The design and fabrication of a high power THz quantum cascade laser (QCL), with electrically controllable transverse mode is presented. The switching of the beam pattern results in dynamic beam switching using a symmetric side current injection scheme. The angular-resolved L-I curves measurements, near-field and far-field patterns and angular-resolved lasing spectra are presented. The measurement results confirm that the quasi-TM01 transverse mode lases first and dominates the lasing operation at lower current injection, while the quasi-TM00 mode lases at a higher threshold current density and becomes dominant at high current injection. The near-field and far-field measurements confirm that the lasing THz beam is maneuvered by 25° in emission angle, when the current density changes from 1.9 kA/cm2 to 2.3 kA/cm2. A two-dimension (2D) current and mode calculation provides a simple model to explain the behavior of each mode under different bias conditions.
©2010 Optical Society of America
After roughly a decade of intense research on terahertz (THz) quantum cascade lasers (QCL), the prototype devices are getting closer to be deployed for various THz applications . Due to sub-wavelength dimension of the laser structure, the emission pattern of the device is inherently diffractive (wide-angle beam) . Focused and controllable emission beam profiles are crucial for many applications . Engineering the laser emission beam pattern is demonstrated using grating [4,5], photonic crystals  and external mode converters such as horn antennas [7,8], Si lenses , plasmonics  and hollow dielectric waveguides . The THz beam with a divergence angle as low as eight degrees has been recently reported by employing a third order grating on a ridge waveguide . Although the beam shape of the laser has been engineered and steered using different designs of photonic crystal structures, dynamically controllable beam emission from a single THz QCL has not been achieved yet. In this work we report the bias-controlled tuning of the emission direction of a THz QCL. Beam switching is achieved by selectively exciting different waveguide transverse modes under different current injection schemes.
We focus our study on a Semi-Insulating Surface Plasmon (SI-SP) based THz QCL. In this structure the optical mode profile extends to the semi-insulating substrate and hence is not tightly confined in the active region. The device shows relatively less divergent emission patterns and also higher output power at the expense of higher optical loss . The top contact is a metal layer directly on the top of the ridge waveguide and the bottom contacts consist of two Au metal layers besides the ridge waveguide, sitting on a 400 nm thick n+ GaAs layer which is underneath the QCL active region (see Fig. 1 ). The substrate is electrically insulating, the current is therefore laterally injected into the quantum-well active region from both sides of the laser ridge through the thin bottom n+ GaAs layer. The side current injection leads to laterally non-uniform distribution of the injected current and electrical potential, giving rise to a laterally non-uniform gain profile. The local gain profile, even though non-uniform, is laterally symmetric due to current injection equally from both sides of the ridge. The lateral non-uniformity of the gain profile plays an important role in deciding which transverse mode can be excited, because of the different extent to which the transverse modes overlap with the gain profile. As a result, quasi-TM00 or quasi-TM01 may be selectively excited under different current injection. For simplicity from now on, we call these quasi-TM modes as TM mode. In this work, we present the experimental and theoretical results of the near-field and far-field patterns from a SI-SP THz QCL under different current injection. Our results demonstrate that controllable beam switching can be achieved by selectively exciting different transverse modes of the devices. We also present a simplified model of the modal gain that qualitatively explains why the fundamental mode TM00 lases later than TM01 and becomes dominant at high current.
The cascade module of the THz QCL used in this study consists of three quantum wells (GaAs) and three barrier layers (Al0.15Ga0.85As), which is the same as the one reported in . The layer thicknesses are 48/ 96/ 20/ 74/ 42/ 161 Å, where the barriers are indicated in bold fonts. The quantum well of 161 Å is doped with Si dopants to a two-dimensional carrier concentration of 3.6 × 1010 cm−2. The whole QCL structure consists of 216 repeats of this module in sandwich between a 50 nm top and 400 nm bottom n+ GaAs layers doped to 5 × 1018 cm−3 and 3 × 1018 cm−3, respectively. The whole structure is grown on a semi-insulating (SI) GaAs substrate by molecular beam epitaxy. THz wave is generated by a radiative transition between a pair of anti-crossed double-well states. Depopulation of lower lasing state is mediated by coupling to a wide and doped subsequent well, the longitudinal-optical (LO) phonon relaxation and the injection to the following module.
