Gain recovery dynamics and photon-driven transport in quantum cascade lasers

Uniform spike trains in optically injected quantum cascade oscillators

It has been experimentally and theoretically analyzed that noise-induced excitability in quantum well and quantum dot semiconductor laser systems usually produces sharp spike patterns of non-uniform amplitude. In this paper, we experimentally record that a quantum cascade oscillator injected externally with a monochromatic laser beam exhibits a series of highly uniform spike trains, which occur in the proximity of the saddle-node bifurcation. Theoretical analysis based on a properly designed single-mode rate equation model endowed with quantum noise reveals that this high uniformity has its primary origin in the ultrashort carrier lifetime of the quantum cascade laser gain medium that is typically close to 1 ps.

Nonlinear gain models in a quantum cascade laser

Density matrix analysis of a three-state model of quantum cascade laser (QCL) reveals that in this device, the optical gain is composed of the linear part (proportional to population inversion Δn) and the remaining nonlinear part. The nonlinear component non-negligibly contributes even to the small-signal response of the medium. In many attempts to modeling QCLs, the common practice to account for nonlinear gain components is to complement the equation for the gain, g = gcΔn, gc is the gain cross-section, by a compression factor f. In this paper, improved (but still simple) models of the optical gain in QCL are proposed, which preserve the two-component gain structure. With these models, there is no need to solve the Hamiltonian with time-dependent potentials, so that extraordinary numerical loads can be avoided, but simultaneously the essential physics of the phenomena is kept. The improved gain models defined by Eqs. (12), (15) and (16) enable accounting for its nonlinear components while preserving the load-saving, scattering-like approach to light-matter interaction. It is also shown that as long as the populations and dc coherences are determined such that they account for the interaction with the optical field, the small-signal formulation of the gain gives its realistic estimate also for a large optical signal. This conjecture validates the use of non-equilibrium Green's function-based approaches, in which the interaction with the optical field is included through electron-photon selfenergies. The small-signal formulation of the gain can be used in this approach to monitor the saturation process, estimate the clamping flux and the light-current characteristic.

Ultrafast Pulse Generation from Quantum Cascade Lasers

Quantum cascade lasers (QCLs) have broken the spectral barriers of semiconductor lasers and enabled a range of applications in the mid-infrared (MIR) and terahertz (THz) regimes. However, until recently, generating ultrashort and intense pulses from QCLs has been difficult. This would be useful to study ultrafast processes in MIR and THz using the targeted wavelength-by-design properties of QCLs. Since the first demonstration in 2009, mode-locking of QCLs has undergone considerable development in the past decade, which includes revealing the underlying mechanism of pulse formation, the development of an ultrafast THz detection technique, and the invention of novel pulse compression technology, etc. Here, we review the history and recent progress of ultrafast pulse generation from QCLs in both the THz and MIR regimes.

Optimization of gain region in mid-IR ( ≈ 5 μm) QCL

Non-equilibrium Green's function (NEGF) formalism is used to optimize the gain region of a quantum cascade laser (QCL) tailored to emit radiation at ∼5 µm wavelength, originally designed by Evans et al. [Appl. Phys. Lett., 88,051105(2006)10.1063/1.2171476]. The optimization strategy uses electron-photon selfenergies to find characteristics of devices under the "operating conditions," i.e., interacting with the laser field. These conditions can be quite different from the one when the device is in no-lasing state and the unsaturated gain is being optimized. The saturation caused by the optical field can push the structure from strong to weak coupling conditions, what changes laser parameters in a non-linear manner. Moreover, the NEGF method does not require any phenomenological parameters (such as, e.g., the phase relaxation times), so the quantities dependent on these parameters are determined solely on physical grounds. The use of the above procedure for the structure under investigation shows that the increase of the quantum efficiency by 24% and the output power by 83% in comparison to the original design can be achieved when the widths of injection and extraction barriers are changed to their optimal values.

Field-resolved high-order sub-cycle nonlinearities in a terahertz semiconductor laser

The exploitation of ultrafast electron dynamics in quantum cascade lasers (QCLs) holds enormous potential for intense, compact mode-locked terahertz (THz) sources, squeezed THz light, frequency mixers, and comb-based metrology systems. Yet the important sub-cycle dynamics have been notoriously difficult to access in operational THz QCLs. Here, we employ high-field THz pulses to perform the first ultrafast two-dimensional spectroscopy of a free-running THz QCL. Strong incoherent and coherent nonlinearities up to eight-wave mixing are detected below and above the laser threshold. These data not only reveal extremely short gain recovery times of 2 ps at the laser threshold, they also reflect the nonlinear polarization dynamics of the QCL laser transition for the first time, where we quantify the corresponding dephasing times between 0.9 and 1.5 ps with increasing bias currents. A density-matrix approach reproducing the emergence of all nonlinearities and their ultrafast evolution, simultaneously, allows us to map the coherently induced trajectory of the Bloch vector. The observed high-order multi-wave mixing nonlinearities benefit from resonant enhancement in the absence of absorption losses and bear potential for a number of future applications, ranging from efficient intracavity frequency conversion, mode proliferation to passive mode locking.

