Abstract

We report on micropillar-based terahertz lasers with active pillars that are much smaller than the emission wavelength. These micropillar array lasers correspond to scaled-down band-edge photonic crystal lasers forming an active photonic metamaterial. In contrast to photonic crystal lasers which use significantly larger pillar structures, lasing emission is not observed close to high-symmetry points in the photonic band diagram, but in the effective medium regime. We measure stimulated emission at 4 THz for micropillar array lasers with pillar diameters of 5 µm. Our results not only demonstrate the integration of active subwavelength optics in a terahertz laser, but are also an important step towards the realization of nanowire-based terahertz lasers.

© 2014 Optical Society of America

1. Introduction

Periodically arranged light emitting pillars with dimensions on the order of the wavelength can be used as an active photonic crystal structure. Photonic crystal resonators are widely employed for light confinement in lasers due to their large degree of design freedom. As a result of this versatility, different concepts for laser resonators using photonic crystals have emerged in the past. In a defect mode laser light is confined in an intentional single defect of atwo-dimensional photonic crystal [13]. Lasers with very small cavities can be realized with this method. A related approach is to form frequency selective mirrors using stop bands of a photonic crystal [4,5]. Alternatively, active photonic crystals can be designed with an intrinsic feedback mechanism [6] without the need for introducing a defect into the structure [713]. Lasing in these structures typically occurs at band edges of the photonic bands close to high symmetry points, where the photonic density of states is high and the group velocity low, which enhances the gain in active photonic crystals [14].

When such a photonic crystal is scaled-down and feature sizes become significantly smaller than the emission wavelength, eventually the homogenization regime of the photonic bandstructure is reached, where the structure effectively forms a photonic metamaterial. In this long-wavelength limit, the photonic crystal can be considered as a homogeneous effective medium [1719]. It is then possible to fully describe the structure using a dielectric tensor, which is diagonal in the principal set of axes. In the case of transverse magnetic (TM)-modes, where the electric field is parallel to all dielectric interfaces, the effective dielectric constant is simply equal to the weighted average dielectric constant of the structure [20]

εeff=ε1η+ε2(1η),
where ε1 and ε2 are the dielectric constants of the pillar and the host medium, and η is the pillar-filling factor of the array.

In Fig. 1(a) we show the photonic band diagram of a hexagonal pillar array calculated using the plane wave expansion method [21]. The ratio of pillar radius/lattice spacing (r/a) is set to 0.45 in order to achieve a high filling factor. For our experiments only the lowest band is important. In the case of a photonic crystal laser the gain region typically overlaps with band edge states of the lowest photonic band. By scaling down the diameter of the pillars but keeping the ratio r/a constant the photonic band diagram does not change on a normalized frequency scale. However, as shown in Fig. 1(a), the gain spectrum, which is constant on an absolute frequency scale, moves down on the normalized scale when the size of the pillars is reduced. Therefore, if the pillars are small enough the gain region overlaps with the homogenization regime of the photonic structure, where the pillar array can be described using an effective medium approach. The effect of scaling on the electric field distribution is illustrated in Fig. 1(b). We define the effective filling factor as the ratio,

ηeff=ε=ε1dr|E(r)|dr|E(r)|.
It quantifies how strongly the electric field is confined inside the pillars. At the high symmetry points the optical mode is strongly confined yielding a large effective filling factor. In the effective medium regime, however, the electric field distribution is practically homogeneous. Therefore, the effective filling factor of the pillar array converges towards the geometrical filling factor when the pillar diameter is scaled down.

 figure: Fig. 1

Fig. 1 Scaling of a pillar array from a photonic crystal to the effective medium regime. (a) Photonic band diagram of TM-modes calculated for infinitely long pillars in a hexagonal array with r/a = 0.45, ε1 = 13.32 (GaAs) [15], and ε2 = 2.45 (BCB) [16]. Reducing the size of the pillars, while keeping r/a constant, moves down the gain spectrum of the active material towards the effective medium regime. (b) Magnitude of the electric field at several points in the lowest band plotted on a linear scale. In contrast to a large confinement of the electric field in the pillars at the high symmetry points (M, K), practically no confinement is observed in the effective medium regime (A). The effective filling factor calculated using Eq. (2) decreases from 0.89 at the K-point to 0.75 at point ‘A’.

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2. Realization

The scaling concept is independent of wavelength and can, in principle, be realized in an arbitrary spectral region. We demonstrate that in the terahertz range the relatively long wavelengths enable the fabrication of lasers with integrated active structures that are significantly smaller than the emission wavelength. Similar to a terahertz photonic crystal laser, the micropillar array is realized in a top-down way by etching the gain material [10,11]. On the contrary, however, the micropillars are considerably smaller than the emission wavelength. Using this concept photonic metamaterials can be realized, where the propagation of electromagnetic modes can be controlled on a subwavelength scale [22].

While, hole arrays are frequently used for photonic crystal lasers [1,2], terahertz lasers can also be realized using pillar arrays [10,11]. This is due to the fact that low loss double-metal waveguides can be utilized for electrically pumping the pillar array [23]. The pillars are based on quantum cascade laser (QCL) structures, which produce only in-plane emission resulting from the TM-polarization of intersubband transitions. Long wavelengths and therefore large feature sizes allow a fabrication of photonic crystal structures using standard semiconductor processing technologies [24]. We show that the size of the pillars can be scaled far into the subwavelength regime. Due to the unipolar nature of the active material, surface recombination does not negatively influence the device. However, surface depletion can reduce the number of electrons available for current transport, which effectively lowers the current density in the micropillar. This effect is especially important if the pillars are scaled into the nanowire regime [25].

