[Paper Review] Fundamental scaling limits and bandwidth shaping of frequency-modulated combs

M. Roy, Zhifeng Xiao+2 more|arXiv (Cornell University)|Sep 29, 2023

Spectroscopy and Laser ApplicationsChemistry3 citations

TL;DR

This paper introduces diffusive loss shaping—using resonantly coupled loss structures in terahertz quantum cascade lasers—to counteract gain curvature, enabling frequency-modulated combs with bandwidths approaching the intrinsic gain bandwidth limit (80% of single-mode laser bandwidth). The method simultaneously stabilizes combs and enables soliton-like pulsed states, offering a new degree of freedom in active cavity comb engineering.

ABSTRACT

Frequency-modulated (FM) combs based on active cavities like quantum cascade lasers have recently emerged as promising light sources in many spectral regions. Unlike passive modelocking, which uses amplitude modulation to generate amplitude modulation, FM combs use phase modulation to generate phase modulation. They can therefore be regarded as a phase-domain version of passive modelocking. However, while the ultimate scaling laws of passive modelocking have long been known -- Haus showed in 1975 that pulses have a bandwidth proportional to effective gain bandwidth -- the limits of FM combs have been much less clear. Here, we show that FM combs are governed by the same fundamental limits, producing combs whose bandwidths are linear in the effective gain bandwidth. Not only do we show theoretically that the diffusive effect of gain curvature limits comb bandwidth, we also show experimentally how this limit can be increased. By adding carefully designed resonant-loss structures that are evanescently coupled to the cavity of a terahertz laser, we reduce the curvature and increase the effective gain bandwidth of the laser, demonstrating bandwidth enhancement. Our results give a new degree of freedom for the creation of active chip-scale combs and can be applied to a wide array of cavity geometries.

Motivation & Objective

• Address the fundamental bandwidth limitation in frequency-modulated quantum cascade laser combs caused by gain curvature.
• Overcome the instability of FM combs due to intensity fluctuations arising from gain variation.
• Demonstrate a new method to engineer both dispersion and diffusion in active cavity combs for enhanced performance.
• Enable broader, more coherent combs and explore the emergence of pulsed states in QCLs.
• Provide a scalable, cavity-agnostic strategy for bandwidth enhancement in integrated frequency combs.

Proposed method

• Engineer resonant loss structures evanescently coupled to the QCL cavity to shape the effective gain profile.
• Control the size and position of these loss structures to flatten the gain curvature across the lasing spectrum.
• Use active cavity mean-field theory and generalized Lugiato-Lefever equation to model the system dynamics.
• Implement diffusive loss shaping to suppress amplitude fluctuations caused by gain curvature, stabilizing FM comb operation.
• Employ SWIFTS and superconducting bolometers to characterize temporal and spectral coherence and bandwidth.
• Bias the device near the instability threshold to observe transition from FM combs to pulsed states.

Figure 1: a. Effect of gain curvature on FM comb formation. For an FM comb with gain curvature, frequency modulation gives rise to intensity modulation that destabilizes the comb. b. By introducing diffusive loss shaping, in which resonant structures near the cavity reduce the gain curvature and mit

Experimental results

Research questions

• RQ1 How does gain curvature limit the bandwidth of frequency-modulated combs in quantum cascade lasers?
• RQ2 Can resonant diffusive loss shaping effectively counteract the destabilizing effects of gain curvature in QCL combs?
• RQ3 To what extent can comb bandwidth be extended toward the intrinsic gain bandwidth limit using this method?
• RQ4 What role does the interplay between dispersion and diffusion play in enabling stable, broadband comb operation?
• RQ5 Can diffusive loss shaping also promote the formation of soliton-like pulsed states in QCLs?

Key findings

• Diffusive loss shaping enables QCL combs to achieve bandwidths up to 80% of the maximum lasing bandwidth of a single-mode laser, approaching the theoretical limit.
• The method suppresses intensity fluctuations caused by gain curvature, stabilizing frequency-modulated comb operation.
• Coherence across the full comb bandwidth was verified using SWIFTS, demonstrating self-referenced coherence over 700 GHz.
• High dynamic range spectra confirmed simultaneous comb bandwidth of 700 GHz using a superconducting bolometer.
• At bias points near the instability threshold, the system transitions from FM combs to pulsed states with pulses 3–4 times stronger than the continuous-wave portion.
• The strategy is compatible with various cavity geometries, including Fabry-Pérot and ring cavities, and enables dynamic tuning via bias control.

Figure 2: Gain curvature theory. a. Comb bandwidths that can be achieved given a gain bandwidth, provided the optimum dispersion is chosen. The linear relationship demonstrates the necessity of low gain curvature. b. Effect of gain inhomogeneity on FM comb spectra. Even if a coherent comb can form,