Femtosecond pulses from a mid-infrared quantum cascade laser

The quantum cascade laser has evolved to be a compact, powerful source of coherent mid-infrared light; however, its fast gain dynamics strongly restricts the formation of ultrashort pulses. As such, the shortest pulses reported so far were limited to a few picoseconds with some hundreds of milliwatts of peak power, strongly narrowing their applicability for time-resolved and nonlinear experiments. Here we demonstrate an approach capable of producing near-transform-limited subpicosecond pulses with several watts of peak power. Starting from a frequency-modulated phase-locked state, ultrashort high-peak-power pulses are generated via spectral filtering, gain modulation-induced spectral broadening and external pulse compression. We assess their temporal nature by means of a novel asynchronous sampling method, coherent beat note interferometry and interferometric autocorrelation. These results open new pathways for nonlinear physics in the mid-infrared.

Application of High-Speed Quantum Cascade Detectors for Mid-Infrared, Broadband, High-Resolution Spectroscopy

Broadband, high-resolution, heterodyne, mid-infrared absorption spectroscopy was performed with a high-speed quantum cascade (QC) detector. By strictly reducing the device capacitance and inductance via air-bridge wiring and a small mesa structure, a 3-dB frequency response over 20 GHz was obtained for the QC detector, which had a 4.6-μm peak wavelength response. In addition to the high-speed, it exhibited low noise characteristics limited only by Johnson–Nyquist noise, bias-free operation without cooling, and photoresponse linearity over a wide dynamic range. In the detector characterization, the noise-equivalent power was 7.7 × 10⁻¹¹ W/Hz^1/2 at 4.6 μm, and it had good photoresponse linearity up to 250 mW, with respect to the input light power. Broadband and high-accuracy molecular spectroscopy based on heterodyne detection was demonstrated by means of two distributed-feedback 4.5-μm QC lasers. Specifically, several nitrous oxide absorption lines were acquired over a wavelength range of 0.8 cm⁻¹ with the wide-band QC detector.

Unifying Frequency Combs in Active and Passive Cavities: Temporal Solitons in Externally Driven Ring Lasers

Frequency combs have become a prominent research area in optics. Of particular interest as integrated comb technology are chip-scale sources, such as semiconductor lasers and microresonators, which consist of resonators embedding a nonlinear medium either with or without population inversion. Such active and passive cavities were so far treated distinctly. Here we propose a formal unification by introducing a general equation that describes both types of cavities. The equation also captures the physics of a hybrid device-a semiconductor ring laser with an external optical drive-in which we show the existence of temporal solitons, previously identified only in microresonators, thanks to symmetry breaking and self-localization phenomena typical of spatially extended dissipative systems.

Light-enhanced incoherence of electronic transport in quantum cascade lasers

Since their invention in the middle of the 1990s, quantum cascade lasers (QCLs) attract increasing theoretical interest stimulated by their widening applications. One of the key theoretical issues is the optimization of electronic transport which in most of these devices is governed by the injection barrier of QCL heterostructure. In the paper, the nonequilibrium Green’s function formalism is used to study electronic transition through the injection barrier as a function of laser field in the cavity; for the increasing field, a crossover is observed from the strong coupling regime, in which electronic transport through the barrier is coherent, to the weak coupling regime, in which electronic transport gets incoherent. This crossover is characterized by gain recovery time, τ_rec, which takes sub-picosecond values for mid-IR QCLs operating at room temperature. This time is also important for the performance of devices under steady-state conditions; the maximum output power is obtained when the figure of merit, FOM = (g(0)/g_th − 1)/g_cτ_rec [g(0) is the linear response gain, g_th is the threshold gain needed to compensate all losses, g_c is the gain cross-section], reaches maximum. It is shown that the use of this optimization criterion can result in the structures essentially different from those which can be obtained when the optimized quantity is the linear response gain, g(0).

