Method and system for detecting zero expansion temperature of ultra-stable cavity

Abstract

The invention relates to the technical field of optical measurement, in particular to a method and system for detecting the zero expansion temperature of an ultra-stable cavity, and the method comprises the steps: locking a right side band of a laser beam at an (m + 1) th fundamental transverse mode of a target Fabry-Perot cavity through a sideband modulation technology, and locking a left side band subjected to the frequency shift of a preset frequency at an mth fundamental transverse mode, the problem of coupling interference between a TEM00 mode and a TEM01 mode in a traditional scheme is avoided, and the stability of the lock cavity and the detection accuracy are improved; a frequency locking task is transferred to the second acousto-optic modulator, so that the detection process does not need to depend on complex and expensive microwave frequency band locking equipment, and the cost is reduced; the driving frequency corresponding to the offset frequency lock cavity module is determined through the preset frequency and the free spectral range, so that the offset frequency lock cavity module can be adaptively adjusted along with the cavity length, zero expansion temperature detection of ultra-stable cavities with different cavity length specifications is compatible, and the universality of the detection method is improved.

Description

Technical Field

[0001] This application relates to the field of optical measurement technology, and in particular to a method and system for detecting the zero expansion temperature of an ultra-stable cavity. Background Technology

[0002] The ultra-stable Fabry-Perot cavity is a core component of an ultra-stable laser system, and the stability of its cavity length directly determines the stability of the output laser frequency. The zero-expansion temperature of an ultra-stable cavity refers to the specific operating temperature at which the cavity length is least sensitive to temperature changes. Precisely controlling the operating temperature of the ultra-stable cavity within the zero-expansion temperature and its extremely small surrounding range can significantly reduce the impact of temperature drift on the cavity length, thereby providing an extremely high-precision frequency reference for the ultra-stable laser. Therefore, accurate detection of the zero-expansion temperature of the ultra-stable cavity is of paramount importance for ensuring the performance of the ultra-stable laser system.

[0003] In existing technologies, methods for detecting the zero-expansion temperature of ultrastable cavities mainly fall into two categories. The first category is based on absolute frequency reference methods. This method requires comparing the laser frequency locked to the ultrastable cavity with absolute frequency reference systems such as atomic / molecular absorption lines or optical frequency combs. By changing the ultrastable cavity temperature and observing the laser frequency drift, the temperature with the smallest frequency drift rate is determined as the zero-expansion temperature. However, the absolute frequency reference equipment relied upon by this type of method is often complex in structure and expensive, and the detection process is cumbersome and time-consuming, making it difficult to meet the needs of rapid on-site detection. At the same time, it has stringent requirements for the absolute frequency stability of the laser, limiting its application in low-to-medium precision ultrastable laser system detection scenarios.

[0004] The second type is the detection method based on dual transverse mode locking. This method splits the laser beam and locks it onto the TEM00 fundamental transverse mode and the TEM01 first-order transverse mode of the ultrastable cavity, respectively. The zero-expansion temperature is determined by monitoring the change in frequency spacing with temperature, utilizing the correlation between the frequency interval of the two transverse modes and the cavity length. While this method does not require an absolute frequency reference, it has significant drawbacks: Firstly, the frequency interval between the TEM00 and TEM01 modes is small (e.g., only 215MHz for a 5cm plano-concave cavity), requiring extremely high frequency control precision from the modulation device. Secondly, the transverse mode types of the two lasers differ, and coupling interference between the transverse modes easily affects locking stability. Furthermore, the modulation device parameters of this scheme have poor adaptability, making it difficult to meet the detection requirements of ultrastable cavities with different cavity lengths, thus lacking universality.

[0005] In addition, existing technologies attempt to introduce electro-optic modulators to achieve frequency-biased cavity locking, but this requires high-precision locking of the microwave driving frequency of the electro-optic modulator. Microwave frequency locking equipment is expensive, difficult to operate, and susceptible to electromagnetic interference affecting locking accuracy, resulting in high technical barriers and implementation costs in the detection process, which is not conducive to the large-scale promotion and application of the technology.

[0006] Therefore, how to achieve low-cost, high-stability, and highly universal detection of ultra-stable cavity zero expansion temperature without relying on absolute frequency references or requiring high-precision locking of the microwave drive frequency of the electro-optic modulator has become an urgent problem to be solved. Summary of the Invention

[0007] To address the aforementioned technical problems, this application adopts a method for detecting the zero expansion temperature of an ultra-stable cavity, comprising: The laser beam output from the laser is processed by the first acousto-optic modulator to obtain the intermediate laser beam; The middle laser beam is modulated by a frequency-biased cavity-locked module to generate a left and right band; Lock the right band onto the (m+1)th base transverse mode of the target Fabry-Perot cavity; The left band is frequency-shifted to a preset frequency using a second acousto-optic modulator. The frequency-shifted left band is locked onto the m-th fundamental transverse mode of the target Fabry-Perot cavity through the second PDH optical path; Based on the relationship between the driving frequency of the second acousto-optic modulator and the cavity temperature of the target Fabry-Perot cavity, the cavity temperature corresponding to the minimum rate of change of the driving frequency is determined as the target zero expansion temperature of the target Fabry-Perot cavity.

