Abstract

Plasmonic lasers suffer from low output power and divergent beams due to their subwavelength metallic cavities. We developed a phase-locking scheme for such lasers to significantly enhance their radiative efficiency and beam quality. An array of metallic microcavities is longitudinally coupled through traveling plasmon waves, which leads to radiation in a single spectral mode and a diffraction limited single-lobed beam in the surface normal direction. We implemented our scheme for terahertz plasmonic quantum-cascade lasers (QCLs) and measured peak output power in excess of $2\,\,{\rm{W}}$ for a single-mode $3.3\,\,{\rm{THz}}$ QCL radiating in a narrow single-lobed beam, when operated at $58\,\,{\rm{K}}$ in a compact Stirling cooler. We thereby demonstrated an order of magnitude increase in power and thirty-times higher average intensity for monolithic single-mode terahertz QCLs compared to prior work. The number of photons radiated from the cavity outnumber those absorbed within its claddings and semiconductor medium, which constitutes ${\gt}50 \%$ radiative efficiency and is significantly greater than that achieved for previous single-mode mid-infrared or terahertz QCLs.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

High-power sources of terahertz radiation are desired for applications in chemical and biomolecular sensing and spectroscopy such as non-destructive evaluation and detection of explosives and drugs [1], biomedical imaging [2], and remote sensing in astronomy to understand star and galaxy formation [3]. Terahertz semiconductor quantum cascade lasers (QCLs) [4] are closer than ever to achieving many such applications, with a vast potential for commercialization similar to that experienced by mid-IR QCLs [5,6]. Terahertz QCLs with Fabry–Perot cavities with output power in the range of hundreds of milliwatts to multiwatts have been reported in recent years [7,8]; however, such lasers show multimode spectral outputs with poor radiation patterns. Stable single-mode operation in a narrow far-field beam is a consistent requirement across many of the targeted applications. However, progress in the improvement of key characteristics of terahertz QCLs has somewhat stagnated in the past decade, particularly with respect to their maximum operating temperature as well as output power [6,911]. Specifically, the output power of monolithic single-mode terahertz QCLs has not increased much beyond the hundred milliwatt level, which was initially reached eight years ago [12]. Some recent results include terahertz QCLs with hybrid second- and fourth-order distributed feedback (DFB) that achieved 170 mW optical power at 62 K [13], terahertz QCLs with sampled gratings in the top metal layers with 186 mW output power at 10 K [14], and terahertz QCLs with a quasi-crystalline DFB structure with a peak output power of 190 mW at 20 K [15]. The recent development of external-cavity terahertz QCLs is promising, as it significantly enhanced the optical power from single-mode terahertz QCLs to the level of a Watt [16], albeit with the added cost of increased complexity and loss of the flexibility and versatility afforded by monolithic chip-based lasers sources.

Phase locking of an array of optical cavities is a long-established method for scaling up the outcoupled optical power, as well as beam shaping of conventional semiconductor lasers [1719], that continues to be further developed today [20]. It could be all the more relevant for plasmonic lasers that confine long-range surface plasmon polariton (SPP) modes at subwavelength dimensions, leading to poor radiation patterns and low output power [2124]. Terahertz QCLs are another class of plasmonic lasers that overwhelmingly use parallel-plate metallic cavities [25], which have excellent mode confinement but poor radiative outcoupling and divergent beams [26]. Different mechanisms for phase locking of multicavity arrays of metal cavities have been reported for terahertz QCLs toward improvement in their output power, radiative efficiency, and far-field radiation patterns [27,28]. However, prior phase-locking schemes have not yielded better results for output power when compared to DFB methods [9,11,13,14].

In this paper, we describe use of a phase-locking scheme for subwavelength metal cavities in a single-mode terahertz plasmonic QCL to achieve a large radiative efficiency and high-power output in a narrow single-lobed far-field beam. The parallel metallic plates in the cavities sandwich a 10 µm thick quantum cascade GaAs/AlGaAs superlattice active medium with spectral gain at $\nu \sim 3.2 {-} 3.4\,\,{\rm{THz}}$ ($\lambda \sim 88 {-} 94\,\,\unicode{x00B5}{\rm m}$). Hence, the cavities are subwavelength in the dimension orthogonal to the metal plates of the resonant optical cavities, but are kept larger in the other two dimensions. Whereas previously reported phase-locking schemes for semiconductor lasers in the literature primarily relied on lateral coupling of cavities, our method implements a longitudinal coupling mechanism by way of single-sided SPP waves that are established on top of the metal claddings of the cavities and propagate in the surrounding medium as surface waves. The nature of surface waves thus generated is similar to that in Ref. [29]. However, the mechanism of generation of such surface waves and their role in the operation of the QCL differs significantly from that in Ref. [29], since they are not the primary contributor to the radiation from the phase-locked array. The specific periodicity and dimensions of the short cavities in the multicavity array lead to the establishment of an intense in-plane electric field that radiates and interferes constructively in the surface normal direction. Based on this scheme, the record-highest peak output power ($2.03\,\,{\rm{W}}$), slope efficiency (SE) ($1.57\,\,{\rm{W}}/{\rm{A}}$), and peak wall plug efficiency ($2.3 \%$) are reported for single-mode terahertz QCLs. A large differential quantum efficiency of 115 photons per electron is realized for the detected radiation for a fraction of the laser’s dynamic range, which is 52% of the maximum theoretical limit in a QCL superlattice medium that has 221 repeated stages. When accounting for optical transmission loss through the cryostat window as well as the laser’s internal transition efficiency, the outcoupling (radiative) efficiency of the QCL is estimated to be $\gtrsim 60\%$, which indicates approximately 50% more photons are radiated from the cavity compared to those absorbed within its claddings and the semiconductor medium. In contrast, the differential quantum efficiency for all single-mode QCLs in the literature, including mid-IR QCLs, has remained below 38% of the theoretical limit [30] to the best of our knowledge.

2. PHASE LOCKING OF SHORT CAVITIES WITH SURFACE WAVES

The radiation loss coefficient (per unit length) for a Fabry–Perot laser cavity is expressed as

$${\alpha _{{\rm{rad}}}} = \frac{1}{L}\ln \left({\frac{1}{R}} \right),$$
where $L$ is the length of the cavity and $R$ is the reflectivity of each of two end facets of the cavity for the guided wave propagating along its length. The coefficient for total optical loss in the cavity can be written as ${\alpha _{{\rm{tot}}}} = {\alpha _{{\rm{rad}}}} + {\alpha _{{\rm{cav}}}}$, where ${\alpha _{{\rm{cav}}}}$ is the optical loss coefficient due to the cavity itself (that includes absorption losses in the claddings as well as the gain medium). The radiative (outcoupling) efficiency of the laser can then be defined as a ratio ${\eta _{{\rm{rad}}}} = {\alpha _{{\rm{rad}}}}/{\alpha _{{\rm{tot}}}}$ that expresses the radiative fraction of the total number of photons generated in the gain medium of the laser. High-power lasers typically have large dimensions, including longer cavities, to generate more photons. However, increasing $L$ reduces ${\eta _{{\rm{rad}}}}$, since ${\alpha _{{\rm{rad}}}} \propto 1/L$, which leads to diminishing returns in the net optical power if the cavity is made too long. For monolithic terahertz QCLs, the best radiative efficiencies have therefore been demonstrated in the surface emitting configuration [13,27] when ${\alpha _{{\rm{rad}}}}$ is no longer dependent on the cavity dimensions to the first order, and is instead dependent on the design of the periodic photonic structures within the cavity and/or its claddings.

A rather effective way to increase the radiative efficiency for an overall large (long) cavity is by coherently combining radiation from several short-length Fabry–Perot cavities, each of which has a large ${\alpha _{{\rm{rad}}}}$, as in equation Eq. (1). A large number of such cavities in a multicavity array would then lead to high optical power. Figure 1 shows in detail a scheme that allows for phase-locked operation for multiple parallel-plate subwavelength metallic cavities when they are placed in a longitudinal arrangement. Figure 1(a) describes the scheme qualitatively. The longer cavity on the left is a Fabry–Perot cavity that radiates only from its two end facets in the longitudinal ($x$) dimension. However, if shorter cavities are used instead, as shown on right, the effective number of radiating facets is increased. With a specific choice of a certain periodicity in which such short microcavities are placed along $x$, propagating single-sided hybrid SPPs [29] are sustained outside the cavities (in the surrounding medium) if they have a well-defined phase relation with resonant SPP modes inside the parallel-plate cavities. These waves are a combination of long-range SPPs and short-range quasi-cylindrical waves sustained on top of metal films [31]. Radiative apertures [rectangular slits in Fig. 1(a)] could be opened in the top metal cladding of the microcavities to serve a dual purpose. First, radiation from these apertures serves to intensify the hybrid SPP surface waves outside the cavities, which is essential for phase locking to be established. Second, the diffracted field from the apertures could contribute to the radiation in the surface normal direction provided the apertures are placed with appropriate periodicity that allows for constructive interference of the radiation in the vertical ($z$) dimension.

