High-efficiency frequency stabilization device for single-frequency continuous laser

Abstract

The invention discloses an efficient frequency stabilization device for a single-frequency continuous laser, which combines PDH (Pound-Drever-Hall) locking and optical frequency comb locking to achieve frequency stabilization, wherein the PDH locking includes an optical isolator (ISO), an optical fiber electro-optical modulator (EOM), a photodetector (PD), a phase shifter (PS), a radio frequency signal source (RF), a low-pass filter (LPF), and a servo control system (PDHServo); the optical frequency comb locking includes an optical microcavity (WGM), a photodetector (PD), a mixer (Mixer), a radio frequency signal source (RF), a high-pass filter (HPF), a signal amplifier (Amplifier) ​​and an acousto-optic modulator (AOM). In the frequency stabilization process, the PDH locking first performs a rough frequency stabilization on the continuous laser by feedback control to achieve the effect of pre-frequency stabilization, and then further processes it by optical frequency comb locking to achieve efficient frequency stabilization of the single-frequency continuous laser.

Description

Technical Field

[0001] The invention belongs to the technical field of optical fiber lasers, and in particular relates to a high-efficiency frequency stabilizing device for single-frequency continuous lasers. Background Art

[0002] The frequency stability of single-frequency lasers has been of great significance in many fields in recent years, such as spectral lines, optical information storage, fiber-optic hydrophones, etc. It is particularly worth mentioning in the field of precision metrology, in which the unit of time is the most accurate unit among the seven basic units of the International System of Units, and the definition of time by atomic clocks is based on the transition frequency of atoms in the microwave frequency band. For example, a second is the duration of 9192631770 cycles of radiation corresponding to the transition between two hyperfine energy levels of the ground state of cesium atoms (Cs) without interference. The uncertainty level of the cesium fountain clock currently used to reproduce the definition of the second (because the motion of the controlled atoms in the experiment is like a fountain) is as high as 10 -16 With the continuous development of science, this accuracy can no longer meet the requirements of certain fields, such as the measurement of dark matter, gravitational waves, and global navigation and positioning systems, which all require higher accuracy. Therefore, optical atomic or ion clocks have become the best choice. The new generation of atomic or ion optical clocks use quantum transitions in the optical frequency band. The line width of the transition spectrum is very narrow, reaching the sub-hertz to millihertz level, and has very good frequency standard potential. In principle, the accuracy of optical atomic or ion clocks is 5 orders of magnitude higher than that of atomic clocks. In the optical clock system, the ultra-narrow linewidth laser with high frequency stability is used as the local oscillator of the space optical clock. It is one of the three most critical components of the optical clock, which determines the medium- and short-term frequency stability of the space optical clock. At the same time, the space ultra-narrow linewidth laser with high frequency stability is used as the oscillator with the highest frequency stability in the high-precision time and frequency experimental cabinet system of the space station, which can provide high-precision frequency reference for other space science experiments. Therefore, it can be foreseen that promoting the development of single-frequency laser frequency stabilization technology will play a huge positive role in many scientific fields.

[0003] The frequency stabilization of single-frequency lasers can be divided into passive frequency stabilization and active frequency stabilization. At the beginning, the laser is isolated from the outside world, such as using sound insulation, vibration isolation, constant temperature and other measures to passively reduce the impact of the environment on the laser. This is passive frequency stabilization. However, the highest accuracy of this frequency stabilization method is currently only controlled within 10 -8 In order to achieve a better frequency stabilization effect, the frequency of the single-frequency laser must be stabilized through active feedback control, which is called active frequency stabilization.

