to the mode programmable laser generator based on the degenerate cavity, further, the output coupling mirror is arranged at the back focal plane of the second thin lens.
[0021] According to the mode programmable laser generator based on the degenerate cavity, further, the wave plate set includes a half wave plate and a quarter wave plate arranged in parallel, and the half wave plate is arranged between the output coupling mirror and the quarter wave plate.
[0022] According to the mode programmable laser generator based on the degenerate cavity, further, the calculation equation of the resonant frequency of the eigenmode of the resonant cavity is shown in formula 1,
[0023]
[0024] The v qmn is the resonant frequency of the eigenmode of the resonant cavity, the q is the longitudinal mode number of the eigenmode of the resonant cavity, the m is a transverse mode number of the eigenmode of the resonant cavity, the n is another transverse mode number of the eigenmode of the resonant cavity, the c is the speed of light in vacuum, the L is the optical length of the resonant cavity, the A is the position transmission factor of the eigenmode of the resonant cavity, and the D is the angle retention factor of the eigenmode of the resonant cavity, wherein A=D=1.
[0025] According to the mode programmable laser generator based on the degenerate cavity of the application, further, the calculation equation of the spectral line full width at half maximum of the F-P etalon is shown as formula 2,
[0026]
[0027] The △v is the spectral line full width at half maximum of the F-P etalon reflecting surface, the c is the light speed in vacuum, the d is the thickness of the F-P etalon, the θ is the included angle between the normal of the side surface of the F-P etalon and the resonant cavity axis, the R is the reflectivity of the F-P etalon reflecting surface, and μ is the refractive index of the F-P etalon.
[0028] The above technical scheme has the following beneficial effects:
[0029] The application has the advantages of ingenious design and reasonable structure. The side pumping technology is adopted to realize uniform pumping of the working substance of the laser while reducing the complexity of the device. Starting from three degrees of freedom of the optical field, i.e. the transverse mode, the longitudinal mode and the polarization mode, the control of the transverse mode is realized through the multi-transverse mode degenerate characteristics of the self-imaging system, the liquid crystal spatial light modulator and the pinhole aperture limiting mode structure, the control of the longitudinal mode is realized through the F-P etalon, and the control of the polarization mode is realized through the combined wave plate, so that the high-efficiency real-time regulation and control of the laser of any mode are realized. BRIEF DESCRIPTION OF DRAWINGS
[0030] In order to more clearly illustrate the technical solutions of the embodiments of the application, the drawings of the embodiments of the application will be briefly introduced below. The drawings are only used to show some embodiments of the application, and the application is not limited to the drawings.
[0031] Figure 1 is a structural schematic diagram of the mode programmable laser generator based on the degenerate cavity of the embodiment of the application;
[0032] Figure 2 is a structural schematic diagram of the F-P etalon of the embodiment of the application;
[0033] Figure 3 is an experimental result diagram of the mode programmable laser generator based on the degenerate cavity of the embodiment of the application.
[0034] The meanings represented by the serial numbers in the drawings are as follows:
[0035] 1. Liquid crystal spatial light modulator, 2. Gain medium, 3. Pump source, 4. First thin lens, 5. Linear polarizer, 6. Pinhole aperture, 7. F-P etalon, 8. Second thin lens, 9. Output coupling mirror, 10. Half-wave plate, 11. Quarter-wave plate. DETAILED DESCRIPTION
[0036] The exemplary solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art.
[0037] like Figure 1 As shown, the degenerate cavity-based mode programmable laser generator of this embodiment includes a resonant cavity, a 4-f self-imaging system, a gain medium 2, a pinhole aperture 6, a linear polarizer 5, an FP etalon 7, and a waveplate group. The resonant cavity includes the liquid crystal panel of the parallel-arranged liquid crystal spatial light modulator 1 and the output coupling mirror 9; a 4-f self-imaging system is disposed within the resonant cavity, including a first thin lens 4 and a second thin lens 8 arranged coaxially; a gain medium 2 is disposed between the liquid crystal spatial light modulator 1 and the first thin lens 4; a pinhole aperture 6 is disposed between the first thin lens 4 and the second thin lens 8, and the resonant cavity, the 4-f self-imaging system, the gain medium 2, and the pinhole aperture 6 are arranged coaxially; a linear polarizer 5 is disposed between the gain medium 2 and the pinhole aperture 6; an FP etalon is tilted between the pinhole aperture 2 and the second thin lens 8; a waveplate group is disposed outside the resonant cavity near the output coupling mirror 9, and the waveplate group is used to control the polarization mode of the output light field of the resonant cavity; a pump source 3 is disposed on the side of the gain medium, and the pump source 3 is used to provide energy for laser generation.