 

Fig. 1. Longitudinal phase-locking scheme for subwavelength metallic cavities. (a) The scheme that allows for phase-locked operation of multiple parallel-plate subwavelength metallic cavities. The objective of the scheme is to enhance radiation from a long ridge cavity by splitting it into several shorter microcavities, which increases the number of radiating end facets when the microcavities are under phase-locked operation. A specific periodic arrangement of the microcavities and slit-like apertures in the top metal layer of the cavities establishes single-sided SPPs in the surrounding medium of the cavities, which leads to phase-locked operation of the microcavities. The enhanced radiation in the surface normal direction is primarily due to a larger number of radiating end facets for the microcavity array. A secondary contribution of radiation is the slit-like apertures within the microcavities. (b) A specific design of the multicavity QCL array for phase-locked operation. The distance between neighboring microcavities is equal to the wavelength of the single-sided SPPs (${\lambda _{{\rm{SPP}}}}$) that are established in the surrounding medium. Each microcavity is of length $3 \times {\lambda _{{\rm{SPP}}}}$ and has two slit-like apertures in its top metal layer with an inter-aperture spacing of ${\lambda _{{\rm{SPP}}}}$. An illustration of the standing wave of the electric field corresponding to the lowest-loss resonant mode under phase-locked operation is given for both the vertical (${E_z}$) and in-plane (${E_x}$) components of the field. The radiating sites in the microcavity array include the end facets of the microcavities as well as the slit-like apertures, each of which has the same phase for the ${E_x}$ field, which leads to radiation in the surface normal direction.

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The length of the microcavities in the multicavity array is chosen on the basis of two considerations. First, the length is such that the in-plane (${E_x}$) electric field has the same phase at the locations of both end facets, where it is most intense. This allows for constructive interference and radiation in the surface normal dimension of the array. Second, the cavities are kept short enough to keep ${\alpha _{{\rm{rad}}}}$ large, with the goal of realizing ${\alpha _{{\rm{rad}}}} \sim {\alpha _{{\rm{cav}}}}$ to achieve an overall large ${\eta _{{\rm{rad}}}}$. For Fabry–Perot terahertz parallel-plate metallic cavities at 3–4 THz, ${\alpha _{{\rm{rad}}}}$ is in the range $2 {-} 3\,\,{\rm{c}}{{\rm{m}}^{- 1}}$ for a 1 mm long cavity [32]. The coefficient for total optical loss in the cavity ${\alpha _{{\rm{tot}}}}$ has been experimentally measured in the range of ${\sim}10 {-} 15\,\,{\rm{c}}{{\rm{m}}^{- 1}}$ for plasmonic QCLs operating from 3–4 THz [33,34] based on resonant-phonon QCL active regions [35], which means that ${\alpha _{{\rm{tot}}}}$ is almost entirely composed of ${\alpha _{{\rm{cav}}}}$ with a minimal radiative component and ${\eta _{{\rm{rad}}}} \ll 1$. The cavity lengths in the array were thus chosen to be approximately a third of 1 mm, in order to realize ${\alpha _{{\rm{rad}}}} \sim 10\,\,{\rm{c}}{{\rm{m}}^{- 1}}$ for the desired lowest-loss resonant optical mode of the phase-locked array.

The specific design of the phase-locked array and its operational principle are shown in the illustrative diagram in Fig. 1(b). The length of each microcavity is chosen to be ${\sim}3{\lambda _{{\rm{SPP}}}}$, where ${\lambda _{{\rm{SPP}}}}$ is the wavelength of the hybrid SPP surface wave in the surrounding medium, which is determined through finite element method (FEM) simulations. For a resonant mode excited at free-space wavelength $\lambda$, ${\lambda _{{\rm{SPP}}}}\lesssim\lambda$ for the multicavity array surrounded by air or vacuum. ${\lambda _{{\rm{SPP}}}}$ can vary slightly based on the shape of the hybrid SPP mode, which differs from one phase-locked resonant mode to another and hence is not an implicitly deterministic parameter for a given geometry of the microcavities. For a 3.3 THz ($\lambda \sim 91\,\,\unicode{x00B5}{\rm m}$) QCL array design, a periodicity $\Lambda = 324\,\,\unicode{x00B5}{\rm m}$ (corresponding to ${\lambda _{{\rm{SPP}}}} \sim 81\,\,\unicode{x00B5}{\rm m}$) is needed based on results from FEM simulations. As shown below, the experimental lasing frequency of a QCL with this periodicity matches the prediction from the FEM simulation. The distance between neighboring cavities ${d_{{\rm{air}}}} \sim {\lambda _{{\rm{SPP}}}}$ ensures the hybrid SPP mode is periodic from one microcavity to another, which allows for phase locking of the hybrid SPP surface waves to guided SPP modes within the cavities. Slit-like apertures are left open in the top metal cladding at locations where vertical electric field ${E_z}$ has a null for the standing wave inside cavities, and hence the in-plane field ${E_x}$ has a maxima leading to a large diffractive outcoupling from the apertures [36]. The periodicity of the aperture locations is kept at ${\sim}3\lambda /{n_{{\rm{eff}}}}$, which is approximately an integer multiple of the wavelength of the guided SPPs within the semiconductor ($= \lambda /{n_{{\rm{eff}}}}$), where ${n_{{\rm{eff}}}}$ is the effective propagation index of the guided SPPs ($\lesssim 3.6$ in GaAs). The hybrid SPP mode on top of the metal cladding automatically adjusts its shape to comply with this periodicity, such that ${\lambda _{{\rm{SPP}}}} \sim 3\lambda /{n_{{\rm{eff}}}}$ for the global phase-locked resonant optical mode in the multicavity array. In that sense, there is no single parameter that exclusively determines the wavelength $\lambda$ of the resonant mode of the multicavity array. The length of the individual microcavities, the intercavity distance ${d_{{\rm{air}}}}$, or the spacing between adjacent apertures could each be changed individually in the array for lithographic tuning of $\lambda$. A numerical study of the effect of variations in structural design parameters of the array on its ability to excite the desired resonant mode was not conducted as part of this report. However, experimental results for the tuning of the resonant frequency of the array via lithographic variation of the ${d_{{\rm{air}}}}/\Lambda$ parameter within a range of ${\sim}4\,\,\unicode{x00B5}{\rm m}$ (as presented in Section 4) show the robustness of the design scheme to variations in cavity dimensions that might arise due to fabrication with conventional lithography techniques.