[0004] In the early exploration of active frequency stabilization, the biggest problem was frequency discrimination. At first, the reflection characteristics of light of different wavelengths were discriminated using a high-Q FP resonant cavity. However, since the intensity of the reflected light is symmetrical to the resonant frequency of the cavity, it is impossible to distinguish whether the frequency of the incident light is greater than or less than an integer multiple of the resonant frequency by the intensity of the reflected light. After continuous exploration, it was finally discovered that the derivative of the reflection intensity is asymmetric with respect to the resonant frequency. This discovery eventually led to the formation of the famous PDH frequency stabilization technology. However, for PDH technology, its frequency stabilization effect is closely related to the resonant linewidth of the reference resonant cavity and the stability of the cavity length. The smaller the resonant linewidth, the better the frequency stabilization effect, but a small resonant linewidth means an extremely high Q value, which means that there are extremely high requirements for the reflectivity of the cavity mirror of the FP resonant cavity; the better the stability of the cavity length, the better the frequency stabilization effect, but a stable cavity length not only means that the experiment needs to be carried out in a vacuum and seismic isolation environment, but also requires a certain control over the temperature changes generated by the laser. In addition, various factors will also cause residual amplitude modulation in PDH frequency stabilization technology, such as light scattering and parasitic interference between parallel surfaces along the optical path, and rapid changes in residual amplitude modulation caused by temperature and vibration, etc. The noise generated by residual amplitude modulation will directly affect the error signal, thereby affecting the overall frequency stabilization effect.

[0005] Using an optical frequency comb for frequency stabilization is also a representative active frequency stabilization method. In particular, the principle of using the high nonlinearity of an optical microcavity to generate a Kerr frequency comb has been continuously improved in recent years, making this frequency stabilization method easier and more feasible. However, the key to using a frequency comb for frequency stabilization is the stability of the optical frequency comb, which in turn is related to the frequency of the incident light entering the microcavity. For single-frequency lasers with large optical frequency fluctuations, the optical frequency comb generated in the optical microcavity is not stable enough, which also leads to a less than ideal final frequency stabilization effect.

[0006] In summary, the traditional PDH frequency stabilization technology has limited the further improvement of its frequency stabilization accuracy and scope of use due to its high requirements for the experimental environment, high requirements for the reference cavity, and inevitable residual amplitude modulation; and the optical frequency comb frequency stabilization is not suitable for single-frequency lasers with large frequency fluctuations due to the stability of the frequency comb it produces. Summary of the invention

[0007] PDH technology frequency stabilization and optical frequency comb frequency stabilization cannot produce sufficient frequency stabilization accuracy due to their own shortcomings, or extremely harsh environment and device requirements are required to produce sufficient accuracy. The present invention combines the two technologies by using an optical microcavity, which not only overcomes the shortcomings of both within a certain range and greatly reduces the experimental requirements, but also fully utilizes the advantages of both, making the frequency stabilization effect more obvious. The present invention is achieved through the following technical solutions:

[0008] High-efficiency frequency stabilization device for single-frequency continuous laser;

[0009] Including PDH locking structure and optical frequency comb locking structure;

[0010] A single frequency continuous laser to be stabilized is included;

[0011] It includes a first optical coupler and a second optical coupler which play a connecting role; the first optical coupler is a 1×3 optical coupler, and the second optical coupler is a 1×2 optical coupler.

[0012] Wherein, the PDH locking structure includes an optical isolator, an optical fiber type electro-optical modulator, a circulator, a first photodetector, a first mixer, a first radio frequency signal source, a low-pass filter, and a servo control system;

[0013] The optical frequency comb locking structure includes a second photodetector, a second mixer, a second radio frequency signal source, a high pass filter, a signal amplifier, and an acousto-optic modulator;

[0014] The PDH locking structure and the optical frequency comb locking structure are linked together by an optical microcavity; the optical microcavity is used for frequency discrimination and to achieve a pre-frequency stabilization effect, and when entering the optical frequency comb locking structure, a more stable optical frequency comb is generated;

[0015] Optical microcavities are not only used for PDH locking, but also play an important role in optical frequency comb locking. In the PDH locking structure, the optical microcavity plays the role of frequency discrimination to achieve the effect of pre-stabilization; while in optical frequency comb locking, the optical microcavity is responsible for generating the optical frequency comb, and with pre-stabilization, the generated frequency comb can be more stable.

[0016] The single-frequency continuous laser provides seed light to be stabilized, which is divided into three beams via an optical isolator and a first optical coupler, namely a first light beam, a second light beam and a third light beam;

[0017] The third light beam is formed into a sideband through an electro-optic modulator, and then reaches the optical microcavity through a circulator. A part of the light reaches the first photodetector again through the circulator due to reflection and scattering, and is mixed with the radio frequency signal generated by the first radio frequency signal source in the first mixer. After mixing, an error signal is generated, and after the high-frequency signal is filtered out by a low-pass filter, it reaches the servo control system. The servo control system adjusts the cavity length of the single-frequency continuous laser according to the signal to achieve the effect of pre-stabilization.

