Terahertz Frequency Quantum Cascade Lasers Research Articles

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

Recently, the field of optical frequency combs experienced a major development of new sources. They are generally much smaller in size (on the scale of millimetres) and can extend frequency comb emission to other spectral regions, in particular towards the mid- and far-infrared regions. Unlike classical pulsed frequency combs, their mode-locking mechanism relies on four-wave-mixing nonlinear processes, yielding a non-trivial phase relation among the modes and an uncommon emission time profile. 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 (unknown) frequency comb. The technique is applied to characterize both 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 the electric field, intensity profile and instantaneous frequency of the emission. The combined technique of dual-comb multi-heterodyne detection and Fourier-transform analysis allows simultaneous acquisition and monitoring of the phase pattern of a generic frequency comb demonstrating the high degree of coherence of the emission of two quantum cascade laser frequency combs.

Group velocity dispersion analysis of terahertz quantum cascade laser frequency comb

The frequency comb which is characterized by equally-spaced frequency lines with high mode coherence has received much attention since its first demonstration in near-infrared and optical frequency range. In the terahertz frequency range, the electrically-pumped terahertz quantum cascade laser (THz QCL) based on semiconductors is an ideal candidate for achieving frequency comb operation in a frequency range between 1 THz and 5 THz. The group velocity dispersion (GVD) is a key factor for the frequency comb. A higher GVD can pull the frequencies from their equidistant values and limit the comb bandwidth. Therefore the laser dispersion needs to be compensated for in order to make the total GVD sufficiently low and flat, such as using a Gires-Tournois interferometer (GTI) or the double chirped mirror (DCM). However, a successful design still depends on the knowledge of the total GVD in the laser. In this paper, we show how to calculate the GVD in metal-metal waveguide THz QCLs by taking into account the dispersions from the GaAs material, the waveguide, and the laser gain, which conduces to the understanding of the frequency comb behavior. The waveguide loss is modelled by the finite element method. The loss due to intersubband absorption is calculated by Fermi's gold rule. All the losses, i.e., waveguide loss, mirror loss, and intersubband absorption loss, are summed up to calculate the clamped gain. The material loss can be calculated by using the reststrahlen band model. Because of these losses and gain, the refractive index needs to be replaced by a complex refractive index. The real part of the complex refractive index is the refractive index, which can be calculated from the Kramers-Kronig relationship that connects the loss or gain with the refractive index. Then the GVD introduced by the material loss, waveguide loss, and clamped gain can be finally calculated. The results show that the total GVD of THz QCL is approximately –8 × 10<sup>5</sup>~8 × 10<sup>5</sup> fs<sup>2</sup>/mm which is strongly determined by the clamped gain. Finally, the developed numerical model is employed to study the dispersion compensation effect of a GTI mirror which is coupled into a QCL gain cavity. The design of the THz QCL based on GTI structure is more flexible and feasible than that of the DCM. The result shows that by carefully designing the geometry of GTI, the dispersion of a THz QCL can be compensated for, thus achieving the broadband terahertz frequency combs.

Broadband heterogeneous terahertz frequency quantum cascade laser

The authors demonstrate a broadband, heterogeneous terahertz frequency quantum cascade laser by exploiting an active region design based on longitudinal optical-phonon-assisted interminiband transitions. They obtain continuous wave laser emission with a threshold current density of ~120 A/cm 2 , a dynamic range of ~3.1, and an emission spectrum spanning from 2.4 to 3.4 THz at 15 K.

Silver-based surface plasmon waveguide for terahertz quantum cascade lasers.

Terahertz-frequency quantum cascade lasers (THz QCLs) based on ridge waveguides incorporating silver waveguide layers have been investigated theoretically and experimentally, and compared with traditional gold-based devices. The threshold gain associated with silver-, gold- and copper-based devices, and the effects of titanium adhesion layers and top contact layers, in both surface-plasmon and double-metal waveguide geometries, have been analysed. Our simulations show that silver-based waveguides yield lower losses for THz QCLs across all practical operating temperatures and frequencies. Experimentally, QCLs with silver-based surface-plasmon waveguides were found to exhibit higher operating temperatures and higher output powers compared to those with identical but gold-based waveguides. Specifically, for a three-well resonant phonon active region with a scaled oscillator strength of 0.43 and doping density of 6.83 × 1015 cm-3, an increase of 5 K in the maximum operating temperature and 40% increase in the output power were demonstrated. These effects were found to be dependent on the active region design, and greater improvements were observed for QCLs with a larger radiative diagonality. Our results indicate that silver-based waveguide structures could potentially enable THz QCLs to operate at high temperatures.

