Application of convolutional fitting in Fabry-Perot (F-P) resonator linewidth measurement
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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）远小于腔的线宽（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。
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关键词:
- 法布里-玻罗（F-P）腔 /
- 线宽 /
- 卷积拟合
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 Guassian-shaped laser spectrum and Lorentzian-type Fabry-Perot (F-P) cavity. An swept-frequency optical fiber experimental platform is constructed to verify the performance of the two F-P cavities (one is custom-built (Cavity 1) and another is commercial (Cavity 2)) . Firstly, the impact of laser linewidth on the signal profile is quantified through simulations, and the main process of the fitting algorithm is introduced. Secondly, the spectrum of the incident laser is measured via beat-frequency analysis. The experimental results indicated that the spectrum exhibited a Gaussian shape with a linewidth of (11.59 ± 1.23) kHz. Subsequently, the frequency modulation error of the swept-frequency platform is evaluated. Linewidth measurements are conducted on the cavity 1 and cavity 2 using the swept-frequency method. For Cavity 1, the results of Lorentzian fitting and convolutional fitting are (204.1 ± 11.2) kHz and (203.9 ± 11.2) kHz, respectively, showing no significant difference. For Cavity 2, which had a calibrated linewidth of 4.17 kHz, the result of Lorentzian fitting is (8.97 ± 0.42) kHz, while the result of convolutional fitting is (4.42 ± 0.50) kHz. The experimental results demonstrate that when the laser linewidth is comparable to the cavity’s linewidth, this method can accurately measure the true linewidth of the cavity. When the laser linewidth (11.59 kHz) is significantly smaller than the cavity’s linewidth (204.1 kHz), the results obtained using this method are similar to those from the Lorentzian fitting approach. This work broadens the range of options for selecting linewidth measurement equipment for narrow-linewidth Fabry-Pérot (F-P) cavities.
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Key words:
- Fabry-Perot (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 frequency signal, 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号腔线宽测量结果
Table 4. Linewidth measurement results of cavity 2
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 注：激光线宽的参考值由3.1给出，腔线宽的参考值为出厂值
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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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