Radio-frequency enabled comb in ring Quantum Cascade Lasers

. Frequency combs (FC) generated by quantum cascade lasers (QCLs) are a promising tool for precision spectroscopy and gas sensing. Recently, ring QCLs have emerged as a new platform for generating FC with unique advantages over Fabry-Perot geometry. While the bandwidth of such Fabry-Perot devices is determined by the device geometry and dispersion, radio-frequency injected devices with circular geometry enable the exploitation of the full gain bandwidth in a controlled manner. Together with this platform, a predictive analytical model that shows excellent agreement with the experimental data was developed. Our results pave the way for a new approach for frequency comb generation based on fast-gain saturation.

On-chip frequency combs have drawn increasing attention due to their wide possible range of applications in spectroscopy and the intriguing mechanisms that govern their formation [1].The unique nature of the gain mechanisms in quantum cascade lasers facilitates frequency comb generation without external nonlinear cavities, enabling simple on-chip devices suitable for spectroscopy application in the mid-IR and THz frequencies [1].
In the molecular fingerprint region of the midinfrared, Quantum Cascade Lasers (QCLs) provide a flexible platform for developing such combs with high output powers, small device footprints and extensive spectral coverage [2].Due to the fast gain recovery time of QCLs, these types of devices can lase in a frequency comb (FC) regime, with a natural frequency-modulated (FM) and almost constant intensity output [3].The most common FC regime of QCLs is a linearly chirped spectral phase, which maintains approximately a constant intensity over time and thus lower peak power [4].For homodyne spectroscopy, lower peak power is advantageous, but the most critical features are the linewidth and, more importantly, the bandwidth of the laser output.
In a free-running QCL, the comb formation results mainly from the interaction between the forward and backward waves through the cross-steepening terms.Therefore, the bandwidth of such a QCL frequency comb is limited by dispersion, gain curvature, losses, and carrier lifetimes [5] and is thus determined by both active region design and fabrication.Radio-frequency (RF) injection allows for some degree of additional broadening of these combs, thereby providing a powerful way to tune the bandwidth and dynamics of QCLs [6].Here, we propose and experimentally demonstrate a bandwidth-tunable broadband comb source in the mid-IR based on an RF-injected ring-shaped QCL device.We find that low backscattering in such devices supports single-mode action, while RF modulation and fast gain unlock the full spectral potential of these devices.We developed a highly predictive model and found an analytical solution for the output phases.
We designed and fabricated egg-shaped ring-QCLs, where the shape is engineered to create exclusive emission from the tip with the highest curvature (fig.1a).To freely vary the repetition frequencies of the ring lasers while maintaining a reasonable amount of output power, the cavity geometry was slightly adapted from an ideal ring to a Hügelschäffer egg.The devices were processed using a buried-heterostructure process with smooth and defect-free sidewalls (see Fig 1a).This is evident from the occurrence of unidirectional lasing at only (1.00095 ± 0.00010)-times the threshold current (see Fig. 1b), which is indicative of very low backscattering.Therefore, the self-formation of combs due to various nonlinearities is suppressed (fig.1c, top).Only when we introduce RF modulation at the cavity resonance, which translates to a spatiotemporal phase change, an FC with a highly tunable, controllable, and predictable bandwidth proliferates (fig.1c (bottom), d).Utilising the fast gain-saturation of QCLS [8], we developed a highly predictive model for the electric field of the laser, which accurately reproduces the spectrum over different RF injection frequencies (fig.2c).
The model reveals a transition between two distinct lasing regimes: a highly off-resonant regime which is similar to the well-known electro-optical FM frequency combs [7], and a novel on-resonance FM regime, linearly chirped and comprised of only co-propagating modes (Fig. 2c, 2d).We also find an analytical solution of the field's phase (, ) for this regime, which also predicts the measured spectra in such devices: where  1 ,  2 are phase modulation amplitudes that directly depend on the modulation depth and dispersion, and  and ΔΩ are the cavity wavenumber and RF-modulation detuning from resonance, respectively.Unlike the linear instantaneous frequency of free-running QCL ridges, here we find the mathematical signatures of half periods of sinusoidal functions.The solution quantifies the relation between the frequency combs bandwidth and the laser properties and can serve as a design tool for QCL ring frequency-comb devices (see Fig 2c and 2d).This device exhibits unidirectional single-mode lasing in free-running operation over the whole dynamic range (see Fig. 1c, top).Under RF injection, combs with a bandwidth of more than 70 cm -1 and Bessel-shaped spectra can be observed around 15.7619 GHz (see Fig. 1c, bottom) and continuously tuned by varying the RF frequency (see Fig. 1d).We believe that the fast gain that governs the dynamics in this system is key for producing compact, highly tunable and low noise frequency comb devices.For no detuning, the phase is a half-sine ϕ(t)~Nsin(Ωt/2) (blue), for higher detuning the phase is a tilted half-sine ϕ(t)~t+Nsin(Ωt/2) with periodic boundary conditions (red and yellow), and for high enough detuning, the resonant solution is unstable.(c) and (d) Simulated spectra and the corresponding phase different vs. cavity resonance detuning, respectively.The phase different clearly shows two distinct regimes of lasing: far offresonance we find the regular EO comb with ϕ(t)~sin(Ωt), and closer to resonance the laser stabilizes in a linearly chirped FM comb state with ϕ(t)~N1t+N2sin(Ωt/2).

Fig. 1 .
Fig. 1.(a) Ring QCL Device before mounting.This specific device is egg-shaped to produce curvature dependant emission in one point on the ring.(b) Electronic properties: IV (black) and LI (red for clockwise mode, turquoise for counter clockwise mode) indicating unidirectional lasing over the whole dynamic range.(c) Single-mode spectrum of the free-running device (top, blue) and proliferation of a Bessel-shaped frequency comb under RF-injection (bottom, green).(d) Spectral map recorded at 1.5 A for varying injection frequencies (+35 dBm injected power) with broad comb operations at resonance and a symmetrical spectrum at 15.7619 GHz (vertical line; working point of c, bottom).

Fig. 2 .
Fig. 2. Features of RF modulated QCL rings with unidirectional lasing.(a) Analytical solution for off-resonance (by 5MHz) modulation of a QLC ring.(b) Field phase solutions of different detuning frequencies.For no detuning, the phase is a half-sine ϕ(t)~Nsin(Ωt/2) (blue), for higher detuning the phase is a tilted half-sine ϕ(t)~t+Nsin(Ωt/2) with periodic boundary conditions (red and yellow), and for high enough detuning, the resonant solution is unstable.(c) and (d) Simulated spectra and the corresponding phase different vs. cavity resonance detuning, respectively.The phase different clearly shows two distinct regimes of lasing: far offresonance we find the regular EO comb with ϕ(t)~sin(Ωt), and closer to resonance the laser stabilizes in a linearly chirped FM comb state with ϕ(t)~N1t+N2sin(Ωt/2).