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 (ωτ = 0, ωt = ω0), (ωτ = ω0, ωt = ω0), and (ωτ = 2ω0, ωt = ω0) where ω0 denotes the lasing frequency. The peak at ωτ = 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.

Measurement of the emission spectrum of a semiconductor laser using laser-feedback interferometry

The effects of optical feedback (OF) in lasers have been observed since the early days of laser development. While OF can result in undesirable and unpredictable operation in laser systems, it can also cause measurable perturbations to the operating parameters, which can be harnessed for metrological purposes. In this work we exploit this ‘self-mixing’ effect to infer the emission spectrum of a semiconductor laser using a laser-feedback interferometer, in which the terminal voltage of the laser is used to coherently sample the reinjected field. We demonstrate this approach using a terahertz frequency quantum cascade laser operating in both single- and multiple-longitudinal mode regimes, and are able to resolve spectral features not reliably resolved using traditional Fourier transform spectroscopy. We also investigate quantitatively the frequency perturbation of individual laser modes under OF, and find excellent agreement with predictions of the excess phase equation central to the theory of lasers under OF.

Broadband monolithic extractor for metal-metal waveguide based terahertz quantum cascade laser frequency combs

We present a monolithic solution to extract efficiently light from terahertz quantum cascade lasers with metal-metal waveguides suitable for broadband frequency comb applications. The design is optimized for a bandwidth of 400 GHz around a center frequency of 2.5 THz. A five-fold increase in total output power is observed compared to standard metal-metal waveguides. The extractor features a single-lobed far-field pattern and increases the frequency comb dynamical range to cover more than 50% of the laser dynamic range. Frequency comb operation up to a spectral bandwidth of 670 GHz is achieved.

Frequency Tunability and Spectral Control in Terahertz Quantum Cascade Lasers With Phase-Adjusted Finite-Defect-Site Photonic Lattices

We report on the effect of finite-defect-site photonic lattices (PLs) on the spectral emission of terahertz frequency quantum cascade lasers, both theoretically and experimentally. A central π-phase adjusted defect incorporated in the PL is shown to favor emission selectively within the photonic bandgap. The effect of the duty cycle and the longitudinal position of such PLs is investigated, and used to demonstrate three distinct spectral behaviors: single-mode emission from devices in the range 2.2-5 THz, with a side-mode suppression ratio of 40 dB and exhibiting continuous frequency tuning over >8 GHz; discrete tuning between two engineered emission modes separated by ~40 GHz; and multiple-mode emission with an engineered frequency spacing between emission lines.

Temperature-Dependent High-Speed Dynamics of Terahertz Quantum Cascade Lasers

Terahertz frequency quantum cascade lasers offer a potentially vast number of new applications. To better understand and apply these lasers, a device-specific modeling method was developed that realistically predicts optical output power under changing current drive and chip temperature. Model parameters are deduced from the self-consistent solution of a full set of rate equations, obtained from energy-balance Schrodinger–Poisson scattering transport calculations. The model is, thus, derived from first principles, based on the device structure, and is, therefore, not a generic or phenomenological model that merely imitates the expected device behavior. By fitting polynomials to data arrays representing the rate equation parameters, we are able to significantly condense the model, improving memory usage and computational efficiency.

Analysis of Operating Regimes of Terahertz Quantum Cascade Laser Frequency Combs

In recent years, quantum cascade lasers (QCLs) have shown tremendous potential for the generation of frequency combs in the mid-infrared and terahertz portions of the electromagnetic spectrum. The research community has experienced success both in the theoretical understanding and experimental realization of QCL devices, capable of generating stable and broadband frequency combs. Specifically, it has been pointed out that four wave mixing (FWM) is the main comb formation process and group velocity dispersion (GVD) is the main comb-degradation mechanism. As a consequence, special dispersion compensation techniques have been employed, in order to suppress the latter and simultaneously enhance the former processes. Here, we perform a detailed computational analysis of FWM, GVD, and spatial hole burning (SHB), all known to play a role in QCLs, and show that SHB has a considerable impact on whether the device will operate as a comb or not. We therefore conclude that for a successful implementation of a quantum cascade laser frequency comb, one would need to address this effect as well.