When pillar diameters are steadily scaled down, essentially two transitions occur. First, the lattice periodicity becomes significantly smaller than the wavelength, and photons experience a change from band-edge modes, where they can be strongly confined inside the pillar medium, to an effective medium. Secondly, for small enough diameters electrons become confined in-plane leading to an additional quantization of energy levels. Terahertz quantum cascade lasers have experienced a significant improvement since their first demonstration [26], but are still limited to cryogenic temperatures. Currently the best performing THz QCL operates up to 199.5 K [27]. Due to the small energy spacing of upper and lower laser level, it is difficult to achieve population inversion at elevated temperatures in these devices. Especially, thermally activated scattering mechanisms significantly reduce the optical gain with increasing temperature. Due to this fundamental problem, alternative approaches might be necessary. A promising concept is to reduce non-radiative relaxation by introducing a quantum mechanical confinement in the plane of the heterostructure [2830]. This can be realized by replacing the bulk active region with a dense array of semiconductor nanowires. Such devices are clearly the ultimate limit of down-scaling a photonic crystal structure. It can be shown, using high magnetic fields, that the maximum operating temperature of a THz QCL can be significantly increased with an additional lateral quantum mechanical confinement [31]. In order to enter the lateral confinement regime, nanowire diameters on the order of 100 nm are necessary [32]. Recently, electroluminescence from nanowire quantum cascade structures has been demonstrated [33].

In this work, we demonstrate the realization of a terahertz laser based on an array of micropillar emitters, which are significantly smaller than the emission wavelength. The micropillar array laser is a scaled-down version of the photonic crystal laser. Consequently, the optical modes of the resonator are defined by the shape of the micropillar array forming a Fabry-Pérot type of cavity. The gain spectrum is shifted into the effective medium regime in these devices as illustrated in Fig. 1(a).

3. Device design and fabrication

The micropillars are fabricated from a 10 μm thick GaAs/Al0.15Ga0.85As quantum cascade structure grown by molecular beam epitaxy on a semi-insulating GaAs substrate. It consists of 221 cascades with a layer sequence of 16.4/4.5/8.5/2.8/8.5/4.5 nm, with barriers in bold and the first 6.4 nm of the underlined section Si-doped yielding a sheet doping density of 3.3e10 cm−2. The active quantum cascade structure is embedded between two highly doped contact layers with a thickness of 100 nm. The design of this active region is a symmetric version derived from that in Ref. [34], which can be operated in both current directions [35]. It is based on a three-well resonant-phonon depopulation scheme designed for optical gain around 4 THz. The doping profile has been adjusted in order to compensate for dopant migration effects [35].

The pillar array is sandwiched between a metal layer on top and on bottom, forming a double-plasmon waveguide [23]. This provides the vertical optical confinement and allows for homogenous electrical pumping of the gain medium. The fabrication process for the micropillar devices is comparable to that of terahertz photonic crystal lasers [24], but optimized for small feature sizes and large filling factors. A 10 nm thin Ti adhesion layer followed by 400 nm and 1 μm of gold is deposited on the sample wafer and an additional n + GaAs substrate respectively. The sample wafer is than thermo-compressively bonded to the GaAs substrate and the original substrate is removed by mechanical polishing and chemical wet etching. This forms a metal bottom contact and waveguide layer below the active region. Electron-beam lithography and a lift-off technique are then used to define the micropillar array with a 10 nm Ti / 400 nm Au etch mask. The bulk heterostructure is etched into pillar arrays using a highly anisotropic reactive ion etching (RIE) process. This process has been optimized for micropillar arrays with large filling factors and to produce almost vertical sidewalls in order to ensure a constant current density across the pillar. The GaAs/Al0.15Ga0.85As quantum cascade structure is etched using a mixture of SiCl4 and N2 gases in an inductively-coupled plasma (ICP) RIE system. The chamber is kept at a pressure of 5 mTorr, the radio frequency (RF) power is set to 60 W, and an ICP power of 20 W is used. The RF power is optimized to achieve reasonable etch rates and a good selectivity between the etch mask and the active region. A higher RF power results in faster etching but also less selectivity. The sidewall angle is controlled by adjusting the relative gas flows. A gas flow ratio of 6 sccm SiCl4 / 20 sccm N2 yields almost vertical sidewalls in the case of large filling factors. The temperature of the wafer table is kept at 40 °C during the etching process. Etch rates are on the order of 100 nm/min and depend on the filling factor of the array. The bottom gold layer acts as an etch stop layer, which allows the use of different filling factors on a single sample. The micropillar arrays are planarized using benzocyclobutene (BCB), a polymer with low losses in the THz range [16]. After planarization the polymer is removed from the top to uncover the top contacts of the pillars. This etch back step is also performed with reactive ion etching, but using a SF6/O2 plasma mixture. The BCB is etched back just as much as to uncover the top contacts of the micropillars in order to achieve a flat top waveguide layer. Optical lithography is finally used to define a 10 nm Ti / 500 nm Au top contact to complete the double-plasmon waveguide. An important aspect of the top-down approach is that it is fully scalable from photonic crystal devices down to nanowire-based devices [36].

