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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 19 — Sep. 17, 2007
  • pp: 12418–12424
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Terahertz photonic crystal resonators in double-metal waveguides

A. Benz, G. Fasching, Ch. Deutsch, A.M. Andrews, K. Unterrainer, P. Klang, W. Schrenk, and G. Strasser  »View Author Affiliations


Optics Express, Vol. 15, Issue 19, pp. 12418-12424 (2007)
http://dx.doi.org/10.1364/OE.15.012418


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Abstract

We present the design and the fabrication of photonic crystals with a complete bandgap for TM-modes used as a resonator for terahertz quantum-cascade lasers (QCL), which are lasing around 2.7 THz. The emission of the devices with and without a photonic crystal shows a shift in the emission from the gain maximum to the bandgap of the crystal. The devices are built up by a core, which provides the optical gain, and by a surrounding photonic crystal, which acts as a frequency selective mirror. The whole device is processed into a double-metal waveguide.

© 2007 Optical Society of America

1. Introduction

Photonic crystals (PC) have shown their potential for an entirely new field of devices such as surface emitting lasers [1

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, 1374 (2003). [CrossRef] [PubMed]

], polarization independent detectors [2

2. S. Schartner, S. Golka, C. Pflügl, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, “Band structure mapping of photonic crystal intersubband detectors,” Appl. Phys. Lett. 89, 151107 (2006). [CrossRef]

] and single-mode optical fibers [3

3. J. C. Knight, T. A. Birks, P. S. J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547 (1996). [CrossRef] [PubMed]

, 4

4. T. A. Birks, Y. D. West, and P. S. J. Russel, “Endlessly single mode photonic crystal fiber,” Opt. Lett. 22, 961 (1997). [CrossRef] [PubMed]

]. A precise control of the propagation properties for desired frequencies can be designed. To achieve compact sources, the direct integration of the PCs into the devices is the most promising solution. The integration of PCs into classical bandgap lasers is limited due to the strongly increased leakage current and the surface recombination, which are both caused by the enlarged surface of the device in a PC. The quantum-cascade laser (QCL), first reported by Faist [5

5. J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Lasers,” Science 264, 553 (1994). [CrossRef] [PubMed]

], doesn’t have these drawbacks. QCLs are based on inter-subband transitions, which makes them unipolar devices, and therefore have no increased surface recombination. Also, the in-plane emission of the light allows for simple processing of a PC with the standard planar processing technology, which is nowadays a mature and relatively inexpensive technology. These reasons make the QCLs ideal devices for the integration of PCs.

Terahertz (THz) QCLs have reached a high grade of maturity since the first publication by Köhler et al. [6

6. R. Köhler, A. Tredicucci, H. E. Beere, E. H. Lienfield, A. G. Davis, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature (London) 417, 156 (2002). [CrossRef]

]. The available frequencies are now as low as 0.84 THz [7

7. G. Scalari, C. Walther, H. Beere, D. Ritchie, and J. Faist, “Laser emission at 830 and 960 GHz from quantum cascade lasers,” presented at the 9th International Conference on Intersubband Transition in Quantum Wells, Ambleside, Cumbria, U.K., 9-14 September 2007.

], threshold current densities of only 1 A/cm 2 are achievable [8

8. G. Scalari, S. Blaser, J. Faist, H. Beere, E. Linfield, and D. Ritchie, “Terahertz Emission from Quantum Cascade Lasers in the Quantum Hall Regime: Evidence of Many Body Resonances and Localization Effects,” Phys. Rev. Lett. 93, 237403 (2004). [CrossRef] [PubMed]

], the maximum working temperature has been raised to 164 K [9

9. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express 13, 3331 (2004). [CrossRef]

] and peak output powers of 248 mW can be generated [10

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

]. The lasing from discs with sub-wavelength diameters based on high confinement, double-metal waveguides has been demonstrated [11

11. 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, 091113 (2007). [CrossRef]

, 12

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

, 13

13. G. Fasching, V. Tamosiunas, A. Benz, A. M. Andrews, K. Unterrainer, R. Zobl, T. Roch, W. Schrenk, and G. Strasser, “Sub-wavelength microdisk and microring terahertz quantum-cascade lasers,” IEEE J. Quantum Elect. (to be published).

]. This fast development has paved the way for applications like a local oscillator for heterodyne detection [14

14. H.-W. Hübers, S. G. Pavlov, A. D. Semenov, R. Köhler, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and E. H. Linfield, “Terahertz quantum cascade laser as local oscillator in a heterodyne receiver,” Opt. Express 13, 5890 (2005). [CrossRef] [PubMed]

, 15

15. J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshev, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Terahertz heterodyne receiver based on a quantum cascade laser and a superconducting bolometer,” Appl. Phys. Lett. 86, 244104 (2005). [CrossRef]

], real time imaging [16

16. A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Real-time terahertz imaging over a standoff distance (>25 meters),” Appl. Phys. Lett. 89, 141125 (2006). [CrossRef]

] and gas phase spectroscopy [17

17. H.-W. Hübers, S. G. Pavlov, H. Richter, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, and D. A. Ritchie, “High-resolution gas phase spectroscopy with distributed feedback terahertz quantum cascade lasers,” Appl. Phys. Lett. 89, 061115 (2006). [CrossRef]

].