Multi‐Watt high‐power THz frequency quantum cascade lasers

Multi-Watt high-power terahertz (THz) frequency quantum cascade lasers are demonstrated, based on a single, epitaxially grown, 24-μm-thick active region embedded into a surface-plasmon waveguide. The devices emit in pulsed mode at a frequency of ∼4.4 THz and have a maximum operating temperature of 132 K. The maximum measurable emitted powers from a single facet are ∼2.4 W at 10 K and ∼1.8 W at 77 K, with no correction being made for the optical collection efficiency of the apparatus, or absorption by the cryostat polyethylene window.

Quasi-continuous frequency tunable terahertz quantum cascade lasers with coupled cavity and integrated photonic lattice.

We demonstrate quasi-continuous tuning of the emission frequency from coupled cavity terahertz frequency quantum cascade lasers. Such coupled cavity lasers comprise a lasing cavity and a tuning cavity which are optically coupled through a narrow air slit and are operated above and below the lasing threshold current, respectively. The emission frequency of these devices is determined by the Vernier resonance of longitudinal modes in the lasing and the tuning cavities, and can be tuned by applying an index perturbation in the tuning cavity. The spectral coverage of the coupled cavity devices have been increased by reducing the repetition frequency of the Vernier resonance and increasing the ratio of the free spectral ranges of the two cavities. A continuous tuning of the coupled cavity modes has been realized through an index perturbation of the lasing cavity itself by using wide electrical heating pulses at the tuning cavity and exploiting thermal conduction through the monolithic substrate. Single mode emission and discrete frequency tuning over a bandwidth of 100 GHz and a quasi-continuous frequency coverage of 7 GHz at 2.25 THz is demonstrated. An improvement in the side mode suppression and a continuous spectral coverage of 3 GHz is achieved without any degradation of output power by integrating a π-phase shifted photonic lattice in the laser cavity.

Extraction-controlled terahertz frequency quantum cascade lasers with a diagonal LO-phonon extraction and injection stage.

We report an extraction-controlled terahertz (THz)-frequency quantum cascade laser design in which a diagonal LO-phonon scattering process is used to achieve efficient current injection into the upper laser level of each period and simultaneously extract electrons from the adjacent period. The effects of the diagonality of the radiative transition are investigated, and a design with a scaled oscillator strength of 0.45 is shown experimentally to provide the highest temperature performance. A 3.3 THz device processed into a double-metal waveguide configuration operated up to 123 K in pulsed mode, with a threshold current density of 1.3 kA/cm2 at 10 K. The QCL structures are modeled using an extended density matrix approach, and the large threshold current is attributed to parasitic current paths associated with the upper laser levels. The simplicity of this design makes it an ideal platform to investigate the scattering injection process.

Origin of terminal voltage variations due to self-mixing in terahertz frequency quantum cascade lasers

We explain the origin of voltage variations due to self-mixing in a terahertz (THz) frequency quantum cascade laser (QCL) using an extended density matrix (DM) approach. Our DM model allows calculation of both the current-voltage (I-V) and optical power characteristics of the QCL under optical feedback by changing the cavity loss, to which the gain of the active region is clamped. The variation of intra-cavity field strength necessary to achieve gain clamping, and the corresponding change in bias required to maintain a constant current density through the heterostructure is then calculated. Strong enhancement of the self-mixing voltage signal due to non-linearity of the (I-V) characteristics is predicted and confirmed experimentally in an exemplar 2.6 THz bound-to-continuum QCL.

Model for a pulsed terahertz quantum cascade laser under optical feedback.