[0008] In some embodiments, the sum of the frequency difference between the left and right bands and a preset frequency is equal to the free spectral path of the target Fabry-Perot cavity.

[0009] In some embodiments, the frequency-biased cavity-locked module includes an electro-optic modulator and a first PDH optical path. The frequency-biased cavity-locked module modulates the intermediate laser beam to generate a left band and a right band, including: By modulating the middle laser beam with an electro-optic modulator, a composite laser beam containing carrier, left band, and right band frequency components is obtained. The frequency interval between the left band and the carrier is equal to the frequency interval between the carrier and the right band, and is also equal to the driving frequency of the electro-optic modulator.

[0010] In some embodiments, the driving frequency f EOM <FSR / 2, where FSR is the free spectral range of the target Fabry-Perot cavity.

[0011] In some embodiments, the preset frequency Δf satisfies the following condition: Δf = FSR - 2 × f EOM .

[0012] In some embodiments, neither the first PDH optical path nor the second PDH optical path is equipped with an electro-optic modulator.

[0013] In some embodiments, determining the cavity temperature corresponding to the minimum rate of change of the driving frequency as the target zero-expansion temperature of the target Fabry-Perot cavity based on the correspondence between the driving frequency of the second acousto-optic modulator and the cavity temperature of the target Fabry-Perot cavity includes: Adjust the cavity temperature of the target Fabry-Perot cavity, collect the driving frequency data of the second acousto-optic modulator at different cavity temperatures, and establish the correspondence between driving frequency and cavity temperature; The rate of change of the driving frequency is calculated based on the relationship between the driving frequency and the cavity temperature. The cavity temperature corresponding to the minimum absolute value of the rate of change is determined as the target zero expansion temperature of the target Fabry-Perot cavity.

[0014] This application also provides a detection system for the zero expansion temperature of an ultra-stable cavity, including a laser, a first acousto-optic modulator, a frequency-biased cavity-locked module, a second acousto-optic modulator, a second PDH optical path, and a data processing module; Among them, the laser is used to output a laser beam; The first acousto-optic modulator is used to process the laser beam to obtain the intermediate laser beam; The frequency-biased cavity-locked module is used to modulate the middle laser beam to generate the left and right bands; Lock the right band onto the (m+1)th base transverse mode of the target Fabry-Perot cavity; The second acousto-optic modulator enables the left band to achieve frequency shifting to match a preset frequency; The second PDH optical path is used to lock the frequency-shifted left band onto the m-th fundamental transverse mode of the target Fabry-Perot cavity; The data processing module is used to determine the cavity temperature corresponding to the minimum rate of change of the driving frequency of the second acousto-optic modulator as the target zero expansion temperature of the target Fabry-Perot cavity, based on the corresponding relationship between the driving frequency of the second acousto-optic modulator and the cavity temperature of the target Fabry-Perot cavity.

[0015] In some embodiments, the frequency-biased cavity-locked module includes an electro-optic modulator and a first PDH optical path; The electro-optic modulator is used to modulate the middle laser beam to obtain a composite laser beam containing carrier, left band, and right band frequency components. The frequency interval between the left band and the carrier is equal to the frequency interval between the carrier and the right band, and is equal to the driving frequency of the electro-optic modulator.

[0016] In some embodiments, the data processing module includes a temperature regulation module, a frequency acquisition module, and a data processing unit; The temperature control module is used to adjust the cavity temperature of the target Fabry-Perot cavity. The frequency acquisition module is used to acquire the driving frequency data of the second acousto-optic modulator at different cavity temperatures; The data processing unit is used to receive the driving frequency data of the second acousto-optic modulator at different cavity temperatures, establish the correspondence between the driving frequency and the cavity temperature, calculate the rate of change of the driving frequency based on the correspondence between the driving frequency and the cavity temperature, and determine the cavity temperature corresponding to the minimum absolute value of the rate of change as the target zero expansion temperature of the target Fabry-Perot cavity.

