Abstract

Quantum cascade lasers (QCLs) represent a most promising compact source at terahertz (THz) frequencies, but efficiency of their continuous wave (CW) operation still needs to be improved to achieve large-scale exploitation. Here, we demonstrate highly efficient operation of a subwavelength microcavity laser consisting of two evanescently coupled whispering gallery microdisk resonators. Exploiting a dual injection scheme for the laser cavity, single mode CW vertical emission at $3.3\ \textrm {THz}$ is obtained at $10\ \textrm {K}$ with $6.4\ \textrm {mA}$ threshold current and $145\ \textrm {mW/A}$ slope efficiency up to $320\ \mu \textrm {W}$ emitted power measured in quasi-CW mode. The tuning of the laser emission directionality is also obtained by independently varying the pumping strength between the microdisks. By connecting the resonators through a suspended gold bridge, the laser out-coupling efficiency in the vertical direction is strongly enhanced. Owing to the high brightness, low-power consumption and CW operation, the proposed microcavity laser design could allow the realization of high-performance CW THz QCLs ready for massive parallelization.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Terahertz (THz) radiation, namely the frequency range from 300 GHz to 10 THz, is attracting an intense and interdisciplinary research effort across fields as diverse as physics, chemistry, biology and medicine. This is due to the suitability of THz light in metrology, spectroscopy, imaging, information and communication technology [1], for a plethora of technological applications $-$ ranging from environmental monitoring, medical diagnostics and drug discovery to quality check in industrial processes, cultural heritage preservation and stand-off detection of hidden objects for security [2].

A main lever in developing THz technologies is the realization of a THz semiconductor laser source working on intersubband transitions in the conduction band of a quantum cascade active region [3]. THz quantum cascade lasers (QCLs) have shown a continuous and rapid evolution in recent years [4,5], becoming the best performing compact THz source in terms of emitted power [610], broadband [11] or single mode emission [12], beam shaping capabilities [13,14], frequency tunability [15] and low power consumption [16,17], both in pulsed and continuous wave (CW) operation [18,19]. Nevertheless, further improvements of CW THz QCLs in terms of maximum operating temperature and out-coupling efficiency are still needed in order to boost the exploitation of THz technology for large-scale application. While the temperature performance can be directly improved by active region design optimization [20,21], CW operation and out-coupling efficiency can be targeted by engineering the laser cavity [22].

A possible route in this perspective relies on cavity miniaturization. The thermal load will be in fact reduced by the small footprint device, making CW operation more easily achievable. Moreover, the combination of a small cavity volume and high mode quality factors guarantees low laser threshold currents [23,24], reducing the overall power/dissipation requirements. The key challenge in this case is to maximize the out-coupling efficiency while reducing the laser high-Q-factor cavity size. The extra achievement of out-of-plane emission would finally allow to realize arrays of microcavity lasers with high output power, vertical regular far-field patterns and low power consumption.

At THz frequencies, the most suitable element for device miniaturization is represented by the double-metal waveguide, where the active region is sandwiched between two metal layers [25]. This allows totally confining the electromagnetic modes inside the cavity in the vertical direction, ensuring an almost 100$\%$ confinement factor. Moreover, the high impedance mismatch with free space allows to reduce the lateral dimension while preserving at least one TM mode within the laser cavity. This property has been instrumental in the realization of full-3D subwavelength THz QCL microcavities with threshold currents in the milliampere range, and, in some cases, with CW operation and single mode emission. These have been usually based on single microdisk resonators working on whispering gallery (WG) modes [2629], which arise from the total internal reflection of light at the lateral active region-air interface of the cavity. Other more recent examples have instead employed subwavelength lasing defects in a photonic crystal structure [30], or even more extreme miniaturization in electronic circuit elements resonating on inductance-capacitance modes [31]. The main issue of these implementations is the inefficient out-coupling, in the best cases resulting in a few $\mu \textrm {W}$ emitted power in a broad emission pattern. One solution to significantly improve the out-coupling performance has been obtained by implementing appropriate diffraction gratings along the circumference of a microdisk resonator [27].

The design considered in this paper instead starts from the concept of a deeply subwavelength THz dipole-antenna microresonator [16], where the enhancement of the evanescent coupling of two adjacent WG microdisks connected via a metallic wire has yielded a high slope efficiency (up to $160\ \textrm {mW/A}$) and a very regular vertically emitted beam with merely $6\ \textrm {mA}$ of threshold current.

Here, we improve the out-coupling of THz QCL microcavities, by designing a dual injection scheme for the dipole-antenna microresonator concept demonstrating a high CW laser efficiency in the vertical direction. This is obtained starting from a microcavity design without the metallic wire bridge linking the two microdisks [32] and is strongly enhanced when this element is instead included. The potential of both designs of the microcavity laser is investigated and compared.

2. Microcavity design modeling and fabrication

The microcavity design consists of two subwalength WG resonators placed in close proximity. The WG eigenmodes of the microdisks are no longer independent, but they are evanescently coupled to form supermodes living in the whole microcavity [16,32]. Being the system axially symmetric, these supermodes can be labelled as $\textrm {M}_{2n,\pm ,\pm }$, where $2n$ indicates the total number of anti-nodes of the single disk, while the first and the second sign indicates even (+) or odd ($-$) symmetry with respect to mirroring along the $x\textrm {-}$ or $y\textrm {-}$axis, respectively.

In order to provide current injection in the microcavity active region, each disk was connected by an electrode to a separate bonding pad, allowing to independently pump each disk, as schematically shown in Fig. 1(a). This has the advantage of not altering the laser emission via the electrical contacts and the coupling between the resonators, which, in the first demonstration of dipole-antenna resonator [16], was inevitably affected by the injection electrode placed in between the two microdisks.

 figure: Fig. 1.

Fig. 1. (a) Sketch of the device showing the THz microcavity laser constituted by two WG microdisk resonators (labeled as disk A and B) and the dual injection scheme: two distinct electrodes connect each resonator to a different bonding pad, where a bias can be applied from the top metal layer to the bottom ground plane. A SiO$_2$ layer is present below the top metallization of both pads and injection electrodes to prevent current injection in the underneath active region. (b) Simulated spatial distribution of the electric-field $z$-component ($E_z$) in the $xy$-plane for the calculated microcavity modes in the spectral range of interest. (c) Simulated far-field profiles in $yz$-plane of the calculated microcavity eigenmodes. Vertical and lateral directions are defined as $z$- and $y$-axes, respectively.

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Full-wave finite element simulations using an open system approximation were performed to investigate the effect of the presence of the injection electrodes on the microcavity supermodes. We calculated the eigenfrequencies and corresponding eigenmodes for a microcavity with $20\ \mu \textrm {m}$-radius disks with a gap distance of $12.5\ \mu \textrm {m}$. The $11\ \mu \textrm {m}$-thick active region of average complex refractive index $n_{\textrm {AR}}=3.55+0.02$ was encapsulated between $200\ \textrm {nm}$-thick gold layer with refractive index $n_{\textrm {Au}}=225+i319$. This microcavity resonates at approximatively 3.3 THz with supermodes of group $\textrm {M}_6$. As highlighted in Fig. 1(b), by intersecting each disk with the injection bridge along the direction perpendicular to the disks alignment ($y\textrm {-}$direction), the electric field spatial distribution of the supermodes ($\textrm {M}_{6-+}$ and $\textrm {M}_{6--}$, which presents a field antinode at the connection point with the electrode) is perturbed. Indeed, a portion of the supermode electric-field is also confined in the injection electrodes, determining lower confinement for the electric field $z$-component and lower waveguide quality factors compared to the odd eigenmodes in $y\textrm {-}$direction ($\textrm {M}_{6+-}$ and $\textrm {M}_{6++}$). The latter have an antinode in the crossing point and thus are more efficiently confined inside the microdisks active region. Importantly, this allows to preserve the quality factor and far-field coupling of the eigenmode $\textrm {M}_{6+-}$. Presenting a dipole electric-field distribution between the disks, this mode is expected to provide the desired out-of-plane emission (see the red curve in Fig. 1(c)). This constituted the main reason for the choice to work on $\textrm {M}_{6}$-supermodes; in fact, as shown in [16] by simulations, WG-modes of higher or lower order do not guarantee the same out-coupling efficiency in the vertical direction. Furthermore, for the selected range of operation, microcavities resonating in $\textrm {M}_{6}$-modes represent a good compromise between the emitted power and overall power consumption for continuous wave operation.

 figure: Fig. 2.