A sufficient wide ridge waveguide is needed to accommodate TM01 lateral mode. We selected 150 μm wide ridges for this purpose. With this ridge width, loss of TM00 and TM01 are comparable and are lower than TM02 mode loss. The ridge waveguide structure of the surface plasmon THz QCL device is fabricated using a dry etching process. The ridge waveguide is etched down to roughly ~10 μm in depth, which allows the exposure of the 400 nm thick n+ GaAs layer for depositing the bottom contacts. The dry etch is targeted to stop at the boundary of active region and n+ region. Metal layers of Pd/Ge/Ti/Pt/Au (55/100/25/50/300 nm) is deposited for the top contact (on top of the ridge) and the bottom contacts (on both sides of the ridge). The bottom contacts are 13 μm away from the edges of the ridge on both sides, respectively, to yield efficient and laterally symmetrical current injection. The SI GaAs substrate of the samples is then thinned down to 150 μm to facilitate heat dissipation from the active region to a heat sink underneath . The sample is cleaved into laser bars with a ~1 mm long Fabry-Perot resonator. The laser bars are indium soldered (epi-layer side up) onto an oxygen-free copper package, wire bonded to the top and both sides of the ridge and then mounted in a closed-cycle Helium cryostat for measurements .
3. Results and discussions
Figure 2(a) shows the light-current (L-I) and voltage-current (V-I) characteristics of the QCL device in pulsed operation (with a 25 Hz repetition rate and a 200 ns pulse width) and under different heat-sink temperatures ranging from 10 K to 90 K. The V-I plot is measured using a four point technique, in which the four contact points are on the device to and side metal contact pads. The Golay cell detector collects 40° cone of the output THz light. The inset of Fig. 2(a) shows light collection scheme. The laser device starts to lase at J th = 1.83 kA/cm2 (13.4 V), at 10 K. As the current density further increases to ~2.0 kA/cm2 (13.9 V), the L-I curve shows a kink – an increase in slope efficiency. This L-I kink at 2.0 kA/cm2 is not related to the alignment of subbands between neighboring cascade modules, because no significant kinks are observed in the voltage-current (V-I) curve in the corresponding current density region. The slope kink is consistently observed in the L-I curves at temperatures ranging from 10 K to 90K. As will be revealed by further experimental and theoretical studies, the two distinct slopes in the L-I curves are attributed to the excitation of two different transverse modes (TM00 and TM01) in the laser device. The kink in the V-I curve at V ≈10 V and J ≈1.2 kA/cm2 is due to the indirect coupling of the injector state with the collector state, where the transparency condition is approximately reached [highlighted by horizontal arrow in Fig. 2(a)] .
An iris is then used to confine THz emission inside a collection cone with a solid-angle of 13°. This experiment measures angular-resolved L-I curve, with a confined collection cone angle. Figure 2(b) shows two L-I curves measured at 10 K along two different emission directions. The TM00 mode curve is measured along the normal direction of the laser facet and the TM01 mode curve is measured at an angle of 25° off the normal direction [see the inset of Fig. 2(b)]. The two L-I curves show different threshold current density. The TM01 mode curve has a threshold current density of 1.83 kA/cm2, which is the same as the one of the non-angular-resolved L-I curve in Fig. 2(a). The TM00 mode curve has a higher threshold current density of ~2.0 kA/cm2, matching the current density at which the kink is observed in the non-angular-resolved L-I curve in Fig. 2(a).