3. FINITE ELEMENT MODELING

To assist in describing the operation of the phase-locked array, Fig. 2(a) shows an eigenmode spectrum of an array that is similar to one that was experimentally implemented with seven microcavities, computed using an FEM solver [37]. The specific details of the modeling are the same as those in Ref. [13], in which the computed loss is the sum of the loss at the absorbing boundaries due to radiation (outcoupling). By analyzing the eigenfrequencies, their corresponding radiation losses, and the electric field distribution, the lasing frequency as well as the far-field beam patterns can be estimated. The simulated structure of the phase-locked array has a periodicity of $\Lambda = 324\,\,\unicode{x00B5}{\rm m}$ for microcavity placement along the longitudinal ($x$) dimension and an intercavity spacing of ${d_{{\rm{air}}}} = \Lambda /4$. The two-dimensional (2D) simulation effectively solves for cavities of infinite width (along the $y$ dimension), which is a good approximation for wide ($\gg \lambda$) cavities used in experimental implementation. The occurrence of bandgaps in the resonant mode spectra is indicative of a DFB effect arising due to the periodicity of the overall array that results in the coupling of forward- and backward-propagating hybrid SPP surface waves. In this case, the desired mode (with the desired periodicity of the phase-locked SPP modes, as illustrated in Fig. 1) with an intense hybrid SPP mode in the surrounding medium is excited as the lowest-loss mode in the multicavity array. For the mode shown, ${\sim}73\%$ of the total electrical energy density is in confined SPP modes within the microcavities, and the remaining fraction exists in hybrid SPPs in the surrounding medium. As in DFB lasers, the global intensity envelope of the hybrid SPP mode shows the maximum intensity at the central microcavity that decays toward either longitudinal end of the multicavity array along the $x$ dimension, which leads to modal discrimination making it the lowest-loss eigenmode. This is evident from the intensity of the field radiated in the surface normal direction in Fig. 2(b), which is strongest in the middle of the array. The computed plots of ${E_z}$ and ${E_x}$ components of the electric fields are similar to that in the illustrative schematic in Fig. 1(b). The intense in-plane field ${E_x}$ (which leads to radiation from the array) at both end facets of the microcavities clearly distinguishes this scheme from surface-emitting DFB terahertz QCLs [12,13,36]. A radiative loss of ${\alpha _{{\rm{rad}}}} \sim 9.5\,\,{\rm{c}}{{\rm{m}}^{- 1}}$ is estimated for the lowest-loss mode, which is approximately twice that in the DFB QCL structure that led to the previous best result for radiative efficiency in terahertz QCLs [13]. The slit-like apertures implemented in the top metal layer also contribute to the overall radiative loss, as can be seen in Fig. 2(b), due to the presence of the in-plane (${E_x}$) field in the apertures. When the energy density due to ${E_x}$ is integrated in a $80\,\,\unicode{x00B5}{\rm m} \times 80\,\,\unicode{x00B5}{\rm m}$ square region outside the quantum cascade gain medium for both the end facets and apertures of the central microcavity, it is estimated that ${\sim}35\%$ of the outcoupled radiation in the phase-locked arrays is from the apertures.

 

Fig. 2. Finite-element simulation results for phase-locked microcavity array at terahertz frequencies. (a) The eigenmode spectrum computed by finite-element simulations for the multicavity array in Fig. 1, with GaAs as the active medium (${n_a} = 3.6$) and air as the surrounding medium (${n_s} = 1$). Simulations are done in 2D (i.e., cavities of infinite width) for seven 10 µm thick cavities with periodicity $\Lambda = 324\,\,\unicode{x00B5}{\rm m}$ and intercavity spacing ${d_{{\rm{air}}}} = \Lambda /4$. Two equally spaced 9 µm wide apertures are implemented in the top metal cladding for each microcavity. The eigenmode spectrum shows frequencies and radiation loss for the resonant cavity modes of the phase-locked array. The lowest-loss mode occurs at 3.3 THz, and its radiative loss is ${\sim}9.5 {\rm{c}}{{\rm{m}}^{- 1}}$. The metal layers and the active medium are modeled as lossless to get an accurate estimation of the radiative loss. (b) Electric field distribution of the resonant mode for both ${E_z}$ and ${E_x}$ components (the ${E_y}$ component is nonexistent for wide cavities). The in-phase ${E_x}$ field at the locations of the end facets and the apertures leads to highly efficient radiation in the surface normal direction, with a single-lobed beam profile. Insets show the electric field distribution near the central microcavity of the phase-locked array.

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4. EXPERIMENTAL RESULTS

An active medium of terahertz QCLs based on a three-well resonant phonon design with a ${\rm{GaAs}}/{\rm{A}}{{\rm{l}}_{{{0}}{\rm{.15}}}}{\rm{G}}{{\rm{a}}_{{{0}}{\rm{.85}}}}{\rm{As}}$ superlattice [design RT3W221YR16A, molecular beam epitaxy (MBE) wafer VB841] is used for experimental implementation of the laser array, with a layer sequence of 57/18.5/31/9/28.5/16.5 (starting from the injector barrier), where the thicknesses are in monolayers (MLs; $1\,\,{\rm{ML}} = 2.825$ Å), and was grown by MBE with 221 cascaded periods, leading to an overall thickness of 10 µm. The design is similar to the three-well QCL design in Refs. [38,39], with minor modifications to achieve peak gain centered around a frequency of 3.3 THz. The QCL superlattice has an average $n$-doping of $5.7e15\,\,{\rm{c}}{{\rm{m}}^{- 3}}$ and is surrounded by 0.1 µm and 0.05 µm thick highly doped GaAs contact layers doped at $5e18\,\,{\rm{c}}{{\rm{m}}^{- 3}}$ on either side of the superlattice. A 200 nm thick ${\rm{A}}{{\rm{l}}_{{{0}}{\rm{.55}}}}{\rm{G}}{{\rm{a}}_{{{0}}{\rm{.45}}}}{\rm{As}}$ layer was grown as an etch-stop layer preceding the entire stack.

The fabrication process is described next. Metallic waveguides were fabricated using a standard thermocompression wafer bonding technique. Following wafer bonding and substrate removal, positive-resist lithography was used to selectively etch away the 0.1 µm thick highly doped GaAs layer from almost all locations where top metal cladding would exist on individual cavities via an ${{\rm{H}}_2}{{\rm{SO}}_4}{:}{{\rm{H}}_2}{{\rm{O}}_2}{:}{{\rm{H}}_2}{\rm{O}}$ etchant in a 1:8:80 concentration. A 10 to 15 µm wide highly doped GaAs layer below the top metal cladding was left unetched in the regions close to the lateral facets of each microcavity and both longitudinal and lateral facets of the bonding pads, serving as the longitudinal and lateral absorbing boundary, to ensure the excitation of the desired mode as the lowest-loss lasing mode, as described in Ref. [29]. A sequence of Ti/Cu/Au was deposited as the top (20/200/100 nm) metallic layers, in which image-reversal lithography was implemented to form metallic gratings. Phase-lock array cavities were then processed via inductively coupled plasma dry etching using ${\rm{BC}}{{\rm{l}}_3}$, ${\rm{C}}{{\rm{l}}_2}$, and Ar etchant in 20 sccm, 5 sccm, and 5 sccm (sccm denotes cubic centimeters per minute at standard temperature and pressure) with ${\rm{Si}}{{\rm{O}}_2}$ as mask. The substrate was then mechanically polished down to a thickness of 300 µm to improve heat sinking. A Ti/Cu/Au ($20/250/100\,\,{\rm{nm}}$) contact was also used as the backside metal contact for the final fabricated QCL chips to assist in soldering.

Experimental results from a representative terahertz QCL implemented with the phase-locking scheme in the pulsed mode of operation are shown in Fig. 3. Microcavities were combined on both lateral sides so they could be electrically biased simultaneously with few bonding pads. There is no optical coupling in those narrow connection regions. The scanning electron microscope image of the fabricated and mounted QCL chip in Fig. 3(b) shows several QCLs of varying dimensions located side by side. Figure 3(c) shows light–current ($L {-} I$) curves versus heat sink temperature for the best-performing QCL in terms of peak output power. A current–voltage ($I {-} V$) curve measured at 58 K is also shown. The results presented here are from a QCL with overall dimensions of $10\,\,\unicode{x00B5}{\rm m} \times 500\,\,\unicode{x00B5}{\rm m} \times 2.2\,\,{\rm{mm}}$ consisting of seven microcavities. The QCL emits in single mode at ${\sim}3.3\,\,{\rm{THz}}$ at most bias conditions (except close to threshold, when it also excites a second, weaker spectral mode). The spectra as a function of bias are plotted in the inset Fig. 3(c). This QCL operated up to a maximum temperature of 132 K, whereas the best Fabry–Perot QCLs fabricated from the same wafer operated up to 159 K. For the light–current–voltage measurements, the QCLs were biased, with rectangular pulses of 400 ns duration repeated at 10 kHz, which was further electrically gated at a 50% duty cycle with a 1 kHz square wave. The effective duty cycle under such a pulsed biasing scheme is 0.2%.