Fig. 2. Main stages of the fabrication process. (1) Metal markers for fine alignment realized through EBL and thermal evaporation. (2) Insulating pattern for pads and injection electrodes obtained via the sputtering deposition of a $180\ \textrm {nm}$-thick SiO$_2$ layer, aligned EBL of a polymer mask and final wet etching in BOE. (3) Top metallization of the microcavity, bonding pads and injection electrodes realized through a second aligned EBL and thermal evaporation of $5/200/40\ \textrm {nm}$ Cr/Au/Ni. (4) SEM image of the THz microcavity laser finally obtained through ICP-RIE. The electric field spatial distribution (out-of-plane component) of the lasing microcavity supermode is superimposed to the microcavity.

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Starting from the simulated design, we realized microcavities with two $20\ \mu \textrm {m}$-radius microdisks displaced by $12.5\ \mu \textrm {m}$, each one connected by $3\ \mu \textrm {m}$-wide injection electrodes to a different bonding pad at about 2 wavelengths distance from the resonators. The active region is an $11\ \mu \textrm {m}$-thick GaAs/AlGaAs QCL heterostructure with a bound-to-continuum design and phonon injection/extraction stage [33], as exploited for the first prototype of dipole-antenna microresonator [16]. As routinely performed in double-metal waveguide QCL processing, the top Cr/Au $5/500\ \textrm {nm}$ metallized active region surface was thermo-compressively wafer-bonded to a highly doped (n+) $300\ \mu \textrm {m}$-thick GaAs substrate covered with the same amount of metal. This created the double-metal waveguide for the microcavity, where the homogeneous bottom metallization constitutes the ground plane. The structure was then mechanically lapped and wet-etched to remove the original active region substrate and provide access to the highly doped contact layer of the active region. The fabrication then proceeded with the steps reported in Fig. 2. The first two processes were the sputtering of a $180\ \textrm {nm}$-thick SiO$_2$ layer and an electron-beam lithography (EBL) to define a negative polymeric resist mask on it. The following wet etching in a buffered-HF solution created the SiO$_2$ elements onto which we realized both injection electrodes and bonding pads. This was crucial in order to electrically insulate these conductive elements from the active region, and avoid the underneath current injection while ensuring the current flow in the microcavity heterostructure. A further EBL was then performed with a positive polymeric resist to define the microdisks, electrodes and bonding pads metallization through a subsequent thermal evaporation of Cr/Au/Ni $5/200/40\ \textrm {nm}$ metal layers. The last Ni layer was used as the etching mask for the final inductively coupled plasma reactive ion etching (ICP-RIE) with a Cl$_2$, BCl$_3$ and Ar (3/1/10) mixture. From both experimental evidence and simulations, we observed that an etching depth $>9\ \mu \textrm {m}$ provides an efficient lateral confinement for light which guarantees the lasing action. The results presented in this work were obtained from microcavities with $\sim 10\ \mu \textrm {m}$-high sidewalls. A complete dry etching of the active region was not performed in order to prevent the possible risk of damaging the double-metal waveguide due a process longer than the etching time of the Ni-mask layer. Moreover, the ICP-RIE recipe was calibrated to create a slight undercut of the resonator sidewalls. This was exploited to automatically suspend the thin metallic bridge linking the two microdisks of the second microcavity design, as later shown in the discussion. The same dry etching recipe was performed for all different devices in order to have the same sidewall profile (i.e. optical loss due to disk interface scattering) and final device dimension (i.e. resonating frequencies) for each prototype, thus ensuring comparable experimental results across devices.

3. Experimental results

The fabricated devices were soldered on a Cu holder via a In-Ag alloy paste, electrically wedge-bonded with Al contacts and subsequently mounted in a continuous-flow liquid-He cryostat. The $50\ \textrm {nm}$-thick gold layer evaporated over the bottom of the device substrate allowed to achieve a good ohmic contact with the grounded Cu holder, enabling current injection by applying a positive bias to the device top metallization. For all the reported measurements, the devices were powered using a double-channel source-meter unit. The emitted power was detected using a Golay cell and its absolute value was measured using a calibrated pyroelectric detector. The microcavity lasers were driven by directly modulating the bias current at $19\ \textrm {Hz}$ with $50\%$ duty cycle. This modulation was then used as reference for a lock-in amplifier used to analyze the output signal of the detector. The emission spectra were acquired by a Fourier transform infrared (FTIR) spectrometer with a spectral resolution of $2.1\ \textrm {GHz}$ using the internal deuterated triglycine sulfate (DTGS) detector. In this case, the devices were powered in CW operation.

The microcavity design in Fig. 2 was tested by independently injecting the same amount of current in each microdisk. The current-voltage (IV) characteristic measured at 10 K in this configuration is reported in the inset of Fig. 3(a). The identical IV-curves of the two disks demonstrate their equal electronic transport. This ensures an equal current flow into the two microdisks when pumping the whole microcavity with a single circuit. In the latter case, the IV and LI characteristics for both vertical and lateral emission (corresponding to the $z$- and $y$-direction, respectively, as defined in Fig. 1(c)) are shown in Fig. 3(a) by a blue and red curve, respectively. A threshold current of about $6.4\ \textrm {mA}$ is observed (corresponding to a current density of $290\ \textrm {A/cm}^2$) at a voltage bias of $12.1\ \textrm {V}$, followed by a visible slight reduction of the device differential resistance induced by the onset of stimulated emission. Accordingly, the threshold for each single microdisk is $3.2\ \textrm {mA}$, that is half of the threshold current for the whole microcavity. The microcavity laser dominantly emits in the vertical direction with a constant slope efficiency of $\sim 145\ \textrm {mA/W}$ and a peak output power of about $320\ \mu \textrm {W}$ at around $8.6\ \textrm {mA}$ ($384\ \textrm {A/cm}^2$). For larger injected current, the power starts to rapidly decrease as the active region band alignment is lost. At the same time, the lateral emission similarly evolves with a peak power of $16\ \mu \textrm {W}$ and slope efficiency around $7\ \textrm {mW/A}$. The vertical to lateral peak output power ratio is $\eta \sim 20$, while the overall wall-plug efficiency is $\sim 0.29\%$. As expected from the linearly constant increase of power, the acquired spectra, shown for several injected currents in Fig. 3(b), reveal single mode emission at $\sim 3.3\ \textrm {THz}$ throughout the entire laser dynamic range for both vertical and lateral directions (see the inset of Fig. 3(b)). In agreement with simulations, the microcavity is able to emit in the vertical direction in the supermode identified as the M$_{6+-}$-mode. The discrepancy in maximum emitted power ($+\ 28 \%$) of the presented device with respect the first prototype of dipole-antenna resonator [16] can be imputed to a better alignment with the active region gain peak plus a $10 \%$ larger device area ($20\ \mu \textrm {m}$ microdisk radius here against $19\ \mu \textrm {m}$ in [16]). The $9 \%$ lower slope efficiency measured in this work is instead related to less efficient cavity out-coupling due to the absence of the bridge which enhances the microdisks coupling, as it will be highlighted for the following measurements. Finally, a similar temperature performance ($\sim \ 65\ \textrm {K}$) is observed between the two resonator designs.

 figure: Fig. 3.