[0017] Compared with existing technologies, this application has at least the following advantages: By using a frequency-shifting cavity-locking process, the right band of the first locked laser beam is locked to the (m+1)th fundamental transverse mode of the target Fabry-Perot cavity. Simultaneously, by using a preset frequency shift and a second PDH optical path, the left band is locked to the mth fundamental transverse mode of the target Fabry-Perot cavity. This results in a dual-fundamental transverse mode locking structure with a spacing of one free spectral range between the left and right bands, avoiding the coupling interference problem between the TEM00 and TEM01 modes in traditional dual-transverse mode schemes, significantly improving the stability of the cavity-locking system and the accuracy of zero-expansion temperature detection. Furthermore, by employing a second acousto-optic modulator to achieve frequency shifting of the left band to a preset frequency, the high-precision locking of the microwave drive frequency of the electro-optic modulator is replaced, thereby transferring the frequency locking task to… The second acousto-optic modulator eliminates the need for complex and expensive microwave frequency locking equipment in the detection process, reducing equipment investment costs and operational technical barriers. It also mitigates the impact of electromagnetic interference on locking accuracy, simplifying and facilitating the detection process. By determining the driving frequency of the biased cavity locking module using a preset frequency and the free spectral range of the target Fabry-Perot cavity, the module can be adaptively adjusted according to cavity length, making it compatible with zero-expansion temperature detection of ultra-stable cavities of different lengths. Furthermore, by monitoring the relationship between the driving frequency of the second acousto-optic modulator and cavity temperature, and using the temperature corresponding to the minimum rate of change of the driving frequency as the zero-expansion temperature, the detection process no longer relies on an absolute frequency reference, reducing the requirements for the absolute frequency stability of the laser and significantly improving the universality of the detection method. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A schematic diagram of a method for detecting the zero expansion temperature of an ultra-stable cavity provided in an embodiment of this application; Figure 2 A schematic diagram of the structure of a detection system for the zero expansion temperature of an ultra-stable cavity provided in an embodiment of this application; Figure 3A schematic diagram of the laser beam frequency in an ultrastable cavity zero expansion temperature detection system provided in this application embodiment; Among them, 1 is the laser, 2 is the frequency-biased cavity-locked module, 3 is the second PDH optical path, 4 is the target Fabry-Perot cavity, 5 is the data processing module, AOM1 is the first acousto-optic modulator, AOM2 is the second acousto-optic modulator, EOM is the electro-optic modulator, 21 is the first PDH optical path, 51 is the temperature adjustment module, 52 is the frequency acquisition module, and 53 is the data processing unit. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It is understood that, where appropriate, the terms used to distinguish similar objects can be interchanged so that this application can also implement other embodiments besides the illustrated or described embodiments. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or server that includes a series of steps or modules is not necessarily limited to those steps or modules explicitly listed, but may include other steps or modules not explicitly listed or inherent to these processes, methods, products, or devices.

[0022] This embodiment provides a method for detecting the zero expansion temperature of an ultra-stable cavity. In some embodiments, such as... Figure 1 As shown, the method for detecting the zero expansion temperature of the ultra-stable cavity includes: S1, the laser beam output from the laser is processed by the first acousto-optic modulator to obtain the intermediate laser beam; S2 modulates the middle laser beam through a frequency-locked cavity module to generate a left and right band; S3, lock the right side band onto the (m+1)th base transverse mode of the target Fabry-Perot cavity; S4, the left band is frequency shifted to a preset frequency by the second acousto-optic modulator; S5, the frequency-shifted left band is locked onto the m-th fundamental transverse mode of the target Fabry-Perot cavity through the second PDH optical path; S6. Based on the relationship between the driving frequency of the second acousto-optic modulator and the cavity temperature of the target Fabry-Perot cavity, determine the cavity temperature corresponding to the minimum rate of change of the driving frequency as the target zero expansion temperature of the target Fabry-Perot cavity.

[0023] The laser beam is a stable laser output from a laser generator.

[0024] In some embodiments, the laser includes at least one or more of narrow linewidth semiconductor lasers and fiber lasers.

[0025] The first acousto-optic modulator is a laser frequency modulation device based on the acousto-optic effect. It consists of an acousto-optic medium, a transducer, and a sound absorber. It is used to perform acousto-optic modulation on the laser beam to achieve an initial frequency shift of the laser, while also playing an auxiliary role in intensity adjustment and optical path switching. Specifically, the first acousto-optic modulator utilizes the acousto-optic effect of sound waves forming a refractive index grating in the acousto-optic medium. When the laser passes through, diffraction occurs, resulting in a frequency shift, which modulates the frequency of the laser beam to obtain an intermediate laser beam.

[0026] In some embodiments, the first acousto-optic modulator includes at least one or more of a fused silica acousto-optic modulator and a heavy flint glass acousto-optic modulator.

[0027] The frequency-biased cavity-locking module has modulation and cavity-locking functions. After modulating the central laser, a first locked laser beam with left and right sideband frequency components and a carrier wave is obtained, where the carrier wave frequency is equal to the initial frequency of the central laser beam. The left and right sidebands serve as the laser basis for locking onto different fundamental transverse modes of the target Fabry-Perot cavity. Specifically, the right sideband is cavity-locked to the (m+1)th fundamental transverse mode of the target Fabry-Perot cavity.

[0028] The second acousto-optic modulator can precisely shift the frequency of the left-side laser beam of the first locked laser beam through the acousto-optic effect, compensating for the frequency difference between the left-side laser beam and the m-th fundamental transverse mode of the target Fabry-Perot cavity, so that the frequency-shifted left-side beam has the frequency conditions to resonate with the target Fabry-Perot cavity mode, and enters the locking state.