 

Fig. 3. Experimental results for a surface-emitting terahertz QCL. (a) A schematic of the phase-locked QCL array as it was implemented for final fabrication. The microcavities are connected through both lateral sides by narrow metallic strips, which create absorbing regions that selectively make higher-order lateral modes in the cavities more lossy. (b) A scanning electron microscope image of the fabricated QCL arrays. The insets show the ${\sim}15\,\,\unicode{x00B5}{\rm m}$ wide lateral absorbing regions composed of an exposed thin highly doped GaAs contact layer. (c) Experimental lasing characteristics ($L\! -\! I$ and $I\! -\! V$) of a representative phased-locked array QCL with seven microcavities, each with the dimensions $10\,\,\unicode{x00B5}{\rm m} \times 243\,\,\unicode{x00B5}{\rm m} \times 500\,\,\unicode{x00B5}{\rm m}$, at different heat sink temperatures. The inset shows QCL spectra at varying electrical bias at 58 K. (d) Far-field radiation pattern of the QCL measured close to its peak operating bias. The single-lobed beam has a FWHM of ${3.2^ \circ} \times {11.5^ \circ}$.

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Under similar conditions but without a 1000 Hz electric gate (0.4% duty cycle), the absolute power was calibrated using a thermopile power meter (Scientech AC2500 with AC25H), as is reported, without any corrections or focusing optics used in this process. A peak optical power of $2030 \pm 10\,\,{\rm{mW}}$ was detected for the QCL at 58 K, which equates to a peak wall plug efficiency of 2.3% for corresponding bias conditions. An SE of $1566 \pm 10\,\,{\rm{mW/A}}$ is estimated from the slope of approximately the first half of the dynamic range at 58 K, in which the $L\! -\! I$ is linear. To understand the significance of this result, a discussion about the SE of a QCL is in order. The SE of a QCL is expressed as

$$\frac{{d{P_{{\rm{out}}}}}}{{dI}} = \frac{{\hbar \omega}}{q}\;{N_p}\;{\eta _{\rm{i}}}\;{\eta _{{\rm{rad}}}},$$
where ${P_{{\rm{out}}}}$ is the output power, $I$ is the bias current, $\hbar \omega$ is the photon energy, $q$ is the fundamental electronic charge, ${N_p}$ is the number of repeat stages in the QCL, ${\eta _{{i}}}$ is the internal quantum efficiency of the QCL superlattice, which is affected by the injection efficiency as well as the radiative transition efficiency in the QCL superlattice [40], and ${\eta _{{\rm{rad}}}} = {\alpha _{{\rm{rad}}}}/({\alpha _{{\rm{rad}}}} + {\alpha _{{\rm{cav}}}})$ is the aforementioned radiative efficiency of the cavity. The slope of the $L {-} I$ decreases at higher bias currents, which is likely due to a reduction in ${\eta _{{i}}}$ as the electron gas becomes hotter in the quantum wells of the superlattice, which reduces the lifetime of the upper radiative subband due to thermally activated phonon scattering [38]. For the QCL in Fig. 3(c), a maximum value of ${\eta _{{i}}}{\eta _{{\rm{rad}}}} \sim 0.52$ is estimated for the detected power. In comparison, all previously published single-mode terahertz [13] and mid-IR QCLs [30] have remained below 0.32 and 0.38, respectively, for the ${\eta _{{i}}}{\eta _{{\rm{rad}}}}$ value to the best of our knowledge. When correcting for 92%–94% transmission through a 0.47 mm thick TPX (polymethylpentene) window of the cryostat, ${\eta _{{i}}}{\eta _{{\rm{rad}}}}\gtrsim 0.55$ is estimated. A conservative estimate of ${\eta _{{i}}} \sim 0.92$ is obtained for the QCL band structure by assuming a unity injection efficiency and using only longitudinal optical phonon scattering with a somewhat arbitrary electron temperature of 100 K for the upper laser subband and an effective tunneling time for the lower laser subband, as described in Ref. [41], to compute the radiative transition efficiency. Hence, a conservative estimate of ${\eta _{{\rm{rad}}}} \sim 0.60$ is obtained for the terahertz QCL shown. This result demonstrates that the radiative outcoupling from the cavity as characterized by ${\alpha _{{\rm{rad}}}}$ exceeds the optical loss coefficient in the cavity ${\alpha _{{\rm{cav}}}}$ by about 50%. In the fabricated QCL, ${\alpha _{{\rm{rad}}}}$ could easily be different from that predicted in the FEM simulations by several ${\rm{c}}{{\rm{m}}^{- 1}}$, especially since it depends critically on the width of the apertures and the overall extent of the metal claddings on top of the QCL cavities. An exact estimate of the absolute value of ${\alpha _{{\rm{rad}}}}$ is difficult to obtain for the fabricated QCLs.
 

Fig. 4. Lithographic tuning of the phase-locked QCL arrays. (a) Measured spectra from three different phase-locked QCLs with the same periodicity of the microcavities ($\Lambda = 324\,\,\unicode{x00B5}{\rm m}$) but slightly different ${d_{{\rm{air}}}}/\Lambda$ values, where ${d_{{\rm{air}}}}$ is the intercavity spacing. All the QCLs consist of seven microcavities and are biased similarly at an operating temperature of 58 K. (b) Measured spectra from three different phase-locked QCLs with different periodicity of the microcavities but a fixed ${d_{{\rm{air}}}}/\Lambda = 0.25$. The QCLs are located adjacent to each other on the fabricated wafer. All QCLs show robust single-mode operation from threshold to high peak bias.

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The power output for this QCL was also measured with a larger duty cycle of 4% (pulses of 400 ns duration repeated at 100 kHz). Peak output power of 1.99 W was detected at 58 K, which is slightly lower than the power measurement with a 0.4% duty cycle and is arguably due to greater electrical power dissipation in the microcavity array.

The experimental far-field beam pattern for the phase-locked array QCL is shown in Fig. 3(d). Diffraction-limited single-lobed far-field beams were measured in both the lateral ($x$) and vertical ($y$) dimensions. Far-field beam patterns were measured with a pyroelectric detector mounted on a 2D motorized scanning stage, which was placed 45 cm from the phase-locked array, with maximum scan angle of ${\pm}{26.5^ \circ}$ in both directions. The device was operated near the peak power at 10 kHz with a 300 ns pulse duration and electronically modulated with pulse trains at 1000 Hz (0.15% duty cycle). The full width at half-maximum (FWHM) for the QCL presented in Fig. 3(c) is ${\sim}{3.2^ \circ} \times {11.5^ \circ}$, which is narrower in the $x$ dimension due to a large cavity width of ${\sim}0.5\;{\rm{mm}}$. The robustness of the phase-locking scheme and its capability for lithographic tuning was verified by slightly changing the duty cycle ${d_{{\rm{air}}}}/\Lambda$ and keeping $\Lambda$ as a constant for different QCLs fabricated on the same semiconductor chip. Spectra from multiple such QCLs using a Fourier transform IR spectrometer (Bruker, VERTEX 70v) are shown in Fig. 4(a). All of the QCLs show single-mode operation over the entire dynamic range, and the lasing frequencies scale linearly with the duty cycle. As discussed earlier, lithographic tuning could also be realized by changing other design parameters. This was verified by changing the periodicity $\Lambda$ while keeping the duty cycle ${d_{{\rm{air}}}}/\Lambda$ constant. The spectra for multiple QCLs like this are shown in Fig. 4(b), where, yet again, robust single-mode operation is realized over the entire dynamic range of the QCLs, and the emission frequencies scale linearly with $\Lambda$.

5. CONCLUSION

In this article, we described a phase-locking scheme for metallic subwavelength cavities in a plasmonic laser that can achieve large radiative efficiency and output power. When implemented for terahertz plasmonic QCLs, the record-highest peak output power (to our knowledge) is reported for single-mode terahertz QCLs, and the record-highest radiative efficiency is estimated among all single-mode QCLs (including mid-IR QCLs) reported to date. The method leads to stable single-mode spectral operation and a diffraction-limited single-lobed far-field beam for the laser. There are two unique aspects to the scheme. First, it leads to longitudinal phase locking of a multicavity array, which differs distinctly from other phase-locking schemes for semiconductor lasers in the literature, which predominantly rely on lateral coupling of multiple cavities. Second, it generates coherent single-sided SPPs propagating as surface waves in the surrounding medium of metal cavities with a large vertical spatial extent, which could lead to the development of new modalities for spectroscopic sensing and wavelength tunability [42] due to access to a coherent SPP wave on top of the plasmonic laser’s cavity.

