Arbitrary laser frequency modulation algorithm based on iterative on-the-fly deconvolution

TL;DR

This work addresses precise laser frequency modulation by introducing an on-the-fly deconvolution framework that iteratively estimates the laser transfer function and synthesizes arbitrary target modulations. By operating in the Fourier domain, it combines two iterative schemes—Newton's method and the secant method—with digital waveform implementation to converge toward the desired modulation patterns, demonstrated on FMCW-like and square-frequency-shift targets. Experimental proof-of-principle with an external-cavity diode laser shows convergence within about 10 iterations and frequency-precision approaching the laser noise floor, highlighting the method's potential for in-situ recalibration in field environments. The approach offers a low-complexity, hardware-friendly tool that can complement existing predistortion and servo-control strategies, with clear paths for enhancement via spectral filtering and higher-bandwidth laser platforms for broader practical deployment.

Abstract

I present a general laser modulation control algorithm. I implement the LIDAR Frequency Modulated Continuous Wave (FMCW) scheme as a special case of study. My proposal applies to any arbitrary modulation pattern and is based on an iterative algorithm that infers the laser transfer function in order to perform on-the-fly deconvolution. I present an experimental proof-of-principle using an external-cavity diode laser, the accuracy of which I analyse by comparing the obtained frequency response with a targeted modulation pattern. In addition to the FMCW scheme, I am also testing square wave modulations, which are more demanding in terms of bandwidth.

Figures (6)

• Figure 1: Right column: converge of the algorithm after 10 iterations for the target FMCW pattern $V_T^\mathrm{FMCW}$ with a rise time $\tau=600$ ns (red dashed line). Left column: I represent the input modulation signal $U_n$ for the first ( $U_0$ as the initial guess, first line), second ($U_1$, second line), fifth ($U_4$, third line ) and tenth ($U_9$, last line) iteration.
• Figure 2: Converge of the algorithm after 10 iterations for the target FS pattern $V_T^\mathrm{FS}$ (red dashed line) with the same representation as Fig. \ref{['fig:converge_fmcw']} and same rise time $\tau=600$ ns.
• Figure 3: Frequency precision, defined as the RMSD error for the target function, converge after 10 iterations for the FCMW (left panel) and the FS patterns (right panel). For each pattern, I compare the first-order Newton's method (black curve and symbols), already illustrated in Figs. \ref{['fig:converge_fmcw']} and \ref{['fig:converge_fs']}, and the second-order secant method (magenta curve and symbols). The 130 kHz noise floor is represented as a black dashed line. The rise time $\tau=600$ ns is unchanged. The RMSD values at the last iteration are summarised in Table.\ref{['table:rmsd']}.
• Figure 4: Frequency precision as a function of $\tau$ for each pattern and method with the same colour code as in Fig.\ref{['fig:converge_compar']}.
• Figure 5: Poor converge of the algorithm after 10 iterations for the target FS pattern with a rise time $\tau=400$ ns. I only represent the frequency response and not the input modulation signal $U_n$. The Newton's and secant methods are plotted on the left and right columns respectively.