The integration of PCs into the active region of THz-QCLs profits from the mature QCL technology and also from the wavelength, typically 100 µm, as the period of the PC has to be in the range of the wavelength. That makes it possible to use standard optical lithography with a resolution of approximately 0.5 µm to process the structures. Resonators based on PCs have been analyzed theoretically [18

18. 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. Exp. 15, 5948 (2007). [CrossRef]

] and have already been used successfully for mid-IR QCLs [1

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, 1374 (2003). [CrossRef] [PubMed]

, 19

19. D. M. Tennant, R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, F. Capasso, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Fabrication methods for a quantum cascade photonic crystal surface emitting laser,” J. Vac. Sci. Technol. B 21, 2907 (2003). [CrossRef]

, 20

20. K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” Appl. Phys. Lett. 84, 4146 (2004). [CrossRef]

] and THz-QCLs [21

21. G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101, 081726 (2007). [CrossRef]

]. The previously used PC did not have a full bandgap for TM-modes, but the devices did lase at band edges at high-symmetry points in the band structure. At these points the group velocity is very low, which means that the modes are localized inside the resonator. This corresponds to a high feedback for these frequencies. Due to the narrow stop band the devices mostly lase single mode. The integration of PCs with a full bandgap for TM-modes in the active region of THz-QCLs with a surface plasmon waveguide has been reported by Dunbar et al. [22

22. L. A. Dunbar, V. Moreau, R. Ferrini, R. Houdr, 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, 8960 (2005). [CrossRef] [PubMed]

], but due to the confinement of 0.35 of the surface plasmon waveguide, the mode is guided mostly in the substrate and not in the PC. The mode mismatch between the pillars and the surrounding air leads to losses due to out of plane scattering. Nonetheless, the devices showed stable single mode emission in the whole dynamic range of the QCL.

Here we present the integration of a PC with a complete bandgap for TM-modes into a THz-QCL. The PC is embedded in the double-metal waveguide of the QCL, therefore the confinement of the mode in the PC is nearly 100 %. PCs can further reduce the losses for a certain frequency range due to their high reflectivity for frequencies within the bandgap. If the gain maximum of the active region and the bandgap of the PC overlap, no changes in the emission are observable. If they don’t overlap, the effects on the spectra are dramatic. The modes are shifted from the gain maximum into the bandgap of the PC. The frequencies in the gain maximum experience now higher losses due to the increased transmission of the PC. Therefore the emission can be tuned to nearly any frequency in the whole gain region of the active zone and allows lasing beside the gain maximum.

2. Design and fabrication

The PCs in our measurements are built up by dielectric rods surrounded by air. Such structures have a complete bandgap for TM-modes [23

23. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751 (1999). [CrossRef]

], which is the polarization of the inter-subband transitions in a QCL. The PC has been processed by standard planar technology resulting in a 2-dimensional (2D) PC, therefore the light can only be confined in 2D. The confinement in the vertical direction is provided by a slab waveguide. Though the waveguide creates a 3-dimensional (3D) problem, for the simulation of the band structure of the PC only a 2D lattice of infinitely high, dielectric rods surrounded by air has been used. The accuracy of the 2D-model is excellent due to the strong confinement in the vertical direction, only the first order mode can propagate. Also the out of plane leakage, from which a dielectric slab waveguide suffers heavily [23

23. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751 (1999). [CrossRef]

], is suppressed by the uninterrupted metal layers. Therefore, the situation inside the double-metal waveguide is very close to the ideal 2D system. Direct measurements of the band structure of 2D-PCs embedded in a plasmonic waveguide with a confinement of 0.87, a value comparable to our confinement, prove the excellent agreement with the calculated 2D band structure [2

2. S. Schartner, S. Golka, C. Pflügl, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, “Band structure mapping of photonic crystal intersubband detectors,” Appl. Phys. Lett. 89, 151107 (2006). [CrossRef]

].

All the PCs used for our measurements have a ratio of r/a of 0.3, where r is the radius of the pillars and a the period of the crystal. Four different periods of the PC, from 22.18 to 35.49 µm, have been processed. The refractive index used for the simulation is 3.9, this value has been obtained by measurements on distributed feedback structures with the same waveguide and is a typical value for the simulation of PCs in the THz spectral region [22

22. L. A. Dunbar, V. Moreau, R. Ferrini, R. Houdr, 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, 8960 (2005). [CrossRef] [PubMed]

]. A simulated band structure, using the MIT Photonic-Bands [24

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

], is shown in Fig. 1(a). The first bandgap spans from 0.2 to 0.28, the second one from 0.37 to 0.48 in terms of the normalized frequency f·a/c, where f is the frequency and c the speed of light.