The observed change of THz emission direction suggests different transverse modes are excited when the device is biased at different currents [19,20]. To confirm this hypothesis of transverse mode change, we use a FLIR Photon 640 micro-bolometer camera to capture the near-field emission pattern at the laser facet. The original lens of the camera is replaced by a Tsurupica lens with 80% transparency at the lasing wavelength. A biconvex spherical lens with a focal length of 50 mm and diameter of 45 mm was chosen for this experiment. The lens tube is purged using dry nitrogen in order to minimize atmospheric vapor absorption. By ignoring spherical aberration, the spatial resolution of the optical system, as defined by diffraction, is already 150 μm. Therefore, the shape of the modal field cannot be well resolved. The recorded images are dominated by diffraction effect of the lens (at the origin of the concentric rings). For high order modes the image is dominated by interferences between the different sections of the opposite signed field. Despite the fact the optical setup could be further improved, for convenience we call these images as “near-field”; they are useful to qualitatively identify the excited lateral modes. The near-field pattern images at the laser facet are captured with a 2.5 time magnification (numerical aperture of 0.64). Figure 3(a) to 3(c) shows the near-field pattern measurement under different current injections (a: I = 2.9 A; b: I = 3.2 A; and c: I = 3.4 A), corresponding to the A, B, C points, labeled in the L-I curve in Fig. 2(a).
Figure 3(a) shows clearly that the transverse mode at the laser facet at (I = 2.9 A, point A) has two lobes (~90 μm apart), indicating a TM01 mode is excited in the waveguide. On the contrary, Fig. 3(c) (I = 3.4 A, point C) shows only one strong lobe at the center of the ridge, which is assigned to a TM00 mode. As for the intermediate current injection at I = 3.2 A (point B), the observed near-field pattern appears as the combination of the TM01 and TM00 modes. The measured near-field patterns show with no doubt that the different transverse modes are excited at different current injections. The TM01 mode is first excited at a lower current, while the TM00 mode (the fundamental mode) is excited at a higher current. The TM01 and TM00 modes can co-exist at an intermediate current injection.
The far-field emission pattern is the direct Fourier transform of the corresponding transverse modes at the laser emission facet. The two lobes in the TM01 mode are theoretically supposed to have opposite phase . The two opposite-phase lobes of the TM01 mode should lead to destructive interference along the normal direction of the laser facet (ϕ = 0° and θ = 0°, as defined in Fig. 1) at far-field, which can be verified by experimentally measuring the far-field emission patterns of the device. The results are shown in Fig. 3(d) to 3(f). As expected at a lower injection current (I = 2.9 A) when only the TM01 mode is excited, the far-field beam pattern [Fig. 3(d)] shows a minimum along the normal direction of the laser facet (θ = 0°). The laser emission is diverged to off-normal directions at angles of θ = ± 25° and beyond, respectively. This suggests that two lobes of TM01 mode have opposite phase and are located approximately apart. The non-symmetric far-field pattern might be caused by packaging asymmetry, where non-similar environment exists on each side of the waveguide facet. Along the vertical direction (ϕ) the far-field beam pattern is mainly distributed under the active region junction plane (ϕ < 0), same as . This is because a big portion of the transverse mode extends from the active region into the underneath semi-insulating substrate. When the device is biased at 3.4 A, only the fundamental mode TM00 is excited. Correspondingly, the far-field patter is mainly focused at the angle of θ = 0° [Fig. 3(f)]. At the intermediate current injection level (I = 3.2 A) when both TM00 and TM01 co-exist, the far-field beam pattern [Fig. 3(e)] displays combined features, as shown in Fig. 3(d) and 3(f).