[0038] The resonant cavity formed by the liquid crystal spatial light modulator 1 and the output coupling mirror 9 extends the working length of the gain medium 2 by reflecting light back and forth within the cavity. Furthermore, the liquid crystal panel of the spatial light modulator 1 loads a computational hologram to control the loss in different regions of the target mode within the resonant cavity, suppressing non-target modes and achieving transverse mode control of the laser.
[0039] The first thin lens 4 and the second thin lens 8 form a 4-f self-imaging system, which enables the light field of the liquid crystal spatial light modulator 1 to be self-reproduced on the output coupling mirror 8 after a single-pass transit, reducing the diffraction loss of higher-order modes and enabling the cavity to support multi-transverse mode resonance.
[0040] As a transverse mode selector, the pinhole aperture 6 increases the loss of higher-order modes in the spectral plane, increases the mode loss spacing, reduces the number of oscillating modes for modes with the same quality factor, and controls the number of transverse modes.
[0041] Linear polarizer 5 is used to control the polarization state of the light field.
[0042] The FP etalon 7 uses longitudinal filtering of the optical field by adjusting its angle and length to achieve controllable longitudinal mode output.
[0043] Half-wave plate 10 controls the polarization direction of the light field, quarter-wave plate 11 controls the ellipticity and chirality of the resonant cavity output light field, and the combination of the two wave plates can achieve polarization mode control.
[0044] Gain medium 2 is used to achieve population inversion and increase the optical energy density, and determines the wavelength of the laser.
[0045] Pump source 3 acts as an energy source, emitting photons to pump the electrons in the gain medium from the ground state to the high energy level to achieve population inversion.
[0046] Optionally, the liquid crystal spatial light modulator 1 adopts a high-power phase-type liquid crystal spatial light modulator, loads a calculated hologram to match the corresponding light field mode, or realizes amplitude modulation of the target light field through the chessboard grating method and the blazed grating method.
[0047] Optionally, the liquid crystal spatial light modulator 1 adopts a high-power amplitude-type spatial light modulator.
[0048] Optionally, the gain medium 2 is in a cylindrical or cuboid shape.
[0049] Optionally, the gain medium 2 can be a solid gain medium doped with neodymium ions (Nd 3+ ), such as neodymium-doped yttrium aluminum garnet laser crystal (Nd:YAG), neodymium-doped yttrium lithium fluoride crystal (Nd:YLF), and neodymium-doped yttrium vanadate crystal (Nd:YVO4), with a concentration of 0.8at%-1.2at% and a thickness of 1-3mm.
[0050] Optionally, the gain medium 2 can be a quantum well material.
[0051] Optionally, the gain medium 2 and the pump source 3 are arranged together between the liquid crystal spatial light modulator 1 and the thin lens 4, or between the thin lens 8 and the output coupling mirror 9.
[0052] Further, the linear polarizer 5 needs to have high transmittance for the laser wavelength. Optionally, the linear polarizer 5 can adopt a dichroic polarizing lens or a crystal polarizing lens or a wire grid polarizing lens. In addition, the laser wavelength range here is 800nm-1600nm.
[0053] Optionally, the laser wavelength is 808nm, 1064nm or 1550nm.
[0054] Optionally, the pump source 3 can adopt a high-power device such as a xenon lamp or a semiconductor laser.
[0055] As shown in Figure 1 , the first thin lens 4 and the second thin lens 8 are both circular and are both convex lenses.
[0056] Optionally, the first thin lens 4 and the second thin lens 8 can adopt a biconvex lens or a plano-convex lens with a focal length of 20 cm or 30 cm, and the surfaces of the first thin lens 4 and the second thin lens 8 need to be coated with a high-transmittance film layer for the laser wavelength. In addition, the laser wavelength range here is 800 nm-1600 nm.
