Interference Fringe Mitigation in Short-Delay Self-Heterodyne Laser Phase Noise Measurements

TL;DR

The paper tackles fringe-induced distortions in short-delay self-heterodyne laser phase-noise measurements by introducing a data-driven PN-PSD equalization that uses Kernel Ridge Regression to learn a smooth $S_{\phi}(f)$ without assuming a specific laser model. This learned model feeds a PSE filter that suppresses interference fringes and yields accurate PN-PSD estimates, even for lasers with complex or unknown lineshapes. The approach is validated through simulations and two experimental measurements, showing close agreement with reference heterodyne data where available and clean PSDs where no reference exists. Its minimal hardware requirements and flexible digital processing make it a practical improvement for routine phase-noise characterizations across diverse laser types.

Abstract

Self-heterodyne techniques are widely used for laser phase noise characterization due to their simple experimental setup and the removed need for a reference laser. However, when investigating low-noise lasers, optical delay paths shorter than the laser coherence length become necessary. This introduces interference patterns that distort the measured phase noise spectrum. To compensate for this distortion, we introduce a robust data-driven digital signal processing routine that integrates a kernel-based regression model into a phase noise power spectral density (PN-PSD) equalization framework. Unlike conventional compensation methods that rely on simplified phase noise models, our approach automatically adapts to arbitrary laser lineshapes by using Kernel Ridge Regression with automatic hyperparameter optimization. This approach effectively removes the interference artifacts and provides accurate PN-PSD estimates. We demonstrate the method's accuracy and effectiveness through simulations and via experimental measurements of two distinct low-noise lasers. The method's applicability to a broad range of lasers, minimal hardware requirements, and improved accuracy make this approach ideal for improving routine phase noise characterizations.

Figures (5)

• Figure 1: a) Typical experimental setup for short-delay self-heterodyne laser phase noise measurements. b) A spectrum of an experimentally detected signal.
• Figure 2: Visualization of the conventional approach to compensate for interference in SDSH measurements. At the interference fringes of $S_{\Delta\phi}(f)$, the conventional estimate $\hat{S}_{\phi, \text{INV}}(f)$ diverges away from the true PN-PSD $S_{\phi, true}(f)$.
• Figure 3: Visualization of the data-driven PN-PSD equalization technique. The grey regions indicate the frequency bands excluded from training due to SNR thresholding, here with $T_{\mathrm{SNR}} = 5$ dB. Given a set of training samples $f_T$, the KRR estimate $\hat{S}_{\phi, \text{KRR}}(f)$ almost perfectly overlaps with the true PN-PSD $S_{\phi, true}(f)$, which results in a very accurate final PSE estimate $\hat{S}_{\phi, \text{PSE}}(f)$. Notably, $\hat{S}_{\phi, \text{PSE}}(f)$ does not diverge at the position of the interference fringes.
• Figure 4: Hyperparameter grid search using grouped n-fold cross-validation, where $N_{train}=600$, $n=8$ and $G=25$. The green cross indicates the optimal set of hyperparameters. As the KRR is performed using logarithmic scaling, the MSE is calculated in logarithmic scaling as well.
• Figure 5: Application of the equalization method to experimental measurements. a) Phase noise PSD estimates of a commercial fiber laser. b) zoom of marked region in a). c) Phase noise PSD estimates of a custom-built, externally stabilized DFB laser. d) zoom of marked region in c).