[0029] The second PDH optical path precisely locks the frequency of the frequency-shifted left band to the m-th fundamental transverse mode of the target Fabry-Perot cavity. In this way, the left and right bands form a dual TEM00 fundamental transverse mode locking structure with a spacing of 1 times the free spectral range (FSR), thereby enabling the monitoring of cavity length changes through frequency correlation of the dual cavity modes.

[0030] In some embodiments, the sum of the frequency difference between the left and right bands and a preset frequency is equal to the free spectral path of the target Fabry-Perot cavity.

[0031] In some embodiments, the second PDH optical path is a frequency-stabilized optical path composed of a photodetector, a phase detector, a servo controller, and optical coupling components (such as a collimating lens and a polarizer).

[0032] Furthermore, the zero-expansion temperature of the target Fabry-Perot cavity is the temperature at which the cavity length changes the slowest with temperature. Changes in the cavity length of the target Fabry-Perot cavity directly cause a shift in the cavity mode frequency, which in turn causes a change in the driving frequency of the second acousto-optic modulator. Therefore, the cavity temperature at which the driving frequency of the second acousto-optic modulator changes at the smallest rate is the target zero-expansion temperature of the target Fabry-Perot cavity.

[0033] In the above method, the right band of the first locked laser beam is locked to the (m+1)th fundamental transverse mode of the target Fabry-Perot cavity through frequency-shifting cavity locking. Simultaneously, the left band is locked to the mth fundamental transverse mode of the target Fabry-Perot cavity through preset frequency shifting and the second PDH optical path. This creates a dual-fundamental transverse mode locking structure with a spacing of one free spectral range between the left and right bands, avoiding the coupling interference problem between the TEM00 and TEM01 modes in traditional dual-transverse mode schemes. This significantly improves the stability of the locked cavity and the accuracy of zero-expansion temperature detection. Furthermore, by employing a second acousto-optic modulator to achieve preset frequency shifting of the left band, the high-precision locking of the microwave drive frequency of the electro-optic modulator is replaced, thus transferring the frequency locking task to the second acousto-optic modulator. The device eliminates the need for complex and expensive microwave frequency locking equipment in the detection process, reducing equipment investment costs and mitigating the impact of electromagnetic interference on locking accuracy, thus simplifying and facilitating the detection process. By determining the driving frequency of the biased cavity locking module through a preset frequency and the free spectral range of the target Fabry-Perot cavity, the biased cavity locking module can be adaptively adjusted according to the cavity length, making it compatible with zero expansion temperature detection of ultra-stable cavities of different lengths. Furthermore, by monitoring the relationship between the driving frequency of the second acousto-optic modulator and the cavity temperature, and using the temperature corresponding to the minimum rate of change of the driving frequency as the zero expansion temperature, the detection process does not need to rely on an absolute frequency reference, reducing the requirements for the absolute frequency stability of the laser and significantly improving the universality of the detection method.

[0034] In some embodiments, the frequency-biased cavity-locked module includes a first PDH optical path of an electro-optic modulator, which modulates the intermediate laser beam to generate a left band and a right band, including: The central laser beam is modulated by an electro-optic modulator to obtain a composite laser beam containing carrier, left-side, and right-side frequency components. The frequency interval between the left-side and carrier bands is equal to the frequency interval between the carrier and right-side bands, and is also equal to the driving frequency of the electro-optic modulator. In other words, the frequencies of the left and right sidebands are symmetrical with respect to the carrier frequency, and the frequency interval is determined by the driving frequency of the electro-optic modulator. The carrier frequency is equal to the center frequency of the central laser beam.

[0035] Among them, the electro-optic modulator is a laser modulation device based on the electro-optic effect. When modulating the middle laser beam, it can obtain a composite laser beam containing the carrier, left band, and right band, thereby providing a multi-frequency laser for the frequency-locked cavity. The driving frequency of the electro-optic modulator determines the frequency difference between the left / right band and the carrier.

[0036] In some embodiments, the electro-optic modulator includes at least one or more of lithium niobate integrated electro-optic modulators and bulk material electro-optic modulators. Furthermore, the electro-optic modulator can be classified as a phase modulator or an amplitude modulator; this embodiment uses a phase modulator.

[0037] The first PDH optical path is also a frequency-stabilized optical path composed of a photodetector, phase detector, servo controller, and optical coupling components (such as collimating lenses and polarizers). It is used for cavity-locking processing based on the right-side band, so that the processed first locked laser beam is precisely locked to the (m+1)th fundamental transverse mode of the target Fabry-Perot cavity, ensuring long-term stable binding of the laser frequency and cavity mode. In some embodiments, a fiber-integrated PDH optical path or a free-space PDH optical path can be selected according to the laser power.

[0038] In some embodiments, the driving frequency of the electro-optic modulator is determined based on a preset frequency and the free spectral range of the target Fabry-Perot cavity.

