Application Cases

Experiment Title: Application in Optical Filter Cavity

Testing Equipment: High Voltage Amplifier, Optical Isolator, Photodetector, Phase Modulator, Spectrum Analyzer, etc.

Experiment Process:

Figure 1: Schematic diagram of the experimental setup for analyzing the acoustic noise characteristics of the optical filter cavity. OI: Optical Isolator; EOM: Electro-Optic Phase Modulator; BS: Beam Splitter; PBS: Polarizing Beam Splitter; MC: Mode Cleaner; PD1-3: Photodetector; HV: High Voltage Amplifier; SA: Spectrum Analyzer; ADC: Analog-to-Digital Conversion; DAC: Digital-to-Analog Conversion; FPGA: Field Programmable Gate Array.

Figure 1 illustrates the experimental setup. The 1550nm laser output from the fiber laser passes through the optical isolator OI and the homemade phase modulator EOM and is split into two beams. The reflected light is sent to the photodetector PD3 for intensity noise analysis, while the transmitted light is incident on the mode cleaner MC. The MC is a three-mirror ring cavity with two plane mirrors having a transmission rate of 1% for the 1550nm laser and a concave mirror that completely reflects the laser (>99.95%). The cavity has a fineness of 275 and a linewidth of 2.5MHz. After locking the cavity length using the Pound-Drever-Hall (PDH) method, the power transmission rate is close to 90%. In the PDH control loop, a signal generator produces two 34.3MHz high-frequency signals, one for driving the EOM and the other mixed with the output signal of the resonant photodetector PD1 through a mixer. After demodulation by a low-pass filter, the feedback control error signal is obtained. It then passes through a digital PID controller based on FPGA and a high voltage amplifier before being fed back to the piezoelectric ceramic of the MC to achieve cavity length locking. The output laser from the MC is attenuated in power and directly enters the photodetector PD2 for intensity noise analysis. The input power to PD2 and PD3 is maintained at 1mW during the experiment.

Experimental Results:

Figure 2: The intensity noise spectra of the laser (orange curve) and the output field of the MC cavity after cavity length locking (other colored curves). (a) Power noise spectra for frequencies ranging from 3-300kHz, with RBW: 10kHz and VBW: 50Hz; (b) Power noise spectra for frequencies less than 3kHz, with RBW: 10Hz and VBW: 1Hz.

As shown in Figure 2, the power noise spectra of a 1mW laser power are presented. Further studies have revealed that noise coupling is mainly introduced through two pathways: (1) additional noise introduced by the PDH locking loop; (2) the MC converting the phase noise of the input beam into intensity noise. In response to these two noise coupling issues, the following research work has been carried out.

In conjunction with the critical proportionality method, a specific implementation plan for optimizing the PI control parameters in the MC has been summarized. (1) First, an initial value is assigned to the proportional gain kP and the integral gain kI, as shown by curve a in Figure 2(b); (2) Then,  kP is gradually increased. The working state of the loop is observed through the transfer function test process or the noise spectrum of the MC output field, until the loop exhibits obvious oscillation; (3) Next, kPis gradually decreased until the control loop oscillation just disappears. The value of kP at this time is noted, and it is set to be 45%-70% of the recorded value, as shown by curve b in Figure 2(b); (4) Subsequently, kI is gradually increased until the loop oscillates; (5) kI is gradually decreased until the oscillation disappears, and its value is recorded. It is then set to be 10%-30% of the recorded value, as shown by curve c in Figure 2(b); (6) Finally, by observing the power noise spectrum output by PD2, the optimal PI parameters are searched near the setting value obtained in step 5 until the noise level reaches the lowest point. At this time, any further adjustment of the PI parameters will increase the noise, thereby achieving the optimal PI parameter setting, as shown by curve d in Figure 2(b). At this stage, the loop gain reaches the optimal value. The response speed can quickly correct system errors and achieve a stable state, thus suppressing the periodic low-frequency oscillation signals in curves a-c.

During the tuning of the PI parameters, when analyzing frequencies greater than 3kHz, changes in the PI parameters do not affect the amplitude of the intensity noise, as shown in Figure 2(a). However, when analyzing frequencies less than 3kHz, as the PI parameters approach the optimal values, the intensity noise of the optical field gradually approaches the lowest noise level, as shown in Figure 2(b). By testing the control loop transfer function, it was found that during the process of optimizing the PI parameters, the open-loop transfer function test results show (as shown in Figure 3) that the loop feedback control bandwidth gradually increases from 290Hz to 2kHz (optimal bandwidth). The closed-loop transfer function test results show (as shown in Figure 4) that the low-frequency noise suppression level of the control loop is improved by about 30dB. The detailed parameters are shown in Table 1.

Table 1: Parameters of the Experiment

Figure 3: Amplitude and Phase Diagram of the System Open-Loop Transfer Function

Figure 4: Amplitude Diagram of the Closed-Loop System Transfer Function

However, as seen from Figures 2(a) and (b), even under the optimal feedback control parameters, the low-frequency noise (<100kHz) of the output field of the MC is still higher than the laser's background noise. The main reason is that the intensity noise of the output field of the MC is determined by both the intensity noise and phase noise of the input field. Since the phase noise of the fiber laser is higher than its intensity noise, the phase noise of the input field is coupled into the intensity noise of the output field through the MC, thereby increasing the intensity noise of the output field. Additionally, laser pointing noise is also converted into intensity noise through the MC, degrading the intensity noise of the output field. In future work, a high-finesse ultra-stable optical resonator will be used as a reference benchmark. By locking the laser to the ultra-stable cavity, phase noise will be suppressed. Measures such as using a vibration isolation platform, adding a shielding cover to the device, temperature control of the entire device, and coupling the spatially transmitted laser beam into a fiber will be adopted to suppress pointing noise. By suppressing phase noise and pointing noise, the intensity noise of the MC output field will be reduced to the background noise level.

High Voltage Amplifier Recommendation: ATA-214

Figure: Specifications of the ATA-214 High Voltage Amplifier

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