Abstract

The dynamics of a multimode quantum cascade laser, are studied in a model based on effective semiconductor Maxwell-Bloch equations, encompassing key features for the radiation-medium interaction such as an asymmetric frequency dependent gain and refractive index as well as the phase-amplitude coupling provided by the linewidth enhancement factor. By considering its role and that of the free spectral range, we find the conditions in which the traveling wave emitted by the laser at the threshold can be destabilized by adjacent modes, thus leading the laser emission towards chaotic or regular multimode dynamics. In the latter case our simulations show that the field oscillations are associated to self-confined structures which travel along the laser cavity, bridging mode-locking and solitary wave propagation. In addition, we show how a RF modulation of the bias current leads to active mode-locking yielding high-contrast, picosecond pulses. Our results compare well with recent experiments on broad-band THz-QCLs and may help in the understanding of the conditions for the generation of ultrashort pulses and comb operation in mid-IR and THz spectral regions.

Highlights

  • The multimode dynamics of Mid-IR and THz Quantum Cascade Lasers (QCLs) became a focus of interest for the realization of pulsed regimes and frequency combs for a number of applications including time-resolved measurements, frequency mixing, high-precision spectroscopy etc. [1]- [12]

  • We consider a unidirectional ring cavity configuration; this hypothesis allows us to show that phase-amplitude coupling and mode competition can provide, even in absence of Spatial Hole Burning (SHB) typical of Fabry-Perot (FP) configurations considered e.g. in [13, 20], a radically lower threshold for coherent multimode dynamics than what predicted by the Risken-Nummedal-Graham-Haken (RNGH) instability [28,29,30], which is typical of two-levels laser

  • In Fig. 4.a, just above threshold (μ = 1.002μth with μth = μth(k = 0) = 1), we find as expected the emission of TW0, affected by a self–oscillation, whose signature is seen in the beat note spectrum (BNS) peak at 0.062 (quite close to the normalized free spectral range (FSR) = (2πc/nl)τd = 0.0628 that corresponds to a frequency separation of 100GHz in physical units) and the presence of higher angular frequencies separated by FSR

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Summary

Introduction

The multimode dynamics of Mid-IR and THz Quantum Cascade Lasers (QCLs) became a focus of interest for the realization of pulsed regimes and frequency combs for a number of applications including time-resolved measurements, frequency mixing, high-precision spectroscopy etc. [1]- [12]. We consider a unidirectional ring cavity configuration; this hypothesis allows us to show that phase-amplitude coupling (associated to the LEF) and mode competition can provide, even in absence of SHB typical of Fabry-Perot (FP) configurations considered e.g. in [13, 20], a radically lower threshold for coherent multimode dynamics than what predicted by the Risken-Nummedal-Graham-Haken (RNGH) instability [28,29,30], which is typical of two-levels laser In this regard, we observe that unidirectional lasing in ring cavities in QCLs has been demonstrated in both a monolithically integrated cavity and an external one [31, 32].

Effective Semiconductor Bloch Equations
Free running traveling wave solutions
Traveling wave selection at threshold
Effect of RF modulation
Active mode-locking
Conclusion

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