The micropillars are arranged in a hexagonal lattice with array sizes up to 1000 x 120 μm. The array forms a Fabry-Pérot type of resonator similar to standard bulk THz quantum cascade laser ridges. The main difference is that the bulk gain region is replaced by the micro-pillar array forming an effective medium. Devices with different pillar diameters (2–5 µm), filling factors, and array dimensions are fabricated. A schematic of the device and fully processed micropillar array laser devices are shown in Fig. 2.

 figure: Fig. 2

Fig. 2 (a) Schematic illustration of the micropillar array terahertz laser. The densely packed pillar array is sandwiched between two metal layers and forms a ridge-waveguide. The space between the pillars is filled with a low-loss polymer. (b) Scanning electron microscope images of fabricated micropillar array lasers with pillar diameters of 5 µm. Inset: Facet of the laser ridge (top), and closer view of a micropillar before planarization (bottom).

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4. Experimental results

In previous experiments, terahertz photonic crystal devices did not show any lasing when they were scaled down far enough that the gain region was no longer overlapping with photonic band edges [10,11]. If this was due to the fact that optical losses were too high or due to other mechanisms remained unclear. In principle, one expects a transition from the distributed feedback mechanism of the photonic crystal to a cavity defined by the boundaries of the pillar array, forming an effective gain medium. We investigate structures with subwavelength feature sizes and high packing densities in order to achieve lasing emission in micropillar array devices.

The fabricated devices are indium-soldered to a copper plate, wire-bonded and mounted in a continuous flow helium cryostat for controlling the heat sink temperature. We measure light-current-voltage (LIV) characteristics for the devices in pulsed mode in order to prevent excessive heating effects. Devices are operated with a voltage pulser, typically using a pulse width of 300 ns and a repetition frequency of 100 kHz. The light emitted by the devices is collected from a single facet and measured with a far-infrared DTGS detector. The spectra are recorded with a Bruker Vertex 80 Fourier-transform infrared (FTIR) spectrometer in continuous-scan mode, which is purged with nitrogen gas to reduce water absorption.

In Fig. 3(a) the current-voltage (IV) characteristics of micropillar arrays with different pillar diameters are compared. As a reference also the IV of a bulk structure is shown. Due to the effect of surface depletion, the current density decreases with decreasing pillar diameter. The current density in the bulk structure is used as a reference, and the size of the effective current channel is calculated for each pillar diameter, as shown in the inset of Fig. 3(a). (Variations in the contact resistance vertically shift the IVs, and are accounted for by comparing current densities at equal electric fields, through locating the parasitic alignment using the second derivative of the IV.) With this calculation we estimate a surface depletion width of approximately 170 nm. In the case of the larger pillar diameters this does not drastically reduce the effective current channel. However, if the pillars are scaled to nanowire dimensions, a higher doping density or surface passivation [25] needs to be used in order to account for this effect.

 figure: Fig. 3

Fig. 3 (a) Comparison of the current-voltage (IV) characteristic of a bulk structure and micropillar arrays with various pillar diameters. The current density in the micropillar arrays is calculated using the physical dimensions of the pillars. Surface states are causing a partial carrier depletion in the micropillars, which significantly reduces the current density for small pillar diameters. The inset shows the effective diameters available for charge transport depending on the physical diameters of the micropillars, including a linear fit to the data. A surface depletion width of approximately 170 nm can be extracted from the decreasing current density. (b) Low-temperature light-current-voltage (LIV) characteristics of a 120 x 1000 x 10 µm micropillar array laser with a pillar size of 5 µm and a filling factor of 0.75 (r/a = 0.45). The current density is given as the density in the micropillars calculated from the measured current and the filling factor of the array.

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In fact, micropillar array devices with a pillar diameter of 5 µm, a filling factor of 0.75, and a size of 1000 x 120 x 10 µm show stimulated emission. The high packing density is necessary to provide sufficient gain to overcome the losses of the waveguide. Light-current-voltage (LIV) characteristics of such a micropillar array laser are presented in Fig. 3(b). Thecurrent density is given as the average current density in the pillar. Lasing emission is observed up to a maximum heat sink temperature of 55 K. The observed threshold current density Jth is approximately 0.65 kA/cm2. Compared to bulk reference devices with a Jth of approximately 0.75 kA/cm2, the threshold current density is slightly reduced. However, due to the relatively low doping density of the active region, the current density in the micropillars is reduced by the effect of surface depletion, which decreases the number of electrons available for charge transport. The measured decrease in the threshold current density perfectly agrees with the estimated surface depletion width. The current density in the micropillar array laser is calculated using the physical size of the pillars. Taking only the effective current channel into account results in similar threshold current densities.

