Micro-cavity optical comb frequency stabilization system based on saturated absorption spectrum and CPT effect

Abstract

The invention discloses a micro-cavity optical comb frequency stabilization system based on a saturated absorption spectrum and a CPT effect, and belongs to the field of micro-cavity optical combs and wavelength frequency stabilization. The device comprises a microcavity optical comb module, a pump light source module, a saturated absorption spectrum frequency stabilization module and a CPT frequency stabilization module. The pump light module comprises a pump laser and an optical amplifier. The saturated absorption spectrum frequency stabilization module comprises an atomic gas chamber physical system and a light path used for achieving the saturated absorption effect. Micro-cavity optical comb excitation is achieved through a thermal tuning method, a sideband is generated by modulating pump light, decoupling of micro-cavity optical comb repetition frequency and micro-cavity optical comb pump light is achieved based on the micro-cavity injection locking principle, and the micro-cavity optical comb repetition frequency is equal to alkali metal atom ground state hyperfine energy level frequency difference. The CPT frequency stabilization module comprises an atomic air chamber physical system, the CPT effect is excited through microcavity optical comb pump light and sideband light of the microcavity optical comb pump light, and the repetition frequency of the microcavity optical comb is referred to the atomic transition frequency. Two degrees of freedom of the micro-cavity optical comb are stabilized based on the saturated absorption spectrum and the CPT effect, so that frequency stabilization of the micro-cavity optical comb is realized.

Description

Technical Field

[0001] The present invention relates to a frequency stabilization system based on a microcavity optical comb, in particular to a frequency stabilization system based on a saturated absorption spectrum and a CPT effect, and belongs to the field of microcavity optical comb and laser frequency stabilization. Background Art

[0002] The optical frequency comb is a periodic pulse sequence in the time domain and a comb with equal frequency intervals in the frequency domain. The comb teeth (frequency components) are coherent and have a stable phase relationship. Based on the fact that the optical frequency comb can achieve frequency linking from optical frequency to microwave, it is regarded as the most effective optical frequency measurement tool and has a wide range of applications in the fields of spectroscopy and laser precision measurement. In particular, the invention of the f-2f self-reference locking technology of the optical frequency comb has greatly improved the frequency stability of the optical frequency comb, making each frequency component of the optical frequency comb traceable, so that the optical frequency comb can play a huge role in the field of precision measurement and metrology. In recent years, with the development of a new generation of high-speed optical communications and microwave photonic technologies, a higher repetition rate of the optical frequency comb is needed to meet system requirements. The microcavity optical comb generated by the high-quality factor microcavity based on continuous light pumping provides a new technical possibility. When the pump laser is in red detuning, a microcavity Kerr soliton optical frequency comb can be realized based on the microcavity. While having the coherence of the optical frequency comb teeth, the comb teeth have narrow linewidth characteristics due to the filtering effect of the microcavity. And because the microcavity size is small and the free spectral range is large, a microcavity optical comb with a very high repetition rate can be generated, which greatly expands the application range of optical frequency combs. However, it is extremely difficult for a microcavity optical comb to obtain an octave, and it is difficult to achieve self-reference locking of the optical frequency comb based on the f-2f method. The existing technical solution is based on the dual-comb interlocking of an octave microcavity optical comb with a terahertz repetition rate and a microwave repetition rate microcavity optical comb to achieve full-frequency domain frequency stabilization of the optical frequency comb. The system is complex and difficult. On the other hand, since the microcavity optical comb belongs to a complex dynamic system, the repetition frequency of the microcavity optical comb and the pump light are coupled together and cannot be tuned independently. This further increases the difficulty of frequency stabilization of the microcavity optical comb. Summary of the invention

[0003] The purpose of the present invention is to provide a microcavity optical comb frequency stabilization system based on saturation absorption spectrum and CPT effect. Based on the principle of heat-assisted laser, the microcavity optical comb is excited by the method of microcavity thermal tuning, and the microcavity injection locking effect is used to realize the decoupling of the repetition frequency of the microcavity optical comb and the pump light. Based on the saturation absorption spectrum and the CPT effect, the pump light and the repetition frequency of the microcavity optical comb are locked respectively. Based on the characteristic that the comb tooth spacing of the microcavity optical comb is equal to the repetition frequency of the microcavity optical comb, by stabilizing the comb tooth spacing and the pump comb teeth, each comb tooth of the microcavity optical comb is referenced to the atomic transition frequency, thereby realizing the frequency stabilization of the microcavity optical comb. The present invention can reduce the loop noise of the frequency stabilization system and improve the frequency stability of the frequency stabilization system.

