Application of convolutional fitting in Fabry-Perot (F-P) resonator linewidth measurement experiments
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摘要:
针对传统扫频法因激光线宽引入的测量误差，基于激光光谱（高斯型）与法布里-珀罗（F-P）谐振腔（洛伦兹型）的卷积特性，提出了基于卷积拟合的信号分析方法，搭建了扫频实验平台，对自制F-P腔（1号腔）和进口F-P腔（2号腔）进行验证。首先，结合仿真分析量化了激光线宽对信号轮廓的影响，并介绍了拟合算法的主要流程。其次，通过拍频对入射激光光谱进行测量。实验结果表明其光谱呈高斯形，线宽为 (11.59±1.23) kHz。接下来，评估了扫频平台的频率调制误差，使用扫频法对两台F-P腔进行了线宽测量，并对比了洛伦兹拟合与卷积拟合结果，其中，1号腔的洛伦兹与卷积拟合结果分别为 (204.1±11.2) kHz和 (203.9±11.2) kHz，差异不显著。2号腔的标定线宽为4.17 kHz,洛伦兹拟合的结果为 (8.97±0.42) kHz，卷积拟合的结果为(4.42±0.50) kHz。实验结果表明，当激光线宽与腔的线宽相近时，本方法能够准确地测量出腔的真实线宽，当激光线宽（11.59 kHz）远小于腔（204.1 kHz）时，本方法的结果与洛伦兹拟合方法相近。本工作为窄线宽F-P腔线宽测量提供了更多选择。
Abstract:To address the measurement errors introduced by laser linewidth in the traditional swept-frequency methods, a signal analysis approach based on convolution fitting is proposed leveraging the convolutional characteristics of Gaussian-shaped laser spectrum and Lorentzian-type Fabry-Perot (F-P) resonant. An experimental platform employing two F-P cavities (one custom-built and one commercial) is constructed to verify the performance of the custom-bulit F-P cavity. The paper demonstrates three key advancements: (1) the impact of laser width on the signal profle is quantified through simulation, and the Quantitative simulations established laser linewidth impacts on signal profiles, coupled with a dedicated fitting algorithm; 2) Beat-frequency characterization revealed a Gaussian laser lineshape with (11.59 ± 1.23) kHz linewidth; 3) Comparative analysis of Lorentzian versus convolutional fitting across different linewidth regimes showed critical performance differences. For Cavity 1 (204.1 kHz nominal), both methods yielded comparable results (Lorentzian: 204.1 ± 11.2 kHz; Convolutional: 203.9 ± 11.2 kHz), while for Cavity 2 (4.17 kHz reference), convolutional fitting achieved superior accuracy (4.42 ± 0.50 kHz vs. Lorentzian's 8.97 ± 0.42 kHz). The methodology effectively recovers true linewidths when laser and cavity linewidths are spectrally comparable, and converges with Lorentzian fitting when laser linewidth (11.59 kHz)
$\ll $ cavity linewidth (204.1 kHz). This approach significantly expands the applicability range of narrow-linewidth F-P cavity measurement systems by relaxing laser source requirements.-
Key words:
- F-P Cavity /
- linewidth /
- convolution fitting
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图 4 数据分箱对信号分辨率的影响。(a)原始光谱数据；(b)分箱数据重建结果
Figure 4. Effects of data binning on signal resolution. (a) Raw spectral data; (b) binned signal reconstruction results
图 8 1号腔激光器频率标定结果。(a)控制压电陶瓷的三角波信号，线性区间为0.24 s；(b)拍频信号，峰峰值为15.69 MHz
Figure 8. Frequency calibration results for cavity 1. (a) Triangular wave signal for controlling the PZT, linear region: 0.24 s; (b) beat the PZT, peak-to-peak: 15.69 MHz
表 1 不同衰减处的激光线宽测量值与理论值对比结果 (RBW=7.5 kHz)
Table 1. Comparison of measured and theoretical laser linewidth values at different attenuation points (RBW=7.5 kHz)
测量结果/Hz 洛伦兹线形 高斯线形 −3 dB 8983 2Δν 1.41Δν −10 dB 16619 6Δν 2.58Δν −20 dB 23806 20Δν 3.65Δν 
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表 2 −20 dB处的激光线宽 (RBW=1 kHz)
Table 2. Laser linewidth at −20 dB (RBW=1 kHz)
序号 测量结果/Hz 1 39595 2 43387 3 48260 4 35266 5 45008
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表 3 10个周期的频率调谐速度
Table 3. Frequency tuning speeds over 10 cycles
序号 调谐速度(MHz/s) 1 65.891 2 67.058 3 64.370 4 64.468 5 64.742 6 67.588 7 64.635 8 64.687 9 67.083 10 67.320 平均值 65.891 标准差 1.396
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表 4 2号腔实验结果：激光线宽的参考值由3.1给出，腔线宽的参考值为出厂值
Table 4. Cavity No. 2 measurement results: the reference value for the laser linewidth is given in section 3.1, and the reference value for the cavity linewidth is the factory value
激光线宽/kHz 腔线宽/kHz G-L拟合 10.84±0.91 4.42±0.50 L拟合 - 8.97±0.42 参考值 11.59±1.23 4.17
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表 5 1号腔线宽测量结果
Table 5. Linewidth measurement results of cavity 1
腔线宽/kHz L拟合 204.1±11.2 G-L拟合 203.9±11.2
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