[0018] A part of the third light beam reaching the optical microcavity undergoes the above-mentioned feedback process, and another part of the light beam forms a Kerr optical frequency comb in the cavity due to the high nonlinearity of the optical microcavity. The Kerr optical frequency comb and the second light beam form a beat frequency in the second photodetector after passing through the second optical coupler. The beat frequency signal is mixed with the second RF signal source through the second mixer, and then the low-frequency signal is filtered out by a high-pass filter. It then reaches the acousto-optic modulator through a signal amplifier, and the first light beam passing through the acousto-optic modulator is frequency-shifted to obtain the first-order diffraction light output, which is the final frequency stabilization result.

[0019] In the optical microcavity, only the light with integer multiples of the cavity's resonant frequency is continuously propagating and the interference is enhanced. When the power of this part of light reaches a certain level, it will excite the nonlinear effect in the cavity, which mainly refers to cascaded four-wave mixing, thereby forming a Kerr frequency comb. The stability of the frequency comb is related to the degree of fit between the incident light frequency and the integer multiples of the optical microcavity's resonant frequency. Among them, the incident light frequency that is different from the integer multiples of the optical microcavity's resonant frequency is reflected back to the photodetector, and an error signal is formed after a series of subsequent processes. After the servo control system, the system changes the cavity length of the original laser, thereby stabilizing the frequency at an integer multiple of the resonant frequency of the optical resonant cavity. After stabilizing the frequency, the stability of the generated optical frequency comb is also improved, forming a stable virtuous cycle.

[0020] Furthermore, the optical isolator and circulator have high isolation, which is used to ensure that no light will return to the electro-optic modulator and the laser after passing through the optical microcavity. The main function is to ensure the stability of the operation of the entire system and the safety of the laser.

[0021] Furthermore, the modulation frequency of the electro-optic modulator is much larger than the value obtained by dividing the free spectrum area of ​​the optical microcavity by the fineness of the cavity, so as to make the position of the sideband far enough from the resonance frequency in the cavity, so that most of the energy of the sideband can be reflected back to the first optical detector, and at the same time, an appropriate error signal that can effectively feedback the frequency fluctuation is obtained. The electro-optic modulator and the RF seed source entering the first mixer 7 have the same frequency, and the frequency needs to be much larger than the value obtained by dividing the resonance line width of the reference cavity by the fineness of the cavity.

[0022] Furthermore, a phase shifter for compensating for delay is installed on any one of the signals between the first photodetector and the first RF signal source and the first mixer. In order to obtain a better error signal, two pure sinusoidal terms need to be generated on the two signals entering the first mixer, but there are almost unequal delays on the two signals. In order to compensate for the delay, a phase shifter is added to one signal.

[0023] Furthermore, the cut-off frequency of the low-pass filter is selected to filter out the double frequency signal generated by the front photodetector. The cut-off frequency of the low-pass filter needs to be controlled to be able to filter out the high-order frequency terms in the power signal.

[0024] Furthermore, the optical microcavity has a specific resonant frequency. When another part of the light in the third light beam passes through the optical microcavity, if the frequency of the incident light is an integer multiple of the resonant frequency of the optical microcavity, it will be continuously reflected on the inner wall of the microcavity, thereby remaining in the cavity and causing interference enhancement, while light of other frequencies will be coupled out of the cavity after propagating in the cavity for a period of time.