Fig. 3. (a) IV and LI characteristics of the THz microcavity laser. The solid blue curve represents the IV characteristic of the microcavity, while both vertical and lateral laser emitted power are reported by the solid and dashed red curve (multiplied by a factor 5), respectively. Inset: IV-characteristics of both microdisks. In both graphs the threshold current is reported by a dashed line. (b) Laser spectra in the vertical direction for different values of injected current. Inset: laser spectrum in the lateral direction for the same current values.

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Moreover, thanks to the independent pumping of each microdisk with respect to the other, the amount of gain and loss in the microcavity can be spatially controlled by injecting a different amount of current in the two disks. We thus investigated the dependence of the microcavity emission by varying the injected current in one microdisk (defined as disk A in Fig. 1(a)) while keeping fixed the current flowing in the other one (labelled as disk B). In this configuration, Fig. 4 shows the IV characteristic of disk A, the dependence of the voltage across disk B against the current in disk A, and both lateral and vertical emitted power. For a fixed injected current of $3.5\ \textrm {mA}$ in disk B, the voltage across this microdisk is inside the range of band alignment ($>12\ V$) and the microcavity emits even if disk A is not biased. Starting to pump disk A, the emitted radiation is observed to increase up to $0.4\ \textrm {mA}$ of injected current, with an $\eta$-ratio of about $5$. As shown in Fig. 4(b)-c for the spectra in the vertical and lateral direction, the microcavity emits at $\sim 3.288\ \textrm {THz}$. Further increasing the current in disk A, a little jump in power is observed, the $\eta$-ratio slightly decreases and the overall emitted power monotonically decreases even increasing the pumping in the system. The discontinuity in power is attributed to mode hopping as in the current range $[0.4, 1.7]\ \textrm {mA}$ the microcavity emits at lower frequency, around $3.275\ \textrm {THz}$. At $\sim 1.7\ \textrm {mA}$ the laser starts again to emit at the initial frequency with a positive jump in power. However, the emitted radiation continues to slightly decrease as the pumping is increased up to $2\ \textrm {mA}$, where the microcavity abruptly stops the emission. No laser emission was observed until a current of $2.9\ \textrm {mA}$ is injected. At this level of disk A pumping, the microcavity starts to emit at a higher frequency ($3.298\ \textrm {THz}$) with a medium slope efficiency of $125\ \textrm {mW/A}$. The maximum peak power of $175\ \mu \textrm {W}$ with a vertical to lateral power ratio of $\sim 17.5$ is obtained at $4.3\ \textrm {mA}$, after which current the emission quickly decreases.

 figure: Fig. 4.

Fig. 4. (a) VI characteristics for each microdisk measured varying the injected current in one resonator (disk A, solid blue curve) while keeping constant to $3.4\ \textrm {mA}$ the injected current in the other one (disk B, dashed blue curve). The emitted power of the whole microcavity both in the vertical ($z$-) and lateral ($y$-) direction is reported by the solid and dashed red curve, respectively. The curve for the lateral emission is multiplied by a factor 5. (b) and (c): laser spectra acquired for different injected currents in disk A from the vertical and lateral direction, respectively.

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This particular behavior of the laser emission (which decreases and even ceases while increasing the pumping) is associated with the presence of a non-Hermitian singularity. Non-Hermitian systems, as optical open cavities featuring gain and loss, and having the property of being parity-time symmetric, can exhibit non-hermitian degeneracies called exceptional points (EPs) [34,35]. At these singularities, two or more system eigenvalues and corresponding eigenvectors coalesce. In many experimental cases, included our system, the levels have a finite energy splitting, resulting in an avoided crossing closed to where the EP would be in the degenerate case. Many non-trivial effects have already been experimentally demonstrated in photonic systems operating in the vicinity of an exceptional point [36,37]. One example is the reversal of the laser pumping dependence which was already demonstrated in a similar coupled resonator system at THz frequencies [32], and reproduced here with a focus on the emission directionality. To demonstrate the presence of EPs in our system, we calculated via FE-simulations the evolution of the microcavity complex eigenvalues as the pumping strength is increased in one disk while keeping a fixed gain in the other one. This was done by varying the refractive index imaginary part of disk A active region ($\textrm {Im}(n_{\textrm {A}})$) from a positive to a negative value (indicating loss and gain, respectively), and by fixing a negative refractive index imaginary part for the disk B active region ($\textrm {Im}(n_{\textrm {B}})=-0.02$). The simulated real and imaginary part of the microcavity eigenvalues are reported in Fig. 5(a). A positive or a negative imaginary part $\textrm {Im}(\omega )$ indicates an eigenvalue $\omega$ which is experiencing effective average gain or loss, respectively, thus defining the supermodes which are more likely to provide laser emission. As Joule heating and all nonlinear effects, like gain pulling, mode competition, spatial hole burning and frequency-dependent coupling between the modes are neglected, the performed simulations only represent a crude approximation of the full problem aiming at qualitatively understand the modes evolution with the pumping strength variation across the microdisks. The four eigenvalues can be divided in two couples of interacting supermodes with respect to the spatial position of the electric field nodes: $\textrm {M}_{6-+}\textrm {-}\textrm {M}_{6--}$ and $\textrm {M}_{6++}\textrm {-}\textrm {M}_{6+-}$, reported with diamond and circle markers, respectively. As the pumping strength is increased in disk A, the eigenvalues in each couple tend to coalesce, both in their real and imaginary parts, until a point where they start to repel each other in their real part, while maintaining a similar positive imaginary part. This is the typical anti-crossing behavior induced by the presence of an EP, which can be adequately reproduced by a two-level model with coupled eigenmodes. By analytically solving the problem as in [35], the experimental results are found in agreement with the presence of two EPs (reported as black markers in Fig. 5), one for each couple of eigenmodes. Assuming a threshold value of $\textrm {Im}(\omega )=10\ \textrm {GHz}$, and when only disk B is pumped, only two modes are expected to provide laser emission. We thus attributed the two low threshold experimentally lasing modes to the $\textrm {M}_{6--}$ and $\textrm {M}_{6+-}$ supermodes with good frequency agreement. As the pumping strength in disk A is increased, both modes pass below the lasing threshold to emerge again after a certain range at higher frequencies. However, only the $\textrm {M}_{6+-}$-mode matches the experimentally lasing mode producing the strong out-of-plane emission. By summing the calculated imaginary part of the eigenfrequencies of the only two modes contributing to the laser emission we can obtain the expected emitted power as a function of the pumping strength. This is shown in Fig. 5(b), which qualitatively reproduces the experimental LI characteristic of Fig. 4(a). The $\textrm {M}_{6+-}$-mode emission is thus turned from a weakly directional emission into a strongly vertical and highly efficient one by simply varying the pumping strength of only one microdisk, as confirmed by the calculated far-field profiles in the inset of Fig. 5(b).

 figure: Fig. 5.

Fig. 5. Microcavity eigenfrequency finite-element simulations varying the amount of gain/loss in disk A while keeping constant the gain in disk B. (a) Imaginary part versus real part of the microcavity eigenfrequencies sweeping the refractive index imaginary part from a positive (indicating loss, $\textrm {Im}(n_{\textrm {A}})=0.05$) to a negative value (indicating gain, $\textrm {Im}(n_{\textrm {A}})=-0.05$). The refractive index imaginary part in disk B is kept fixed at $\textrm {Im}(n_{\textrm {B}})=-0.02$. Experimentally lasing and non-lasing modes are presented by face- and edge-colored markers, respectively. The horizontal dashed line represents a hypothetical lasing threshold of $\textrm {Im}(\omega )=10\ \textrm {GHz}$. The position of the calculated exceptional points is also reported: EP1 and EP2 are associated with the eigenvalue couple reported via diamond and circle markers, respectively. (b) Calculated emitted power as a function of the refractive index imaginary part of disk A obtained with the assumed lasing threshold. Inset: Simulated far-field profiles for the $\textrm {M}_{6+-}$-mode for Im$(n_{\textrm {A}})=0.02$ and -0.02.