[0039] In some embodiments, the driving frequency f EOM <FSR / 2, where FSR is the free spectral range of the target Fabry-Perot cavity.

[0040] In order to lock the two sidebands onto the m-th and (m+1)-th fundamental transverse modes of the target Fabry-Perot cavity, respectively, the driving frequency of the electro-optic modulator needs to be set to be less than half of the free spectral range of the target Fabry-Perot cavity.

[0041] In some embodiments, the driving frequency of the electro-optic modulator satisfies the following condition: f EOM =(FSR-Δf) / 2, where Δf is the preset frequency.

[0042] The free spectral range of the target Fabry-Perot cavity characterizes the frequency interval between two adjacent longitudinal modes, and its value is determined by the cavity length. The formula is FSR=c / 2nL, where c is the speed of light, n is the refractive index of the cavity medium, and L is the cavity length.

[0043] The preset frequency, which is the frequency shift amount of the second acousto-optic modulator, is fixed at 300MHz in this embodiment to compensate for the frequency difference between the sideband laser beam and the target Fabry-Perot cavity mode.

[0044] The driving frequency of the electro-optic modulator must be "slightly less than half of the free spectral range (FSR) of the target Fabry-Perot cavity" and match the preset frequency. Therefore, for target Fabry-Perot cavities of different lengths, the driving frequency of the electro-optic modulator can be calculated simply by substituting their FSR values, without needing to readjust the device parameters. This allows for adaptation to the detection requirements of ultra-stable cavities of different specifications, significantly improving the universality of the detection method.

[0045] In some embodiments, neither the first PDH optical path nor the second PDH optical path is equipped with an electro-optic modulator.

[0046] The core of the PDH frequency stabilization optical path is to generate sidebands through phase modulation, phase detection of cavity reflected light, and servo feedback locking. Conventional PDH optical paths will have an independent electro-optic modulator configured in the optical path for phase modulation. However, in this embodiment, the independent electro-optic modulators have been eliminated in both the first and second PDH optical paths. Their modulation function is uniformly undertaken by the system-level electro-optic modulator.

[0047] Specifically, the core reason why the first PDH optical path does not require an independent electro-optic modulator is that the laser has already undergone phase modulation by a system-level electro-optic modulator before entering the first PDH optical path, generating a composite laser beam containing a carrier wave, a left-side band, and a right-side band. The first PDH optical path only needs to complete the cavity-locked loop for phase detection and servo feedback, without the need for an additional electro-optic modulator for secondary modulation.

[0048] The incident laser in the second PDH optical path is the laser beam to be locked after the left-side laser beam is frequency-shifted by the second acousto-optic modulator. The frequency of the laser beam to be locked is precisely matched with the target Fabry-Perot cavity mode, and its phase modulation information can be indirectly transmitted through the modulation of the pre-amplifier electro-optic modulator. Therefore, the second PDH optical path only needs to perform closed-loop control of the cavity locking, and there is no need to independently configure an electro-optic modulator to generate new modulation sidebands.

[0049] In the above approach, the electro-optic modulation device of the detection system is reduced from a system-level electro-optic modulator + electro-optic modulators in two PDHs to only one system-level electro-optic modulator. This not only reduces the number of core optical components, but also eliminates auxiliary equipment such as microwave drive sources and temperature control modules corresponding to the electro-optic modulator. This significantly reduces the hardware cost and optical path integration difficulty of the system, making it easier to deploy in miniaturized form. Furthermore, it reduces cavity-locking errors caused by electromagnetic coupling of microwave drive signals and phase interference of laser modulation, and avoids crosstalk problems between multiple electro-optic modulators.

[0050] In some embodiments, determining the cavity temperature corresponding to the minimum rate of change of the driving frequency as the target zero-expansion temperature of the target Fabry-Perot cavity based on the correspondence between the driving frequency of the second acousto-optic modulator and the cavity temperature of the target Fabry-Perot cavity includes: Adjust the cavity temperature of the target Fabry-Perot cavity, collect the driving frequency data of the second acousto-optic modulator at different cavity temperatures, and establish the correspondence between driving frequency and cavity temperature; The rate of change of the driving frequency is calculated based on the relationship between the driving frequency and the cavity temperature. The cavity temperature corresponding to the minimum absolute value of the rate of change is determined as the target zero expansion temperature of the target Fabry-Perot cavity.

[0051] The cavity length of the target Fabry-Perot cavity changes nonlinearly with temperature, and this change in cavity length directly leads to a shift in the cavity mode resonant frequency. The driving frequency of the second acousto-optic modulator needs to compensate for this frequency shift in real time to maintain the cavity mode locking of the second locked laser beam. Therefore, the driving frequency of the second acousto-optic modulator is strongly correlated with the cavity temperature. By collecting the driving frequency data of the second acousto-optic modulator at different cavity temperatures, the correspondence between the driving frequency and the cavity temperature can be established.