[0025] Furthermore, after the beat frequency signal formed by the second photodetector is mixed with the signal of the second RF signal source, two signal values ​​of the addition and subtraction of the two signals are obtained. The cutoff frequency selection requirement of the subsequent high-pass filter is to filter out the value of the subtraction between the two; the obtained output signal will be locked at a certain frequency of the frequency comb and the sum of the frequency of the second RF signal source. The frequency of the second RF signal source is adjustable, which is used to make the locked signal adjustable within a certain range. The frequency stability of the output signal after frequency stabilization is finally obtained. There is a certain relationship between the frequency stability of the output signal and the second RF signal source. The frequency of the output signal will be locked at a certain frequency of the frequency comb and the sum of the frequency of the second RF signal source. Through this point, if the frequency of the second RF signal source is adjustable, the locked signal can be adjusted within a certain range. In addition, it can be seen that there are requirements for the frequency stability of the second RF signal source. The stronger the frequency stability of the second RF signal source, the better the frequency stabilization effect.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] 1. Traditional PDH frequency stabilization requires an FP resonant cavity with an extremely high Q value to act as a reference cavity in order to obtain sufficient frequency stabilization accuracy, which places very high demands on the reflectivity of the resonant cavity mirror. Not only that, traditional PDH frequency stabilization also needs to work in a vacuum, seismic isolation, and constant temperature environment, which greatly limits the application and development of PDH technology. In addition, the inevitable residual amplitude modulation of PDH technology will also affect the final frequency stabilization effect. Because the present invention only uses PDH for pre-frequency stabilization, the frequency stabilization accuracy of PDH does not have a great impact on the final frequency stabilization effect compared to traditional PDH technology, thereby greatly reducing the requirements for the reference cavity and working environment used.

[0028] 2. The stability of the traditional frequency comb is related to the frequency incident to the microcavity, so the generated frequency comb is not stable, which greatly affects the final frequency stabilization effect. The present invention combines PDH technology with the optical frequency comb by using an optical microcavity, and adds PDH before the optical frequency comb structure to pre-stabilize the incident light, which greatly improves the stability of the generated frequency comb, thereby improving the frequency stabilization effect of the frequency comb.

[0029] 3. Traditional frequency stabilization technology lacks frequency tuning means, which greatly reduces the application range of the laser after frequency stabilization. The final frequency stabilization structure of the present invention partially relies on the local RF signal source, which can have a larger tuning range while ensuring its stability, thereby increasing the practicality of the laser after frequency stabilization.

[0030] 4. Compared with the spatial structure of some frequency stabilization technologies, the optical path of the present invention adopts an all-fiber structure, which greatly simplifies the system structure and has lower loss and higher efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for describing the embodiments are briefly introduced below.

[0032] Figure 1 It is a schematic diagram of the device of the present invention.

[0033] Figure 2 This is a diagram of light propagation in the optical microcavity of the present invention with a frequency that is an integer multiple of the resonance frequency.

[0034] Figure 3 This is a typical error signal diagram generated by PDH frequency stabilization in the present invention.

[0035] In the figure, a single-frequency continuous laser 1, a first optical coupler 3, a second optical coupler 13, an optical isolator 2, a fiber-type electro-optic modulator 4, a circulator 5, a first photodetector 6, a first mixer 7, a first radio frequency signal source 9, a low-pass filter 10, a servo control system 11, a second photodetector 14, a second mixer 15, a second radio frequency signal source 16, a high-pass filter 17, a signal amplifier 18, an acousto-optic modulator 19, an optical microcavity 12, and a phase shifter 8. DETAILED DESCRIPTION

[0036] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0037] like Figure 1 As shown: a single-frequency continuous laser 1, a first optical coupler 3, a second optical coupler 13, an optical isolator 2, a fiber-type electro-optic modulator 4, a circulator 5, a first photodetector 6, a first mixer 7, a first radio frequency signal source 9, a low-pass filter 10, a servo control system 11, a second photodetector 14, a second mixer 15, a second radio frequency signal source 16, a high-pass filter 17, a signal amplifier 18, an acousto-optic modulator 19, an optical microcavity 12, and a phase shifter 8.

[0038] like Figure 2As shown: In an optical microcavity, when the optical path length of a circle is an integer multiple of the wavelength, the light wave will be enhanced by interference and remain in the cavity, while the light that is not an integer multiple will be reflected or scattered. The light power that continuously propagates in the cavity is continuously enhanced, which will stimulate the cascade four-wave mixing effect in the cavity, thereby forming a Kerr frequency comb.

[0039] like Figure 3 As shown in the figure: when the frequency of the laser to be stabilized is higher than the integral multiple of the resonance frequency of the reference cavity, the error signal is greater than zero; when the frequency of the laser to be stabilized is lower than the integral multiple of the resonance frequency of the reference cavity, the error signal is less than zero; when the frequency of the laser to be stabilized is equal to the integral multiple of the resonance frequency of the reference cavity, the error signal is equal to zero. According to the error signal, the servo control system can accurately adjust the cavity length of the laser.