[0004] The objective of the present invention is achieved through the following technical solutions:

[0005] The microcavity optical comb frequency stabilization system based on saturation absorption spectrum and CPT effect disclosed in the present invention comprises a microcavity optical comb module, a pump light source module, a saturation absorption spectrum frequency stabilization module, and a CPT frequency stabilization module. The pump light module comprises a pump laser and an optical amplifier. The saturation absorption module comprises a first atomic gas chamber physical system and an optical path for realizing the saturation absorption effect. The microcavity optical comb module comprises a microcavity optical comb pump light and an auxiliary laser, and realizes microcavity optical comb excitation by a thermal tuning method, generates sidebands by modulating the pump light, and realizes the decoupling of the microcavity optical comb repetition frequency and the microcavity optical comb pump light based on the principle of microcavity injection locking. The microcavity optical comb repetition frequency is equal to the frequency difference of the ground state hyperfine energy level of the alkali metal atom, which is used to excite the CPT effect. The CPT frequency stabilization module comprises a second atomic gas chamber physical system, and excites the CPT effect by the microcavity optical comb pump light and its sideband light, so that the repetition frequency of the microcavity optical comb is referenced to the atomic transition frequency. The two degrees of freedom of the microcavity optical comb are stabilized based on the saturation absorption spectrum and the CPT effect, so as to realize the frequency stabilization of the microcavity optical comb.

[0006] The pump light source module emits pump light, which is split into the first pump light and the second pump light. The first pump light enters the saturated absorption spectrum frequency stabilization module after frequency doubling. The saturated absorption spectrum frequency stabilization module uses the saturated absorption spectrum method to discriminate the frequency of the first pump light, and controls the output frequency of the pump light source module through PID feedback, thereby achieving frequency stabilization of the pump light source.

[0007] The microcavity optical comb module uses the microcavity optical comb pump light and auxiliary laser of the second pump light splitting as input. Based on the principle of thermally assisted laser, the microcavity optical comb is excited by the method of thermally tuning the microcavity. The photodetector detects the microcavity optical comb and obtains microwaves equal to the repetition frequency of the microcavity optical comb. The microcavity optical comb pump light is modulated by microwaves to generate sideband light, which constitutes coherent two-color light. The coherent two-color light is split to generate the first coherent two-color light and the second coherent two-color light. The first coherent two-color light is injected into the microcavity, and based on the principle of microcavity injection locking, the repetition frequency of the microcavity optical comb is decoupled from the pump light of the microcavity optical comb. The second coherent two-color light is frequency-doubled and injected into the CPT frequency stabilization module to realize the frequency discrimination of the repetition frequency of the microcavity optical comb. The repetition frequency of the microcavity optical comb is regulated by the method of PID feedback control of the frequency of the auxiliary laser, thereby realizing the frequency stabilization of the repetition frequency of the microcavity optical speed.

[0008] The first atomic gas cell physics system and the second atomic gas cell physics system use the same atoms and the same fine energy level transition lines.

[0009] Since the free spectral range of the microcavity is equal to the repetition frequency of the microcavity light comb, the repetition frequency of the microcavity light comb is equal to half of the frequency difference of the ground state hyperfine energy levels of the atoms used by designing the free spectral range of the microcavity.

[0010] In the microcavity optical comb module, the auxiliary laser is shifted to the blue end by an acousto-optic frequency shifter to compensate for the thermal effect of the microcavity. The pump light of the microcavity optical comb is first modulated by a phase modulator to produce sidebands, and then split to produce the first coherent two-color light and the second coherent two-color light. Among them, the first coherent two-color light provides gain to compensate for the dissipation of the microcavity.