[0052] Specifically, the target Fabry-Perot cavity undergoes uniform temperature adjustment, for example, by 0.5℃, to ensure data uniformity. The temperature adjustment range must cover the theoretical range of zero expansion temperature and be adapted to the cavity material. After stabilizing at each temperature point for 5-10 minutes to eliminate the cavity's thermal hysteresis effect, the driving frequency of the second acousto-optic modulator is synchronously acquired using a frequency acquisition module (such as a frequency counter) to form a "cavity temperature-driving frequency" dataset. Then, a continuous curve of the driving frequency changing with the cavity temperature is generated through a fitting algorithm, thus establishing the temperature-frequency correspondence.

[0053] The frequency change rate characterizes the fluctuation amplitude of the driving frequency of the second acousto-optic modulator under the unit cavity temperature change. Its essence is the first derivative of the temperature-frequency fitting curve, which can quantitatively reflect how fast the cavity length changes with temperature. The established temperature-frequency correspondence is calculated interval by interval difference to obtain the rate of change of the driving frequency in each cavity temperature interval, and the absolute value of the rate of change is taken.

[0054] Since the zero expansion temperature of the ultra-stable cavity is the temperature point at which the cavity length is least sensitive to temperature changes, the temperature coefficient of the cavity length approaches 0, and the rate of change of the corresponding cavity mode frequency also approaches 0. This is reflected in the driving frequency of the second acousto-optic modulator, i.e., the absolute value of its rate of change is the smallest. Therefore, the cavity temperature corresponding to the minimum absolute value of the rate of change is determined as the target zero expansion temperature of the target Fabry-Perot cavity.

[0055] This application also provides a detection system for the zero expansion temperature of an ultra-stable cavity, such as... Figure 2 As shown, the detection system for the zero expansion temperature of the ultra-stable cavity includes a laser 1, a first acousto-optic modulator AOM1, a frequency-biased cavity-locking module 2, a second acousto-optic modulator AOM2, a second PDH optical path 3, and a data processing module 5. Laser 1 is used to output a laser beam; The first acousto-optic modulator AOM1 is used to process the laser beam to obtain the intermediate laser beam; The frequency-biased cavity-locking module 2 is used to modulate the middle laser beam to generate a left band and a right band, and lock the right band onto the (m+1)th fundamental transverse mode of the target Fabry-Perot cavity; wherein, the frequency of the middle laser beam is V0, the frequency of the right band is G1, and the frequency of the left band is G2.

[0056] The second acousto-optic modulator AOM2 is used to shift the frequency of the left band to a preset frequency; after the frequency shift, the frequency of the left band is G3.

[0057] The second PDH optical path 3 is used to lock the frequency-shifted left band onto the m-th fundamental transverse mode of the target Fabry-Perot cavity 4; The data processing module is used to determine the cavity temperature corresponding to the minimum rate of change of the driving frequency of the second acousto-optic modulator AOM2 as the target zero expansion temperature of the target Fabry-Perot cavity 4 based on the correspondence between the driving frequency of the second acousto-optic modulator AOM2 and the cavity temperature of the target Fabry-Perot cavity 4.

[0058] in, Figure 2 The middle arrow indicates the direction of the laser beam.

[0059] In some embodiments, such as Figure 2 As shown, the frequency-biased cavity-locked module 2 includes an electro-optic modulator EOM and a first PDH optical path 21; Among them, the electro-optic modulator EOM is used to modulate the middle laser beam to obtain a composite laser beam containing carrier, left band and right band frequency components; the frequency interval between the left band and the carrier is equal to the frequency interval between the carrier and the right band, and is equal to the driving frequency of the electro-optic modulator. The first PDH optical path 21 is used to lock the right band onto the m+1 fundamental transverse modes of the target Fabry-Perot cavity.

[0060] In some embodiments, such as Figure 2 As shown, the data processing module 5 includes a temperature regulation module 51, a frequency acquisition module 52, and a data processing unit 53; Among them, the temperature regulation module 51 is used to regulate the cavity temperature of the target Fabry-Perot cavity 4; Frequency acquisition module 52 is used to acquire the driving frequency data of the second acousto-optic modulator AOM2 at different cavity temperatures; The data processing unit 53 is used to receive the driving frequency data of the second acousto-optic modulator AOM2 at different cavity temperatures, establish the correspondence between the driving frequency and the cavity temperature, calculate the rate of change of the driving frequency based on the correspondence between the driving frequency and the cavity temperature, and determine the cavity temperature corresponding to the minimum absolute value of the rate of change as the target zero expansion temperature of the target Fabry-Perot cavity 4.

[0061] Specifically, the temperature adjustment module 51 is used to perform equal-gradient temperature adjustment on the target Fabry-Perot cavity 4, for example, 0.5℃, to ensure data uniformity; the temperature adjustment range needs to cover the theoretical range of zero expansion temperature and be adapted to the cavity material.

