Theory of Frequency-Modulated Combs in Lasers with Spatial Hole Burning, Dispersion, and Kerr Nonlinearity

Abstract

Frequency modulated (FM) frequency combs constitute an exciting alternative to generate equidistant spectra. The full set of Maxwell-Bloch equations is reduced to a single master equation for FM combs with fast dynamics to provide insight into the governing mechanisms behind phase-locking. It reveals that the recently observed linear frequency chirp is caused by the combined effects of spatial hole burning, group velocity dispersion and Kerr due to asymmetric gain. The comparison to observation in various semiconductor lasers suggests that the linear chirp is general to self-starting FM combs.

RF Injection of THz QCL Combs at 80 K Emitting over 700 GHz Spectral Bandwidth

“…The fact that we often observe the high-phase noise instead of the harmonic state indicates that there must be additional parameters influencing the locking mechanism. Other factors to be taken into account are the relatively long upper state life time of the laser (surely longer than 40 ps [30] measured in our previous, less diagonal design), which would result in an intermediate behaviour between AM and FM comb regimes, and the spatial hole burning [31]. The latter is probably reduced for lower temperatures due the particular photon-driven transport in these devices, which leads to a low differential conductance even though the low-loss subwavelength waveguides leads to higher fields.…”

Mode-locked short pulses from an 8 μm wavelength semiconductor laser

“…Both synchronization frequencies are probed by applying modulation to the laser. In order to model the cavity dynamics, we use a fully coherent master equation 35 (Supplementary Section 1). This single equation for the complex field replaces the entire Maxwell-Bloch system 36,37 and reliably predicts the spectral shape, phase relationship and pulse width observed experimentally (Fig.…”

Frequency noise correlation between the offset frequency and the mode spacing in a mid-infrared quantum cascade laser frequency comb

“…As a result of the very short upper state lifetime of the gain medium, these comb sources do not generate optical pulses, but deliver a fairly constant output power [8] that is associated to a frequency-modulated (FM) spectrum. A recent model proposed by Opacak and Schwarz describes the formation of FM combs with the combined contributions of spatial hole burning, gain saturation and a minimum group velocity dispersion or Kerr nonlinearity due to gain asymmetry [9]. The FM nature of QCL combs has made the self-referencing method not possible so far and no detection of the offset frequency of a MIR QCL comb has ever been reported to the best of our knowledge, even if the full phase stabilization of a THz QCL comb to a CEO-free metrological THz comb was recently demonstrated [10].…”