Retrieval of phase relation and emission profile of quantum cascade laser frequency combs

The major development recently undergone by quantum cascade lasers has effectively extended frequency comb emission to longer-wavelength spectral regions, i.e. the mid and far infrared. Unlike classical pulsed frequency combs, their mode-locking mechanism relies on four-wave mixing nonlinear processes, with a temporal intensity profile different from conventional short-pulses trains. Measuring the absolute phase pattern of the modes in these combs enables a thorough characterization of the onset of mode-locking in absence of short-pulses emission, as well as of the coherence properties. Here, by combining dual-comb multi-heterodyne detection with Fourier-transform analysis, we show how to simultaneously acquire and monitor over a wide range of timescales the phase pattern of a generic frequency comb. The technique is applied to characterize a mid-infrared and a terahertz quantum cascade laser frequency comb, conclusively proving the high degree of coherence and the remarkable long-term stability of these sources. Moreover, the technique allows also the reconstruction of electric field, intensity profile and instantaneous frequency of the emission.Comment: 20 pages. Submitted to Nature Photonic

Modeling techniques for quantum cascade lasers

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schr\"odinger equation and Schr\"odinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function (NEGF) formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures

Unified theory for frequency combs in ring and Fabry-Perot quantum cascade lasers: an order-parameter equation approach

We present a unified model to describe the dynamics of optical frequency combs (OFCs) in quantum cascade lasers (QCLs), incorporating both ring and Fabry-P\'erot (FP) cavity configurations. The model derives a modified complex Ginzburg-Landau equation (CGLE), leveraging an order parameter approach and is capable of capturing the dynamics of both configurations, thus enabling a comparative analysis. In the modified CGLE, a nonlinear integral term appears which is associated with the coupling between counterpropagating fields in the FP cavity and whose suppression yields the ring model, which is known to be properly described by a conventional CGLE. We show that this crucial term holds a key role in inhibiting the formation of harmonic frequency combs (HFCs), associated to multi-peaked localized structures, due to its anti-patterning effect. We provide in support a comprehensive campaign of numerical simulations, in which we observe a higher occurrence of HFCs in the ring configuration compared to the FP case. Furthermore, the simulations demonstrate the model's capability to reproduce experimental observations, including the coexistence of amplitude and frequency modulation, linear chirp, and typical dynamic scenarios observed in QCLs. Finally, we perform a linear stability analysis of the single-mode solution for the ring case, confirming its consistency with numerical simulations and highlighting its predictive power regarding the formation of harmonic combs

Nozaki–Bekki solitons in semiconductor lasers

Optical frequency-comb sources, which emit perfectly periodic and coherent waveforms of light1, have recently rapidly progressed towards chip-scale integrated solutions. Among them, two classes are particularly significant-semiconductor Fabry-Perot lasers2-6 and passive ring Kerr microresonators7-9. Here we merge the two technologies in a ring semiconductor laser10,11 and demonstrate a paradigm for the formation of free-running solitons, called Nozaki-Bekki solitons. These dissipative waveforms emerge in a family of travelling localized dark pulses, known within the complex Ginzburg-Landau equation12-14. We show that Nozaki-Bekki solitons are structurally stable in a ring laser and form spontaneously with tuning of the laser bias, eliminating the need for an external optical pump. By combining conclusive experimental findings and a complementary elaborate theoretical model, we reveal the salient characteristics of these solitons and provide guidelines for their generation. Beyond the fundamental soliton circulating inside the ring laser, we demonstrate multisoliton states as well, verifying their localized nature and offering an insight into formation of soliton crystals15. Our results consolidate a monolithic electrically driven platform for direct soliton generation and open the door for a research field at the junction of laser multimode dynamics and Kerr parametric processes.Free-running stable optical dissipative solitons, called Nozaki-Bekki solitons, are created in a ring semiconductor laser; their spontaneous formation with tuning of laser bias eliminates the need for an external optical pump