System and method for optimizing residual amplitude noise in Pound-Drever-Hall system

Abstract

The invention provides a method for removing residual amplitude noise in a Pound-Drever-Hall (PDH) laser frequency stabilization system based on a crystal birefringence theory and an orthogonal demodulation scheme. Comprising the following steps: analyzing a reason for generating residual amplitude noise in a system based on a crystal birefringence theory, and optimizing a PDH model; the method further optimizes the system according to the noise generation reason elaborated by the model, and comprises the following steps: firstly, adding a polarization controller in the system to restrain a laser input signal aiming at the problem that the laser incident polarization angle is not fixed; secondly, aiming at the problem that the phase of a demodulation signal is not clear due to signal phase drift, an orthogonal demodulation system is established, and updating of the demodulation phase is completed by analyzing the signal phase in real time; and finally, establishing a system based on the work, and optimizing the PDH frequency tracking system. According to the method, the problems of frequency stabilization point blanking, error curve distortion and the like caused by residual amplitude noise in a traditional PDH scheme can be solved, and the problems of low final optimization tracking precision and poor long-term stability are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of precision instrument manufacturing and precision detection, and more specifically, relates to a PDH (Pound-Drever-Hall) laser frequency stabilization method and device for optimizing residual amplitude noise of an electro-optical modulator based on crystal birefringence theory and an orthogonal demodulation scheme. Background Art

[0002] Laser frequency stabilization technology can ensure that the frequency of the laser beam is highly stable. Through frequency stabilization technology, the measurement error caused by laser frequency fluctuation can be reduced and the ranging accuracy can be improved. In the fields of long-distance measurement, industrial automation, robot navigation, etc., the accuracy of laser ranging directly affects the overall performance and reliability of the system. In the field of spectral analysis, laser frequency stabilization technology can provide a high-precision laser source, which greatly improves the sensitivity and reliability of spectral analysis. In the fields of communications, military navigation, etc., the high-precision measurement capability of resonant fiber gyroscopes is crucial. The application of laser frequency stabilization technology has significantly improved the navigation and positioning accuracy in these fields. The importance of laser frequency stabilization technology in the field of high-precision measurement and high-precision sensing is self-evident. It is not only a key technology to improve the accuracy of measurement and sensing, but also an important force to promote technological progress and industrial upgrading in related fields.

[0003] In the process of achieving laser frequency stabilization using Pound-Drever-Hall (PDH) technology, it is crucial to solve the residual amplitude modulation (RAM) noise. PDH technology achieves high stability of laser frequency by locking the laser frequency to the resonant frequency of a high-fineness Fabry-Perot (FP) cavity. However, the existence of RAM noise limits the further improvement of laser frequency stability. In order to overcome this problem, researchers have conducted in-depth research on the formation mechanism of RAM, analyzed the parameters that affect the size of RAM, and developed a variety of methods to actively suppress RAM noise. These methods include modulating the laser carrier using multi-frequency synthesis technology, optimizing the PDH error signal by adjusting the phase of the modulation frequency signal, and thus effectively suppressing RAM noise. However, the current mechanism for the generation of RAM is not sufficient, and it is impossible to effectively remove RAM. It is necessary to pay attention to and solve the RAM noise problem to ensure the stability and accuracy of the laser frequency. Summary of the invention

[0004] To achieve the above objectives, a PDH system based on crystal birefringence theory and orthogonal demodulation scheme is proposed, including the following steps:

[0005] (1) Using lasers, electro-optic modulators, resonant cavities, photodetectors, digital-to-analog converters, analog-to-digital converters, and demodulation modules implemented based on FPGAs, as well as laser PZT driver modules, a traditional PDH system is built together;

[0006] (2) Based on the crystal birefringence theory, the signal transmission process of the PDH system is re-derived, the mechanism of residual amplitude noise caused by laser not incident along the crystal optical axis is explained, and a new PDH error signal model under the action of residual amplitude noise is established;

[0007] (3) Based on the new model, an overall optimization scheme is designed. A fixed-angle polarization control module is added in hardware to constrain the polarization angle of the incident laser. In software, the traditional demodulation module is optimized to an orthogonal demodulation module to obtain the error signal reflecting the laser frequency and the resonant frequency of the resonant cavity in the new system built based on the new model.

[0008] (4) Use FPGA to build a PID control module to output control signals to the laser PZT to complete the adjustment of the laser, thereby achieving laser frequency stabilization.