The photonic band diagram for this structure is shown in Fig. 4(a). Due to the large filling factor, the structure does not form a pronounced photonic band gap, but local gaps at the high symmetry points. However, since the lasing emission is expected in the effective medium regime of the lowest photonic band, the band gap is not important. As a result of the down-scaling, the gain maximum is shifted downwards in the photonic band diagram and lasing can no longer take place at the band edges, but only in the effective medium regime. The gain maximum of the active region at 4 THz corresponds to a normalized frequency of fa/c = 0.073. To confirm that the devices are indeed lasing in the effective medium regime, spectral measurements are performed on the micropillar devices. Figure 4(b) shows the lasing spectra of a micropillar array laser for different applied biases. The emission frequency of the device is around 4 THz with one dominant mode shifting to higher frequency with increasing bias. The emission at 4 THz is proof of lasing in the effective medium regime of the photonic band. Therefore, the resonator is no longer defined by the distributed feedback of a photonic crystal but the Fabry-Pérot resonator defined by the boundaries of the array.

 figure: Fig. 4

Fig. 4 Laser output spectra of a 120 x 1000 x 10 µm micropillar array laser with a pillar size of 5 µm and a filling factor of 0.75 (r/a = 0.45). The measurements are performed at a heat sink temperature of 5 K. (a) Overlay of the emission spectrum with the photonic band diagram. In contrast to photonic crystal lasers, high-symmetry points of the photonic lattice are far outside the gain region and no lasing is observed at these points. The emission frequency of approximately 4 THz corresponds to a normalized frequency (fa/c) of about 0.07. (b) The two dominant emission modes with slightly varying frequency close to the operation points of the two output maxima in the LI-curve of Fig. 3. The spectra are vertically shifted for clarity.

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Bulk reference devices show lasing up to a maximum operating temperature of 158 K, with a negative bias, and 150 K, with a positive bias applied to the top contact. We ascribe the difference in temperature performance between bulk and micropillar array devices to the fact that, on the one hand, there is less gain medium present in the micropillar array lasers, and, on the other hand, additional loss mechanisms are introduced. Due to the effect of surface depletion, the physical filling factor of 0.75 is reduced for a micropillar array with pillar diameters of 5 µm to an effective filling factor of 0.65, when only the area of current flow is considered. Even though, the polymer, which is used for filling up the space between the pillars, has low losses in the THz spectral range, they are not negligible [16]. In the case of the double metal waveguide used for the devices, the waveguide loss increases from 8.86 cm−1 in a regular bulk device to 12.22 cm−1 for the micropillar array laser with a filling factor of 0.75 and planarized using BCB. In contrast to band-edge photonic crystal lasers the optical mode is not strongly confined to the pillars, but homogeneously distributed. Therefore, absorption losses in the planarization material play an important role for micropillar array lasers. In contrast to bulk reference devices, the top waveguide is not perfectly flat. This roughness, resulting from the planarization procedure, potentially causes additional waveguide losses. However, these losses might be reduced by using alternative processing schemes that do not rely on a planarization layer [11]. Although, the structure is designed to be symmetric with respect to the operating direction, devices show lasing only with a negative bias polarity applied to the top contact. When applying a positive bias to the top contact, we measure spontaneous emission on top of a thermal background radiation from heating up the device. In this operating direction, the active region does not provide sufficient gain to overcome the optical losses in the micropillar array device preventing any lasing. This dependence of the optical gain on the operating direction is in agreement with earlier findings [35]. The relatively small difference in the maximum operating temperature depending on the operating direction for bulk devices indicates that the difference in optical gain at lower temperatures is significantly larger than at higher temperatures. This can be explained by the fact that differences in impurity scattering are at lower temperatures even more important than at higher operating temperatures, because at higher temperatures lifetimes are increasingly dominated by phonon scattering. Pillar arrays with diameters smaller than 5 µm and filling factors below 0.75 show spontaneous emission with both bias polarities. Due to higher losses and less gain material present in these devices stimulated emission is not possible.

5. Conclusion

In conclusion, we demonstrate a micropillar array terahertz laser with pillar sizes that are much smaller than the emission wavelength. This not only represents the successful realization of a micropillar effective medium device, but even constitutes a new class of devices with active structures that are designable on a subwavelength scale. The device is essentially realized by scaling down a photonic crystal structure to the effective medium regime. Both, the lateral confinement of photons as well as the confinement of electrons have to be considered in this scaling. While photons experience a transition from confined modes to an effective medium, electrons are more and more confined with decreasing pillar sizes. This will eventually lead to quantum confinement effects, if the pillar diameters are small enough. Therefore, not only new kinds of devices may be realized using this concept, but also conventional terahertz laser devices can benefit.

A great challenge in the realization of the devices is to provide sufficient gain inside the cavity to overcome the optical losses of the waveguide. This can only be achieved with relatively high pillar-packing densities. Therefore, a reduction of the optical losses is crucial for the realization of nanowire-based devices with limited filling factors. The issue of high waveguide losses may be addressed using alternative planarization materials or processing techniques. The polymer used for filling up the space between the micropillars (BCB) has non-negligible absorption losses at the emission frequency, and the planarization method used in the experiments does not yield perfectly flat top waveguides. A reduction of the waveguide losses, by avoiding polymers to fill up the space between pillars and reducing the top waveguide roughness, is likely to enhance the performance of these devices. Improvements of the waveguide design will be necessary to achieve a device performance comparable to bulk devices. The scaling-concept is independent of the spectral region. Therefore, the effect of an increase in waveguide losses due to the down-scaling might be significantly less pronounced for other frequency ranges.

Regarding potential applications, we believe that the scaling into the effective medium regime opens up new opportunities for devices using concepts of active subwavelength optics, including graded-index devices and graded photonic crystals [22]. The possibility of designing active material structures on a subwavelength level also allows for exciting novel device designs. Since the active region is not connected anymore, each pillar can be pumped individually. Thus, the pumping geometry can be changed dynamically to realize novel laser control concepts or simply to pump more efficiently. Scaling down the micropillars into the nanowire regime will eventually even lead to lateral quantum confinement effects. A quantization of energy levels in the plane of the semiconductor heterostructure can significantly increase the lifetimes of intersubband transitions leading to an increase of the maximum operating temperatures. The realization of the micropillar array laser represents an important step towards the realization of nanowire-based devices.

