1. Introduction

Terahertz quantum cascade lasers (THz QCLs) [1] have witnessed a remarkable progress [2] since their first demonstration in 2002. Despite their cryogenic operation temperatures, they have been employed as radiation sources in spectroscopy [3], imaging [4,5] and heterodyne systems [6,7]. Their resonators are based on surface plasmon waveguides, either in single-metal [1], or double-metal configuration [8]. In the latter case, the gain material is sandwiched between two metallic layers. The two surface-plasmons at the metal-dielectric interfaces form a mode of transverse-magnetic (TM) nature, which ideally matches the selection rules of intersubband transitions. This waveguide has a confinement factor close to unity, while keeping the losses moderate, and has been shown to perform significantly better at higher operating temperatures [9]. From an application point of view, however, lasers based on double-metal waveguides, due to the large impedance mismatch at the facet and the intrinsically strong divergence of the beam, typically present low radiative and collection efficiencies. The search for double-metal resonator designs with better performances has therefore been a major topic for THz QCL development, leading to the implementation of horn antennas [10], hyperhemispherical silicon lenses [11], or photonic crystals [12–14] and linear gratings for vertical emission [15–17]. The latter were implemented simply by fabricating slits in the top metallization. Surface emission is particularly appealing, because the devices are significantly easier to fabricate, allow two-dimensional integration and on-chip testing. For these so-called second order distributed feedback (DFB) resonators the waveguide is perturbed with a periodicity corresponding to the guided wavelength. Their application to THz QCLs was studied theoretically in [18], where it was pointed out that the two eigenmodes of the grating are characterized by their different symmetry with respect to the grating. For second order gratings, this symmetry determines whether a mode is coupled out vertically or not. Unfortunately, the optical losses of the two modes differ accordingly, to the extent that the non-radiative mode is always the only one excited above lasing threshold. In real devices, surface emission can be obtained by the use of appropriate boundary conditions [17], or, to a smaller extent, because of the finite length of the grating [16,19]. The suppression of surface emission in an infinite device is caused by the field components of the mode interfering destructively in the far-field, a consequence of the mode symmetry. The breaking of this symmetry, e.g. by bending of the grating in a circular device, leads to considerable surface emission, as demonstrated in [20]. Considering the far-field, linear devices show a different angular distribution along and perpendicular to the ridge axis [17]. While the former is controlled by the length of the grating, the latter is given by the lateral extent of the mode profile in the waveguide and basically diffraction-limited. Circular devices instead, if their mode has a constant phase-relation to the grating all along the ring, should have a circularly symmetric far-field. The extension of the lobe is then determined by the ratio of device diameter and free-space wavelength, because the far-field is generated by interference between photons originating from opposite sides of the ring diameter [20]. This will in turn increase the collection efficiencies with standard optics. Surface-emitting ring resonators were recently demonstrated for mid-IR QCLs [21,22]. The second work reported a laser operating on a DFB resonance, with the corresponding narrow far-field distribution. In the present work, we investigate DFB ring resonators for THz QCLs, i.e. we describe the extension of the concept described in [20] to obtain low-divergence, high-power devices.

2. Modeling

For the design of the ring resonator, we use a commercial finite element solver (Comsol Multiphysics) to solve Maxwell’s equation formulated as an eigenfrequency problem. A full three dimensional simulation is beyond the presently available computational power, not only because we consider resonators extending over many wavelengths (1mm vs. 30 μm), but also because THz QCLs use metallic layers for mode confinement, which are typically three orders of magnitude thinner than the free-space wavelength. Thus, the eigenfrequencies are here computed for a segment of the ring corresponding to one period, and, furthermore, the metallic layers are only taken into account through appropriately shaped boundaries, similarly to the simplification described in [19]. While this is useful for the design of the ring and grating in the top metallization, obviously it does not yield the eigenmodes with different periodicity or non-circular symmetry. For the latter, one would need to apply periodic boundary conditions with a non-zero phase. To compute the far-field, we extract both the magnetic and the electric near-field in a plane of the segment 2 µm above the grating, reconstruct the full near-field of the device with linear transformations, and apply the Stratton-Chu formula to obtain the far-field.