[0040] Specific:

[0041] Firstly, the frequency stabilization process of the PDH locking structure in this technology is introduced.

[0042] Assume that the output of the single-frequency continuous laser 1 to be stabilized is:

[0043] E in =E0e iωt (1)

[0044] After electro-optic modulator 2:

[0045] E eom =E0e i(ωt+βsinΩt) (2)

[0046] Using Bessel function expansion we get:

[0047] E emo ≈E0[J0(β)e iωt +J1(β)e i(ω+Ω)t -J1(β)e i(ω-Ω)t ] (3)

[0048] If the modulation frequency of the electro-optic modulator 2 is large enough, the two sidebands generated are far enough from the resonant frequency of the optical microcavity 12, and most of the energy of the sidebands will be reflected back. In addition, some of the energy of the frequency that resonates in the microcavity will also "leak" out. Assume that the light reflected back after passing through the microcavity is E ref , the reflection function F(ω) of the microcavity is defined as

[0049]

[0050] Assuming the single-frequency laser output power is P0, then:

[0051] P0≡|E0| 2 (5)

[0052] Assume that the optical power of those frequencies that are far away from the microcavity resonance frequency and are quickly reflected back is P s ; and those that resonate in the cavity, the power that "leaks" out is P c , then according to the law of conservation of energy:

[0053] P c +2P s ≈P0 (6)

[0054] According to equations (1), (3), and (4), we can get the light E reflected from the microcavity: ref for:

[0055] E ref =E0[F(ω)J0(β)e iωt +F(ω+Ω)J1(β)e i(ω+Ω)t -F(ω-Ω)J1(β)e i(ω-Ω)t ] (7)

[0056] After mixing, we get:

[0057]

[0058] In order to obtain a suitable signal, the only term we are interested in in equation (8) is the sine term in the Ω term. Other high-order terms and cosine terms will be filtered out in the selection of a suitable modulation frequency and the subsequent combination of mixing and filtering. For example, the modulation frequency of the electro-optic modulator 4 is selected to be relatively large, so that the generated sideband is far enough from the resonance frequency. At this time, the reflectivity of the microcavity for the two sidebands is strong enough, that is, F(ω±Ω)=-1; then we can get:

[0059] F(ω)F * (ω+Ω)-F * (ω)F(ω-Ω)=-i2Im{F(ω)} (9)

[0060] It can be seen that formula (9) is a pure imaginary number. At this time, for formula (8), the cosine term is zero, and only the sine term remains. The cosine term in the Ω term in the power signal is well filtered out, and formula (8) becomes:

[0061]

[0062] At this time, the error signal ε can be obtained as:

[0063]

[0064] For the subsequent mixing process, if the two signals of the first mixer 7 are both sinusoidal, the mixing process can be simplified as follows:

[0065]

[0066] Using the same RF signal source, Ω' is equal to Ω at this time, then the 2Ω term will be filtered out by the subsequent low-pass filter 10 together with the 2Ω term generated by equation (8), and the Ω-Ω' term will become the servo control system 11 after the DC signal arrives.

[0067] Next, the frequency stabilization process of the optical frequency comb part of this technology is introduced.

[0068] Assume that the single-frequency continuous optical frequency to be stabilized is f CW , assuming it is smaller than the closest mode f in the frequency comb n , then the two will form a beat frequency in the photodetector, the frequency of the beat frequency is f Beat for:

[0069] f Beat =f n -f CW (13)

[0070] After passing through the second mixer 15 and the high-pass filter 17, the frequency f AOM for:

[0071] f AOM =f Lo +f Beat =f Lo +f n -f CW (14)

[0072] After diffraction by the acousto-optic modulator 19, the first-order diffraction result is taken as the final output:

[0073] f 1st =f CW +f AOM =f Lo +f n (15)

[0074] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail.

