Broadband THz quantum cascade laser frequency combs with surface emission and inverse-designed facet reflectors

. We present a planarized waveguide cavity with an integrated broadband output coupler that improves both the output power and far-field properties of THz quantum cascade laser frequency combs. The laser mirror reflectivity can be tuned by the shape of the end facet, which is obtained with an efficient inverse design algorithm, where the structure is iteratively updated to match the desired figure of merit. Surface emission is achieved with a broadband patch-array antenna, and all the components have been optimized for octave-spanning emission spectra (2-4 THz). Experimentally, we demonstrate a broadband surface-emitting THz quantum cascade laser frequency comb with optical bandwidths of up to 800 GHz, surface emission into a narrow beam with divergence below (20° x 20°) and a peak power of 13 mW.


Introduction
Terahertz (THz) quantum cascade lasers (QCLs) [1] are compact sources of broadband THz radiation, appealing for use in coherent spectroscopy, communications, and sensing, as they can operate as frequency combs [2] and dual combs [3].We recently developed a planarized waveguide platform for THz QCLs, where the active material is embedded in a low-loss polymer BCB and covered by an extended top metallization [4].Besides improved dispersion, RF and thermal properties, it enables the co-integration of active and passive components on the same photonic chip.
In simple ridge waveguide devices, the laser mirrors are formed by cleaved facets.Due to a large impedance mismatch between the guided and free space optical mode, this results in relatively large reflectivities (around 70% at a frequency of 3 THz), limiting the slope efficiency and output power.Since the waveguide thickness is subwavelength, this also results in poor farfield properties, which are highly divergent and frequency-dependent.While these challenges have been addressed in the last decade, the existing solutions are either frequency selective (DFBs, photonic crystals [5]) or non-monolithic, requiring additional post-processing and mounting steps (lenses [6], antennas [7]).
In this work, we designed, fabricated and characterized planarized waveguide cavities which simultaneously improve the far-field pattern and output power, all designed for octave-spanning spectra (2-4 THz), suitable for broadband comb devices and monolithically integrated on the same photonic chip.

Surface emission with a broadband antenna
First, we improve the far-field properties by connecting the end facet of a ridge waveguide to a passive waveguide which is coupled to a broadband patch array antenna for surface emission (see illustration in Fig. 1(a)).The antenna design was based on the narrowband structure from Ref. [8] but re-optimized for octave-spanning emission spectra (2-4 THz), where both the beam divergence and beam steering with frequency were minimized.
In Fig. 1(b) we show the results of far-field measurements on a broadband device in pulsed mode, where the emission is spanning around 1 THz.The measurements were performed with a pyroelectric detector on a motorized scanning stage, and the sample was mounted on a flow cryostat cold finger at a heat sink temperature of 20 K.The far-field pattern features a central lobe with a full-width half-maximum (FWHM) beam divergence below (20° x 20°).
By connecting the active waveguide and the antenna with a passive waveguide, we have decoupled the laser cavity from the output coupler, which enables us to design the laser mirror reflectivity independently from the outcoupling mechanism.

Inverse-designed waveguide facets
Next, we address the naturally high end facet reflectivities of THz QCLs which limit the slope efficiency and output power.By coupling the active planarized waveguide to a passive waveguide (metallized stripe on top of the BCB polymer connecting to the antenna), the end facet reflectivity is already reduced to around 23% at a frequency of 3 THz.To have more precise control over the desired end facet reflectivity, we used an inverse design method based on the adjoint optimization approach [9].Specifically, we use shape optimization, where the outline shape of the end facet is iteratively updated to match the desired figure of merit.The optimization parameters define the position of control points on the end facet which then connect into a smooth global shape by spline interpolation.The optimization is coupled with a full-wave optics simulation environment (Ansys Lumerical).
We present the results of a device with an inversedesigned end facet reflectivity of 10% over an octavespanning spectrum (2-4 THz).Simulation results are shown in Fig. 2(a), where the resulting reflectivity (green line) matches well with the target reflectivity (dashed line).The reflectivity of a simple flat planarized facet is also shown (blue line).
Experimentally, we characterized a planarized ridge waveguide with a width of 40 μm and a length of 2.5 mm, with a 10% reflectivity inverse-designed facet and coupled to a surface-emitting antenna.The back facet is cleaved for a high-reflectivity back mirror to minimize total mirror losses and keep the threshold current density low.In Fig. 2(b), we show the measured frequency comb spectrum at a heat sink temperature of 20 K.The spectrum spans around 800 GHz and the strong single RF beatnote at the roundtrip frequency of 15.44 GHz is shown in the inset.In Fig. 2(c) are the measured LIV curves of the same device in pulsed mode (10% duty cycle) and a heat sink temperature of 20 K, featuring a peak power of 13 mW.The measured slope efficiency is improved by more than a factor of five compared to devices processed on the same epilayer with a cleaved front facet.

Conclusion
In conclusion, we presented a planarized waveguide laser cavity with inverse-designed end facets coupled to a patch array antenna for surface emission, suitable for octavespanning comb operation.All the components are monolithically integrated on the same chip and show improved output powers and far-field intensities both in simulation and experiment.

Fig. 1 .
Fig. 1.(a) Illustration of the fabricated device.A planarized ridge waveguide is terminated by an inverse-designed waveguide facet and coupled to a passive waveguide which is connected to a broadband patch array antenna, with the simulated far-field of the surface emission beam superimposed.The inset shows an SEM image of the 10% reflectivity inverse-designed facet after dry etching (before planarization with a losloss polymer BCB).(b) Far-field measurement of a broadband antennacoupled device in pulsed mode, where the emission spectrum was spanning around 1 THz.The measured beam divergence is below (20° x 20°).

Fig. 2 .
Fig. 2. (a) Simulation results of the reflectivity for a flat planarized facet (blue) and an inverse-designed planarized facet (green) with a target reflectivity of 10% (dashed) over an octave-spanning spectrum (2-4 THz).(b) Measured comb spectrum in continuous-wave at a heatsink temperature of 20 K, spanning around 800 GHz and with a single strong RF beatnote at the roundtrip frequency of 15.44 GHz (inset).(c) Measured LIV characteristics of the same device (ridge width of 40 μm and a length of 2.5 mm) in pulsed mode (10% duty cycle) at a heat sink temperature of 20 K, with a peak power of around 13 mW.