[0062] After stabilizing at each temperature point for 5-10 minutes to eliminate the cavity thermal hysteresis effect, the frequency acquisition module 52 (such as a frequency counter) synchronously acquires the driving frequency of the second acousto-optic modulator AOM2 to form a "cavity temperature-driving frequency" dataset. Then, the fitting algorithm in the data processing unit 53 generates a continuous curve of the driving frequency changing with the cavity temperature, completes the establishment of the temperature-frequency correspondence, and calculates the fluctuation amplitude of the driving frequency of the second acousto-optic modulator AOM2 under a unit cavity temperature change, obtains the rate of change of the driving frequency in each cavity temperature range, and determines the cavity temperature corresponding to the minimum absolute value of the rate of change as the target zero expansion temperature of the target Fabry-Perot cavity 4.

[0063] The temperature control module 51, the frequency acquisition module 52, and the data processing unit 53 are electrically connected to each other.

[0064] As described above, the right band of the first locked laser beam is locked onto the (m+1)th fundamental transverse mode of the target Fabry-Perot cavity via the frequency-shifting cavity-locking module 2, while the left band is locked onto the mth fundamental transverse mode of the target Fabry-Perot cavity via the second acousto-optic modulator AOM2 and the second PDH optical path 3. This creates a dual-fundamental transverse mode locking structure with a spacing of one free spectral range between the left and right bands, avoiding the coupling interference problem between the TEM00 and TEM01 modes in traditional dual-transverse mode schemes. This significantly improves the stability of the cavity-locking structure and the accuracy of zero-expansion temperature detection. By using the second acousto-optic modulator AOM2 to perform a preset frequency shift operation on the left band, the high-precision locking of the microwave drive frequency of the electro-optic modulator is replaced, thus transferring the frequency locking task to the second acousto-optic modulator AOM2. 2. This eliminates the need for complex and expensive microwave frequency locking equipment in the detection system, reducing equipment investment costs and mitigating the impact of electromagnetic interference on locking accuracy, thus simplifying and facilitating the detection system. By determining the driving frequency of the frequency-shifting cavity-locking module through a preset frequency and the free spectral range of the target Fabry-Perot cavity 4, the frequency-shifting cavity-locking module can be adaptively adjusted according to the cavity length, making it compatible with zero-expansion temperature detection of ultra-stable cavities with different cavity length specifications. Furthermore, the data processing module 5 monitors the relationship between the driving frequency of the second acousto-optic modulator AOM2 and the cavity temperature, and uses the temperature corresponding to the minimum rate of change of the driving frequency as the zero-expansion temperature. This eliminates the need for an absolute frequency reference in the detection system, reducing the requirements for the absolute frequency stability of the laser and significantly improving the universality of the detection system.

[0065] In some embodiments, taking a Fabry-Perot cavity with a length of 5 cm as an example... Figure 3 The diagram shows the frequencies of each laser beam. The Fabry-Perot cavity has an FSR of 3 GHz and a preset frequency Δf of 300 MHz. Therefore, the driving frequency f of the electro-optic modulator EOM is... EOM =(FSR-Δf) / 2=1.35GHz.

[0066] The intermediate laser beam is modulated using a frequency-locked cavity module to generate a left and right band. The frequency interval between the left band and the carrier is equal to the frequency interval between the carrier and the right band, and is equal to the driving frequency of the electro-optic modulator, 1.35 GHz. Furthermore, the difference between the frequency V0 of the intermediate laser beam and the frequency G2 of the left band is 1.35 GHz, and the difference between the frequency G1 of the right band and the frequency V0 of the intermediate laser beam is also 1.35 GHz.

[0067] The right band is locked to the TEM00 in the target Fabry-Perot cavity via the first PDH optical path. (m+1) superior.

[0068] The left side of the TEM00 is connected to the target Fabry-Perot cavity. mThe frequency difference is exactly 300MHz, which can be compensated by frequency shifting to a preset frequency (300MHz) through a second acousto-optic modulator.

[0069] While specific embodiments of this application have been described in detail by way of examples, those skilled in the art should understand that the examples are for illustrative purposes only and not intended to limit the scope of this application. Those skilled in the art should also understand that various modifications can be made to the embodiments without departing from the scope and spirit of this application. The scope of this application is defined by the appended claims.

Claims

1. A method for detecting the zero expansion temperature of an ultra-stable cavity, characterized in that, The method for detecting the zero expansion temperature of the ultra-stable cavity includes: The laser beam output from the laser is processed by the first acousto-optic modulator to obtain the intermediate laser beam; The middle laser beam is modulated by a frequency-biased cavity-locking module to generate a left band and a right band; Lock the right side band onto the (m+1)th base transverse mode of the target Fabry-Perot cavity; The left band is frequency-shifted to a preset frequency using a second acousto-optic modulator; The frequency-shifted left band is locked onto the m-th fundamental transverse mode of the target Fabry-Perot cavity via the second PDH optical path; Based on the correspondence between the driving frequency of the second acousto-optic modulator and the cavity temperature of the target Fabry-Perot cavity, the cavity temperature corresponding to the minimum rate of change of the driving frequency is determined as the target zero expansion temperature of the target Fabry-Perot cavity.