Acknowledgments

The authors acknowledge the support by the Austrian Science Fund FWF (SFB IR-ON F25, DK CoQuS W1210), the Austrian Nano Initiative project (PLATON), and the Austrian Society for Microelectronics (GMe). We also would like to thank Markus Geiser from ETH Zürich for his support with regard to the fabrication of the devices.

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32. T. Grange, “Nanowire terahertz quantum cascade lasers,” arXiv:1301.1258 [cond–mat.mes–hall] (2013).

33. M. I. Amanti, A. Bismuto, M. Beck, L. Isa, K. Kumar, E. Reimhult, and J. Faist, “Electrically driven nanopillars for THz quantum cascade lasers,” Opt. Express 21(9), 10917–10923 (2013). [CrossRef]   [PubMed]  

34. 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(13), 131105 (2009). [CrossRef]  

35. C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013). [CrossRef]  

36. M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013). [CrossRef]  

References

  • View by:

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  2. R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
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  3. M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, and O. Painter, “Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap,” Opt. Express 15(10), 5948–5965 (2007).
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  4. L. A. Dunbar, V. Moreau, R. Ferrini, R. Houdré, L. Sirigu, G. Scalari, M. Giovannini, N. Hoyler, and J. Faist, “Design, fabrication and optical characterization of quantum cascade lasers at terahertz frequencies using photonic crystal reflectors,” Opt. Express 13(22), 8960–8968 (2005).
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  5. A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, and G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
    [Crossref] [PubMed]
  6. M. Notomi, H. Suzuki, and T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
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  7. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
    [Crossref]
  8. M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
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  9. H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
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  10. H. Zhang, L. A. Dunbar, G. Scalari, R. Houdré, and J. Faist, “Terahertz photonic crystal quantum cascade lasers,” Opt. Express 15(25), 16818–16827 (2007).
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    [Crossref] [PubMed]
  12. Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
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    [Crossref]
  16. E. Perret, N. Zerounian, S. David, and F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
    [Crossref]
  17. S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
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    [Crossref]
  20. D. J. Bergman and D. Stroud, “Physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
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    [Crossref] [PubMed]
  23. K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
    [Crossref]
  24. H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, and R. Houdré, “Design and fabrication technology for high performance electrical pumped terahertz photonic crystal band edge lasers with complete photonic band gap,” J. Appl. Phys. 108(9), 093104 (2010).
    [Crossref]
  25. M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, and T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
    [Crossref]
  26. 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] [PubMed]
  27. 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(4), 3866–3876 (2012).
    [Crossref] [PubMed]
  28. N. S. Wingreen and C. A. Stafford, “Quantum-dot cascade laser: proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33(7), 1170–1173 (1997).
    [Crossref]
  29. C.-F. Hsu, J. -S. O, P. Zory, and D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).
  30. E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
    [Crossref] [PubMed]
  31. S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, and K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
    [Crossref]
  32. T. Grange, “Nanowire terahertz quantum cascade lasers,” arXiv:1301.1258 [cond–mat.mes–hall] (2013).
  33. M. I. Amanti, A. Bismuto, M. Beck, L. Isa, K. Kumar, E. Reimhult, and J. Faist, “Electrically driven nanopillars for THz quantum cascade lasers,” Opt. Express 21(9), 10917–10923 (2013).
    [Crossref] [PubMed]
  34. 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(13), 131105 (2009).
    [Crossref]
  35. C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
    [Crossref]
  36. M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
    [Crossref]

2013 (4)

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, and K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[Crossref]

M. I. Amanti, A. Bismuto, M. Beck, L. Isa, K. Kumar, E. Reimhult, and J. Faist, “Electrically driven nanopillars for THz quantum cascade lasers,” Opt. Express 21(9), 10917–10923 (2013).
[Crossref] [PubMed]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (2)

B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
[Crossref] [PubMed]

H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, and R. Houdré, “Design and fabrication technology for high performance electrical pumped terahertz photonic crystal band edge lasers with complete photonic band gap,” J. Appl. Phys. 108(9), 093104 (2010).
[Crossref]

2009 (5)

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, and T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[Crossref]

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

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(13), 131105 (2009).
[Crossref]

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, and G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[Crossref] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[Crossref] [PubMed]

2008 (3)

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[Crossref] [PubMed]

H. Yasuda and I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. 47(3), 1632–1634 (2008).
[Crossref]

E. Perret, N. Zerounian, S. David, and F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[Crossref]

2007 (3)

2005 (1)

2003 (1)

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

2002 (2)

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] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[Crossref]

2001 (3)

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[Crossref] [PubMed]

M. Notomi, H. Suzuki, and T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
[Crossref]

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[Crossref]

2000 (1)

C.-F. Hsu, J. -S. O, P. Zory, and D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

1999 (4)

P. Halevi, A. A. Krokhin, and J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82(4), 719–722 (1999).
[Crossref]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[Crossref]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[Crossref]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

1997 (1)

N. S. Wingreen and C. A. Stafford, “Quantum-dot cascade laser: proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33(7), 1170–1173 (1997).
[Crossref]

1996 (1)

1993 (1)

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[Crossref] [PubMed]

1992 (1)

D. J. Bergman and D. Stroud, “Physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[Crossref]

Amanti, M. I.