Angular-resolved lasing spectra of the device at 10 K measured at the aforementioned three injection current levels once again reveal that two different transverse modes are excited. The spectra are measured along two different directions: θ = 0° and θ = 25° along which the TM00 and TM01 modes are found to radiate strongest, respectively. The two sets of spectra (in total 6) are shown in Fig. 4 . All spectra are normalized to unity in peak intensity. The two spectra at I = 2.9 A (θ = 0° and θ = 25°) have a main peak at 124.3 cm−1 and a much weaker Fabry-Perot (FP) side mode at 121.8 cm−1. The FP longitudinal wavelengths are given by Fig. 4(a)] looks similar to each other, while the absolute power at θ = 0° is much weaker than that at θ = 25°. The two lasing peaks at 124.3 and 121.8 cm−1 belong to the same longitudinal Fabry-Perot mode family of the TM01 transverse mode. As the current rises to I = 3.2 A, a new peak at 120.9 cm−1 appears in both angular-resolved spectra [Fig. 4(b)]. The wave number difference between this new peak and the peak at 124.3 cm−1 is 3.4 cm−1, which is not an integer product of the TM01 FP mode spacing (1.25 cm−1). Apparently, they do not belong to the same FP longitudinal mode family. The lasing emission at 120.9 cm−1 has the main peak at θ = 0° direction, while it is much weaker at θ = 25°, indicating that this lasing wavelength is from the TM00 transverse mode. The peak at 124.3 cm−1 of the TM01 mode dominates at θ = 25°, while is very weak but still observable at θ = 0° direction. The spectrum measurement result again confirms the co-existence of TM00 and TM01 modes at this current injection level (I = 3.2 A). The different FP longitudinal wavelengths of the TM00 and TM01 modes are attributed to slightly different effective refractive indices of these two transverse modes. With further increasing the current to 3.4 A, the peak at 120.9 cm−1 dominates at both θ = 0° and θ = 25° directions. The peak at 124.3 cm−1 disappears at θ = 0°, however, it is still observable at θ = 25°. The lasing spectra show that even at I = 3.4 A, both TM00 and TM01 are excited in the laser waveguide, nevertheless the TM00 is dominant. The results of the angular-resolved lasing spectra agree with the earlier observation of the near-field and far-field patterns.
4. Simulation of far-field pattern
To confirm that the experimental observations of the far-field pattern measurements are really due to the excitation of the TM00 and TM01 modes, the HFSS (Finite Element Method) simulation software is employed to calculate the far-field beam patterns from the 3D model of ridge waveguide structure as depicted in Fig. 1. HFSS was used as a 3-D Driven-Modal solver. The first two modes of SI-SP waveguide were separately calculated by an embedded 2-D eigenmode solver. These two modes were then separately used to excite one facet of the laser structure. Exact truncation boundary conditions were considered for the other facets. As compared to most published analyses based on simplifying assumptions, in this work, the far radiation fields are rigorously calculated from the modal field distributions over the entire 1 mm length of the structure. The conductivity of the contact metal and n+ GaAs layers is calculated using Drude model with relaxation times of 60 fs and 100 fs, respectively . The active region is modeled as a 10 μm thick GaAs layer with a background doping concentration of 8.15 × 1015 cm−3 and a Drude relaxation time of 500 fs. Despite the considerable computational complexity due to large mesh size and multi-resolution nature of the structure for the 3D simulation, the full length of the laser ridge (1 mm) is used in the accurate simulation of the fringes . Figure 5(a) shows the simulated far-field pattern of the TM00 mode. The laser beam is mainly focused in an emission cone around θ = 0° and φ = −10° direction, which agrees well with the experimental results shown in Fig. 3(f). Figure 5(b) shows the simulated far-field pattern of TM01 mode. The multiple-ring pattern of the simulated results resembles the experimental observation, whereas the experimental result [Fig. 3(d)] only shows the central-most ring due to the angular limit of the experimental setup collection cone. The simulation results confirm that the excited modes in the laser waveguide are TM00 and TM01 modes.
5. Simplified modal gain model
As mentioned before, the laser ridge is sufficiently wide (w = 150 μm) to support multiple transverse modes. However, among these, the particular transverse mode, which is excited, is the one with sufficient optical modal gain Gij [23,24] given by,,Fig. 1), Eij(x,y) and Hij(x,y) are the lateral electric and magnetic field profile of the ijth transverse mode respectively, M(x,y) is the normalized 2D mode power density, and g(x,y) is the local non-uniform gain. Equations (2a) and (2b) assume the gain is proportional to the fraction of power that overlaps with the gain medium. As pointed out by Robinson et. al. in , this is correct for TM or quasi-TM modes, as long as the lateral confinement of the mode is not too strong. Because the SI-SP modes are mostly confined in the substrate, Eq. (2b) results in less than 2% error.
