The Fabry-Perot cavity,which is composed of two or more mirrors with high reflectivity,plays an important,multifunctional role in quantum optical experiments,such as in selecting and stabilizing the laser frequency [
Laser & Optoelectronics Progress, Volume. 60, Issue 15, 1536001(2023)
[in Chinese]
The combination of an optical cavity and a proportional-integral (PI) controller is commonly used in experimental quantum optical fields. In this study, an optimal PI controller for an optical cavity was designed based on the average-squared value of the error signal. The controller was implemented using a field-programmable gate array (FPGA) data acquisition board and LabVIEW software. The overall gain of the controller is optimized by adopting the cavity transmission as an optical power reference, such that the cavity locking performance does not degrade as the optical power varies.
1 Introduction
The Fabry-Perot cavity,which is composed of two or more mirrors with high reflectivity,plays an important,multifunctional role in quantum optical experiments,such as in selecting and stabilizing the laser frequency [
However,the Fabry-Perot cavity is susceptible to the surrounding temperature and mechanical noise. Therefore,in most applications,it is locked on the resonance of the incident laser,or the laser frequency is locked to a specially fabricated,very stable cavity. Cavity detuning was measured and fed back using a proper controller. Schemes discriminating the error of cavity length include Pound-Drever-Hall locking[
In recent decades,digital locking of optical cavities has been widely adopted. Digital locking has several advantages over other analog devices. It provides good scalability and integration,which are particularly important in complicated experimental systems[
Proportional-integral(PI)controllers are widely used in many applications owing to their simplicity and effectiveness. Extensive research has been conducted on PI parameter tuning,such as the Ziegler-Nichols parameter tuning [
In this study,an optimal PI controller for the cavity was designed and implemented using a reconfigurable I/O device and LabVIEW programming(LabVIEW FPGA,NI-7833R). The controller parameters are optimized by minimizing the average squared error signal of the system. The total gain of the controller is optimized by adopting the cavity transmission as the optical power reference,such that the cavity-locking performance will not degrade as the optical power varies.
2 Experimental setup
The traditional Pound-Drever-Hall(PDH)technique [
Figure 1.Experimental setup diagram
The mirrors have a power transmittance of T=10%,T=0.1%,and radii of curvature of 30 mm and infinity,respectively.
The reflected light was picked off using a 50% beam splitter and detected using a wideband photodetector(PD1). The subsequent photocurrent was demodulated with reference to the same local oscillator used to modulate the laser. After passing through a low-pass filter,the demodulated signal was used as the error signal for cavity detuning. The laser transmitted through the optical cavity was detected by another photodetector(PD2),and the subsequent photocurrent was used as a reference for optical power. The error signal and optical power reference are sent to an analog-to-digital converter and converted into digital signals. The digital program of the controller running on the FPGA was composed and debugged using the LabVIEW software.
The programming output was converted to an analog signal by a digital-to-analog converter connected to a high-voltage amplifier and then to the cavity PZT to drive cavity detuning.
A schematic of the control system is shown in
Figure 2.Schematic diagram of closed-loop feedback control
3 The controller and experimental result
The mathematical expression of discrete PI can be written as
where
The PI controller program has two external inputs:the error signal and the reference of the optical power in the cavity. The gain of the plant is proportional to the optical power in the cavity[
The experimental results of parameter scanning are shown in
Figure 3.Hot spot of the average squared error signal
This experiment was performed using a Moku:Lab instrument to measure the frequency response. As shown in
Figure 4.Frequency response diagram of the system
Figure 5.Error signal spectrum
To verify the control capability of the designed digital control system under the condition of laser power variation,the incident laser was intensity modulated by a
Figure 6.Cavity transmission power and error signal. (a) Adapted overall gain; (b) non-adapted overall gain
4 Conclusion
A digital proportional-integral controller was designed and implemented for the optical cavity. The overall gain of the controller was optimized in the case of laser power variations. The proportional and integral gains of the controller were optimized by minimizing the average square of the error signal. The measured frequency response showed that the cavity length was robustly controlled against disturbances,and the spectrum of the error signal indicated that the controller provided good noise suppression. The entire system exhibits good long-term stability. This digital control system can provide the basis for a more complicated optical system.
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Xian Liu, Zehui Zhai, Jianli Liu, Xufei Han. [J]. Laser & Optoelectronics Progress, 2023, 60(15): 1536001
Category: Information
Received: Apr. 26, 2023
Accepted: May. 4, 2023
Published Online: Aug. 11, 2023
The Author Email: Liu Xian (zhzehui@sxu.educn), Zhai Zehui (zhzehui@sxu.educn), Liu Jianli (zhzehui@sxu.educn), Han Xufei (zhzehui@sxu.educn)