Claims

1. An efficient frequency stabilization device for single-frequency continuous laser, characterized by: Including PDH locking structure and optical frequency comb locking structure; It includes a single-frequency continuous laser (1) to be stabilized; It comprises a first optical coupler (3) and a second optical coupler (13) which play a connecting role; wherein the PDH locking structure comprises an optical isolator (2), an optical fiber electro-optic modulator (4), a circulator (5), a first photodetector (6), a first mixer (7), a first radio frequency signal source (9), a low-pass filter (10), and a servo control system (11); The optical frequency comb locking structure comprises a second photodetector (14), a second mixer (15), a second radio frequency signal source (16), a high pass filter (17), a signal amplifier (18), and an acousto-optic modulator (19); The PDH locking structure and the optical frequency comb locking structure are linked together by an optical microcavity (12); the optical microcavity (12) is used for frequency discrimination and achieving a pre-frequency stabilization effect, and when entering the optical frequency comb locking structure, a more stable optical frequency comb is generated; The single-frequency continuous laser (1) provides seed light to be stabilized, which is divided into three beams through an optical isolator (2) and a first optical coupler (3), namely a first light beam, a second light beam and a third light beam; the third light beam forms a sideband through an electro-optic modulator (4), and then reaches the optical microcavity (12) through a circulator (5); a portion of the light reaches the first photodetector (6) again through the circulator (5) due to reflection and scattering, and is mixed with the radio frequency signal generated by the first radio frequency signal source (9) in the first mixer (7), and an error signal is generated after mixing, and then reaches the servo control system (11) after filtering out the high-frequency signal through a low-pass filter (10); the servo control system (11) adjusts the cavity length of the single-frequency continuous laser (1) according to the signal to achieve a pre-stabilization effect; Another part of the third light beam that reaches the optical microcavity (12) forms a Kerr optical frequency comb in the cavity due to the high nonlinearity of the optical microcavity (12). The Kerr optical frequency comb and the second light beam form a beat frequency in the second photodetector (14) after passing through the second optical coupler (13). The beat frequency signal and the second radio frequency signal source (16) are mixed through the second mixer (15). The low-frequency signal is filtered out through a high-pass filter (17). The signal amplifier (18) reaches the acousto-optic modulator (19). The first light beam that passes through the acousto-optic modulator (19) is frequency-shifted to obtain a first-order diffracted light output, which is the final frequency stabilization result. After the beat frequency signal generated by the second photoelectric detector (14) is mixed with the signal of the second radio frequency signal source (16), two signal values ​​of the addition and subtraction of the two signals are obtained, and the cutoff frequency of the subsequent high-pass filter (17) is selected to filter out the subtraction value of the two signals; The obtained output signal will be locked to the sum of a certain frequency of the frequency comb and the frequency of the second radio frequency signal source (16), and the frequency of the second radio frequency signal source (16) is adjustable, so as to make the locked signal adjustable within a certain range.

2. The high-efficiency frequency stabilization device for a single-frequency continuous laser according to claim 1, characterized in that: The optical isolator (2) and the circulator (5) both have a high degree of isolation, and are used to ensure that no light passes through the optical microcavity (12) and returns to the electro-optic modulator (4) and the laser (1).

3. The high-efficiency frequency stabilization device for a single-frequency continuous laser according to claim 1, characterized in that: The modulation frequency of the electro-optic modulator (4) is much larger than the value obtained by dividing the free spectral range of the optical microcavity (12) by the fineness of the cavity, so as to make the position of the sideband far enough from the resonance frequency in the cavity, so that most of the energy of the sideband can be reflected back to reach the first optical detector (6), and at the same time obtain an appropriate error signal that can efficiently feedback the frequency fluctuation situation.

4. The high-efficiency frequency stabilization device for a single-frequency continuous laser according to claim 1, characterized in that: A phase shifter (8) for compensating for delay is installed on any one of the signals between the first photodetector (6) and the first radio frequency signal source (9) and the first mixer (7).

5. The high-efficiency frequency stabilization device for a single-frequency continuous laser according to claim 1, characterized in that: The cut-off frequency of the low-pass filter (10) is selected so as to filter out the double frequency signal generated by the front photoelectric detector (6).

6. The high-efficiency frequency stabilization device for a single-frequency continuous laser according to claim 1, characterized in that: The optical microcavity (12) has a specific resonant frequency, and when another part of the light in the third light beam passes through the optical microcavity (12), if the frequency of the incident light is an integer multiple of the resonant frequency of the optical microcavity (12), it will be continuously reflected on the inner wall of the microcavity, thereby remaining in the cavity and causing interference enhancement, while light of other frequencies will be coupled out of the cavity after propagating in the cavity for a period of time.

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