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We then fabricated another microcavity, now including a suspended gold bridge linking the two microdisk resonators, which is expected to produce a strong enhancement of the device out-coupling performance [16]. An example of the fabricated microcavities with this design is shown in Fig. 6(a). This was realized using the previously described fabrication procedure. The $12.5\ \mu \textrm {m}$-long, $1\ \mu \textrm {m}$-wide and $\sim 200\ \textrm {nm}$-thick gold bridge was suspended via the calibrated ICP-RIE etching with a lateral to vertical etching rate ratio of about $0.06$. The measured IV and LI characteristics are reported in Fig. 6(b), while the FTIR-acquired spectra in the vertical and lateral direction are shown Fig. 6(c)-d, respectively. These results are obtained by equally pumping both microdisks at a temperature of $10\ \textrm {K}$. A $5\ \textrm {mA}$ ($225\ \textrm {A/cm}^2$) threshold current is observed, associated with the emission of two lasing modes at 3.26 and $3.275\ \textrm {THz}$. FE-simulations reveal that the two low threshold modes should correspond to $\textrm {M}_{6++}$ and $\textrm {M}_{6--}$ modes, whose electric field spatial distributions are shown in Fig. 7(a). In this case, the $\textrm {M}_{6--}$ mode should be able to reach the lasing threshold even if its electric field overlaps with the injection bridges, thanks the total removal of the active region underneath the injection bridges by the undercut of the ICP-RIE, which lowers the total mode losses. The initial laser emission presents a slope efficiency of $18\ \textrm {mW/A}$ with a vertical to lateral peak power ratio of 2.5 until an injected current $>6.4\ \textrm {mA}$ ($288\ \textrm {A/cm}^2$). The low slope-efficiency can be attributed to the high radiative quality factor calculated for the two lasing modes ($\textrm {Q}_{\textrm {rad}} \sim 380$ and 320 for $\textrm {M}_{6++}$ and $\textrm {M}_{6--}$, respectively), while the low vertical to lateral power ratio is in agreement with the simulated far-field emission shown in Fig. 7(b) where a spread emission with a strong radial component can be observed. Above $6.4\ \textrm {mA}$ the emission abruptly changes with a huge increase in the vertical out-coupling efficiency. A high slope efficiency of $\sim 900\ \textrm {mW/A}$ is achieved. The presence of the gold bridge improves the radiation efficiency of the bare coupled WG resonators microcavity by a factor $\sim 6$, improving also with respect to the previous demonstration of the dipole-antenna microresonator [16], where the gold wire was not-completely suspended. Moreover, a vertical to lateral power ratio of $\sim 26$ is obtained with a vertical peak output power of $\sim 360\ \mu \textrm {W}$ at $6.8\ \textrm {mA}$ ($306\ \textrm {A/cm}^2$), resulting in $\sim 0.08\ \textrm {W}$ power consumption and a $>0.44\ \%$ wall-plug efficiency.

 figure: Fig. 6.

Fig. 6. (a) SEM of the fabricated THz microcavity with a suspended gold bridge linking the two microdisks. The $E_{\textrm {z}}$-spatial distribution of the vertically emitting mode ($\textrm {M}_{+-}$-mode) is superimposed. (b) VI and LI characteristics. Emitted power in the out-of-plane ($z$-direction) and in-plane (with a multiplication factor of 10) directions are reported via a solid and a dashed red curve, respectively. (c), (d) Spectra measured in the out-of-plane and in-plane direction, respectively, for several values of injected current.

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 figure: Fig. 7.

Fig. 7. Simulated modes of the THz microcavity with the suspended gold bridge. (a) Spatial distribution of the electric-field $z$-component ($E_z$) in the $xy$-plane for the three eigenmodes ($\textrm {M}_{6++}$, $\textrm {M}_{6--}$ and $\textrm {M}_{6+-}$) experimentally showing lasing action. (b) Relative far-field profiles in the $yz$-plane.

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A slope efficiency improvement is expected from the lower radiative quality factor $Q_{\textrm {rad}}$ achieved for the $\textrm {M}_{6+-}$-mode when the suspended bridge is present, i.e. $Q_{\textrm {rad}}=160$ and 250 for the connected and separated microdisks, respectively. As both microcavity designs have approximatively the same total quality factor ($Q_{\textrm {tot}}\sim 50$), this implies an increase of the radiation efficiency ($\propto Q_{\textrm {tot}}/Q_{\textrm {rad}}$) by a factor $\sim 1.55$. Even though this value is in good agreement with a calculated average slope efficiency of $\sim 200\ \textrm {mW/A}$ for the microcavity with connected microdisks (a factor $\sim 1.4$ bigger than that obtained for the microcavity without the suspended bridge), it does not quantitatively explain the measured slope efficiency. However, the strong increase in emission power and directionality coincides with the disappearance of the mode at lower frequency and the simultaneous onset of a vertically emitting lasing mode at $3.315\ \textrm {THz}$, which is expected matching with the calculated $\textrm {M}_{6+-}$-mode, shown in Fig. 7(a). This could qualitatively explain the abrupt change in slope efficiency as the mode hopping could have made the population inversion already present for $\textrm {M}_{6--}$-mode available for $\textrm {M}_{6+-}$-mode, thus leading to the fast power increase of the latter.

The $\textrm {M}_{6+-}$-mode contributes for $80\%$ of the emitted power with a vertical to lateral emission contrast $\eta >160$. The rest of the emission is produced by the $\textrm {M}_{6--}$-mode which still continues to emit with a more pronounced radiation efficiency in the vertical direction. The experimental mode emission directionality is also qualitatively confirmed by the simulated far-field profiles of the three lasing modes reported in Fig. 7(b). Moreover, CW laser emission is clearly observed up to $68\ \textrm {K}$, a slightly higher temperature with respect to the microcavity without the bridge due to a $1.8\ \textrm {mA}$ lower current at peak power. No significant variation on the laser emission is observed in this case by differently pumping the two microdisks as the estimated $\le 1\Omega$ bridge resistance implies an almost equal current flowing in the disks while connected in parallel. In order to obtain a pump induced control of the laser emission profile, active region designs with larger dynamic range, able to achieve a higher pump imbalance between the microdisks, should be exploited.

4. Conclusions

A THz QCL microcavity consisting of two evanescently coupled WG microdisk resonators is proved to produce a highly efficient CW vertical emission. In particular, a scheme for the current injection inside the microcavity active region is engineered in such a way to independently pump each microdisk. An injection bridge connected to each microdisk is theoretically and experimentally shown not to detrimentally alter the out-coupling performance of the radiating microcavity supermode providing out-of-plane emission.

For a cavity with separated microdisks, a $145\ \textrm {mW/A}$ CW slope efficiency in the vertical direction is achieved at $3.3\ \textrm {THz}$ up to $320\ \mu \textrm {W}$ emitted power with $8.6\ \textrm {mA}$ injected current, corresponding to a wall-plug efficiency of $0.29 \%$. Moreover, in this cavity configuration, the injection scheme allows to arbitrarily control the pumping strength across the microdisks. The effects on the laser emission associated with the presence of an EP in the system are shown and confirmed by simulations. This has been explored by varying the injected current in one microdisk while keeping fixed the pumping strength above laser threshold in the other one. Apart from the already known reversal in the laser pumping dependence, the improvement of the vertical emission efficiency of one lasing mode is demonstrated. As the mode evolves through a system EP, the initial spread emission is turned into a strongly directional vertical one. This offers the possibility to arbitrarily modify the laser emission directionality by simply varying the pumping strength between the microdisks.