A peak output power of 2.03 W is detected for a surface-emitting 3.3 THz QCL operating at 58 K in the pulsed mode of operation. The QCL radiates in a single-lobed far-field beam with a FWHM divergence of ${3.2^ \circ} \times {11.5^ \circ}$. Due to the high power and narrow beam, the average intensity within the FWHM contour at a fixed distance for this QCL is ${\sim}40$ times the previous best achieved for a DFB terahertz QCL [13] and ${\sim}30$ times that estimated for a phase-locked array terahertz QCL [28]. A slope-efficiency of up to $1.57\,\,{\rm{W/A}}$ was measured that corresponds to a differential quantum efficiency of 115 photons reaching the detector per electron transported through the QCL superlattice, which is 52% of the maximum theoretical limit for the QCL. The radiative efficiency, which is the fraction of total generated photons that are radiated to free space, is expected to be even higher ($\gtrsim 60\%$). This result makes it the first single-mode QCL (including mid-IR QCLs), to our knowledge, in which more photons are radiated than are absorbed as optical losses within the cavity. Finally, robust single-mode operation and lithographic tuning across a bandwidth of ${\sim}140\,\,{\rm{GHz}}$ are demonstrated for a range of QCLs fabricated on the same semiconductor chip. The advantage of this scheme lies in its ease of implementation, which does not require tight tolerances for fabrication, as well as the possibility of scaling the optical power output further by increasing the lateral size of the cavities and number of elements in the multicavity array.

Funding

National Science Foundation (ECCS 1351142, ECCS 1609168).

Acknowledgment

The semiconductor lasers were fabricated at the nanofabrication facility of the Center for Photonics and Nanoelectronics at Lehigh University. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc. The views expressed in the paper do not necessarily represent the views of the U.S. DOE or the United States Government.

Disclosures

SK and YJ: Office of Technology Transfer at Lehigh University (P).

REFERENCES

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2. E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D 39, R301–R310 (2006). [CrossRef]  

3. P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. 50, 910–928 (2002). [CrossRef]  

4. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002). [CrossRef]  

5. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994). [CrossRef]  

6. M. S. Vitiello, G. Scalari, B. Williams, and P. D. Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23, 5167–5182 (2015). [CrossRef]  

7. M. Brandstetter, C. Deutsch, M. Krall, H. Detz, D. C. MacFarland, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “High power terahertz quantum cascade lasers with symmetric wafer bonded active regions,” Appl. Phys. Lett. 103, 171113 (2013). [CrossRef]  

8. L. H. Li, L. Chen, J. R. Freeman, M. Salih, P. Dean, A. G. Davies, and E. H. Linfield, “Multi-watt high-power THz frequency quantum cascade lasers,” Electron. Lett. 53, 799–800 (2017). [CrossRef]  

9. C. Sirtori, S. Barbieri, and R. Collombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7, 691–701 (2013). [CrossRef]  

10. G. Liang, T. Liu, and Q. J. Wang, “Recent developments of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 23, 1200118 (2017). [CrossRef]  

11. Y. Zeng, B. Qiang, and Q. J. Wang, “Photonic engineering technology for the development of terahertz quantum cascade lasers,” Adv. Opt. Mater. 8, 1900573 (2019). [CrossRef]  

12. G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, “Efficient power extraction in surface-emitting semiconductor lasers using graded photonic heterostructures,” Nat. Commun. 3, 952 (2012). [CrossRef]  

13. Y. Jin, L. Gao, J. Chen, C. Wu, J. L. Reno, and S. Kumar, “High power surface emitting terahertz laser with hybrid second- and fourth-order Bragg gratings,” Nat. Commun. 9, 1407 (2018). [CrossRef]  

14. F.-Y. Zhao, Y.-Y. Li, J.-Q. Liu, F.-Q. Liu, J.-C. Zhang, S.-Q. Zhai, N. Zhuo, L.-J. Wang, S.-M. Liu, and Z.-G. Wang, “Sampled grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 114, 141105 (2019). [CrossRef]  

15. S. Biasco, A. Ciavatti, L. Li, A. G. Davies, E. H. Linfield, H. Beere, D. Ritchie, and M. S. Vitiello, “Highly efficient surface-emitting semiconductor lasers exploiting quasi-crystalline distributed feedback photonic patterns,” Light Sci. Appl. 9, 54 (2020). [CrossRef]  

16. C. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum cascade VECSEL with watt-level output power,” Appl. Phys. Lett. 113, 011104 (2018). [CrossRef]  

17. D. R. Scifres, R. D. Burnham, and W. Streifer, “Phase-locked semiconductor laser array,” Appl. Phys. Lett. 33, 1015–1017 (1978). [CrossRef]  

18. J. Katz, S. Margalit, and A. Yariv, “Diffraction coupled phase-locked semiconductor laser array,” Appl. Phys. Lett. 42, 554–555 (1983). [CrossRef]  

19. D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced ‘leaky’ waveguides (antiguides),” Appl. Phys. Lett. 53, 464–466 (1988). [CrossRef]  

20. M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019). [CrossRef]  

21. M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009). [CrossRef]  

22. K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18, 8790–8799 (2010). [CrossRef]  

23. Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012). [CrossRef]  

24. R. F. Oulton, “Surface plasmon lasers: sources of nanoscopic light,” Mater. Today 15(1-2), 26–34 (2012). [CrossRef]  

25. B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 µm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003). [CrossRef]  

26. A. J. L. Adam, I. Kašalynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions,” Appl. Phys. Lett. 88, 151105 (2006). [CrossRef]  

27. T. Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10, 541–547 (2016). [CrossRef]  

28. A. Khalatpour, J. L. Reno, and Q. Hu, “Phase-locked photonic wire lasers by π coupling,” Nat. Photonics 13, 47–53 (2019). [CrossRef]  

29. C. Wu, S. Khanal, J. L. Reno, and S. Kumar, “Terahertz plasmonic laser radiating in an ultra-narrow beam,” Optica 3, 734–740 (2016). [CrossRef]  

30. W. Zhou, Q.-Y. Lu, D.-H. Wu, S. Slivken, and M. Razeghi, “High-power, continuous-wave, phase-locked quantum cascade laser arrays emitting at 8 µm,” Opt. Express 27, 15776–15785 (2019). [CrossRef]  

31. P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2, 551–556 (2006). [CrossRef]  

32. S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005). [CrossRef]  

33. D. Burghoff, C. W. I. Chan, Q. Hu, and J. L. Reno, “Gain measurements of scattering-assisted terahertz quantum cascade lasers,” Appl. Phys. Lett. 100, 261111 (2012). [CrossRef]  

34. D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105, 181118 (2014). [CrossRef]  

35. B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003). [CrossRef]  

36. S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, Q. Hu, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15, 113–128 (2007). [CrossRef]  

37. COMSOL Multiphysics, version 4.4, A Finite-Element Partial Differential Equation Solver.

38. S. Kumar, Q. Hu, and J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94, 131105 (2009). [CrossRef]  

39. S. Fathololoumi, E. Dupont, C. W. I. Chan, Z. R. Wasilewski, S. R. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. C. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express 20, 3866–3876 (2012). [CrossRef]  

40. J. Faist, “Wallplug efficiency of quantum cascade lasers: critical parameters and fundamental limits,” Appl. Phys. Lett. 90, 253512 (2007). [CrossRef]  

41. S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009). [CrossRef]  

42. C. Wu, Y. Jin, J. L. Reno, and S. Kumar, “Large static tuning of narrow-beam terahertz plasmonic lasers operating at 78 K,” APL Photon. 2, 026101 (2017). [CrossRef]  