[0009] In order to improve the accuracy of the PDH frequency tracking system, the modulation coefficient of the electro-optical modulator in step (1) is 1.082 radians, so that the energy of the modulated signal is mainly concentrated on the carrier and the positive and negative first-order sidebands, thereby ensuring the signal-to-noise ratio.

[0010] In order to improve the accuracy of the PDH frequency tracking system, the coupling ratio of the optical fiber resonant cavity in step (1) is selected as 99:1 to obtain higher resonant cavity finesse, and the material of the resonant cavity is selected as polarization-maintaining fiber to avoid mode splitting caused by scattering noise.

[0011] In order to improve the accuracy of the PDH frequency tracking system, the sampling frequencies of the digital-to-analog converter and the analog-to-digital converter in step (1) are both 250 MHz / s, with an accuracy of 16.

[0012] The data processing module constructed by FPGA in step (1) includes a bandpass filter, a mixer, and a low-pass filter. The demodulated PDH error signal can be expressed as shown in formula (1):

[0013]

[0014] Re represents the real part of the signal, Im represents the imaginary part of the signal, is the intensity of the input laser signal, F(ω), F(ω-Ω), and F(ω+Ω) are the reflection coefficient expressions of the resonant cavity at frequencies ω, ω-Ω, and ω+Ω, respectively. mod is the demodulation phase, where cosφ mod The term is called the absorption term, sinφ mod is called the dispersion term. When the demodulation phase is When , the signal contains only dispersion terms.

[0015] Based on the crystal birefringence theory, when the laser is not incident along the optical axis of the electro-optical crystal in step (2), the PDH error can be expressed as shown in formula (2):

[0016]

[0017] Where T 1 The residual amplitude noise caused by the laser not being incident along the crystal optical axis can be expressed as shown in formula (3):

[0018]

[0019] in: is the modulation coefficient of o-light and e-light, is the phase delay caused by natural crystal birefringence, and A and B are parameters that reflect the polarization information of the laser input signal.

[0020] In step (3), the traditional demodulation module is optimized to be an orthogonal demodulation module. Specifically, the error signal output by the photodetector is passed through a bandpass filter, and the extracted error signal is divided into two, and mixed with the sine signal and the cosine signal respectively. The mixing result includes a frequency doubling signal and a DC signal, which are respectively passed through a low-pass filter, and the square root of the sum of the two signals is taken as the final PDH error signal. The inverse tangent function of the two signals can obtain the phase of the current signal. By acquiring the phase of the current signal in real time, the phase of the demodulated signal is updated in real time, thereby reducing the error caused by the phase change of the error signal.

[0021] In step (4), FPGA is used to build a PID control module to output a control signal to the laser PZT to complete the adjustment of the laser. Specifically, a closed-loop transfer function of the entire PDH system is established to design the proportional, differential, and integral parameters of the PID. Combined with the error signal output by the demodulation module, the PID parameters are used to control the laser PZT as an actuator to eliminate the error, that is, to complete the laser frequency stabilization. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flow chart of the PDH system built based on the crystal birefringence theory and orthogonal demodulation scheme;

[0023] Figure 2 This is the structure diagram of the PDH system based on the crystal birefringence theory and orthogonal demodulation scheme;

[0024] Figure 3 It is the schematic diagram of the orthogonal demodulation scheme; DETAILED DESCRIPTION

[0025] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, a residual amplitude noise optimization system and method in a Pound-Drever-Hall system of the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0026] See also Figure 1 , which is a structural diagram of the PDH system provided by the present application and constructed based on the crystal birefringence theory and orthogonal demodulation scheme, specifically including a laser, a polarization controller, an optical isolator, an electro-optic modulator, a resonant cavity, and a data processing module built by FPGA, a laser PZT, a digital-to-analog converter and an analog-to-digital converter. Among them, the laser, polarization controller, optical isolator, electro-optic modulator, resonant cavity and photodetector constitute the optical path part, and the FPGA, PZT, analog-to-digital converter and digital-to-analog converter constitute the circuit part. In particular, the present application adds a polarization controller to constrain the polarization state of the laser signal in the system, and optimizes the traditional demodulation module to orthogonal demodulation to eliminate the error curve distortion problem caused by signal phase instability.