In order to calculate the 2D non-uniform gain profile, g(x,y), we start from calculating voltage and current distribution by solving the 2D Poisson’s equation as25]. The vertical conductivity of active region (σy) depends on the applied vertical electric field (Ey) . To measure the vertical conductivity of the active region, it is required to conduct a four point measurement of the V-I curve of a device (preferably a non-lasing device), in which current is injected and flows vertically. For this purpose, a fabricated THz QCL with a metal-metal waveguide structure and the same active region material is employed. In such a structure, the current flows vertically through the active region from the top metal contact to the bottom metal contact without lateral spreading. As the current simulation results will be eventually used to calculate the gain, it is important to use the V-I of a non-lasing device to derive the conductivity. For this purpose, we fabricated a small micro-disc and cleaved it in half. Such a structure is expected to show very high waveguide loss, and hence destroy or strongly damp the lasing; nevertheless we observed very weak lasing form it. The vertical conductivity of the active region material is derived form measured V-I curve of this device. The final vertical conductivity used for the active region is in form of
The inset of Fig. 6 shows the measured DC vertical conductivity of the active region versus vertical electric field. We used COMSOL simulator to solve the Eq. (3) and calculate the current spreading at various applied voltages, for the 2D structure shown in Fig. 1. Figure 6 shows the lateral distribution of the vertical current, Jy, under different applied voltages, across the middle of the active region (5 μm below the top of the ridge). Two dashed lines show the corresponding current density levels, at which the TM01 and TM00 modes reach the lasing threshold (Fig. 2). Due to the bottom current injection configuration of the laser device, the lateral current density distribution, Jy(x), is not uniform. As observed in Fig. 6, Jy(x) is maximum at the two lateral edges of the ridge and is minimum at the center. The inset of Fig. 6 also compares the measured V-I curve shown in Fig. 2(a) with the simulated one. The simulated current agrees with the measurement results with a less than 1.5% mean square error.
In order to link the simulated current density to the local gain distribution, g(x,y), it is required to estimate the intrinsic gain of the active material versus the vertical current density. To do so, we started from the L-I characteristic of a metal-metal THz QCL, where the current distribution in the active region is uniform. The threshold gain for such a device is estimated to be 40 cm−1 . It is also shown in  that the transparency current density occurs after the alignment of the injection and collector states. The alignment is indicated by the bump in Fig. 2(a) V-I (horizontal arrow). For the gain material under study, the transparency current density (Jtr) is ~1.2 kA/cm2. Assuming the Lorentzian gain model for the THz QCL active region, the gain becomes proportional to the population inversion (Δn). If the leakage tunneling time from the upper lasing state to the excited state of the phonon well, called wrong extraction channel, is much larger than the upper lasing state lifetime, the current efficiency for population inversion, Δn/J, is weakly dependent on the electric field, and therefore, population inversion increases linearly with current. For the sake of simplicity, we used such a linear approximation between the transparency point and threshold, even though we have demonstrated theoretically that the shunting effect by the wrong extraction channel cannot be neglected in our three-well design with vertical transitions . Above the threshold, we assumed the emitted power is proportional to (Δn/ Δnth-1), where Δn is the population inversion if no photon were present in the cavity, and Δnth is the population inversion at threshold. Even though not strictly correct according to our ballistic model , this last approximation is reasonable.
By applying all of above assumptions and combining with the measured L-I curve, the intrinsic gain versus current density is extracted and shown in Fig. 7 . This curve is used to calculate the 2D local gain distribution at various applied voltages, in combination with simulated 2D current density profile. For current densities below 2 kA/cm2, at which g(x,y) ∝ (Jy(x,y) – Jtr), the local gain distribution, g(x,y), has a similar lateral profile as that of Jy(x,y). At higher current densities (>2.5 kA/cm2) and below the negative differential resistance of the laser, the local gain diminishes probably due to the different detuning at the injection and extraction sides . Since TM00 and TM01 modes have different distribution profile along the lateral direction of the device ridge, they overlap with the laterally non-uniform material gain profile to different extents, leading to different modal gains of these two modes. By controlling the current injection, one can favor one modal gain, while hold up the other one. As a result, the TM00 and TM01 modes can be selectively turned on under different biases.