The focus in the design lies on the top metallization, which acts not only as a periodic structure for distributed feedback, but also for vertical out-coupling of the resonator energy and electrical contact. For the latter, the slits in the top metallization should be considerably smaller than the waveguide thickness, in order to maintain uniform current injection. At the same time, the slit width is an important parameter for the design of the radiative losses of the resonator [18]. Analysis of the surface emission obtained in previous circular grating devices with large slits [20] showed that the surface emission stems from the magnetic field of the lasing mode below the metallic edges forming the slits. We therefore added a pumping segment in the center of each slit, creating a configuration where each period consists of two slits. Figure 1(a) shows a typical computed spectrum obtained for a segment of a ring with a diameter of 960 μm, 97 periods, and thickness of 11 μm. It is dominated by the resonance of the mode whose electric field is symmetric with respect to the grating. The inset shows the design of the segment and the field distribution of the eigenmode. At the inner border of the ridge, a stripe with higher imaginary part of the refractive index was added to account for the zone in the actual device that was left unmetalized. This acts as an absorber, which selectively introduces losses to modes with more than one radial lobe (similar to higher order transverse mode suppression described in [19]). To further investigate this design, we computed the frequency and radiative efficiency of the eigenmodes with only one radial lobe, as a function of double-slit separation, keeping the grating period constant. The results, shown in Fig. 1(b), are reminiscent of the results obtained in a linear double-slit structure of the same kind (not shown), but with the important difference that also the mode with symmetric electric field distribution shows finite surface losses (solid line). As described in [20], the bending of the grating suppresses the destructive interference, thus causing a vertical power flow for this resonator mode. The contrast is most obvious for the case of the first order grating (slit separation 50%), which, in the linear case, is well known not to provide surface emission for any mode symmetry. In the devices presented here, we chose the distance between two slits at 30% of the total period. In this parameter range, the quality factor of the asymmetric mode is strongly reduced due to its large surface losses (resonance at 3.1 THz); we therefore obtain the favorable spectrum of Fig. 1(a). The radiative efficiency of around 12% for the symmetric mode, on the other hand, is lower than for larger slit separation, where one could, with a narrow spectral gain profile, take advantage of the large mode separation (~400 GHz) to obtain single mode emission. Since the radiative efficiency affects both lasing threshold and slope efficiency, maximizing device power by the choice of optimum surface losses is difficult if, like in the case of THz QCLs, the waveguide losses and gain vs. current characteristics are not well known. Note that the ratio of waveguide thickness and wavelength strongly influences the photon lifetime, thus a thinner waveguide leads to a higher radiative efficiency.

 

Fig. 1 (a) Spectrum computed for a segment of a ring with 97 periods and a diameter of 960 um. The eigenmode whose field distribution is shown corresponds to the dominant resonance. The distance between two slits is chosen at 30% of the total period. The SEM micrograph shows a few periods of a fabricated grating. (b) Resonance frequencies and radiative efficiencies of the modes with symmetric and asymmetric electric field distribution with respect to the grating, plotted as solid and dashed lines respectively, as a function of slit distance at constant period (segment size). The ring radius in these plots is slightly larger. The resonance at 3.1 THz in panel (a) corresponds to the asymmetric eigenmode. Note the radiative efficiency of the symmetric mode at 10-20%, which would instead vanish in the entire parameter range in the case of a linear infinite grating.

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3. Fabrication and measurements