[0011] The spectrum output by the microcavity optical comb module is a soliton optical frequency comb. On the one hand, the tooth spacing of the soliton optical frequency comb is equal to the repetition frequency of the microcavity optical comb, and the repetition frequency of the microcavity optical frequency comb is referenced to the atomic transition frequency through the CPT frequency stabilization module; on the other hand, the pump light corresponds to a tooth of the soliton optical frequency comb, and the pump light is referenced to the saturated absorption spectrum frequency stabilization module. Based on the characteristics of the soliton optical frequency comb, the frequency stability of the pump light is transmitted by the stable tooth spacing, realizing the frequency stabilization of the microcavity optical frequency comb.

[0012] Beneficial effects:

[0013] 1. The microcavity optical comb frequency stabilization system based on saturation absorption spectrum and CPT effect disclosed in the present invention is based on the principle of thermally assisted laser, uses the method of microcavity thermal tuning to realize the microcavity optical comb, and uses the microcavity injection locking effect to realize the decoupling of the repetition frequency of the microcavity optical comb and the wavelength of the pump light. It makes it possible to stabilize the frequency of the microcavity optical comb by stabilizing the pump light and the repetition frequency of the microcavity optical comb. Therefore, it is not necessary to expand the microcavity optical comb to the octave, avoiding the shortcomings of the f-2f optical comb frequency stabilization, and reducing the difficulty of microcavity optical comb frequency stabilization and system complexity.

[0014] 2. Most of the existing laser frequency stabilization is based on atomic clocks and needs to pass through some microwave links to achieve frequency stabilization. The microcavity optical comb frequency stabilization system based on saturated absorption spectrum and CPT effect disclosed in the present invention uses saturated absorption spectrum to stabilize the pump light frequency and uses CPT frequency stabilization to stabilize the repetition frequency of the microcavity optical comb, thus achieving full optical link frequency stabilization, low system noise and strong anti-interference ability. At the same time, the microcavity optical comb and CPT frequency stabilization system have the potential for miniaturization and chipization, and have advantages in small volume and low power consumption application scenarios.

[0015] 3. The microcavity optical comb frequency stabilization system based on saturated absorption spectrum and CPT effect disclosed in the present invention adopts the method of stabilizing the repetition frequency of the microcavity optical comb and the comb teeth of the pump light, and transmits the frequency stability of the pump light source to other optical comb teeth through the stable repetition frequency, thereby achieving full spectrum frequency stability. It can realize multi-wavelength standard application. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Schematic diagram of the microcavity optical comb frequency stabilization system based on saturation absorption spectrum and CPT effect of the present invention;

[0017] It is divided into four modules: a-saturated absorption spectrum frequency stabilization module; b-microcavity optical comb module; c-CPT frequency stabilization module; d-pump light source module.

[0018] Among them, a-saturated absorption spectrum frequency stabilization module includes: 1-first photodetector, 2-first beam splitter, 3-first atomic gas chamber, 4-first magnetic shielding tube, 5-second beam splitter, 6-first lens, 7-first frequency doubling crystal. a-31-first reflector, a-32-second reflector, a-33-third reflector.

[0019] b- microcavity optical comb module includes: 9- third beam splitter, 10- suppressed carrier single sideband modulator, 11- acousto-optic modulator, 12- fourth beam splitter, 13- first EDFA, 14- second EDFA, 15- first polarization controller, 16- second polarization controller, 17- first circulator, 18- second circulator, 19- second photodetector, 20- third photodetector, 21- fifth beam splitter, b- 34- fourth reflector, 39- second PID, 41- signal source, 42- phase-locked amplifier.

[0020] The c-CPT frequency stabilization module includes: 22-the second frequency doubling crystal, 23-the second lens, 24-the adjustable optical attenuator, 25-the 1 / 4 wave plate, 26-the sixth beam splitter, 27-the second atomic gas chamber, 28-the fourth photodetector, 29-the second magnetic shielding tube, 30-the fifth photodetector, c-35-the fifth reflector, c-36-the sixth reflector, 40-the third PID.