We considered also a microcavity design where the microresonators are connected by a suspended gold bridge. The presence of this metallic element is demonstrated to strongly enhance the microcavity out-coupling performance. A directional vertical emission with a maximum slope efficiency of $900\ \textrm {mW/A}$ is obtained, corresponding to a 6.2 enhancement with respect to the same device without the gold wire. Moreover, the complete suspension of the gold bridge allows a significant improvement with respect to previous devices with a single injection electrode crossing the gold wire [16]. A peak output power up to $360\ \mu \textrm {W}$ at $6.8\ \textrm {mA}$ injected current ($305\ \textrm {A/cm}^2$) is obtained at $3.31\ \textrm {THz}$ in a very subwavelength device dimension (mode volume to cube wavelength ratio of $\sim 0.03$), corresponding to a mere $0.09\ \textrm {W}$ power consumption and a $0.44 \%$ wall-plug efficiency.

By using state-of-art designs for THz QC active regions [21], the miniaturized device dimension in connection with the very low threshold current could allow to achieve record CW temperature operation. Owing to its high out-of-plane brightness and highly efficient CW operation the proposed design of THz QCL microcavity could pave the way towards the realization of CW-driven high temperature THz QCLs made of arrays of massively parallelized subwavelength emitters.

Funding

North Atlantic Treaty Organization Science for Peace and Security Programme (G5721).

Acknowledgments

The authors would like to thank Dr. M. S. Vitiello for fruitful discussions.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in each figure of this paper are not publicly available at this time but can be obtained from the authors upon request.

References

1. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]  

2. S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017). [CrossRef]  

3. 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(6885), 156–159 (2002). [CrossRef]  

4. M. S. Vitiello, G. Scalari, B. Williams, and P. De Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23(4), 5167–5182 (2015). [CrossRef]  

5. M. S. Vitiello and A. Tredicucci, “Physics and technology of terahertz quantum cascade lasers,” Adv. Phys.: X 6(1), 1893809 (2021). [CrossRef]  

6. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42(2), 89–91 (2006). [CrossRef]  

7. L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. Davies, and E. Linfield, “Terahertz quantum cascade lasers with> 1 w output powers,” Electron. Lett. 50(4), 309–311 (2014). [CrossRef]  

8. 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, “High power-efficiency terahertz quantum cascade laser,” Chin. Phys. B 25(8), 084206 (2016). [CrossRef]  

9. C. A. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum cascade vecsel with watt-level output power,” Appl. Phys. Lett. 113(1), 011104 (2018). [CrossRef]  

10. Y. Jin, J. L. Reno, and S. Kumar, “Phase-locked terahertz plasmonic laser array with 2 w output power in a single spectral mode,” Optica 7(6), 708–715 (2020). [CrossRef]  

11. M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave-spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2015). [CrossRef]  

12. M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009). [CrossRef]  

13. L. Xu, C. A. Curwen, P. W. Hon, Q.-S. Chen, T. Itoh, and B. S. Williams, “Metasurface external cavity laser,” Appl. Phys. Lett. 107(22), 221105 (2015). [CrossRef]  

14. T.-Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10(8), 541–546 (2016). [CrossRef]  

15. C. A. Curwen, J. L. Reno, and B. S. Williams, “Broadband continuous single-mode tuning of a short-cavity quantum-cascade vecsel,” Nat. Photonics 13(12), 855–859 (2019). [CrossRef]  

16. L. Masini, A. Pitanti, L. Baldacci, M. S. Vitiello, R. Degl’Innocenti, H. E. Beere, D. A. Ritchie, and A. Tredicucci, “Continuous-wave laser operation of a dipole antenna terahertz microresonator,” Light: Sci. Appl. 6(10), e17054 (2017). [CrossRef]  

17. C. A. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum-cascade patch-antenna vecsel with low power dissipation,” Appl. Phys. Lett. 116(24), 241103 (2020). [CrossRef]  

18. S. Biasco, K. Garrasi, F. Castellano, L. Li, H. E. Beere, D. A. Ritchie, E. H. Linfield, A. G. Davies, and M. S. Vitiello, “Continuous-wave highly-efficient low-divergence terahertz wire lasers,” Nat. Commun. 9(1), 1122–1128 (2018). [CrossRef]  

19. X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with 0.23 w in continuous wave mode,” AIP Adv. 6(7), 075210 (2016). [CrossRef]  

20. L. Bosco, M. Franckié, G. Scalari, M. Beck, A. Wacker, and J. Faist, “Thermoelectrically cooled thz quantum cascade laser operating up to 210 k,” Appl. Phys. Lett. 115(1), 010601 (2019). [CrossRef]  

21. A. Khalatpour, A. K. Paulsen, C. Deimert, Z. R. Wasilewski, and Q. Hu, “High-power portable terahertz laser systems,” Nat. Photonics 15(1), 16–20 (2021). [CrossRef]  

22. Y. Zeng, B. Qiang, and Q. J. Wang, “Photonic engineering technology for the development of terahertz quantum cascade lasers,” Adv. Opt. Mater. 8(3), 1900573 (2020). [CrossRef]  

23. S. McCall, A. Levi, R. Slusher, S. Pearton, and R. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992). [CrossRef]  

24. L. He, Ş. K. Özdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photonics Rev. 7(1), 60–82 (2013). [CrossRef]  

25. B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007). [CrossRef]  

26. G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87(21), 211112 (2005). [CrossRef]  

27. L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009). [CrossRef]  

28. L. A. Dunbar, R. Houdré, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, “Small optical volume terahertz emitting microdisk quantum cascade lasers,” Appl. Phys. Lett. 90(14), 141114 (2007). [CrossRef]  

29. Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. Beere, J. Alton, and D. Ritchie, “Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range,” Appl. Phys. Lett. 90(9), 091113 (2007). [CrossRef]  

30. A. Klimont, A. Ottomaniello, R. Degl’Innocenti, L. Masini, F. Bianco, Y. Wu, Y. D. Shah, Y. Ren, D. Jessop, A. Tredicucci, H. Beere, and D. Ritchie, “Line-defect photonic crystal terahertz quantum cascade laser,” J. Appl. Phys. 126(15), 153104 (2019). [CrossRef]  

31. C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010). [CrossRef]  

32. M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5(1), 4034–4037 (2014). [CrossRef]  

33. M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009). [CrossRef]  

34. W. Heiss, “Exceptional points of non-hermitian operators,” J. Phys. A: Math. Gen. 37(6), 2455–2464 (2004). [CrossRef]  

35. M.-A. Miri and A. Alu, “Exceptional points in optics and photonics,” Science 363(6422), eaar7709 (2019). [CrossRef]  

36. Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “Parity–time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019). [CrossRef]  

37. M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108(17), 173901 (2012). [CrossRef]  

References

  • View by:

  1. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
    [Crossref]
  2. S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
    [Crossref]
  3. 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(6885), 156–159 (2002).
    [Crossref]
  4. M. S. Vitiello, G. Scalari, B. Williams, and P. De Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23(4), 5167–5182 (2015).
    [Crossref]
  5. M. S. Vitiello and A. Tredicucci, “Physics and technology of terahertz quantum cascade lasers,” Adv. Phys.: X 6(1), 1893809 (2021).
    [Crossref]
  6. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42(2), 89–91 (2006).
    [Crossref]
  7. L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. Davies, and E. Linfield, “Terahertz quantum cascade lasers with> 1 w output powers,” Electron. Lett. 50(4), 309–311 (2014).
    [Crossref]
  8. 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, “High power-efficiency terahertz quantum cascade laser,” Chin. Phys. B 25(8), 084206 (2016).
    [Crossref]
  9. C. A. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum cascade vecsel with watt-level output power,” Appl. Phys. Lett. 113(1), 011104 (2018).
    [Crossref]
  10. Y. Jin, J. L. Reno, and S. Kumar, “Phase-locked terahertz plasmonic laser array with 2 w output power in a single spectral mode,” Optica 7(6), 708–715 (2020).
    [Crossref]
  11. M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave-spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2015).
    [Crossref]
  12. M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
    [Crossref]
  13. L. Xu, C. A. Curwen, P. W. Hon, Q.-S. Chen, T. Itoh, and B. S. Williams, “Metasurface external cavity laser,” Appl. Phys. Lett. 107(22), 221105 (2015).
    [Crossref]
  14. T.-Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10(8), 541–546 (2016).
    [Crossref]
  15. C. A. Curwen, J. L. Reno, and B. S. Williams, “Broadband continuous single-mode tuning of a short-cavity quantum-cascade vecsel,” Nat. Photonics 13(12), 855–859 (2019).
    [Crossref]
  16. L. Masini, A. Pitanti, L. Baldacci, M. S. Vitiello, R. Degl’Innocenti, H. E. Beere, D. A. Ritchie, and A. Tredicucci, “Continuous-wave laser operation of a dipole antenna terahertz microresonator,” Light: Sci. Appl. 6(10), e17054 (2017).
    [Crossref]
  17. C. A. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum-cascade patch-antenna vecsel with low power dissipation,” Appl. Phys. Lett. 116(24), 241103 (2020).
    [Crossref]
  18. S. Biasco, K. Garrasi, F. Castellano, L. Li, H. E. Beere, D. A. Ritchie, E. H. Linfield, A. G. Davies, and M. S. Vitiello, “Continuous-wave highly-efficient low-divergence terahertz wire lasers,” Nat. Commun. 9(1), 1122–1128 (2018).
    [Crossref]
  19. X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with 0.23 w in continuous wave mode,” AIP Adv. 6(7), 075210 (2016).
    [Crossref]
  20. L. Bosco, M. Franckié, G. Scalari, M. Beck, A. Wacker, and J. Faist, “Thermoelectrically cooled thz quantum cascade laser operating up to 210 k,” Appl. Phys. Lett. 115(1), 010601 (2019).
    [Crossref]
  21. A. Khalatpour, A. K. Paulsen, C. Deimert, Z. R. Wasilewski, and Q. Hu, “High-power portable terahertz laser systems,” Nat. Photonics 15(1), 16–20 (2021).
    [Crossref]
  22. Y. Zeng, B. Qiang, and Q. J. Wang, “Photonic engineering technology for the development of terahertz quantum cascade lasers,” Adv. Opt. Mater. 8(3), 1900573 (2020).
    [Crossref]
  23. S. McCall, A. Levi, R. Slusher, S. Pearton, and R. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
    [Crossref]
  24. L. He, Ş. K. Özdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photonics Rev. 7(1), 60–82 (2013).
    [Crossref]
  25. B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
    [Crossref]
  26. G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87(21), 211112 (2005).
    [Crossref]
  27. L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
    [Crossref]
  28. L. A. Dunbar, R. Houdré, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, “Small optical volume terahertz emitting microdisk quantum cascade lasers,” Appl. Phys. Lett. 90(14), 141114 (2007).
    [Crossref]
  29. Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. Beere, J. Alton, and D. Ritchie, “Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range,” Appl. Phys. Lett. 90(9), 091113 (2007).
    [Crossref]
  30. A. Klimont, A. Ottomaniello, R. Degl’Innocenti, L. Masini, F. Bianco, Y. Wu, Y. D. Shah, Y. Ren, D. Jessop, A. Tredicucci, H. Beere, and D. Ritchie, “Line-defect photonic crystal terahertz quantum cascade laser,” J. Appl. Phys. 126(15), 153104 (2019).
    [Crossref]
  31. C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010).
    [Crossref]
  32. M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5(1), 4034–4037 (2014).
    [Crossref]
  33. M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
    [Crossref]
  34. W. Heiss, “Exceptional points of non-hermitian operators,” J. Phys. A: Math. Gen. 37(6), 2455–2464 (2004).
    [Crossref]
  35. M.-A. Miri and A. Alu, “Exceptional points in optics and photonics,” Science 363(6422), eaar7709 (2019).
    [Crossref]
  36. Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “Parity–time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019).
    [Crossref]
  37. M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108(17), 173901 (2012).
    [Crossref]

2021 (2)

M. S. Vitiello and A. Tredicucci, “Physics and technology of terahertz quantum cascade lasers,” Adv. Phys.: X 6(1), 1893809 (2021).
[Crossref]

A. Khalatpour, A. K. Paulsen, C. Deimert, Z. R. Wasilewski, and Q. Hu, “High-power portable terahertz laser systems,” Nat. Photonics 15(1), 16–20 (2021).
[Crossref]

2020 (3)

Y. Zeng, B. Qiang, and Q. J. Wang, “Photonic engineering technology for the development of terahertz quantum cascade lasers,” Adv. Opt. Mater. 8(3), 1900573 (2020).
[Crossref]

Y. Jin, J. L. Reno, and S. Kumar, “Phase-locked terahertz plasmonic laser array with 2 w output power in a single spectral mode,” Optica 7(6), 708–715 (2020).
[Crossref]

C. A. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum-cascade patch-antenna vecsel with low power dissipation,” Appl. Phys. Lett. 116(24), 241103 (2020).
[Crossref]

2019 (5)

C. A. Curwen, J. L. Reno, and B. S. Williams, “Broadband continuous single-mode tuning of a short-cavity quantum-cascade vecsel,” Nat. Photonics 13(12), 855–859 (2019).
[Crossref]

L. Bosco, M. Franckié, G. Scalari, M. Beck, A. Wacker, and J. Faist, “Thermoelectrically cooled thz quantum cascade laser operating up to 210 k,” Appl. Phys. Lett. 115(1), 010601 (2019).
[Crossref]

A. Klimont, A. Ottomaniello, R. Degl’Innocenti, L. Masini, F. Bianco, Y. Wu, Y. D. Shah, Y. Ren, D. Jessop, A. Tredicucci, H. Beere, and D. Ritchie, “Line-defect photonic crystal terahertz quantum cascade laser,” J. Appl. Phys. 126(15), 153104 (2019).
[Crossref]

M.-A. Miri and A. Alu, “Exceptional points in optics and photonics,” Science 363(6422), eaar7709 (2019).
[Crossref]

Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “Parity–time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019).
[Crossref]

2018 (2)

S. Biasco, K. Garrasi, F. Castellano, L. Li, H. E. Beere, D. A. Ritchie, E. H. Linfield, A. G. Davies, and M. S. Vitiello, “Continuous-wave highly-efficient low-divergence terahertz wire lasers,” Nat. Commun. 9(1), 1122–1128 (2018).
[Crossref]

C. A. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum cascade vecsel with watt-level output power,” Appl. Phys. Lett. 113(1), 011104 (2018).
[Crossref]

2017 (2)

L. Masini, A. Pitanti, L. Baldacci, M. S. Vitiello, R. Degl’Innocenti, H. E. Beere, D. A. Ritchie, and A. Tredicucci, “Continuous-wave laser operation of a dipole antenna terahertz microresonator,” Light: Sci. Appl. 6(10), e17054 (2017).
[Crossref]

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

2016 (3)