Devices were fabricated from the same wafer used in [19,20], a 200 stage resonant-phonon structure. The wafer and a doped host substrate were covered with 10/300 nm of Ti/Au and wafer bonded using a thermo-compression method. The original substrate was then removed by a combination of lapping and etching. Rings of various diameters (910 to 1020 μm) were fabricated by optical lithography and lift-off in a thermally evaporated Ti/Au metallization. The top contact in the slit region was etched with a H₃PO₄/H₂O₂/H₂O 3/1/50 solution with the metal as a self-aligned mask and a circular resist mask to maintain the contact layer on the inner circumference of the ring as an absorber. The use of Ti as an adhesion layer is crucial in order to prevent fast etching along the metal-semiconductor interface and thus metal lift-off. The ring mesas are etched with inductively coupled plasma (ICP), using a gas mixture of BCl₃/Cl₂/Ar with a photoresist mask and a Si carrier wafer. After substrate thinning, devices were soldered to copper bars with an In/Ag alloy and wire bonded. The number of bonds is a trade-off between uniform pumping and introduction of defects into the grating structure. We observed a dual mode spectrum in some devices with two bonds, which then became single mode upon adding another two bonds. This could be a consequence of non-uniform current densities along the ring. An alternative explanation could be that the bonds introduce additional defects into the grating structure and therefore change the spectral properties of the resonator. In future devices, the additional bond wires could simply be avoided by fabricating a thicker top metallization, which was only ~5/50 nm of Ti/Au in the present devices. Finally, devices were mounted on the cold finger of a continuous-flow liquid-helium cryostat for the measurement. Spectra were recorded with an f/1 Picarin lens and a Fourier transform infrared spectrometer in rapid scan mode, with a DTGS detector, and at the maximum resolution of 0.125 cm⁻¹. Light-current curves were obtained with a Golay-cell with a 6 mm diameter PE-window positioned 30 mm away from the device surface (resulting in a maximum collection angle of ~6° from the vertical), while the devices were driven with an Avtech AVR-3HF-B power supply with a 35 Ω resistor in series. No collection optics was employed. The far-fields were obtained by spherically scanning a pyroelectric detector of 1 mm² size at a distance of ~8 cm, while the device was driven with an Agilent 8114A and a transformer for impedance matching. The 25 mm diameter cryostat window was located 25 mm from the sample, equivalent to a maximum accessible angle of 26.5° with respect to the device axis.

4. Results

Figure 2(a) shows a fabricated device. The centers of the two slits belonging to one period have a spacing equal to 30% of the period, for which we compute a radiative efficiency of ~12% for the dominant resonance (see Fig. 1). Figure 2(b) shows the light-current characteristics of a device with a resonance frequency close to the maximum of the gain curve. 10 mW peak power are obtained at a duty cycle of 2%, with a slope efficiency of 25 mW/A. This is in good agreement with other lasers fabricated from the same growth, where 50 mW/A were observed from devices with ~24% computed radiative efficiency [20]. Lasing ceases at 100 K, somewhat below the 130 K observed in unpatterned disk lasers. The inset shows the spectrum of the same device at a current of 1.8 A; the device is single mode with a side-mode suppression ratio of more than 20 dB. The same behavior was observed at all temperatures; only at currents just above threshold, we observed a second mode close to the dominant one. Figure 3(a) shows the computed far-field for the mode shown in Fig. 1(a). For symmetry reasons, the field components interfere destructively on the device axis. The concentric rings in the far-field can be understood from an analysis following Young’s double slit experiment, considering the opposite ridges of the ring as two slits with anti-symmetric field distribution. Their angular position is determined by sin(2θ) = 2(n + 1/2)λ/d, where θ is the angle between device axis and free-space wavevector, λ is the free-space wavelength, and d is the device diameter. This explains why we expect a stronger divergence for our THz devices (λ/d≈1/10) than for the devices in [22], where λ/d≈1/100. The device from which we obtained the data of Fig. 2(b) was then mounted in a different setup to measure the far-field, where we also repeated the spectral measurements for verification. Results for the central cone (~15° from the vertical) of the far-field are shown in Fig. 3(b) with the laser nominally under the same driving conditions: a semicircular pattern with a relatively strong peak on one side was observed. The asymmetry could be due to the non-uniformly distributed mode along the ring, as discussed in detail below, or due to near-field distortions introduced by the asymmetric wire-bonding. We also note that the measured spectrum is no longer perfectly single-mode (see Fig. 3(b)), making the interpretation of the pattern even more complex.

 

Fig. 2 (a) A SEM picture of a fabricated device. (b) Light-current characteristics of a ring with a diameter of 960 µm, driven with 800 ns pulses at 25 kHz repetition rate. The inset shows a spectrum on a logarithmic scale of the device driven with the above settings at a current of 1.8 A.