Andrews, A. M.

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[Crossref]

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, and G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[Crossref] [PubMed]

A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, and G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
[Crossref] [PubMed]

Aniel, F.

E. Perret, N. Zerounian, S. David, and F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[Crossref]

Arriaga, J.

P. Halevi, A. A. Krokhin, and J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82(4), 719–722 (1999).
[Crossref]

Bahriz, M.

Ban, D.

Barbieri, S.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[Crossref] [PubMed]

Bastard, G.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Beck, M.

Beere, H. E.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[Crossref] [PubMed]

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] [PubMed]

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(6885), 156–159 (2002).
[Crossref] [PubMed]

Benz, A.

Bergman, D. J.

D. J. Bergman and D. Stroud, “Physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[Crossref]

Bismuto, A.

Botez, D.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, and T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[Crossref]

C.-F. Hsu, J. -S. O, P. Zory, and D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

Brandstetter, M.

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[Crossref]

Capasso, F.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[Crossref]

Carpenter, B. A.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Chan, C. T.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[Crossref] [PubMed]

Chan, C. W. I.

Chassagneux, Y.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[Crossref] [PubMed]

Cho, A. Y.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[Crossref]

Chutinan, A.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[Crossref]

Colombelli, R.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[Crossref] [PubMed]

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, and O. Painter, “Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap,” Opt. Express 15(10), 5948–5965 (2007).
[Crossref] [PubMed]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[Crossref]

Crisafulli, O.

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Datta, S.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[Crossref] [PubMed]

David, S.

E. Perret, N. Zerounian, S. David, and F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[Crossref]

Davies, A. G.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[Crossref] [PubMed]

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] [PubMed]

de Vaulchier, L.-A.

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, and K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[Crossref]

Detz, H.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[Crossref]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[Crossref]

Deutsch, C.

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[Crossref]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[Crossref]

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, and K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[Crossref]

Deutsch, Ch.

Dodabalapur, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[Crossref]

Dunbar, L. A.

Dupont, E.

Faist, J.

Fasching, G.

Fathololoumi, S.

Ferreira, R.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Ferrini, R.

Gajic, R.

Giovannini, M.

Gmachl, C.

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[Crossref]

Gmachl, C. F.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

Grange, T.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Guldner, Y.

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, and K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[Crossref]

Halevi, P.

P. Halevi, A. A. Krokhin, and J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82(4), 719–722 (1999).
[Crossref]

Helm, M.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Hingerl, K.

Ho, K. M.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[Crossref] [PubMed]

Hosako, I.

H. Yasuda and I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. 47(3), 1632–1634 (2008).
[Crossref]

Houdré, R.

Hoyler, N.

Hsu, C.-F.

C.-F. Hsu, J. -S. O, P. Zory, and D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

Hu, Q.

Hwang, H. Y.

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[Crossref]

Imada, M.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[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(6885), 156–159 (2002).
[Crossref] [PubMed]

Isa, L.

Isic, G.

Jianglin, Y.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[Crossref] [PubMed]

Jirauschek, C.

Joannopoulos, J.

Joannopoulos, J. D.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[Crossref]

Johnson, S.

Khandekar, A. A.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, and T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[Crossref]

Khanna, S. P.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[Crossref] [PubMed]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Klang, P.

Köhler, R.

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] [PubMed]

Krall, M.

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, and K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[Crossref]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[Crossref]

Krokhin, A. A.

P. Halevi, A. A. Krokhin, and J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82(4), 719–722 (1999).
[Crossref]

Kuech, T. F.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, and T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[Crossref]

Kumar, K.

Kumar, S.

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(13), 131105 (2009).
[Crossref]

Laframboise, S. R.

Lalanne, P.

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Linfield, E. H.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[Crossref] [PubMed]

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] [PubMed]

Liu, H. C.

Liu, H. Y.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Maëro, S.

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, and K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[Crossref]

Maineult, W.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[Crossref] [PubMed]

Matsubara, H.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[Crossref] [PubMed]

Mátyás, A.

Meier, M.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[Crossref]

Mekis, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[Crossref]

Moreau, V.

Murata, M.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[Crossref]

Nalamasu, O.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[Crossref]

Noda, S.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[Crossref] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[Crossref]

Nojima, S.

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[Crossref]

Notomi, M.

M. Notomi, H. Suzuki, and T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
[Crossref]

O, J. -S.

C.-F. Hsu, J. -S. O, P. Zory, and D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Painter, O.

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, and O. Painter, “Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap,” Opt. Express 15(10), 5948–5965 (2007).
[Crossref] [PubMed]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Perret, E.

E. Perret, N. Zerounian, S. David, and F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[Crossref]

Porter, N. E.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Rathi, M. K.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, and T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[Crossref]

Reimhult, E.

Reno, J. L.

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(13), 131105 (2009).
[Crossref]

Ritchie, D. A.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[Crossref] [PubMed]

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] [PubMed]

Rossi, 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(6885), 156–159 (2002).
[Crossref] [PubMed]

Saito, H.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[Crossref] [PubMed]

Sasaki, G.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[Crossref]

Scalari, G.

Scherer, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Schrenk, W.