[0021] d- pump light source module includes: 8- the seventh beam splitter, 37- a narrow linewidth laser, 38- a first PID. DETAILED DESCRIPTION

[0022] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0023] Embodiment 1:

[0024] like Figure 1As shown, the present embodiment discloses a microcavity optical comb frequency stabilization system based on saturated absorption spectrum and CPT effect, including a microcavity optical comb module b, a pump light source module d, a saturated absorption spectrum frequency stabilization module a, and a CPT frequency stabilization module c. The pump light module d includes a narrow linewidth laser 37 with a wavelength of 1550nm as a pump laser, and its output power is greater than 100mW. The saturated absorption module a includes a first beam splitter 2, a first atomic gas chamber 3, a first magnetic shielding tube 4, a second beam splitter 5, a first lens 6, and a first frequency doubling crystal 7. The first reflector a-31, the second reflector a-32, and the third reflector a-33 constitute a first atomic gas chamber physical system. The first photodetector 1 is used to detect the signal light of the saturated absorption spectrum, and is used to realize the saturated absorption spectrum frequency discrimination. The microcavity optical comb module b includes a light beam 2-2 as a microcavity optical comb pump light, a light beam 2-1 as an auxiliary laser, and a thermal tuning method to realize microcavity optical comb excitation. The light beam 2-2 is modulated by a carrier suppression single sideband modulator 10 as a coherent two-color light. Based on the principle of microcavity injection locking, the repetition frequency of the microcavity optical comb and the decoupling of the microcavity optical comb pump light are realized. The repetition frequency of the microcavity optical comb is equal to 87 The frequency difference of the ground state hyperfine energy level of Rb atom is used to stimulate the CPT effect. The CPT frequency stabilization module c includes a second atomic gas chamber physical system consisting of a second lens 23, an adjustable optical attenuator 24, a 1 / 4 wave plate 25, a sixth beam splitter 26, a second atomic gas chamber 27, a second magnetic shielding tube 29, a fifth reflector c-35, and a sixth reflector c-36. The coherent two-color light composed of the microcavity optical comb pump light and its sideband light is split by the fourth beam splitter 12, and the generated light beam 2-2-2 is multiplied by the second frequency doubling crystal 22 to stimulate the CPT effect, thereby referencing the repetition frequency of the microcavity optical comb to the atomic transition frequency. Based on the saturated absorption spectrum and the CPT effect, the two degrees of freedom of the microcavity optical comb are stabilized, thereby achieving frequency stabilization of the microcavity optical comb.

[0025] The working method of a microcavity optical comb frequency stabilization system based on saturated absorption spectrum and CPT effect disclosed in this embodiment is as follows:

[0026] First, the pump light source module d emits pump light, and the pump light passes through the seventh beam splitter 8 and is split into beam 1 as the first pump light and beam 2 as the second pump light, wherein beam 1 is frequency-doubled by the first frequency-doubling crystal 7, and then reflected by the first reflector a-31, focused by the first lens 6, and split into beam 1-1 by the second beam splitter 5 as alkali metal atom pump light, and then reflected by the second reflector a-32, the third reflector a-33 and the first beam splitter 2 into the first atomic gas chamber 3; beam 1-2 directly enters the first atomic gas chamber 3 as detection light, and detects the saturated absorption signal through the first photodetector 1, realizing the frequency discrimination function of the saturated absorption spectrum stabilization module. The narrow linewidth laser 37 is controlled by the first PID 38 to realize the frequency stabilization of the pump light source module d.