[0057] Optionally, the laser wavelength is 808 nm, 1064 nm or 1550 nm.
[0058] Optionally, the diameter of the first thin lens 4 and the second thin lens 8 is 25.4 cm or 50.8 cm.
[0059] As shown in Figure 1 , the back focal plane of the first thin lens 4 coincides with the front focal plane of the second thin lens 8 to become a common focal plane.
[0060] As shown in Figure 1 , the pinhole diaphragm 6 is arranged at the common focal plane of the first thin lens 4 and the second thin lens 8.
[0061] Optionally, the pinhole diaphragm 6 can adopt a square diaphragm or a circular diaphragm structure, and the aperture is continuously adjustable in the range of 1 mm-10 mm.
[0062] As shown in Figure 1 , the liquid crystal spatial light modulator 1 is located at the front focal plane of the first thin lens 4.
[0063] As shown in Figure 1 , the output coupling mirror 9 is arranged at the back focal plane of the second thin lens 8.
[0064] Optionally, the output coupling mirror 9 can adopt a reflection:transmission split ratio of 5:5, 6:4, 7:3, etc., and the surface of the output coupling mirror 9 needs to be coated with a reflection and transmission film layer for the laser wavelength, and the diameter is 25.4 cm, 50.8 cm. In addition, the wavelength range here is 800 nm-1600 nm.
[0065] Optionally, the laser wavelength is 808 nm, 1064 nm or 1550 nm.
[0066] Optionally, the F-P etalon 7 can adopt a solid single-cavity etalon or an air gap etalon.
[0067] As shown in Figure 1 , the wave plate set includes a half-wave plate 10 and a quarter-wave plate 11 arranged in parallel, and the half-wave plate 10 is arranged between the output coupling mirror 9 and the quarter-wave plate 11.
[0068] Optionally, the half-wave plate 10 can adopt a zero-order wave plate or a true zero-order wave plate or a multi-order wave plate or a quartz wave plate or a polymer wave plate or an air gap wave plate.
[0069] Optionally, the quarter-wave plate 11 can be a zero-order wave plate or a true zero-order wave plate or a multi-order wave plate or a quartz wave plate or a polymer wave plate or an air gap wave plate.
[0070] In the present application, the calculation equation of the resonant frequency of the resonant cavity eigenmode is shown in Formula 1,
[0071]
[0072] where v qmn is the resonant frequency of the resonant cavity eigenmode, q is the longitudinal mode order number of the resonant cavity eigenmode, m is a transverse mode order number of the resonant cavity eigenmode, n is another transverse mode order number of the resonant cavity eigenmode, c is the speed of light in vacuum, L is the optical length of the resonant cavity, A is the position transmission factor of the resonant cavity eigenmode, D is the angle retention factor of the resonant cavity eigenmode, and A = D = 1.
[0073] In the present application, the resonant cavity regulates the transverse mode as follows:
[0074] By bringing A = D = 1 into Formula 1, we can obtain: It can be seen from this that the resonant frequency v qmn of the eigenmode of the resonant cavity in the present application is only related to the speed of light in vacuum c, the optical length L of the resonant cavity, and the longitudinal mode order number q, and is independent of the two transverse mode order numbers m and n. This indicates that all the transverse mode patterns in the resonant cavity are completely degenerate, and the frequency is independent of the transverse mode order number, so the resonant cavity of the device supports the resonance of any transverse mode.
[0075] On this basis, the liquid crystal spatial light modulator 1 is used to load the calculation hologram of the target transverse mode in the resonant cavity, and is matched with the phase of the transverse mode of the resonant cavity, so as to realize the lasing of the target transverse mode in the resonant cavity.
[0076] In addition, in order to avoid the lasing of other high-order modes, the pinhole diaphragm 6 is used to realize the transverse mode loss control in the resonant cavity, and the principle is as follows: the total loss of the laser mode TEMmn is shown in Formula 2,
[0077]
[0078] where γ mn represents the total loss of the laser mode TEMmn in the resonant cavity, represents the additional loss of each additional element in the resonant cavity, represents the diffraction loss of the laser mode TEMmn in the resonant cavity, represents the sum of the transmission loss, absorption, scattering loss, etc. of each optical element. In the different laser modes of the 4-f self-imaging system, and are basically the same, and The light intensity distribution of the target mode can be adjusted. Therefore, the pinhole diaphragm 6 is introduced into the resonant cavity as a high-order mode loss, so that it cannot oscillate because the loss does not meet the laser oscillation condition.