[0027] See also Figure 2 :The system workflow diagram provided for this application, the system workflow is as follows: after the system is powered on, the programmable logic gate array (FPGA) of the system circuit part first transmits the initial voltage control information to the laser PZT, so that the laser performs a small range frequency sweep, and the signal is transmitted backward, through the optical path part composed of a polarization controller, an optical isolator, an electro-optical modulator and a resonant cavity, and the error signal is obtained by using a photodetector. This process realizes the open-loop control of the laser; secondly: the error signal is processed by using an orthogonal demodulation module composed of a dual mixer built by using FPGA, that is, it is passed to the FPGA for data processing through an analog-to-digital converter (AD), firstly the error signal is band-pass filtered, the required first-order error signal is extracted, and then the error signal intensity and real-time phase are obtained through the orthogonal demodulation module. Finally: the PID (proportional differential integral) control module finally outputs the PID control signal to the laser PZT control module through the digital-to-analog converter (DA) to complete the closed-loop control of the laser.

[0028] See also Figure 3, which is the schematic diagram of the orthogonal demodulation scheme provided by the present application. Specifically, the error signals of the laser and the resonant cavity obtained by the photodetector are divided into two, and the direct digital frequency synthesizer (DDS) module is built by FPGA as a signal generator to synchronously output one cosine signal and one sine signal, both of which have a frequency of 10MHz. The cosine signal and the sine signal are also used as reference signals in demodulation. The error signal and the two reference signals are mixed in mixer 1 and mixer 2 respectively, and the two output signals are respectively passed through low-pass filter 1 and low-pass filter 2 to obtain the in-phase component and orthogonal component of the PDH error signal. The current phase angle can be obtained by solving the inverse tangent function of the two signals, and this angle is fed back to the signal generator to complete the real-time update of the demodulated signal phase, reducing the error caused by the phase change of the error signal.

Claims

1. A system and method for optimizing residual amplitude noise in a Pound-Drever-Hall system, characterized in that: The following steps are involved: (1) A PDH system consisting of a single-frequency laser with a wavelength of 1550 nm, an optical isolator, an electro-optic modulator, a resonant cavity, a photodetector, a programmable logic gate array (FPGA), a digital-to-analog converter, an analog-to-digital converter, and a PZT actuator was constructed. The laser, polarization controller, electro-optic modulator, and resonant cavity constituted the optical path part, which was used to obtain an optical signal that could reflect the error between the laser resonant frequency and the resonant cavity resonant frequency; the photodetector converted the error signal from an optical signal to an electrical signal, which was then passed to the FPGA for processing through an analog-to-digital converter; an orthogonal demodulation module consisting of a mixer, a phase shifter, and a low-pass filter was constructed based on the FPGA to complete the processing of the error signal, and a PID control module was constructed using the FPGA to output the control signal; the control signal controlled the laser PZT via the digital-to-analog conversion module, and finally completed the control of the laser. (2) Based on the crystal birefringence theory, the residual amplitude noise caused by the incident laser deviating from the principal axis of the electro-optical crystal is quantitatively analyzed in actual situations to optimize the PDH model. (3) According to the PDH system optimization model obtained in step (2), the polarization effect is optimized and a polarization control module is added to the system to fix the polarization angle of the laser output signal. (4) Based on the PDH system optimization model obtained in step (2), an orthogonal demodulation module is constructed to optimize the problem of signal curve distortion caused by unstable error signal phase and fixed demodulation phase, which in turn leads to the blanking of the stable frequency point.

2. A residual amplitude noise optimization system and method in a Pound-Drever-Hall system according to claim 1, characterized in that: The laser obtained in step (1) is a narrow linewidth laser with a wavelength of 1550nm, the modulation coefficient of the electro-optic modulator is 1.082 radians, and the modulation frequency is 10MHz, ensuring that the energy of the laser after modulation is concentrated on the carrier and the positive and negative first-order sidebands to obtain the best signal-to-noise ratio; the resonant cavity is a resonant cavity built by an optical fiber ring, and the fineness of the resonant cavity is ensured by optimizing parameters such as material and coupling ratio to ensure system accuracy; FPGA builds a direct digital synthesis module to complete the modulation of the electro-optic modulator, and at the same time builds mixing, phase shifting, and low-pass to complete the processing of the error signal, and finally realizes the regulation of the laser through the built PID module output control module.