Frequency-Modulated Combs Obey a Variational Principle

Laser dynamics encompasses universal phenomena that can be encountered in many areas of physics, such as bifurcation and chaos, mode competition, resonant nonlinearities, and synchronization-or locking-of oscillators. When a locking process occurs in a multimode laser, an optical frequency comb is produced, which is an optical spectrum consisting of equidistant modes with a fixed phase relationship. Describing the formation of self-starting frequency combs in terms of fundamental laser equations governing the field inside the cavity does not allow one, in general, to grasp how the laser synchronizes its modes. Our finding is that, in a particular class of lasers where the output is frequency modulated with small or negligible intensity modulation, a greatly simplified description of self-locking exists. We show that in quantum cascade lasers-solid-state representatives of these lasers characterized by an ultrashort carrier relaxation time-the frequency comb formation obeys a simple variational principle, which was postulated over 50 years ago and relies on the maximization of the laser output power. The conditions for the breakdown of this principle are also experimentally identified, shedding light on the behavior of many different types of lasers, such as dye, diode, and other cascade lasers. This discovery reveals that the formation of frequency-modulated combs is an elegant example of an optimization problem solved by a physical system.

Radio frequency transmitter based on a laser frequency comb

Since the days of Hertz, radio transmitters have evolved from rudimentary circuits emitting around 50 MHz to modern ubiquitous Wi-Fi devices operating at gigahertz radio bands. As wireless data traffic continues to increase, there is a need for new communication technologies capable of high-frequency operation for high-speed data transfer. Here, we give a proof of concept of a compact radio frequency transmitter based on a semiconductor laser frequency comb. In this laser, the beating among the coherent modes oscillating inside the cavity generates a radio frequency current, which couples to the electrodes of the device. We show that redesigning the top contact of the laser allows one to exploit the internal oscillatory current to drive a dipole antenna, which radiates into free space. In addition, direct modulation of the laser current permits encoding a signal in the radiated radio frequency carrier. Working in the opposite direction, the antenna can receive an external radio frequency signal, couple it to the active region, and injection lock the laser. These results pave the way for applications and functionality in optical frequency combs, such as wireless radio communication and wireless synchronization to a reference source.

Temporal characteristics of quantum cascade laser frequency modulated combs in long wave infrared and THz regions

We consider here a time domain model representing the dynamics of quantum cascade lasers (QCLs) generating frequency combs (FCs) in both THz and long wave infrared (LWIR λ = 8-12µm) spectral ranges. Using common specifications for these QCLs we confirm that the free running laser enters a regime of operation yielding a pseudo-randomly frequency modulated (FM) radiation in the time domain corresponding to FCs with stable phase relations in the frequency domain. We provide an explanation for this unusual behavior as a consequence of competition for the most efficient regime of operation. Expanding the model previously developed in [Opt. Eng. 57(1), 011009 (2017)] we analyze the performance of realistic THz and LWIR QCLs and show, despite the vastly different scale of many parameters, that both types of lasers offer very similar characteristics, namely FM operation with an FM period commensurate with the gain recovery time and an FM amplitude comparable with the gain bandwidth. We also identify the true culprit behind pseudo-random dynamics of the FM comb to be spatial hole burning, rather than the more pervasive spectral hole burning.

The harmonic state of quantum cascade lasers: origin, control, and prospective applications [Invited]

The recently discovered ability of the quantum cascade laser to produce a harmonic frequency comb has attracted new interest in these devices for both applications and fundamental laser physics. In this review we present an extensive experimental phenomenology of the harmonic state, including its appearance in mid-infrared and terahertz quantum cascade lasers, studies of its destabilization induced by delayed optical feedback, and the assessment of its frequency comb nature. A theoretical model explaining its origin as due to the mutual interaction of population gratings and population pulsations inside the laser cavity will be described. We explore different approaches to control the spacing of the harmonic state, such as optical injection seeding and variation of the device temperature. Prospective applications of the harmonic state include microwave and terahertz generation, picosecond pulse generation in the mid-infrared, and broadband spectroscopy.

Two-dimensional coherent spectroscopy of a THz quantum cascade laser: observation of multiple harmonics

Two-dimensional spectroscopy is performed on a terahertz (THz) frequency quantum cascade laser (QCL) with two broadband THz pulses. Gain switching is used to amplify the first THz pulse and the second THz pulse is used to probe the system. Fourier transforms are taken with respect to the delay time between the two THz pulses and the sampling time of the THz probe pulse. The two-dimensional spectrum consists of three peaks at (ω_τ = 0, ω_t = ω₀), (ω_τ = ω₀, ω_t = ω₀), and (ω_τ = 2ω₀, ω_t = ω₀) where ω₀ denotes the lasing frequency. The peak at ω_τ = 0 represents the response of the probe to the zero-frequency (rectified) component of the instantaneous intensity and can be used to measure the gain recovery.