[0079] Through the cooperation between the multi-transverse mode degeneracy characteristics of the 4-f self-imaging system, the phase control ability of the liquid crystal spatial light modulator 1 and the additional loss of the pinhole diaphragm 6, the adjustment of any order transverse mode in the resonant cavity is realized.
[0080] In this application, the calculation equation of the full width at half maximum of the spectrum line of the F-P etalon is shown in formula 3,
[0081]
[0082] △v is the full width at half maximum of the spectrum line of the F-P etalon, c is the speed of light in vacuum, d is the thickness of the F-P etalon, θ is the included angle between the normal of the side surface of the F-P etalon and the axis of the resonant cavity, R is the reflectivity of the F-P etalon, and μ is the refractive index of the F-P etalon.
[0083] In this application, the resonant cavity adjusts the longitudinal mode as follows:
[0084] The F-P etalon 7 is arranged obliquely between the pinhole diaphragm 6 and the second thin lens 8, so as to avoid the formation of parasitic oscillation of the F-P etalon 7 in the resonant cavity.
[0085] In addition, the F-P etalon 7 has extremely high transmission to the longitudinal mode of the resonant cavity with a frequency , θ is the included angle between the normal of the side surface of the F-P etalon and the axis of the resonant cavity, c is the speed of light in vacuum, d is the thickness of the F-P etalon, and q is the longitudinal mode number.
[0086] In the resonant cavity, by adjusting the thickness and the inclination angle of the F-P etalon 7, the light that does not meet the maximum transmission condition of the etalon is attenuated, so as to realize the adjustment of the longitudinal mode frequency, the free spectral range and the full width at half maximum in the resonant cavity.
[0087] In this application, the resonant cavity adjusts the polarization mode as follows:
[0088] The linear polarizer 5 is arranged between the first thin lens 4 and the pinhole diaphragm 6, and at this time, the light emitted from the output coupling 9 of the resonant cavity is linearly polarized light. When the linearly polarized light passes through the half-wave plate 10, the polarization direction of the linearly polarized light is deflected, that is, the polarization direction of the linearly polarized light is adjusted by using the half-wave plate 10.
[0089] Subsequently, the light passes through the quarter-wave plate 11. If the fast axis of the quarter-wave plate 11 is consistent with the polarization direction of the incident light, the emergent light passing through the quarter-wave plate 11 is still linearly polarized light. At this time, the quarter-wave plate 11 needs to be adjusted so that the fast axis of the quarter-wave plate 11 is inconsistent with the polarization direction of the incident light, so that the emergent light passing through the quarter-wave plate 11 becomes elliptically polarized light or circularly polarized light.
[0090] Through the cooperation of the half-wave plate 10 and the quarter-wave plate 11, the control of any polarization mode in the resonant cavity is realized.
[0091] As shown in the figure, the normalized gray value in the figure represents the light intensity, and each light spot represents a single independent mode. The number of modes is 12, indicating that the spatial light modulator can realize the control of the laser mode. Figure 3
[0092] The technical scheme of the present application is described above in conjunction with the drawings. Obviously, the specific implementation of the present application is not limited by the above manner. Any non-essential improvement or direct application of the inventive concept and technical scheme to other occasions is within the protection scope of the present application.
[0093] In the description of the present application, it should be understood that the expressions of "first", "second" are used to describe the elements of the present application, and do not represent any order, quantity or importance limitation, but only to distinguish one component from another.
[0094] It should be noted that when an element is described as "connected", "coupled" or "linked" to another element, it can mean that it is directly connected, coupled or linked to the other element, but it should be understood that there can be intermediate elements between the two. That is, it covers both direct connection and indirect connection.