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, “High power-efficiency terahertz quantum cascade laser,” Chin. Phys. B 25(8), 084206 (2016).
[Crossref]

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with 0.23 w in continuous wave mode,” AIP Adv. 6(7), 075210 (2016).
[Crossref]

T.-Y. Kao, J. L. Reno, and Q. Hu, “Phase-locked laser arrays through global antenna mutual coupling,” Nat. Photonics 10(8), 541–546 (2016).
[Crossref]

2015 (3)

L. Xu, C. A. Curwen, P. W. Hon, Q.-S. Chen, T. Itoh, and B. S. Williams, “Metasurface external cavity laser,” Appl. Phys. Lett. 107(22), 221105 (2015).
[Crossref]

M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave-spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2015).
[Crossref]

M. S. Vitiello, G. Scalari, B. Williams, and P. De Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23(4), 5167–5182 (2015).
[Crossref]

2014 (2)

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. Davies, and E. Linfield, “Terahertz quantum cascade lasers with> 1 w output powers,” Electron. Lett. 50(4), 309–311 (2014).
[Crossref]

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5(1), 4034–4037 (2014).
[Crossref]

2013 (1)

L. He, Ş. K. Özdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photonics Rev. 7(1), 60–82 (2013).
[Crossref]

2012 (1)

M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108(17), 173901 (2012).
[Crossref]

2010 (1)

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010).
[Crossref]

2009 (3)

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[Crossref]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[Crossref]

2007 (4)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[Crossref]

L. A. Dunbar, R. Houdré, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, “Small optical volume terahertz emitting microdisk quantum cascade lasers,” Appl. Phys. Lett. 90(14), 141114 (2007).
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Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. Beere, J. Alton, and D. Ritchie, “Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range,” Appl. Phys. Lett. 90(9), 091113 (2007).
[Crossref]

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

2006 (1)

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42(2), 89–91 (2006).
[Crossref]

2005 (1)

G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87(21), 211112 (2005).
[Crossref]

2004 (1)

W. Heiss, “Exceptional points of non-hermitian operators,” J. Phys. A: Math. Gen. 37(6), 2455–2464 (2004).
[Crossref]

2002 (1)

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(6885), 156–159 (2002).
[Crossref]

1992 (1)

S. McCall, A. Levi, R. Slusher, S. Pearton, and R. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[Crossref]

Alton, J.

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. Beere, J. Alton, and D. Ritchie, “Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range,” Appl. Phys. Lett. 90(9), 091113 (2007).
[Crossref]

Alu, A.

M.-A. Miri and A. Alu, “Exceptional points in optics and photonics,” Science 363(6422), eaar7709 (2019).
[Crossref]

Amanti, M. I.

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010).
[Crossref]

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[Crossref]

Andrews, A. M.

G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87(21), 211112 (2005).
[Crossref]

Appleby, R.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Baldacci, L.

L. Masini, A. Pitanti, L. Baldacci, M. S. Vitiello, R. Degl’Innocenti, H. E. Beere, D. A. Ritchie, and A. Tredicucci, “Continuous-wave laser operation of a dipole antenna terahertz microresonator,” Light: Sci. Appl. 6(10), e17054 (2017).
[Crossref]

Beck, M.

L. Bosco, M. Franckié, G. Scalari, M. Beck, A. Wacker, and J. Faist, “Thermoelectrically cooled thz quantum cascade laser operating up to 210 k,” Appl. Phys. Lett. 115(1), 010601 (2019).
[Crossref]

M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave-spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2015).
[Crossref]

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010).
[Crossref]

M. I. Amanti, G. Scalari, R. Terazzi, M. Fischer, M. Beck, J. Faist, A. Rudra, P. Gallo, and E. Kapon, “Bound-to-continuum terahertz quantum cascade laser with a single-quantum-well phonon extraction/injection stage,” New J. Phys. 11(12), 125022 (2009).
[Crossref]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[Crossref]

Beere, H.

A. Klimont, A. Ottomaniello, R. Degl’Innocenti, L. Masini, F. Bianco, Y. Wu, Y. D. Shah, Y. Ren, D. Jessop, A. Tredicucci, H. Beere, and D. Ritchie, “Line-defect photonic crystal terahertz quantum cascade laser,” J. Appl. Phys. 126(15), 153104 (2019).
[Crossref]

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. Beere, J. Alton, and D. Ritchie, “Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range,” Appl. Phys. Lett. 90(9), 091113 (2007).
[Crossref]

Beere, H. E.

S. Biasco, K. Garrasi, F. Castellano, L. Li, H. E. Beere, D. A. Ritchie, E. H. Linfield, A. G. Davies, and M. S. Vitiello, “Continuous-wave highly-efficient low-divergence terahertz wire lasers,” Nat. Commun. 9(1), 1122–1128 (2018).
[Crossref]

L. Masini, A. Pitanti, L. Baldacci, M. S. Vitiello, R. Degl’Innocenti, H. E. Beere, D. A. Ritchie, and A. Tredicucci, “Continuous-wave laser operation of a dipole antenna terahertz microresonator,” Light: Sci. Appl. 6(10), e17054 (2017).
[Crossref]

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[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(6885), 156–159 (2002).
[Crossref]

Beltram, F.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics 3(1), 46–49 (2009).
[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(6885), 156–159 (2002).
[Crossref]

Benz, A.

G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87(21), 211112 (2005).
[Crossref]

Bianco, F.

A. Klimont, A. Ottomaniello, R. Degl’Innocenti, L. Masini, F. Bianco, Y. Wu, Y. D. Shah, Y. Ren, D. Jessop, A. Tredicucci, H. Beere, and D. Ritchie, “Line-defect photonic crystal terahertz quantum cascade laser,” J. Appl. Phys. 126(15), 153104 (2019).
[Crossref]

Biasco, S.

S. Biasco, K. Garrasi, F. Castellano, L. Li, H. E. Beere, D. A. Ritchie, E. H. Linfield, A. G. Davies, and M. S. Vitiello, “Continuous-wave highly-efficient low-divergence terahertz wire lasers,” Nat. Commun. 9(1), 1122–1128 (2018).
[Crossref]

Booske, J.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Bosco, L.

L. Bosco, M. Franckié, G. Scalari, M. Beck, A. Wacker, and J. Faist, “Thermoelectrically cooled thz quantum cascade laser operating up to 210 k,” Appl. Phys. Lett. 115(1), 010601 (2019).
[Crossref]

Brandstetter, M.

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5(1), 4034–4037 (2014).
[Crossref]

Castellano, F.

S. Biasco, K. Garrasi, F. Castellano, L. Li, H. E. Beere, D. A. Ritchie, E. H. Linfield, A. G. Davies, and M. S. Vitiello, “Continuous-wave highly-efficient low-divergence terahertz wire lasers,” Nat. Commun. 9(1), 1122–1128 (2018).
[Crossref]

Castro-Camus, E.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Cerjan, A.

M. Liertzer, L. Ge, A. Cerjan, A. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108(17), 173901 (2012).
[Crossref]

Chassagneux, Y.

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. Beere, J. Alton, and D. Ritchie, “Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range,” Appl. Phys. Lett. 90(9), 091113 (2007).
[Crossref]

Chen, L.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. Davies, and E. Linfield, “Terahertz quantum cascade lasers with> 1 w output powers,” Electron. Lett. 50(4), 309–311 (2014).
[Crossref]

Chen, Q.-S.

L. Xu, C. A. Curwen, P. W. Hon, Q.-S. Chen, T. Itoh, and B. S. Williams, “Metasurface external cavity laser,” Appl. Phys. Lett. 107(22), 221105 (2015).
[Crossref]

Chu, W.