2. The method for detecting the zero expansion temperature of an ultra-stable cavity according to claim 1, characterized in that, The sum of the frequency difference between the left and right bands and the preset frequency is equal to the free spectral path of the target Fabry-Perot cavity.

3. The method for detecting the zero expansion temperature of an ultra-stable cavity according to claim 1, characterized in that, The frequency-shifting cavity-locked module includes an electro-optic modulator and a first PDH optical path. The modulation of the intermediate laser beam through the frequency-shifting cavity-locked module to generate a left band and a right band includes: The intermediate laser beam is modulated by the electro-optic modulator to obtain a composite laser beam containing carrier, left band, and right band frequency components, wherein the frequency interval between the left band and the carrier is equal to the frequency interval between the carrier and the right band, and is equal to the driving frequency of the electro-optic modulator.

4. The method for detecting the zero expansion temperature of an ultra-stable cavity according to claim 3, characterized in that, The driving frequency f EOM <FSR / 2, where FSR is the free spectral range of the target Fabry-Perot cavity.

5. The method for detecting the zero expansion temperature of an ultra-stable cavity according to claim 4, characterized in that, The preset frequency Δf satisfies the following condition: Δf=FSR-2×f EOM 。 6. The method for detecting the zero expansion temperature of an ultra-stable cavity according to claim 3, characterized in that, Neither the first PDH optical path nor the second PDH optical path is equipped with an electro-optic modulator.

7. The method for detecting the zero expansion temperature of an ultra-stable cavity according to claim 1, characterized in that, The step of determining the cavity temperature corresponding to the minimum rate of change of the driving frequency as the target zero-expansion temperature of the target Fabry-Perot cavity based on the correspondence between the driving frequency of the second acousto-optic modulator and the cavity temperature of the target Fabry-Perot cavity includes: Adjust the cavity temperature of the target Fabry-Perot cavity, collect the driving frequency data of the second acousto-optic modulator at different cavity temperatures, and establish the correspondence between driving frequency and cavity temperature; The rate of change of the driving frequency is calculated based on the relationship between the driving frequency and the cavity temperature. The cavity temperature corresponding to the minimum absolute value of the rate of change is determined as the target zero expansion temperature of the target Fabry-Perot cavity.

8. A detection system for the zero expansion temperature of an ultra-stable cavity, characterized in that, The detection system for the zero expansion temperature of the ultra-stable cavity includes a laser, a first acousto-optic modulator, a frequency-biased cavity-locked module, a second acousto-optic modulator, a second PDH optical path, and a data processing module. The laser is used to output a laser beam; The first acousto-optic modulator is used to process the laser beam to obtain an intermediate laser beam; The frequency-shifting cavity-locking module is used to modulate the middle laser beam to generate a left band and a right band; Lock the right side band onto the (m+1)th base transverse mode of the target Fabry-Perot cavity; The second acousto-optic modulator causes the left band to achieve a frequency shift that conforms to a preset frequency; The second PDH optical path is used to lock the frequency-shifted left band onto the m-th fundamental transverse mode of the target Fabry-Perot cavity; The data processing module is used to determine the cavity temperature corresponding to the minimum rate of change of the driving frequency of the second acousto-optic modulator as the target zero expansion temperature of the target Fabry-Perot cavity, based on the correspondence between the driving frequency of the second acousto-optic modulator and the cavity temperature of the target Fabry-Perot cavity.

9. The detection system for zero expansion temperature of an ultra-stable cavity according to claim 8, characterized in that, The frequency-shifting cavity-locking module includes an electro-optic modulator first PDH optical path; The electro-optic modulator is used to modulate the intermediate laser beam to obtain a composite laser beam containing carrier, left band, and right band frequency components. The frequency interval between the left band and the carrier is equal to the frequency interval between the carrier and the right band, and is equal to the driving frequency of the electro-optic modulator.

10. The detection system for zero expansion temperature of an ultra-stable cavity according to claim 8, characterized in that, The data processing module includes a temperature regulation module, a frequency acquisition module, and a data processing unit. The temperature control module is used to adjust the cavity temperature of the target Fabry-Perot cavity; The frequency acquisition module is used to acquire the driving frequency data of the second acousto-optic modulator at different cavity temperatures; The data processing unit is used to receive the driving frequency data of the second acousto-optic modulator at different cavity temperatures, establish the correspondence between the driving frequency and the cavity temperature, calculate the rate of change of the driving frequency based on the correspondence between the driving frequency and the cavity temperature, and determine the cavity temperature corresponding to the minimum absolute value of the rate of change as the target zero expansion temperature of the target Fabry-Perot cavity.

Images