In the last step, we simulate the 2D mode profile for each mode, as defined in Eq. (2b). The inset of Fig. 8 shows the simulated mode profile in the active region for the TM00 and TM01 modes, using the COMSOL simulator. These two mode distributions are inserted into the Eq. (2a), together with the calculated voltage dependant non-uniform local gain distribution to calculate the total reserve of gain. Each mode (TMij) reaches the threshold when the reserve of gain increases up to the total modal loss (αtot-ij = αm-ij + αw-ij). We call such a figure of merit the net modal gain of the material and define it as
To estimate the waveguide loss for each mode, we use the imaginary parts of corresponding effective index from the eigenmode solution of the Maxwell’s equation. The modal mirror loss (αm) is directly related to the modal reflectivity at the laser facet, which depends on the modal index and angle. A good approximation of the modal reflectivity is obtained by decomposing the main component of the electric field in a series plane waves by 2D Fourier transform. The coefficient of each of these waves is multiplied by the Fresnel reflection coefficient applied separately for contributions parallel and perpendicular to the plane of incidence. The total reflected field is then reconstructed by inverse Fourier transform; and the reflectivity is estimated by averaging the ratio of the reflected field intensity over the incident field. The mirror loss and the waveguide loss for different modes are, therefore, given by and , where R is the calculated reflectivity and β is the imaginary part of the propagation constant . Table 1 lists the calculated modal waveguide and mirror loss values. Lower mirror loss of TM01 can be explained using ray optics approach for a polarization perpendicular to the plane of incidence; the higher order mode impinges on the facet at a larger incident angle and hence is more reflective . Lower waveguide loss of TM01 mode originates from smaller overlap of this mode with the active region and the n+ layer underneath it.
Figure 8 shows the calculated net gain versus applied voltage for each mode. When the device is biased at a lower bias (lower current injection), the gain profile has maxima near the edges of the waveguide, which spatially overlaps more with the TM01 mode than with the TM00 mode. As a result, the TM01 mode possesses higher net gain than the TM00 mode and reaches the lasing threshold first. This explains why the experimental results show that the TM01 mode has a lower simulated threshold current density of Jth = 2.04 kA/cm2 (compared to experimental value of Jth = 1.83 kA/cm2) and starts to lase first. As the current injection continues to increase, the local gain in the center part of the ridge increases, which contributes more to the modal gain of the TM00 mode and brings it to the threshold point. According to this simplified model, the TM00 mode starts to lase at Jth = 2.11 kA/cm2 which is close to experimental (Jth = 2 kA/cm2). Further increase of the current injection renders the local current density at the lateral edges of the waveguide to exceed the maximum current density – beyond which the quantum wells become absorptive rather than emissive. Consequently, the net modal gain of the TM01 mode degrades and the lasing emission from the TM01 mode saturates. The TM00 mode is less affected by this gain-reduction process, because the maxima for lateral distribution of the current (on the edges) and TM00 mode profile (on the center) do not overlap. As observed in Fig. 2(a), the TM00 mode dominates at a current injection of J = 2.25 kA/cm2 (V ≈14.5 V), which is also consistent with the simulated graph in Fig. 8. The discrepancy between the simulated and the measured Jth for each mode can be attributed to various sources of error such as, underestimation of the total loss (particularly for TM01 mode) and the estimated intrinsic gain of the active region, etc.
We designed and fabricated a high power THz QCL, which exhibits electrically controllable dynamic beam switching using a symmetric side current injection scheme. The angular-resolved L-I curves measurements, near-field and far-field patterns and angular-resolved lasing spectra all confirm that the TM01 transverse mode lases first and dominates the lasing operation at lower current injection, while the TM00 mode lases at a higher threshold current density and becomes dominant at high current injection. Because of the different near-field patterns at the laser emission facet of the TM00 and TM01 transverse modes, the far-field of the laser shows two lobes of radiation at horizontal angles of θ = ± 25° when operating in TM01 mode under lower current injection and single lobe radiation at θ = 0° when operating in TM00 mode under higher current injection. The THz emission beam of the device can be easily and dynamically maneuvered by switching the applied device bias. The experimental results are in qualitatively reasonable agreement with the results of the simplified model of the modal gain.
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