References

  • View by:
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  • |

  1. J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20, S266–S280 (2005).
    [Crossref]
  2. E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D 39, R301–R310 (2006).
    [Crossref]
  3. P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. 50, 910–928 (2002).
    [Crossref]
  4. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
    [Crossref]
  5. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
    [Crossref]
  6. M. S. Vitiello, G. Scalari, B. Williams, and P. D. Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23, 5167–5182 (2015).
    [Crossref]
  7. M. Brandstetter, C. Deutsch, M. Krall, H. Detz, D. C. MacFarland, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “High power terahertz quantum cascade lasers with symmetric wafer bonded active regions,” Appl. Phys. Lett. 103, 171113 (2013).
    [Crossref]
  8. L. H. Li, L. Chen, J. R. Freeman, M. Salih, P. Dean, A. G. Davies, and E. H. Linfield, “Multi-watt high-power THz frequency quantum cascade lasers,” Electron. Lett. 53, 799–800 (2017).
    [Crossref]
  9. C. Sirtori, S. Barbieri, and R. Collombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7, 691–701 (2013).
    [Crossref]
  10. G. Liang, T. Liu, and Q. J. Wang, “Recent developments of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 23, 1200118 (2017).
    [Crossref]
  11. Y. Zeng, B. Qiang, and Q. J. Wang, “Photonic engineering technology for the development of terahertz quantum cascade lasers,” Adv. Opt. Mater. 8, 1900573 (2019).
    [Crossref]
  12. G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, “Efficient power extraction in surface-emitting semiconductor lasers using graded photonic heterostructures,” Nat. Commun. 3, 952 (2012).
    [Crossref]
  13. Y. Jin, L. Gao, J. Chen, C. Wu, J. L. Reno, and S. Kumar, “High power surface emitting terahertz laser with hybrid second- and fourth-order Bragg gratings,” Nat. Commun. 9, 1407 (2018).
    [Crossref]
  14. F.-Y. Zhao, Y.-Y. Li, J.-Q. Liu, F.-Q. Liu, J.-C. Zhang, S.-Q. Zhai, N. Zhuo, L.-J. Wang, S.-M. Liu, and Z.-G. Wang, “Sampled grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 114, 141105 (2019).
    [Crossref]
  15. S. Biasco, A. Ciavatti, L. Li, A. G. Davies, E. H. Linfield, H. Beere, D. Ritchie, and M. S. Vitiello, “Highly efficient surface-emitting semiconductor lasers exploiting quasi-crystalline distributed feedback photonic patterns,” Light Sci. Appl. 9, 54 (2020).
    [Crossref]
  16. C. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum cascade VECSEL with watt-level output power,” Appl. Phys. Lett. 113, 011104 (2018).
    [Crossref]
  17. D. R. Scifres, R. D. Burnham, and W. Streifer, “Phase-locked semiconductor laser array,” Appl. Phys. Lett. 33, 1015–1017 (1978).
    [Crossref]
  18. J. Katz, S. Margalit, and A. Yariv, “Diffraction coupled phase-locked semiconductor laser array,” Appl. Phys. Lett. 42, 554–555 (1983).
    [Crossref]
  19. D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced ‘leaky’ waveguides (antiguides),” Appl. Phys. Lett. 53, 464–466 (1988).
    [Crossref]
  20. M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019).
    [Crossref]
  21. M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
    [Crossref]
  22. K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18, 8790–8799 (2010).
    [Crossref]
  23. Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
    [Crossref]
  24. R. F. Oulton, “Surface plasmon lasers: sources of nanoscopic light,” Mater. Today 15(1-2), 26–34 (2012).
    [Crossref]
  25. B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 µm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
    [Crossref]
  26. A. J. L. Adam, I. Kašalynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions,” Appl. Phys. Lett. 88, 151105 (2006).
    [Crossref]
  27. T. Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10, 541–547 (2016).
    [Crossref]
  28. A. Khalatpour, J. L. Reno, and Q. Hu, “Phase-locked photonic wire lasers by π coupling,” Nat. Photonics 13, 47–53 (2019).
    [Crossref]
  29. C. Wu, S. Khanal, J. L. Reno, and S. Kumar, “Terahertz plasmonic laser radiating in an ultra-narrow beam,” Optica 3, 734–740 (2016).
    [Crossref]
  30. W. Zhou, Q.-Y. Lu, D.-H. Wu, S. Slivken, and M. Razeghi, “High-power, continuous-wave, phase-locked quantum cascade laser arrays emitting at 8 µm,” Opt. Express 27, 15776–15785 (2019).
    [Crossref]
  31. P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2, 551–556 (2006).
    [Crossref]
  32. S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005).
    [Crossref]
  33. D. Burghoff, C. W. I. Chan, Q. Hu, and J. L. Reno, “Gain measurements of scattering-assisted terahertz quantum cascade lasers,” Appl. Phys. Lett. 100, 261111 (2012).
    [Crossref]
  34. D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105, 181118 (2014).
    [Crossref]
  35. B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003).
    [Crossref]
  36. S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, Q. Hu, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15, 113–128 (2007).
    [Crossref]
  37. COMSOL Multiphysics, version 4.4, A Finite-Element Partial Differential Equation Solver.
  38. S. Kumar, Q. Hu, and J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94, 131105 (2009).
    [Crossref]
  39. S. Fathololoumi, E. Dupont, C. W. I. Chan, Z. R. Wasilewski, S. R. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. C. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express 20, 3866–3876 (2012).
    [Crossref]
  40. J. Faist, “Wallplug efficiency of quantum cascade lasers: critical parameters and fundamental limits,” Appl. Phys. Lett. 90, 253512 (2007).
    [Crossref]
  41. S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
    [Crossref]
  42. C. Wu, Y. Jin, J. L. Reno, and S. Kumar, “Large static tuning of narrow-beam terahertz plasmonic lasers operating at 78 K,” APL Photon. 2, 026101 (2017).
    [Crossref]

2020 (1)

S. Biasco, A. Ciavatti, L. Li, A. G. Davies, E. H. Linfield, H. Beere, D. Ritchie, and M. S. Vitiello, “Highly efficient surface-emitting semiconductor lasers exploiting quasi-crystalline distributed feedback photonic patterns,” Light Sci. Appl. 9, 54 (2020).
[Crossref]

2019 (5)

F.-Y. Zhao, Y.-Y. Li, J.-Q. Liu, F.-Q. Liu, J.-C. Zhang, S.-Q. Zhai, N. Zhuo, L.-J. Wang, S.-M. Liu, and Z.-G. Wang, “Sampled grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 114, 141105 (2019).
[Crossref]

Y. Zeng, B. Qiang, and Q. J. Wang, “Photonic engineering technology for the development of terahertz quantum cascade lasers,” Adv. Opt. Mater. 8, 1900573 (2019).
[Crossref]

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019).
[Crossref]

A. Khalatpour, J. L. Reno, and Q. Hu, “Phase-locked photonic wire lasers by π coupling,” Nat. Photonics 13, 47–53 (2019).
[Crossref]

W. Zhou, Q.-Y. Lu, D.-H. Wu, S. Slivken, and M. Razeghi, “High-power, continuous-wave, phase-locked quantum cascade laser arrays emitting at 8 µm,” Opt. Express 27, 15776–15785 (2019).
[Crossref]

2018 (2)

Y. Jin, L. Gao, J. Chen, C. Wu, J. L. Reno, and S. Kumar, “High power surface emitting terahertz laser with hybrid second- and fourth-order Bragg gratings,” Nat. Commun. 9, 1407 (2018).
[Crossref]

C. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum cascade VECSEL with watt-level output power,” Appl. Phys. Lett. 113, 011104 (2018).
[Crossref]

2017 (3)

G. Liang, T. Liu, and Q. J. Wang, “Recent developments of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 23, 1200118 (2017).
[Crossref]

L. H. Li, L. Chen, J. R. Freeman, M. Salih, P. Dean, A. G. Davies, and E. H. Linfield, “Multi-watt high-power THz frequency quantum cascade lasers,” Electron. Lett. 53, 799–800 (2017).
[Crossref]

C. Wu, Y. Jin, J. L. Reno, and S. Kumar, “Large static tuning of narrow-beam terahertz plasmonic lasers operating at 78 K,” APL Photon. 2, 026101 (2017).
[Crossref]

2016 (2)

C. Wu, S. Khanal, J. L. Reno, and S. Kumar, “Terahertz plasmonic laser radiating in an ultra-narrow beam,” Optica 3, 734–740 (2016).
[Crossref]

T. Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10, 541–547 (2016).
[Crossref]

2015 (1)

2014 (1)

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105, 181118 (2014).
[Crossref]

2013 (2)

M. Brandstetter, C. Deutsch, M. Krall, H. Detz, D. C. MacFarland, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “High power terahertz quantum cascade lasers with symmetric wafer bonded active regions,” Appl. Phys. Lett. 103, 171113 (2013).
[Crossref]

C. Sirtori, S. Barbieri, and R. Collombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7, 691–701 (2013).
[Crossref]

2012 (5)

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, “Efficient power extraction in surface-emitting semiconductor lasers using graded photonic heterostructures,” Nat. Commun. 3, 952 (2012).
[Crossref]