Optical feedback effects in lasers may be useful or problematic, depending on the type of application. When semiconductor lasers are operated using pulsed-mode excitation, their behavior under optical feedback depends on the electronic and thermal characteristics of the laser, as well as the nature of the external cavity. Predicting the behavior of a laser under both optical feedback and pulsed operation therefore requires a detailed model that includes laser-specific thermal and electronic characteristics. In this paper we introduce such a model for an exemplar bound-to-continuum terahertz frequency quantum cascade laser (QCL), illustrating its use in a selection of pulsed operation scenarios. Our results demonstrate significant interplay between electro-optical, thermal, and feedback phenomena, and that this interplay is key to understanding QCL behavior in pulsed applications. Further, our results suggest that for many types of QCL in interferometric applications, thermal modulation via low duty cycle pulsed operation would be an alternative to commonly used adiabatic modulation.

On-chip, self-detected terahertz dual-comb source

We present a directly generated on-chip dual-comb source at terahertz (THz) frequencies. The multi-heterodyne beating signal of two free-running THz quantum cascade laser frequency combs is measured electrically using one of the combs as a detector, fully exploiting the unique characteristics of quantum cascade active regions. Up to 30 modes can be detected corresponding to a spectral bandwidth of 630 GHz, being the available bandwidth of the dual comb configuration. The multi-heterodyne signal is used to investigate the equidistance of the comb modes showing an accuracy of 10−12 at the carrier frequency of 2.5 THz.

Diffuse-Reflectance Spectroscopy Using a Frequency-Switchable Terahertz Quantum Cascade Laser

We demonstrate diffuse-reflectance (DR) spectroscopy of powders using a discretely-tunable terahertz-frequency quantum cascade laser (THz QCL) with a heterogeneous active region. DR signatures were obtained at frequencies of 3.06, 3.21, 3.28, and 3.35 THz, and the relative absorption coefficients were inferred at each frequency using a Kubelka-Munk (KM) scattering model. The spectral lineshapes reproduce the absolute Beer-Lambert (BL) absorption spectra of a range of materials, which were also measured using conventional transmission-mode THz time-domain spectroscopy. It is shown that the DR technique works reliably for materials that include pharmaceutical compounds and foodstuffs, with BL absorption coefficients in the range 2-10 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . This method is potentially suitable for automated material identification, without any requirement for a priori knowledge of the refractive index or scattering properties of the sampled material.

Gain recovery time in a terahertz quantum cascade laser

The gain recovery time of a bound-to-continuum terahertz frequency quantum cascade laser, operating at 1.98 THz, has been measured using broadband terahertz-pump-terahertz-probe spectroscopy. The recovery time is found to reduce as a function of current density, attaining a value of 18 ps as the laser is brought close to threshold. We attribute this reduction to improved coupling efficiency between the injector state and the upper lasing level as the active region aligns.

Improving the Out-Coupling of a Metal-Metal Terahertz Frequency Quantum Cascade Laser Through Integration of a Hybrid Mode Section into the Waveguide

A hybrid mode section is integrated into the end of the metal-metal waveguide of a terahertz (THz) frequency quantum cascade laser (QCL) by removing sub-wavelength portions of the top metal layer. This allows a hybrid mode to penetrate into the air, which reduces the effective index of the mode and improves the out-coupling performance at the facet. The transmission of the hybrid section is further increased by ensuring its length fulfills the criterion for constructive interference. These simple modifications to a 2.5-THz metal-metal QCL waveguide result in a significant increase in the output emission power. In addition, simulations show that further improvements in out-coupling efficiency can be achieved for lower frequencies with effective refractive indices close to the geometric mean of the indices of the metal-metal waveguide and air.

Mechanically robust waveguide‐integration and beam shaping of terahertz quantum cascade lasers

Terahertz-frequency quantum cascade lasers (THz QCLs) have numerous potential applications as 1–5 THz radiation sources in space science, biomedical and industrial sensing scenarios. However, the key obstacles to their wide-scale adoption outside laboratory environments have included their poor far-field beam quality and the lack of mechanically robust schemes that allow integration of QCLs with THz waveguides, mixers and other system components. A block integration scheme is presented, in which a continuous-wave ∼3.4 THz double-metal QCL is bonded into a precision-machined rectangular waveguide within a copper heat-sink block. This highly reproducible approach provides a single-lobed far-field beam profile with a divergence of ≲20°, and with no significant degradation in threshold current or in the range of operating temperatures.