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，对两台F-P腔进行验证。首先，结合仿真量化了激光线宽对信号轮廓的影响，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，使用扫频法对自制F-P腔（1号腔）和进口F-P腔（2号腔）进行了线宽测量，并对比了洛伦兹拟合与卷积拟合的结果，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，当激光线宽与腔相近时，本方法能够很好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。本工作拓宽了窄线宽F-P腔线宽测量设备选择范围。
Abstract:To address measurement inaccuracies in traditional swept-frequency methods caused by laser linewidth effects, this study proposes a convolution-based signal analysis approach that accounts for the convolutional relationship between Gaussian-shaped laser spectra and Lorentzian-type Fabry-Perot (F-P) resonator responses. An experimental platform employing two F-P cavities (one custom-built and one commercial) demonstrated three key advancements: 1) 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 2 入射激光线宽对信号轮廓的影响
Figure 2. Impact of laser linewidth on F-P cavity lineshape distortions
图 4 数据分箱：左图为分箱前，右图为分箱后
Figure 4. Data binning effects on signal resolution Raw spectral data | Binned signal reconstruction
图 6 激光线宽测量结果(a)分辨带宽7.5 kHz；(b) 分辨带宽1 kHz
Figure 6. Laser Linewidth Results (a) RBW=7.5 kHz; (b) RBW=1 kHz
图 8 1号腔激光器频率标定实验(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 for Cavity 1 (a) Triangular wave (PZT control), linear region: 0.24 s; (b) Beat signal, peak-to-peak: 15.69 MHz.
表 1 不同衰减处的激光线宽 (RBW=7.5 kHz)
Table 1. Comparison of measured laser linewidth with theoretical value (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 speed 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 by 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. Cavity No.1 linewidth measurement results
腔线宽/kHz L拟合 204.1±11.2 G-L拟合 203.9±11.2
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