[0027] Light beam 2 is used as the second pump light to pump the microcavity optical comb module b. The second pump light is split by the third beam splitter 9 to form light beam 2-2 as the microcavity optical comb pump light and light beam 2-1 as the auxiliary laser. The two pump the microcavity from both ends of the microcavity chip. Light beam 2-2 is modulated by the suppressed carrier single-sideband modulator 10 to produce coherent two-color light, and is split by the fourth beam splitter 12. Light beam 2-2-1 is amplified by the first EDFA 13, and injected into the microcavity through the first polarization controller 15 and the first circulator 17. Light beam 2-1 is frequency-shifted by 80MHz by the acousto-optic modulator 11, amplified by the second EDFA 14, and injected into the microcavity from the other end through the second polarization controller 16 and the second circulator 18. The power of the first EDFA 13 and the second EDFA 14 is adjusted to match, and the power is monitored by the second photodetector 19. The microcavity is tuned by the method of thermal tuning until the microcavity optical comb at the port of the second circulator 18. The output light beam is split into light beam a and light beam b by the fifth beam splitter 21. Light beam b is output as a microcavity optical comb. Light beam a is detected by the third photodetector 20 to obtain a microwave signal equal to the repetition frequency of the microcavity optical comb. The microwave signal is used to drive the suppressed carrier single sideband modulator 10 to realize the closed-loop modulation of the light beam 2-2 to generate sideband light and form coherent dichromatic light. The fourth beam splitter 12 generates light beam 2-2-1 as the first coherent dichromatic light and light beam 2-2-2 as the second coherent dichromatic light. The first coherent dichromatic light is injected into the microcavity, and based on the microcavity injection locking principle, the repetition frequency of the microcavity optical comb is decoupled from the pump light of the microcavity optical comb. The second coherent dichromatic light is frequency-doubled by the second frequency-doubling crystal 22, reflected by the sixth reflector c-36, focused by the second lens 23, and regulated by the adjustable optical attenuator 24. It is adjusted to circular polarization by the 1 / 4 wave plate 25, split by the sixth beam splitter 26, and the light reflected by the fifth reflector c-35 is controlled by the fifth photodetector 30 and the third PID40 to stabilize the optical power of the adjustable optical attenuator 24. Another light is directly injected into the 87 The second atomic gas chamber 27 of the Rb atom detects the CPT transmission signal light through the fourth photodetector 28 to achieve frequency discrimination. Phase-sensitive demodulation differentiation is performed through the phase-locked amplifier 42, and the output frequency of the 80MHz signal source is feedback-controlled by the second PID39, thereby realizing the repetition frequency stabilization of the microcavity optical comb based on the CPT frequency stabilization module c. While the signal source 41 outputs a signal to modulate the 80MHz signal source, it provides a reference signal to the phase-locked amplifier 42 to support the phase-sensitive demodulation differentiation function. The auxiliary laser of the microcavity optical comb module b is frequency-shifted to the blue end through the acousto-optic frequency shifter 11 to compensate for the thermal effect of the microcavity. In addition, the first coherent two-color light provides a gain effect to compensate for the dissipation of the microcavity.

[0028] The free spectral range of the microcavity needs to be designed to be 3.417 GHz, so that the repetition frequency of the microcavity optical comb is equal to 87 Half the frequency difference of the ground state hyperfine level of the Rb atom.

[0029] Finally, the spectrum output by the microcavity optical comb module b is a soliton optical frequency comb. On the one hand, the tooth spacing of the soliton optical frequency comb is equal to the repetition frequency of the microcavity optical comb, and the repetition frequency of the microcavity optical comb is referenced to the atomic transition frequency through the CPT frequency stabilization module c; on the other hand, the pump light corresponds to a tooth of the soliton optical frequency comb, and the pump light is referenced to the saturated absorption spectrum stabilization module a. Based on the characteristics of the soliton optical frequency comb, the frequency stability of the pump light is transmitted by the stable tooth spacing, thereby achieving the frequency stabilization of the microcavity optical comb.

[0030] Due to the fixed correspondence between the comb teeth, the repetition frequency of the microcavity optical comb is referenced to the atomic transition spectrum, and a comb tooth is also referenced to the atomic transition, so that the frequency stabilization of the microcavity optical comb can be achieved. The relationship between the mth comb tooth and the nth comb tooth is shown in the following formula:

[0031] f m =f n +(mn)f rep

[0032] where f m represents the frequency of the mth comb tooth, f n represents the frequency of the nth comb tooth, f rep represents the repetition frequency of the microcavity optical comb.

[0033] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A microcavity optical comb frequency stabilization system based on saturated absorption spectrum and CPT effect, characterized in that: It includes a microcavity optical comb module, a pump light source module, a saturated absorption spectrum frequency stabilization module, and a CPT frequency stabilization module; the pump light module includes a pump laser and an optical amplifier; the saturated absorption module includes a first atomic gas chamber physical system and an optical path for realizing the saturated absorption effect; the microcavity optical comb module includes a microcavity optical comb pump light and an auxiliary laser, and the microcavity optical comb excitation is realized by a thermal tuning method, and the sideband is generated by modulating the pump light. Based on the principle of microcavity injection locking, the decoupling of the microcavity optical comb repetition frequency and the microcavity optical comb pump light is realized, and the microcavity optical comb repetition frequency is equal to the frequency difference of the ground state hyperfine energy level of the alkali metal atom, which is used to excite the CPT effect; the CPT frequency stabilization module includes a second atomic gas chamber physical system, and the CPT effect is excited by the microcavity optical comb pump light and its sideband light, so that the repetition frequency of the microcavity optical comb is referenced to the atomic transition frequency; based on the saturated absorption spectrum and the CPT effect, the two degrees of freedom of the microcavity optical comb are stabilized, so as to realize the frequency stabilization of the microcavity optical comb.