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Fig. 3 (a) Computed far-field of the device shown in Fig. 2. The angular position of the rings is determined by d/λ, where d is the ring diameter and λ the free-space wavelength. (b) Measured central portion of the emission far-field. Also shown is a spectrum taken prior to the far-field measurement. The insets show 3D plots of the corresponding panels.

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In any case we can observe that the device seems quite sensitive to operating conditions (pulse shape, optical feedback, temperature stability, bonding etc.), indicating low mode selectivity. To further investigate these aspects, far-field measurements were also performed in a much wider angular range along the horizontal axis. This was achieved measuring multiple far-fields, each taken after rotating the cryostat head by 15°, and joining them together. The absence of false peaks (originating from unwanted reflections, etc.) was verified by checking data collected in the same angular region for two different windows positions. Results are shown in Fig. 4(a) for the same device, though driven this time with shorter pulses (330 ns) at higher repetition rates. Apart from the lower signal-to-noise ratio implied by the time-consuming measurement technique, it is evident that, while a significant fraction of the emission is indeed observed in a relatively small angular spread near the vertical, some non-negligible signal is clearly detected at large angles as well, possibly a consequence of the presence of modes with an undefined phase relation with the grating. These would have a partially asymmetric character and, as shown in Fig. 4(b), the power radiating from the asymmetric mode shows a strong intensity also at large angle from the vertical. The central area of Fig. 4(a) is also qualitatively different from Fig. 3(b), further evidencing the sensitivity to driving conditions. More importantly, however, this intensity distribution is incompatible with the slope efficiency shown in Fig. 2(b), where 25 mW/A were observed within a small collection angle. In fact, assuming the optimistic case in which the Golay detector were aligned on the maximum intensity peak at 11/-18 degrees, and integrating the far–field intensity over the detector field of view (black circle in Fig. 4) for the power comparison, one obtains that the far-field of Fig. 4 would imply a radiative efficiency of at least 20%, even for the ideal internal quantum efficiency of 200 (equal to the number of stages). This provides clear further evidence that the laser oscillates on other modes under these pumping conditions. In Fig. 5 we present data for another device with a slightly larger diameter emitting at 3.21 THz. The reduced peak power of 4 mW, shown in Fig. 5(a) is expected from the spectral gain dependence observed in earlier device series [20]. In this case, however, the device showed a more stable single-mode character in both set-ups. A far-field acquired at 1.7 A, where it was verified one mode dominated the spectrum, is reported in Fig. 5(b). We can now identify the ring shaped structure predicted; the centermost ring is however collapsed into a spot. The distortion could be due to the bonding wires disturbing the near-field, or to the device being slightly non-symmetric. We recall in fact that the near-to-far-field transformation is basically a Fourier transform, which means that a coherent, delocalized near-field leads to a narrow spot in the far-field, whereas small bright spots in the near-field lead to isotropic emission.

 

Fig. 4 (a) Measured far-field of the same device as in Fig. 2(b), driven with 1.65 A, 330 ns pulses at 90 kHz repetition rate. Data are joined from measurements with different cryostat window positions. Under these pumping conditions, a maximum emission at 11/-18 degrees and a considerable angular spread of the power is observed. The black circle indicates the collection angle of the Golay-cell used for acquisition of the light-current characteristics. The colormap is the same as for Fig. 3. (b) Cross section of the computed far-field of the two modes depicted in Fig. 1(b): symmetric (red) and asymmetric (black). Surprisingly, the asymmetric mode presents a large radiating intensity also far from the vertical direction.

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Fig. 5 (a) Light-current characteristics of a ring with a diameter of 990 µm, driven with 800 ns pulses at 12.5 kHz repetition rate. The inset shows a spectrum on a logarithmic scale of the device driven with the above settings at a current of 1.8 A. (b) Measured far-field of the same device. Except for the center ring, the computed far-field of Fig. 3(a) is reasonably reproduced. The non-continuous rings could be due to the bonds covering the grating. The area outside an angle of ~26° (black circle) is shielded by the cryostat window opening. The inset shows a spectrum of the device driven under the same conditions.