D. Burghoff, C. W. I. Chan, Q. Hu, and J. L. Reno, “Gain measurements of scattering-assisted terahertz quantum cascade lasers,” Appl. Phys. Lett. 100, 261111 (2012).
[Crossref]

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

R. F. Oulton, “Surface plasmon lasers: sources of nanoscopic light,” Mater. Today 15(1-2), 26–34 (2012).
[Crossref]

S. Fathololoumi, E. Dupont, C. W. I. Chan, Z. R. Wasilewski, S. R. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. C. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express 20, 3866–3876 (2012).
[Crossref]

2010 (1)

2009 (3)

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[Crossref]

S. Kumar, Q. Hu, and J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94, 131105 (2009).
[Crossref]

S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
[Crossref]

2007 (2)

2006 (3)

A. J. L. Adam, I. Kašalynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions,” Appl. Phys. Lett. 88, 151105 (2006).
[Crossref]

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2, 551–556 (2006).
[Crossref]

E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D 39, R301–R310 (2006).
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2005 (2)

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20, S266–S280 (2005).
[Crossref]

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005).
[Crossref]

2003 (2)

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003).
[Crossref]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 µm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
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2002 (2)

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. 50, 910–928 (2002).
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R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
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1994 (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
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1988 (1)

D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced ‘leaky’ waveguides (antiguides),” Appl. Phys. Lett. 53, 464–466 (1988).
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1983 (1)

J. Katz, S. Margalit, and A. Yariv, “Diffraction coupled phase-locked semiconductor laser array,” Appl. Phys. Lett. 42, 554–555 (1983).
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1978 (1)

D. R. Scifres, R. D. Burnham, and W. Streifer, “Phase-locked semiconductor laser array,” Appl. Phys. Lett. 33, 1015–1017 (1978).
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Adam, A. J. L.

A. J. L. Adam, I. Kašalynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions,” Appl. Phys. Lett. 88, 151105 (2006).
[Crossref]

Andrews, A. M.

M. Brandstetter, C. Deutsch, M. Krall, H. Detz, D. C. MacFarland, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “High power terahertz quantum cascade lasers with symmetric wafer bonded active regions,” Appl. Phys. Lett. 103, 171113 (2013).
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Bachmann, D.

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105, 181118 (2014).
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Ban, D.

Barat, R.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20, S266–S280 (2005).
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Barbieri, S.

C. Sirtori, S. Barbieri, and R. Collombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7, 691–701 (2013).
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Beck, M.

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105, 181118 (2014).
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Beere, H.

S. Biasco, A. Ciavatti, L. Li, A. G. Davies, E. H. Linfield, H. Beere, D. Ritchie, and M. S. Vitiello, “Highly efficient surface-emitting semiconductor lasers exploiting quasi-crystalline distributed feedback photonic patterns,” Light Sci. Appl. 9, 54 (2020).
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Beere, H. E.

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, “Efficient power extraction in surface-emitting semiconductor lasers using graded photonic heterostructures,” Nat. Commun. 3, 952 (2012).
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R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
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Belarouci, A.

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, “Efficient power extraction in surface-emitting semiconductor lasers using graded photonic heterostructures,” Nat. Commun. 3, 952 (2012).
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Beltram, F.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
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Biasco, S.

S. Biasco, A. Ciavatti, L. Li, A. G. Davies, E. H. Linfield, H. Beere, D. Ritchie, and M. S. Vitiello, “Highly efficient surface-emitting semiconductor lasers exploiting quasi-crystalline distributed feedback photonic patterns,” Light Sci. Appl. 9, 54 (2020).
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Botez, D.

D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced ‘leaky’ waveguides (antiguides),” Appl. Phys. Lett. 53, 464–466 (1988).
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Brandstetter, M.

M. Brandstetter, C. Deutsch, M. Krall, H. Detz, D. C. MacFarland, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “High power terahertz quantum cascade lasers with symmetric wafer bonded active regions,” Appl. Phys. Lett. 103, 171113 (2013).
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Burghoff, D.

D. Burghoff, C. W. I. Chan, Q. Hu, and J. L. Reno, “Gain measurements of scattering-assisted terahertz quantum cascade lasers,” Appl. Phys. Lett. 100, 261111 (2012).
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Burnham, R. D.

D. R. Scifres, R. D. Burnham, and W. Streifer, “Phase-locked semiconductor laser array,” Appl. Phys. Lett. 33, 1015–1017 (1978).
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Callebaut, H.

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 µm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
[Crossref]

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003).
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Capasso, F.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
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Chan, C. W. I.

Chang, W.-H.

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
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Chen, H.-Y.

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Chen, J.

Y. Jin, L. Gao, J. Chen, C. Wu, J. L. Reno, and S. Kumar, “High power surface emitting terahertz laser with hybrid second- and fourth-order Bragg gratings,” Nat. Commun. 9, 1407 (2018).
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Chen, L.

L. H. Li, L. Chen, J. R. Freeman, M. Salih, P. Dean, A. G. Davies, and E. H. Linfield, “Multi-watt high-power THz frequency quantum cascade lasers,” Electron. Lett. 53, 799–800 (2017).
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Chen, L.-J.

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Cho, A. Y.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
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Christodoulides, D. N.

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019).
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Ciavatti, A.

S. Biasco, A. Ciavatti, L. Li, A. G. Davies, E. H. Linfield, H. Beere, D. Ritchie, and M. S. Vitiello, “Highly efficient surface-emitting semiconductor lasers exploiting quasi-crystalline distributed feedback photonic patterns,” Light Sci. Appl. 9, 54 (2020).
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Collombelli, R.

C. Sirtori, S. Barbieri, and R. Collombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7, 691–701 (2013).
[Crossref]

Colombelli, R.

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, “Efficient power extraction in surface-emitting semiconductor lasers using graded photonic heterostructures,” Nat. Commun. 3, 952 (2012).
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Curwen, C.

C. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum cascade VECSEL with watt-level output power,” Appl. Phys. Lett. 113, 011104 (2018).
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Dabidian, N.

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Darmo, J.

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105, 181118 (2014).
[Crossref]

Davies, A. G.

S. Biasco, A. Ciavatti, L. Li, A. G. Davies, E. H. Linfield, H. Beere, D. Ritchie, and M. S. Vitiello, “Highly efficient surface-emitting semiconductor lasers exploiting quasi-crystalline distributed feedback photonic patterns,” Light Sci. Appl. 9, 54 (2020).
[Crossref]

L. H. Li, L. Chen, J. R. Freeman, M. Salih, P. Dean, A. G. Davies, and E. H. Linfield, “Multi-watt high-power THz frequency quantum cascade lasers,” Electron. Lett. 53, 799–800 (2017).
[Crossref]

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, “Efficient power extraction in surface-emitting semiconductor lasers using graded photonic heterostructures,” Nat. Commun. 3, 952 (2012).
[Crossref]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
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Dean, P.

L. H. Li, L. Chen, J. R. Freeman, M. Salih, P. Dean, A. G. Davies, and E. H. Linfield, “Multi-watt high-power THz frequency quantum cascade lasers,” Electron. Lett. 53, 799–800 (2017).
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Detz, H.

M. Brandstetter, C. Deutsch, M. Krall, H. Detz, D. C. MacFarland, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “High power terahertz quantum cascade lasers with symmetric wafer bonded active regions,” Appl. Phys. Lett. 103, 171113 (2013).
[Crossref]

Deutsch, C.

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105, 181118 (2014).
[Crossref]

M. Brandstetter, C. Deutsch, M. Krall, H. Detz, D. C. MacFarland, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “High power terahertz quantum cascade lasers with symmetric wafer bonded active regions,” Appl. Phys. Lett. 103, 171113 (2013).
[Crossref]

Dupont, E.

El-Ganainy, R.

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019).
[Crossref]

Faist, J.

D. Bachmann, M. Rösch, C. Deutsch, M. Krall, G. Scalari, M. Beck, J. Faist, K. Unterrainer, and J. Darmo, “Spectral gain profile of a multi-stack terahertz quantum cascade laser,” Appl. Phys. Lett. 105, 181118 (2014).
[Crossref]

J. Faist, “Wallplug efficiency of quantum cascade lasers: critical parameters and fundamental limits,” Appl. Phys. Lett. 90, 253512 (2007).
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J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[Crossref]

Fathololoumi, S.