X. Wang, C. Shen, T. Jiang, Z. Zhan, Q. Deng, W. Li, W. Wu, N. Yang, W. Chu, and S. Duan, “High-power terahertz quantum cascade lasers with 0.23 w in continuous wave mode,” AIP Adv. 6(7), 075210 (2016).
[Crossref]

Clarke, R.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Cocker, T. L.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Colombelli, R.

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. Beere, J. Alton, and D. Ritchie, “Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range,” Appl. Phys. Lett. 90(9), 091113 (2007).
[Crossref]

Cooper, K. B.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Cumming, D. R. S.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Cunningham, J. E.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Curwen, C. A.

C. A. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum-cascade patch-antenna vecsel with low power dissipation,” Appl. Phys. Lett. 116(24), 241103 (2020).
[Crossref]

C. A. Curwen, J. L. Reno, and B. S. Williams, “Broadband continuous single-mode tuning of a short-cavity quantum-cascade vecsel,” Nat. Photonics 13(12), 855–859 (2019).
[Crossref]

C. A. Curwen, J. L. Reno, and B. S. Williams, “Terahertz quantum cascade vecsel with watt-level output power,” Appl. Phys. Lett. 113(1), 011104 (2018).
[Crossref]

L. Xu, C. A. Curwen, P. W. Hon, Q.-S. Chen, T. Itoh, and B. S. Williams, “Metasurface external cavity laser,” Appl. Phys. Lett. 107(22), 221105 (2015).
[Crossref]

Davies, A.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. Davies, and E. Linfield, “Terahertz quantum cascade lasers with> 1 w output powers,” Electron. Lett. 50(4), 309–311 (2014).
[Crossref]

Davies, A. G.

S. Biasco, K. Garrasi, F. Castellano, L. Li, H. E. Beere, D. A. Ritchie, E. H. Linfield, A. G. Davies, and M. S. Vitiello, “Continuous-wave highly-efficient low-divergence terahertz wire lasers,” Nat. Commun. 9(1), 1122–1128 (2018).
[Crossref]

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. A. Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017).
[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(6885), 156–159 (2002).
[Crossref]

De Natale, P.

Dean, P.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. Davies, and E. Linfield, “Terahertz quantum cascade lasers with> 1 w output powers,” Electron. Lett. 50(4), 309–311 (2014).
[Crossref]

Degl’Innocenti, R.

A. Klimont, A. Ottomaniello, R. Degl’Innocenti, L. Masini, F. Bianco, Y. Wu, Y. D. Shah, Y. Ren, D. Jessop, A. Tredicucci, H. Beere, and D. Ritchie, “Line-defect photonic crystal terahertz quantum cascade laser,” J. Appl. Phys. 126(15), 153104 (2019).
[Crossref]

L. Masini, A. Pitanti, L. Baldacci, M. S. Vitiello, R. Degl’Innocenti, H. E. Beere, D. A. Ritchie, and A. Tredicucci, “Continuous-wave laser operation of a dipole antenna terahertz microresonator,” Light: Sci. Appl. 6(10), e17054 (2017).
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Data availability

Data underlying the results presented in each figure of this paper are not publicly available at this time but can be obtained from the authors upon request.

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Figures (7)

Fig. 1.
Fig. 1. (a) Sketch of the device showing the THz microcavity laser constituted by two WG microdisk resonators (labeled as disk A and B) and the dual injection scheme: two distinct electrodes connect each resonator to a different bonding pad, where a bias can be applied from the top metal layer to the bottom ground plane. A SiO$_2$ layer is present below the top metallization of both pads and injection electrodes to prevent current injection in the underneath active region. (b) Simulated spatial distribution of the electric-field $z$-component ($E_z$) in the $xy$-plane for the calculated microcavity modes in the spectral range of interest. (c) Simulated far-field profiles in $yz$-plane of the calculated microcavity eigenmodes. Vertical and lateral directions are defined as $z$- and $y$-axes, respectively.
Fig. 2.
Fig. 2. Main stages of the fabrication process. (1) Metal markers for fine alignment realized through EBL and thermal evaporation. (2) Insulating pattern for pads and injection electrodes obtained via the sputtering deposition of a $180\ \textrm {nm}$-thick SiO$_2$ layer, aligned EBL of a polymer mask and final wet etching in BOE. (3) Top metallization of the microcavity, bonding pads and injection electrodes realized through a second aligned EBL and thermal evaporation of $5/200/40\ \textrm {nm}$ Cr/Au/Ni. (4) SEM image of the THz microcavity laser finally obtained through ICP-RIE. The electric field spatial distribution (out-of-plane component) of the lasing microcavity supermode is superimposed to the microcavity.
Fig. 3.
Fig. 3. (a) IV and LI characteristics of the THz microcavity laser. The solid blue curve represents the IV characteristic of the microcavity, while both vertical and lateral laser emitted power are reported by the solid and dashed red curve (multiplied by a factor 5), respectively. Inset: IV-characteristics of both microdisks. In both graphs the threshold current is reported by a dashed line. (b) Laser spectra in the vertical direction for different values of injected current. Inset: laser spectrum in the lateral direction for the same current values.
Fig. 4.
Fig. 4. (a) VI characteristics for each microdisk measured varying the injected current in one resonator (disk A, solid blue curve) while keeping constant to $3.4\ \textrm {mA}$ the injected current in the other one (disk B, dashed blue curve). The emitted power of the whole microcavity both in the vertical ($z$-) and lateral ($y$-) direction is reported by the solid and dashed red curve, respectively. The curve for the lateral emission is multiplied by a factor 5. (b) and (c): laser spectra acquired for different injected currents in disk A from the vertical and lateral direction, respectively.
Fig. 5.
Fig. 5. Microcavity eigenfrequency finite-element simulations varying the amount of gain/loss in disk A while keeping constant the gain in disk B. (a) Imaginary part versus real part of the microcavity eigenfrequencies sweeping the refractive index imaginary part from a positive (indicating loss, $\textrm {Im}(n_{\textrm {A}})=0.05$) to a negative value (indicating gain, $\textrm {Im}(n_{\textrm {A}})=-0.05$). The refractive index imaginary part in disk B is kept fixed at $\textrm {Im}(n_{\textrm {B}})=-0.02$. Experimentally lasing and non-lasing modes are presented by face- and edge-colored markers, respectively. The horizontal dashed line represents a hypothetical lasing threshold of $\textrm {Im}(\omega )=10\ \textrm {GHz}$. The position of the calculated exceptional points is also reported: EP1 and EP2 are associated with the eigenvalue couple reported via diamond and circle markers, respectively. (b) Calculated emitted power as a function of the refractive index imaginary part of disk A obtained with the assumed lasing threshold. Inset: Simulated far-field profiles for the $\textrm {M}_{6+-}$-mode for Im$(n_{\textrm {A}})=0.02$ and -0.02.
Fig. 6.
Fig. 6. (a) SEM of the fabricated THz microcavity with a suspended gold bridge linking the two microdisks. The $E_{\textrm {z}}$-spatial distribution of the vertically emitting mode ($\textrm {M}_{+-}$-mode) is superimposed. (b) VI and LI characteristics. Emitted power in the out-of-plane ($z$-direction) and in-plane (with a multiplication factor of 10) directions are reported via a solid and a dashed red curve, respectively. (c), (d) Spectra measured in the out-of-plane and in-plane direction, respectively, for several values of injected current.
Fig. 7.
Fig. 7. Simulated modes of the THz microcavity with the suspended gold bridge. (a) Spatial distribution of the electric-field $z$-component ($E_z$) in the $xy$-plane for the three eigenmodes ($\textrm {M}_{6++}$, $\textrm {M}_{6--}$ and $\textrm {M}_{6+-}$) experimentally showing lasing action. (b) Relative far-field profiles in the $yz$-plane.

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