[0095] It should be noted that the use of "one" or "a" and similar words does not necessarily mean a quantity limitation. The words "including" or "containing" and similar words mean that the elements or objects before the words cover the elements or objects listed after the words and their equivalents, without excluding other elements or objects.
[0096] It should be noted that the terms indicating the relative position or location relationship, such as "up", "down", "left", "right", etc. are used only to represent the relative position relationship, which is for the convenience of describing the present application, and the devices or elements referred to must have a specific orientation, be constructed and operated in a specific orientation. When the absolute position of the described object changes, the relative position relationship may also change accordingly.
[0097] While the preferred embodiments of the application have been described above, it should be understood that they have been presented by way of example only, and not limitation. Although the application has been described with regard to only a limited number of embodiments, it should be appreciated that many variations, modifications and alternatives are possible within the scope of the application. Numerous specific details have been set forth in this description in order to provide a thorough understanding of the application. The details disclosed herein are not intended to limit the application; rather they are intended to provide description of the application. Finally, it should be appreciated that certain features of the application that are, for clarity, described above and depicted in the drawings can be provided in less than all of the embodiments of the application. Therefore, the scope of the application is indicated by the appended claims rather than by the description preceding them.
Claims
1. A mode programmable laser generator based on a degenerate cavity, characterized in that, The resonant cavity comprises a liquid crystal panel of a liquid crystal spatial light modulator and an output coupling mirror arranged in parallel; a 4-f self-imaging system arranged in the resonant cavity, the 4-f self-imaging system comprising coaxially arranged first and second thin lenses; a gain medium arranged between the liquid crystal spatial light modulator and the first thin lens; a pinhole diaphragm arranged between the first and second thin lenses, the resonant cavity, 4-f self-imaging system, gain medium and pinhole diaphragm being coaxial; a linear polarizer arranged between the gain medium and the pinhole diaphragm; an F-P etalon arranged obliquely between the pinhole diaphragm and the second thin lens; a wave plate group arranged outside the resonant cavity close to one end of the output coupling mirror, the wave plate group being used to control the polarization mode of the output light field of the resonant cavity; and a pump source arranged at the side of the gain medium, the pump source being used to provide energy for the generation of laser. The first and second thin lenses are both circular and convex.
2. The degenerate cavity based mode programmable laser generator of claim 1, wherein, The back focal plane of the first thin lens coincides with the front focal plane of the second thin lens to form a common focal plane.
3. The degenerate cavity based mode programmable laser generator of claim 2, wherein, The pinhole diaphragm is arranged at the common focal plane.
4. The degenerate cavity based mode programmable laser generator of claim 3, wherein, The liquid crystal spatial light modulator is located at the front focal plane of the first thin lens.
5. The degenerate cavity based mode programmable laser generator of claim 2, wherein, The output coupling mirror is arranged at the back focal plane of the second thin lens.
6. The degenerate cavity based mode programmable laser generator of claim 5, wherein, The wave plate group comprises a half wave plate and a quarter wave plate arranged in parallel, and the half wave plate is arranged between the output coupling mirror and the quarter wave plate.
7. The degenerate cavity based mode programmable laser generator of claim 1, wherein, The calculation equation of the resonant frequency of the eigenmode of the resonant cavity is shown in Formula 1, 8. The degenerate cavity based mode programmable laser generator of claim 1, wherein, the calculation equation of the full width at half maximum of the spectral line of the F-P etalon is shown in Formula 2, The v qmn is the resonance frequency of the eigenmode of the resonator, q is the longitudinal mode number of the eigenmode of the resonator, m is a transverse mode number of the eigenmode of the resonator, n is another transverse mode number of the eigenmode of the resonator, c is the speed of light in vacuum, L is the optical length of the resonator, A is the position transmission factor of the eigenmode of the resonator, and D is the angle holding factor of the eigenmode of the resonator, wherein A = D = 1.
9. The degenerate cavity based mode programmable laser generator of claim 8, wherein, where Δv is the full width at half maximum of the spectral line of the F-P etalon reflecting surface, c is the speed of light in vacuum, d is the thickness of the F-P etalon, θ is the included angle between the normal of the side surface of the F-P etalon and the axis of the resonant cavity, R is the reflectivity of the reflecting surface of the F-P etalon, and μ is the refractive index of the F-P etalon.