Coherent instabilities in a semiconductor laser with fast gain recovery

Abstract

We report the observation of a coherent multimode instability in quantum cascade lasers (QCLs), which is driven by the same fundamental mechanism of Rabi oscillations as the elusive RiskenNummedal-Graham-Haken (RNGH) instability predicted 40 years ago for ring lasers. The threshold of the observed instability is significantly lower than in the original RNGH instability, which we attribute to saturable-absorption nonlinearity in the laser. Coherent effects, which cannot be reproduced by standard laser rate equations, can play therefore a key role in the multimode dynamics of QCLs, and in lasers with fast gain recovery in general.PACS numbers: 42.55. Px, 42.60.Mi, 42.65.Sf The fundamental coherent mechanism that can destabilize a single-mode laser was predicted in the early 60s [1] and was later extended to multi-mode lasers [2,3] where it became known as the RNGH instability. These instabilities became classic landmarks for the general field of nonlinear dynamics [4,5] because they emerge in conceptually the simplest laser model, which in the single-mode case was shown to be equivalent to the Lorentz model of deterministic chaos [6]. Another feature that makes these instabilities so interesting and unique is their coherent nature that involves the polarization of the medium as a nontrivial dynamical variable. Most other physical mechanisms that can drive a laser from a singlemode to a multi-mode regime, such as spatial and spectral hole burning, Q-switching, and saturable absorption [7,8], can be adequately described within the standard rate equation formalism, in which the polarization of the active medium is adiabatically eliminated. The RNGH instability and its single-mode twin cannot be explained by the rate equations. Such coherent effects can be only observed when the polarization is driven faster than or comparable to the dephasing time T 2 [9].The origin of both phenomena is the oscillation of the population inversion at the Rabi frequency Ω Rabi that takes place when the intracavity laser intensity becomes large. This results in a modification of the gain spectrum and the emergence of sidebands separated from the maximum of the gain curve by an amount corresponding to the Rabi frequency. These sidebands can be regarded as a manifestation of parametric gain. The instability sets in when the intracavity power is sufficiently large: the Rabi angular frequency Ω Rabi has to be greater than the relaxation timescales of the gain medium (more precisely, Ω Rabi is sufficiently greater than (T 1 T 2 ) −1/2 , where T 1 is the gain relaxation time). The instability threshold is often called the second laser threshold due to its universal nature.Pioneering theoretical works stimulated extensive experimental studies that finally resulted in the observation of the Lorenz-type chaos in a far-infrared singlemode laser [10]. However, despite almost 40 years of efforts, the experimental demonstration of the multimode RNGH instability has remained somewhat controversial [11,12,13,14,15,16].In lasers with long gain recov...

Time-Resolved Investigations of Electronic Transport Dynamics in Quantum Cascade Lasers Based on Diagonal Lasing Transition

“…Following a standard procedure as given in [29]- [31], the tunnel-assisted lower state emptying rate is expressed as (22) As shown in Fig. 13, given the dephasing time around a few tens of femtoseconds, the computed tunneling rate based on the (22) is approximately two to three times larger than the measurement results.…”

“…(b) Corresponding bandstructure calculation for N433 at a bias corresponding to an applied electric field of 85 kV/cm is displayed. and instabilities [22]. For the experiments reported here, the saturable absorber plays no role, since these effects occur only when the laser is biased far above threshold, and our experiments are mainly concentrated on the laser operation below and just above threshold.…”

Coherent frequency combs produced by self frequency modulation in quantum cascade lasers

“…As a result, some way of locking the modes together must be employed. Yet all the numerous attempts [14][15][16] to mode-lock QCL had limited success, and the practical achievements did not match numerous theoretical predictions. This problem can be traced to the fact that the in the QCL the relaxation time between the upper and lower laser levels (often referred to a "gain recovery time"), τ 21 is measured in picoseconds, and is thus much shorter than the cavity round trip time τ rt that is typically about 50-100ps in a few mm long cavity.…”

Quantum Cascade Laser Frequency Combs

“…Narrowband modulation at the round trip frequency of the output power of continuous wave QCLs were first interpreted using a set of Maxwell-Bloch equation expressed in the time domain [46,61,62]. However, these equations, while well suited to describe the generation and propagation of a pulse in the laser cavity, are ill-conditioned to study the output of a laser that exhibits mostly a frequency modulated output.…”