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[Crossref]

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, and G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[Crossref] [PubMed]

A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, and G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
[Crossref] [PubMed]

Sergent, A. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[Crossref]

Shin, J. C.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, and T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[Crossref]

Sirigu, L.

Sivco, D. L.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[Crossref]

Skolnick, M. S.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Slusher, R. E.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[Crossref]

Soukoulis, C. M.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[Crossref] [PubMed]

Srinivasan, K.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

Stafford, C. A.

N. S. Wingreen and C. A. Stafford, “Quantum-dot cascade laser: proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33(7), 1170–1173 (1997).
[Crossref]

Stehr, D.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Strasser, G.

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, and K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[Crossref]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[Crossref]

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, and G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[Crossref] [PubMed]

A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, and G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
[Crossref] [PubMed]

Stroud, D.

D. J. Bergman and D. Stroud, “Physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[Crossref]

Suzuki, H.

M. Notomi, H. Suzuki, and T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
[Crossref]

Tamamura, T.

M. Notomi, H. Suzuki, and T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
[Crossref]

Tanaka, Y.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[Crossref] [PubMed]

Tennant, D. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

Timko, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[Crossref]

Tokuda, T.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[Crossref]

Tredicucci, A.

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] [PubMed]

Troccoli, M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

Tsvid, G.

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, and T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[Crossref]

Unterrainer, K.

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[Crossref]

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, and K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[Crossref]

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, and G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[Crossref] [PubMed]

A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, and G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
[Crossref] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[Crossref]

Vasic, B.

Wasilewski, Z. R.

Wilson, L. R.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Wingreen, N. S.

N. S. Wingreen and C. A. Stafford, “Quantum-dot cascade laser: proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33(7), 1170–1173 (1997).
[Crossref]

Winnerl, S.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

Yasuda, H.

H. Yasuda and I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. 47(3), 1632–1634 (2008).
[Crossref]

Yoshimoto, S.

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[Crossref] [PubMed]

Zederbauer, T.

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, and K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[Crossref]

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[Crossref]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[Crossref]

Zerounian, N.

E. Perret, N. Zerounian, S. David, and F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[Crossref]

Zhang, H.

Zibik, E. A.

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Zory, P.

C.-F. Hsu, J. -S. O, P. Zory, and D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

Appl. Opt. (1)

Appl. Phys. Lett. (7)

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002).
[Crossref]

S. Maëro, L.-A. de Vaulchier, Y. Guldner, C. Deutsch, M. Krall, T. Zederbauer, G. Strasser, and K. Unterrainer, “Magnetic-field assisted performance of InGaAs/GaAsSb terahertz quantum cascade lasers,” Appl. Phys. Lett. 103(5), 051116 (2013).
[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(13), 131105 (2009).
[Crossref]

C. Deutsch, H. Detz, M. Krall, M. Brandstetter, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Dopant migration effects in terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(20), 201102 (2013).
[Crossref]

M. Notomi, H. Suzuki, and T. Tamamura, “Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps,” Appl. Phys. Lett. 78(10), 1325–1327 (2001).
[Crossref]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).
[Crossref]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).
[Crossref]

IEEE J. Quantum Electron. (1)

N. S. Wingreen and C. A. Stafford, “Quantum-dot cascade laser: proposal for an ultralow-threshold semiconductor laser,” IEEE J. Quantum Electron. 33(7), 1170–1173 (1997).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

C.-F. Hsu, J. -S. O, P. Zory, and D. Botez, “Intersubband quantum-box semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6(3), 491–503 (2000).

J. Appl. Phys. (2)

H. Zhang, G. Scalari, J. Faist, L. A. Dunbar, and R. Houdré, “Design and fabrication technology for high performance electrical pumped terahertz photonic crystal band edge lasers with complete photonic band gap,” J. Appl. Phys. 108(9), 093104 (2010).
[Crossref]

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[Crossref]

J. Electron. Mater. (1)

M. K. Rathi, G. Tsvid, A. A. Khandekar, J. C. Shin, D. Botez, and T. F. Kuech, “Passivation of interfacial states for GaAs- and InGaAs/InP-based regrown nanostructures,” J. Electron. Mater. 38(10), 2023–2032 (2009).
[Crossref]

Jpn. J. Appl. Phys. (1)

H. Yasuda and I. Hosako, “Measurement of terahertz refractive index of metal with terahertz time-domain spectroscopy,” Jpn. J. Appl. Phys. 47(3), 1632–1634 (2008).
[Crossref]

Microelectron. Eng. (1)

E. Perret, N. Zerounian, S. David, and F. Aniel, “Complex permittivity characterization of benzocyclobutene for terahertz applications,” Microelectron. Eng. 85(11), 2276–2281 (2008).
[Crossref]

Nat. Mater. (1)

E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, “Long lifetimes of quantum-dot intersublevel transitions in the terahertz range,” Nat. Mater. 8(10), 803–807 (2009).
[Crossref] [PubMed]

Nature (2)

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] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[Crossref] [PubMed]

Opt. Express (10)

H. Zhang, G. Scalari, M. Beck, J. Faist, and R. Houdré, “Complex-coupled photonic crystal THz lasers with independent loss and refractive index modulation,” Opt. Express 19(11), 10707–10713 (2011).
[Crossref] [PubMed]

H. Zhang, L. A. Dunbar, G. Scalari, R. Houdré, and J. Faist, “Terahertz photonic crystal quantum cascade lasers,” Opt. Express 15(25), 16818–16827 (2007).
[Crossref] [PubMed]

