Staggered Phase Flux for Frequency Comb Shaping in Fast Gain Lasers

The importance of optical frequency combs (OFCs) has steadily grown in fields such as spectroscopy, metrology, timekeeping, microwave synthesis, wavelength division multiplexing, and communication over the past decades [1]. To address the expanding demand for compact OFC generation, various nonlinear optics-based approaches have been developed, mainly based on microresonators, to efficiently produce on-chip combs. Whether the generation of the comb takes place in a nonlinear passive chip or directly inside a semiconductor mode-locked lasers (SMLLs), its applications would benefit greatly from spectral shaping, i.e., reconfiguring the spectrum to achieve a desired intensity distribution. Traditionally, this has been achieved during device fabrication by engineering dispersion and losses, which prevents in-situ control when the OFC device is already in operation. Recent attempts rely on integrated photonic circuit-based reconfigurable spectral filters for OFCs, which complicates the fabrication and integration [2]. In principle, it is possible to shape the spectrum using phase modulation that introduces an electrically controllable coupling between cavity modes. However, since in most OFCs the output is pulsed, the overlap with the modulation signal is reduced and spectral control by phase-modulation-induced mode coupling is very inefficient. Here, we demonstrate in-situ spectral shaping using phase modulation of a ring-shaped semiconductor laser with ultrafast gain recovery times [3]. Using fast-gain lasers, we enable quasi-continuous-wave OFC states, which are extended throughout the whole cavity and experience highly efficient phase modulation. This allows for unprecedented control of the state inside a mirroring cavity. Specifically, we modulate the laser with two radio-frequency tones, at the resonance frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{rep}$</tex> and second harmonic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2 f_{ {rep }}$</tex>. The resulting modulation, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$J_M=A_{1 f_{ {rep }}} \cos \left(2 \pi f_{ {rep }} t\right)+A_{2 f_{{rep }}} \cos \left(4 \pi f_{ {rep }} t+\dot{\phi}\right)$</tex> (Fig. 1A), depends on both the tone amplitudes and their relative phase. Viewing the equally spaced laser cavity modes as sites of a 1D lattice in a synthetic frequency dimension, the two-tone modulation induces nearest-neighbour (NN) and next-nearest-neighbour (NNN) couplings, forming a triangular ladder geometry (Fig. 1B). <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A_{1f_{rep}},A_{2f_{rep}}$</tex> control the NN, NNN coupling strengths respectively, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\phi$</tex> imposes a staggered flux across each triangular lattice plaquette (Fig. 1B). This affects the instantaneous frequency and spectrum of the emitted frequency-modulated comb (Fig. 1C, numerical simulation), both of which depend sensitively on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\phi$</tex> . Experimental results using a ring-shaped Quantum Cascade Laser [4], confirm this, showing tuneable spectral shaping as the phase between modulation tones varies from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0\pi$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2\pi$</tex>.