Mode-locking of a terahertz laser by direct phase synchronization

A novel scheme to achieve mode-locking of a multimode laser is demonstrated. Traditional methods to produce ultrashort laser pulses are based on modulating the cavity gain or losses at the cavity roundtrip frequency, favoring the pulsed emission. Here, we rather directly act on the phases of the modes, resulting in constructive interference for the appropriated phase relationship. This was performed on a terahertz quantum cascade laser by multimode injection seeding with an external terahertz pulse, resulting in phase mode-locked terahertz laser pulses of 9 ps duration, characterized unambiguously in the time domain.

Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation

We demonstrate that the cavity resonance frequency - the round-trip frequency - of Terahertz quantum cascade lasers can be injection-locked by direct modulation of the bias current using an RF source. Metal-metal and single-plasmon waveguide devices with roundtrip frequencies up to 35GHz have been studied, and show locking ranges above 200MHz. Inside this locking range the laser round-trip frequency is phase-locked, with a phase noise determined by the RF-synthesizer. We find a square-root dependence of the locking range with RF-power in agreement with classical injection-locking theory. These results are discussed in the context of mode-locking operation.

Dynamics of actively mode-locked Quantum Cascade Lasers

The impact of upper state lifetime and spatial hole burning on pulse shape and stability in actively mode locked QCLs is investigated by numerical simulations. It is shown that an extended upper state lifetime is necessary to achieve stable isolated pulse formation per roundtrip. Spatial hole burning helps to reduce the pulse duration by supporting broadband multimode lasing, but introduces pulse instabilities which eventually lead to strongly structured pulse shapes that further degrade with increased pumping. At high pumping levels gain saturation and recovery between pulses leads to suppression of mode locking. In the absence of spatial hole burning the laser approaches single-mode lasing, while in the presence of spatial hole burning the mode locking becomes unstable and the laser dynamics does not reach a steady state anymore.

Self-induced transparency modelocking of quantum cascade lasers in the presence of saturable nonlinearity and group velocity dispersion

We consider the impact of saturable nonlinearity and group velocity dispersion on self-induced transparency (SIT) modelocking of quantum cascade lasers (QCLs). We find that self-induced transparency modelocking in QCLs can be obtained in the presence of saturable nonlinearity if the saturable loss or gain is below a critical limit. The limit for the saturable loss is significantly more stringent than the limit for the saturable gain. Stable modelocked pulses are also obtained in the presence of both normal and anomalous group velocity dispersion when its magnitude is below a critical value. The stability limit for the saturable loss becomes less stringent when group velocity dispersion is simultaneously present. However, the stability limit for the saturable gain is not significantly affected. All these limits depend on the ratio of the SIT-induced gain and absorpt n to the linear loss. Realistic values for both the saturable nonlinearity and chromatic dispersion are within the range in which SIT modelocking is predicted to be stable.

Activation energy study of electron transport in high performance short wavelengths quantum cascade lasers

We present a method to study current paths through quantum cascade lasers (QCLs). The temperature dependence of the current is measured at a fixed voltage. At low temperatures we find activation energies that correspond to the energy difference between the injector ground state and the upper laser level. At higher temperatures additional paths with larger activation energies are found. Application of this method to high performance QCLs based on strained InGaAs/InAlAs quantum wells and barriers with different band-offsets allows us to identify individual parasitic current paths through the devices. The results give insight into the transport properties of quantum cascade lasers thus providing a useful tool for device optimization.

Mode-locked pulses from mid-infrared quantum cascade lasers

In this study, we report the unequivocal demonstration of midinfrared mode-locked pulses from quantum cascade lasers. The train of short pulses was generated by actively modulating the current and hence the gain of an edge-emitting quantum cascade laser (QCL). Pulses with duration of about 3 ps at full-width-at-half-maxima and energy of 0.5 pJ were characterized using a second-order interferometric autocorrelation technique based on a nonlinear quantum well infrared photodetector. The mode-locking dynamics in the QCLs was modeled based on the Maxwell-Bloch equations in an open two-level system. Our model reproduces the overall shape of the measured autocorrelation traces and predicts that the short pulses are accompanied by substantial wings as a result of strong spatial hole burning. The range of parameters where short mode-locked pulses can be formed is found.

Continuous voltage tunability of intersubband relaxation times in coupled SiGe quantum well structures using ultrafast spectroscopy

We demonstrate continuous voltage control of the nonradiative transition lifetime in semiconductor heterostructures. The results were obtained by picosecond time-resolved experiments on biased SiGe valence band quantum well structures using a free electron laser. By varying the applied voltage, the intersubband hole relaxation times for quantum well structures were varied by a factor of 2 as the wave functions and their overlaps were tuned. The range of magnitudes for the lifetime indicates a possible route to silicon-based quantum cascade lasers.