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To investigate how the alignment of the metallic grating and the defects introduced by wire-bonding are affecting surface emission patterns, we need a model of the entire ring. To this end, we follow a recent work on electrically pumped photonic crystal devices [23], where the location of the bond-wires in surface emitting THz QCLs has been shown to be very important. The authors have successfully employed a 2D model to compute the resonances of their large devices and explain the surface emission patterns. The approach uses the effective refractive indices of both double-metal and slit region to mimic the device with a structure of infinite extension along the growth axis, which allows the use of a scalar differential equation in 2D. The magnetic field of the eigenmode in the non-metalized area is then considered to be the near-field. After checking this model to be consistent with Fig. 3(a), a misalignment between the center of the semiconductor ring and of the metallic grating was introduced, as well as four missing slits to simulate the bond locations, in order to model the device of Fig. 2(a). Figures 6(a,b) show the electric field of the obtained eigenmode and the corresponding far-field. The imperfections lead to a non-uniform mode distribution along the ring, which then translates into a spot-like emission pattern. As further examples, we also plot the computed far-fields of a device with a perfect grating misaligned by 1 µm, and a perfectly aligned grating with two defects on the x-axis. As expected, all deviations strongly modify the surface emission pattern. In any case, the general directionality of the power does not seem to be affected, in agreement with our experimental observations. We can also assume that the bond wires contribute to the near-field by enlarging the effectively radiating area, which would explain the fact that the spot observed in Fig. 5(b) is narrower than the spots in Fig. 6(b). This effect is of course not included in this simple model. While this approach proves very useful for the understanding of non-perfectly periodic devices, it does not yield the surface losses of a particular mode, and therefore also excludes the calculation of spectra like those shown in Fig. 1.

 

Fig. 6 (a) Electric field along the growth axis computed in a 2D model for the device shown in Fig. 2(a). Slits are suppressed in the location of the bonding pads, and the grating is misaligned by 0.5/-1.5 µm in x/y direction. (b) Corresponding far-field, where the distortions are even stronger than those in the measured far-field (see Fig. 5(b)). (c), (d) Computed far-fields of a device with a grating misaligned by 1 µm in the x-direction, and of a symmetric device with 2 bonding pads on the x-axis respectively. Both deviations from a perfect device qualitatively change the surface emission pattern.

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If the grating is even more shifted with respect to the waveguide, the ring segments have locally different eigenfrequencies. Figure 7 illustrates the consequences as observed in earlier devices. In places where the grating is shifted towards the outer radius of the mesa, the effective period seen by the mode is reduced. The resulting shift of the main resonance can be seen from the computed spectra in Fig. 7(a). Two segments are considered, on opposite sides of a ring with a grating misaligned by 2.5 µm. Because the difference in eigenfrequency is now of the order of the linewidth of the resonator, the mode becomes localized in only one part of the ring. Therefore, the interference effect between opposite ring sides previously described as causing the circular far-field is lost, as can be clearly seen in the measurements of Fig. 7(b).

 

Fig. 7 (a) Resonances of segments of the same dimension, computed for two different radial positions of the grating. (b) Far-field of a device with the metallic grating misaligned with respect to the semiconductor ring by 2-3 um. Due to the effect shown in panel (a), the eigenfrequency is not constant along the ring. Indeed, the mode seems to be localized in the lower left part of the ring, thus the far-field is no longer determined by interference, but rather diffraction limited.

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5. Conclusions and perspectives

We have demonstrated a promising new technology for high power THz QCLs. In future devices, one should further reduce the grating misalignment to the submicron range, but also increase the thickness of the top-metallization to 200-300 nm, in order to ensure a completely symmetric device, both from an electrical and an optical point of view. Finally, the technology employed in [17] to separate the bonds from the grating would eliminate the mode distortions due to the bond pads. More recent heterostructures [9,24] show slope efficiencies up to 60 mW/A in double-metal FP resonators. According to our simulations, a ring resonator with a first order grating, together with a slightly thinner waveguide (~10% of the free-space wavelength) should yield a radiative efficiency of 25%. Considering also the high collection efficiencies achieved, we indeed believe that slope efficiencies of up to 300 mW/A can be reached in these structures. Surface emission then allows large emitter areas by device parallelization, which should pave the way towards compact, narrowband THz sources at the Watt level.