A. Benz, Ch. Deutsch, G. Fasching, K. Unterrainer, A. M. Andrews, P. Klang, W. Schrenk, and G. Strasser, “Active photonic crystal terahertz laser,” Opt. Express 17(2), 941–946 (2009).
[Crossref] [PubMed]

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, and O. Painter, “Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap,” Opt. Express 15(10), 5948–5965 (2007).
[Crossref] [PubMed]

L. A. Dunbar, V. Moreau, R. Ferrini, R. Houdré, L. Sirigu, G. Scalari, M. Giovannini, N. Hoyler, and J. Faist, “Design, fabrication and optical characterization of quantum cascade lasers at terahertz frequencies using photonic crystal reflectors,” Opt. Express 13(22), 8960–8968 (2005).
[Crossref] [PubMed]

A. Benz, G. Fasching, Ch. Deutsch, A. M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, and G. Strasser, “Terahertz photonic crystal resonators in double-metal waveguides,” Opt. Express 15(19), 12418–12424 (2007).
[Crossref] [PubMed]

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(4), 3866–3876 (2012).
[Crossref] [PubMed]

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[Crossref] [PubMed]

B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
[Crossref] [PubMed]

M. I. Amanti, A. Bismuto, M. Beck, L. Isa, K. Kumar, E. Reimhult, and J. Faist, “Electrically driven nanopillars for THz quantum cascade lasers,” Opt. Express 21(9), 10917–10923 (2013).
[Crossref] [PubMed]

Phys. Rev. B Condens. Matter (1)

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B Condens. Matter 48(20), 14936–14943 (1993).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

P. Halevi, A. A. Krokhin, and J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82(4), 719–722 (1999).
[Crossref]

Proc. SPIE (1)

M. Krall, M. Brandstetter, C. Deutsch, H. Detz, T. Zederbauer, A. M. Andrews, W. Schrenk, G. Strasser, and K. Unterrainer, “Towards nanowire-based terahertz quantum cascade lasers: prospects and technological challenges,” Proc. SPIE 8640, 864018 (2013).
[Crossref]

Science (3)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref] [PubMed]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003).
[Crossref] [PubMed]

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).
[Crossref] [PubMed]

Solid State Phys. (1)

D. J. Bergman and D. Stroud, “Physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[Crossref]

Other (1)

T. Grange, “Nanowire terahertz quantum cascade lasers,” arXiv:1301.1258 [cond–mat.mes–hall] (2013).

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Figures (4)

Fig. 1
Fig. 1 Scaling of a pillar array from a photonic crystal to the effective medium regime. (a) Photonic band diagram of TM-modes calculated for infinitely long pillars in a hexagonal array with r/a = 0.45, ε1 = 13.32 (GaAs) [15], and ε2 = 2.45 (BCB) [16]. Reducing the size of the pillars, while keeping r/a constant, moves down the gain spectrum of the active material towards the effective medium regime. (b) Magnitude of the electric field at several points in the lowest band plotted on a linear scale. In contrast to a large confinement of the electric field in the pillars at the high symmetry points (M, K), practically no confinement is observed in the effective medium regime (A). The effective filling factor calculated using Eq. (2) decreases from 0.89 at the K-point to 0.75 at point ‘A’.
Fig. 2
Fig. 2 (a) Schematic illustration of the micropillar array terahertz laser. The densely packed pillar array is sandwiched between two metal layers and forms a ridge-waveguide. The space between the pillars is filled with a low-loss polymer. (b) Scanning electron microscope images of fabricated micropillar array lasers with pillar diameters of 5 µm. Inset: Facet of the laser ridge (top), and closer view of a micropillar before planarization (bottom).
Fig. 3
Fig. 3 (a) Comparison of the current-voltage (IV) characteristic of a bulk structure and micropillar arrays with various pillar diameters. The current density in the micropillar arrays is calculated using the physical dimensions of the pillars. Surface states are causing a partial carrier depletion in the micropillars, which significantly reduces the current density for small pillar diameters. The inset shows the effective diameters available for charge transport depending on the physical diameters of the micropillars, including a linear fit to the data. A surface depletion width of approximately 170 nm can be extracted from the decreasing current density. (b) Low-temperature light-current-voltage (LIV) characteristics of a 120 x 1000 x 10 µm micropillar array laser with a pillar size of 5 µm and a filling factor of 0.75 (r/a = 0.45). The current density is given as the density in the micropillars calculated from the measured current and the filling factor of the array.
Fig. 4
Fig. 4 Laser output spectra of a 120 x 1000 x 10 µm micropillar array laser with a pillar size of 5 µm and a filling factor of 0.75 (r/a = 0.45). The measurements are performed at a heat sink temperature of 5 K. (a) Overlay of the emission spectrum with the photonic band diagram. In contrast to photonic crystal lasers, high-symmetry points of the photonic lattice are far outside the gain region and no lasing is observed at these points. The emission frequency of approximately 4 THz corresponds to a normalized frequency (fa/c) of about 0.07. (b) The two dominant emission modes with slightly varying frequency close to the operation points of the two output maxima in the LI-curve of Fig. 3. The spectra are vertically shifted for clarity.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

ε eff = ε 1 η+ ε 2 (1η),
η eff = ε= ε 1 dr| E( r ) | dr| E( r ) | .

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