Federici, J. F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20, S266–S280 (2005).
[Crossref]

Freeman, J. R.

L. H. Li, L. Chen, J. R. Freeman, M. Salih, P. Dean, A. G. Davies, and E. H. Linfield, “Multi-watt high-power THz frequency quantum cascade lasers,” Electron. Lett. 53, 799–800 (2017).
[Crossref]

Gao, J. R.

A. J. L. Adam, I. Kašalynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions,” Appl. Phys. Lett. 88, 151105 (2006).
[Crossref]

Gao, L.

Y. Jin, L. Gao, J. Chen, C. Wu, J. L. Reno, and S. Kumar, “High power surface emitting terahertz laser with hybrid second- and fourth-order Bragg gratings,” Nat. Commun. 9, 1407 (2018).
[Crossref]

Gary, D.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20, S266–S280 (2005).
[Crossref]

Geluk, E. J.

Gwo, S.

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Hayashida, P.

D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced ‘leaky’ waveguides (antiguides),” Appl. Phys. Lett. 53, 464–466 (1988).
[Crossref]

Hill, M. T.

Hokmabadi, M. P.

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363, 623–626 (2019).
[Crossref]

Hovenier, J. N.

A. J. L. Adam, I. Kašalynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions,” Appl. Phys. Lett. 88, 151105 (2006).
[Crossref]

Hu, Q.

A. Khalatpour, J. L. Reno, and Q. Hu, “Phase-locked photonic wire lasers by π coupling,” Nat. Photonics 13, 47–53 (2019).
[Crossref]

T. Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10, 541–547 (2016).
[Crossref]

D. Burghoff, C. W. I. Chan, Q. Hu, and J. L. Reno, “Gain measurements of scattering-assisted terahertz quantum cascade lasers,” Appl. Phys. Lett. 100, 261111 (2012).
[Crossref]

S. Fathololoumi, E. Dupont, C. W. I. Chan, Z. R. Wasilewski, S. R. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. C. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express 20, 3866–3876 (2012).
[Crossref]

S. Kumar and Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
[Crossref]

S. Kumar, Q. Hu, and J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94, 131105 (2009).
[Crossref]

S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, Q. Hu, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15, 113–128 (2007).
[Crossref]

A. J. L. Adam, I. Kašalynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions,” Appl. Phys. Lett. 88, 151105 (2006).
[Crossref]

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005).
[Crossref]

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015–1017 (2003).
[Crossref]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ≈100 µm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
[Crossref]

Huang, F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20, S266–S280 (2005).
[Crossref]

Hugonin, J. P.

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2, 551–556 (2006).
[Crossref]

Hutchinson, A. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[Crossref]

Iotti, R. C.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref]

Jin, Y.

Y. Jin, L. Gao, J. Chen, C. Wu, J. L. Reno, and S. Kumar, “High power surface emitting terahertz laser with hybrid second- and fourth-order Bragg gratings,” Nat. Commun. 9, 1407 (2018).
[Crossref]

C. Wu, Y. Jin, J. L. Reno, and S. Kumar, “Large static tuning of narrow-beam terahertz plasmonic lasers operating at 78 K,” APL Photon. 2, 026101 (2017).
[Crossref]

Jirauschek, C.

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Other (1)

COMSOL Multiphysics, version 4.4, A Finite-Element Partial Differential Equation Solver.

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Figures (4)

Fig. 1.
Fig. 1. Longitudinal phase-locking scheme for subwavelength metallic cavities. (a) The scheme that allows for phase-locked operation of multiple parallel-plate subwavelength metallic cavities. The objective of the scheme is to enhance radiation from a long ridge cavity by splitting it into several shorter microcavities, which increases the number of radiating end facets when the microcavities are under phase-locked operation. A specific periodic arrangement of the microcavities and slit-like apertures in the top metal layer of the cavities establishes single-sided SPPs in the surrounding medium of the cavities, which leads to phase-locked operation of the microcavities. The enhanced radiation in the surface normal direction is primarily due to a larger number of radiating end facets for the microcavity array. A secondary contribution of radiation is the slit-like apertures within the microcavities. (b) A specific design of the multicavity QCL array for phase-locked operation. The distance between neighboring microcavities is equal to the wavelength of the single-sided SPPs (${\lambda _{{\rm{SPP}}}}$) that are established in the surrounding medium. Each microcavity is of length $3 \times {\lambda _{{\rm{SPP}}}}$ and has two slit-like apertures in its top metal layer with an inter-aperture spacing of ${\lambda _{{\rm{SPP}}}}$. An illustration of the standing wave of the electric field corresponding to the lowest-loss resonant mode under phase-locked operation is given for both the vertical (${E_z}$) and in-plane (${E_x}$) components of the field. The radiating sites in the microcavity array include the end facets of the microcavities as well as the slit-like apertures, each of which has the same phase for the ${E_x}$ field, which leads to radiation in the surface normal direction.
Fig. 2.
Fig. 2. Finite-element simulation results for phase-locked microcavity array at terahertz frequencies. (a) The eigenmode spectrum computed by finite-element simulations for the multicavity array in Fig. 1, with GaAs as the active medium (${n_a} = 3.6$) and air as the surrounding medium (${n_s} = 1$). Simulations are done in 2D (i.e., cavities of infinite width) for seven 10 µm thick cavities with periodicity $\Lambda = 324\,\,\unicode{x00B5}{\rm m}$ and intercavity spacing ${d_{{\rm{air}}}} = \Lambda /4$. Two equally spaced 9 µm wide apertures are implemented in the top metal cladding for each microcavity. The eigenmode spectrum shows frequencies and radiation loss for the resonant cavity modes of the phase-locked array. The lowest-loss mode occurs at 3.3 THz, and its radiative loss is ${\sim}9.5 {\rm{c}}{{\rm{m}}^{- 1}}$. The metal layers and the active medium are modeled as lossless to get an accurate estimation of the radiative loss. (b) Electric field distribution of the resonant mode for both ${E_z}$ and ${E_x}$ components (the ${E_y}$ component is nonexistent for wide cavities). The in-phase ${E_x}$ field at the locations of the end facets and the apertures leads to highly efficient radiation in the surface normal direction, with a single-lobed beam profile. Insets show the electric field distribution near the central microcavity of the phase-locked array.
Fig. 3.
Fig. 3. Experimental results for a surface-emitting terahertz QCL. (a) A schematic of the phase-locked QCL array as it was implemented for final fabrication. The microcavities are connected through both lateral sides by narrow metallic strips, which create absorbing regions that selectively make higher-order lateral modes in the cavities more lossy. (b) A scanning electron microscope image of the fabricated QCL arrays. The insets show the ${\sim}15\,\,\unicode{x00B5}{\rm m}$ wide lateral absorbing regions composed of an exposed thin highly doped GaAs contact layer. (c) Experimental lasing characteristics ($L\! -\! I$ and $I\! -\! V$) of a representative phased-locked array QCL with seven microcavities, each with the dimensions $10\,\,\unicode{x00B5}{\rm m} \times 243\,\,\unicode{x00B5}{\rm m} \times 500\,\,\unicode{x00B5}{\rm m}$, at different heat sink temperatures. The inset shows QCL spectra at varying electrical bias at 58 K. (d) Far-field radiation pattern of the QCL measured close to its peak operating bias. The single-lobed beam has a FWHM of ${3.2^ \circ} \times {11.5^ \circ}$.
Fig. 4.
Fig. 4. Lithographic tuning of the phase-locked QCL arrays. (a) Measured spectra from three different phase-locked QCLs with the same periodicity of the microcavities ($\Lambda = 324\,\,\unicode{x00B5}{\rm m}$) but slightly different ${d_{{\rm{air}}}}/\Lambda$ values, where ${d_{{\rm{air}}}}$ is the intercavity spacing. All the QCLs consist of seven microcavities and are biased similarly at an operating temperature of 58 K. (b) Measured spectra from three different phase-locked QCLs with different periodicity of the microcavities but a fixed ${d_{{\rm{air}}}}/\Lambda = 0.25$. The QCLs are located adjacent to each other on the fabricated wafer. All QCLs show robust single-mode operation from threshold to high peak bias.

Equations (2)

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α r a d = 1 L ln ( 1 R ) ,
d P o u t d I = ω q N p η i η r a d ,

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