3. A residual amplitude noise optimization system and method in a Pound-Drever-Hall system according to claim 1 or claim 2, characterized in that: Step (2) The process of optimizing the PDH model based on the crystal birefringence theory is as follows: When the laser is not incident along the optical axis of the electro-optical crystal, that is, there is an angle α between its polarization direction and the direction perpendicular to the optical axis, the birefringence effect of the crystal will cause the ordinary light o and the extraordinary light e to exist at the same time, and the beat frequency of these two polarization components will modulate the detected light. When considering the above process, assuming that there is an angle β between the laser emission angle and the direction perpendicular to the optical axis, after electro-optic modulation, the signal can be expressed as shown in formula (1): Among them: A=sinαsinβ, B=cosαcosβ, E EOM is the modulated laser signal, E0 is the intensity of the laser signal, ω is the angular frequency of the laser signal, Ω is the modulation frequency, φ o and φ e is the phase delay caused by birefringence, δ o and δ e is the modulation index of o light and e light. When the birefringence of the crystal is not considered, that is, α=β=0, the laser signal after electro-optical modulation is a standard signal, which can be expressed as shown in formula (2): The photodetector is used to detect the light field of the phase modulated light interacting with the optical cavity. The signal can be expressed as shown in formula (3): AND PD =And o +E e (3) Where: E PD is the total signal after the modulated optical signal interacts with the optical cavity, E o is the signal after the interaction between o light and the optical cavity, E e is the signal after the e-light and the optical cavity interact. Finally, the PDH error model including the crystal birefringence can be obtained. The signal can be expressed as shown in formula (4): Where: V PDH is the error signal, Re represents the real part of the signal, Im represents the imaginary part of the signal, φ mod is the demodulation phase, cosφ mod Characterizing the absorption term, sinφ mod Characterize the dispersion term. When the modulation frequency is high, it is characterized as an absorption term, and when the modulation frequency is low, it is characterized as a dispersion term. F(ω), F(ω-Ω), and F(ω+Ω) are the reflection coefficients of the resonant cavity at frequencies of ω, ω-Ω, and ω+Ω, respectively. T1 can be expressed as shown in formula (5): Where: J0 and J1 are the zeroth and first order Bessel functions of the first kind, where Δφ = φ o -φ e Characterizing the phase delay φ caused by birefringence in natural crystals o and φ e The difference between them, A and B are polarization-related parameters.

4. A residual amplitude noise optimization system and method in a Pound-Drever-Hall system according to claims 1 to 3, characterized in that: Step (3) is specifically as follows: Based on the obtained PDH optimization model formula (4) and formula (5) that can explain the residual amplitude noise, it can be known that when the polarization angle is fixed, the error signal can obtain a fixed value. Therefore, a polarization controller is added to the system to constrain the laser incident angle and optimize the impact of polarization instability.

5. A system and method for optimizing residual amplitude noise in a Pound-Drever-Hall system according to claims 1 to 4, characterized in that: From formula (4) and formula (5), we can see that the most influential factor is the demodulation phase φ mod The main reason for the instability of the error curve is that the unstable phase of the output signal leads to unstable demodulation phase. To address this problem, we use FPGA to build a new orthogonal demodulation module to optimize the traditional demodulation module, and optimize the impact of phase jitter through real-time analysis of the error signal phase.

6. A system and method for optimizing residual amplitude noise in a Pound-Drever-Hall system according to claims 1 to 5, characterized in that: The process of building the orthogonal demodulation module in step (5) is as follows: the system uses FPGA to build a direct digital frequency synthesizer module to synchronously output two cosine signals and one sine signal, both of which have a frequency of 10MHz, one cosine signal as the control signal of the electro-optical modulator, and the remaining one cosine signal and one sine signal as the reference signal in the demodulation. The error signal and the two reference signals are mixed in mixer 1 and mixer 2 respectively, and the two output signals are respectively passed through a low-pass filter to obtain the in-phase component and the orthogonal component of the PDH error signal. The inverse tangent function of the two signals can be solved to obtain the current phase angle, thereby completing the real-time update of the demodulation signal phase, solving the problem of the demodulation phase not being fixed, and reducing the error caused by the phase change of the error signal.

7. A system and method for optimizing residual amplitude noise in a Pound-Drever-Hall system according to claims 1 to 6, characterized in that: It includes three modules: the first module is used to complete the acquisition of the original signal of the frequency tracking error. The module is composed of a fiber laser with a band of 1550nm, an electro-optic modulator, a fiber resonant cavity, and a photodetector; the second module uses FPGA to build a frequency discrimination module composed of a bandpass filter, a mixer, and a low-pass filter; the third module is a feedback module composed of a PID control module and a laser PZT. The PID control module controls the laser PZT based on the error signal obtained by the second module to achieve the laser tracking of the resonant frequency of the resonant cavity.

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