2. The microcavity optical comb frequency stabilization system based on saturation absorption spectrum and CPT effect as claimed in claim 1, characterized in that: The pump light source module emits pump light, and the pump light is split into a first pump light and a second pump light. The first pump light enters the saturated absorption spectrum frequency stabilization module after frequency doubling. The saturated absorption spectrum frequency stabilization module uses the saturated absorption spectrum method to discriminate the frequency of the first pump light, and controls the output frequency of the pump light source module through PID feedback, thereby achieving frequency stabilization of the pump light source.

3. The microcavity optical comb frequency stabilization system based on saturation absorption spectrum and CPT effect as claimed in claim 1, characterized in that: The microcavity optical comb module uses the microcavity optical comb pump light and auxiliary laser split by the second pump light as input; based on the principle of thermally assisted laser, the microcavity optical comb is excited by thermally tuning the microcavity; the photodetector detects the microcavity optical comb and obtains microwaves with the same repetition frequency as the microcavity optical comb; Microwaves are used to modulate the microcavity optical comb pump light to generate sideband light, and the two form coherent two-color light; the coherent two-color light is split to generate the first coherent two-color light and the second coherent two-color light; the first coherent two-color light is injected into the microcavity, and based on the microcavity injection locking principle, the repetition frequency of the microcavity optical comb is decoupled from the microcavity optical comb pump light; The second coherent two-color light is frequency-doubled and injected into the CPT frequency stabilization module to realize the frequency discrimination of the repetition frequency of the microcavity optical comb. The repetition frequency of the microcavity optical comb is regulated by the method of PID feedback control of the frequency of the auxiliary laser, thereby achieving the stabilization of the repetition frequency of the microcavity light speed.

4. The microcavity optical comb frequency stabilization system based on saturation absorption spectrum and CPT effect as claimed in claim 1, characterized in that: The first atomic gas cell physics system and the second atomic gas cell physics system use the same atoms and the same fine energy level transition lines.

5. The microcavity optical comb frequency stabilization system based on saturation absorption spectrum and CPT effect as claimed in claim 4, characterized in that: In the microcavity optical comb module, since the free spectral range value of the microcavity is equal to the repetition frequency of the microcavity optical comb, the repetition frequency of the microcavity optical comb is equal to half of the frequency difference of the ground state hyperfine energy levels of the atoms used by designing the free spectral range value of the microcavity.

6. The microcavity optical comb frequency stabilization system based on saturation absorption spectrum and CPT effect as claimed in claim 4, characterized in that: In the microcavity optical comb module, the auxiliary laser is frequency-shifted toward the blue end through an acousto-optic frequency shifter to compensate for the thermal effect of the microcavity. The pump light of the microcavity optical comb is first modulated by a phase modulator to produce sidebands, and then split to produce the first coherent two-color light and the second coherent two-color light. The first coherent two-color light provides gain to compensate for the dissipation of the microcavity.

7. The microcavity optical comb frequency stabilization system based on saturation absorption spectrum and CPT effect as claimed in claim 1, characterized in that: The spectrum output by the microcavity optical comb module is a soliton optical frequency comb; on the one hand, the comb tooth spacing of the soliton optical frequency comb is equal to the repetition frequency of the microcavity optical comb, and the repetition frequency of the microcavity optical frequency comb is referenced to the atomic transition frequency through the CPT frequency stabilization module; on the other hand, the pump light corresponds to a comb tooth of the soliton optical frequency comb, and the pump light is referenced to the saturated absorption spectrum frequency stabilization module; based on the characteristics of the soliton optical frequency comb, the frequency stability of the pump light is transmitted by the stable comb tooth spacing, thereby realizing the frequency stabilization of the microcavity optical frequency comb.

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