Fig. 1. A calculated band structure of the 2D-PC and a schematic of the real device. (a) The plane wave expansion method is used for the simulation. The first two bandgaps for TM-modes are shown, the first one spans from 0.2 to 0.28 [fa/c], the second one from 0.37 to 0.48 [fa/c]. (b) A schematic of the device. The core is surrounded by one period of the PC, corresponding to two rows of pillars. The double-metal waveguide embeds the core and the PC. The inset is showing the principal crystallographic directions in a triangular lattice.
Fig. 2. Schematics of the processing steps (a) after the first RIE etching and (b) after the wafer bonding. The light gray part is the active region, the red one the etch stop layer and the dark gray one the substrate. (a) The core and the PC are etched 10 µm into the active region, 5 µm remain unprocessed. (b) After the substrate removal, gold is deposited on the active region, it is used as a self-aligned etch mask for the second RIE step.

The resonators for our devices are built up by a hexagonal core, which provides the necessary optical gain, and only one unit cell of the PC, corresponding to two rows of pillars, which surround the core. The side length of the core is 250 to 350 µm. A schematic of the devices is shown in Fig. 1(b). The PC acts as a frequency selective mirror, which provides the positive feedback.

Fig. 3. SEM-images of the RIE etched devices and spectra from the reference devices. (a) A fully processed resonator. The top-gold has been used as self-aligned etch mask for the RIE etching. (b) The spectra of the two reference cavities. Sample (1) shows modes between 2.8 and 2.9 THz, sample (2) between 2.45 and 2.7 THz. By applying higher fields, no additional modes are observable.

For the processing various metal deposition steps and reactive ion etching (RIE) steps are required. First gold is sputtered onto the active region defining the core and the PC. A 400 nm thick SiNx layer covers the whole structure and is used as a mask for the first RIE step. This defines the core and the PC at the same time. The structure is etched 10 µminto the active region of the QCL. A 5 µm thin layer of active region remains unprocessed, a schematic after this etching is shown in Fig. 2(a). The QCL is then processed into a double-metal waveguide using a gold-gold thermo-compression bonding [25

25. 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, 211112 (2005). [CrossRef]

]. After the substrate removal, the top-contact can be structured by photo-lithography and gold can be sputtered onto the active region. The 5 µm thin membrane supports the gold, a schematic is shown in Fig. 2(b). This gold is used as a self-aligned etch-mask for the second RIE step, which removes the spare material and finally defines the resonator, a SEM picture of the processed device is shown in Fig. 3(a). Thereby, the core and the PC are embedded in the double-metal waveguide. This results in facet emitting devices as the top and the bottom metal layer are uninterrupted. The waveguide has a strong, optical confinement of the mode in the vertical direction. Therefore the mode is forced to propagate through the PC, no mode spreading into the substrate or leakage through the surface is possible.

Two different samples have been used to fabricate the devices. The active regions are built up by GaAs/Al0.15Ga0.85As heterostructure. Both samples have been grown by molecular beam epitaxy and are based on the longitudinal-optical phonon depopulation of the lower laser state [26

26. B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015 (2002). [CrossRef]

]. The grown sequence is 9.2/3.0/15.5/4.1/6.6/2.7/8.0/5.5 nm where the barriers are marked with bold letters. The two samples differ in the doping density, sample (1) has a sheet density of 8.2×109 cm -2, sample (2) of 5.4×109 cm-2. The active regions consist of 271 cascades each which results in a total thickness of 15 µm. A detailed description of the active regions can be found in reference [27

27. A. Benz, G. Fasching, A. M. Andrews, M. Martl, K. Unterrainer, T. Roch, W. Schrenk, S. Golka, and G. Strasser, “The influence of doping on the performance of terahertz quantum-cascade lasers,” Appl. Phys. Lett. 90, 101107 (2007). [CrossRef]

].

3. Experimental results

The measurements have been performed in pulsed mode operation with a pulse length of 100 ns and a repetition rate of 5 kHz at liquid-He temperature. Two different types of cavities have been processed. The reference cavities are built up only by the hexagonally shaped core, but no surrounding PC. These cavities lase in the frequency range where the active region provides the maximum gain, therefore the effect of the photonic crystal can be isolated. Spectra of the two reference cavities are shown in Fig. 3(b), Sample (1) emits between 2.8 and 2.9 THz, sample (2) between 2.45 and 2.7 THz.

Fig. 4. Spectra of both samples with the periods (a) 22.18 µm and (b) 26.62 µm. The gray shaded area shows the bandgap of the PC. (a) The modes of sample (1) compared to the reference cavity are not changed as they already lie within the bandgap. The spectrum of sample (2) is blue shifted to 2.7 THz and lies now in the gap. The side length of the core is 266.2 µm. (b) Both samples show the same modes as the reference cavities as they lie in the gap. The core has a side length of 213.0 µm.
Fig. 5. Spectra of both samples with the periods (a) 31.05 µm and (b) 35.49 µm. The gray shaded area shows the bandgap of the PC. (a) Sample (1) lases at the band edge at the K-point between the first and the second bandgap. Sample (2) shows nearly the same modes as the reference cavity as they are still in the gap. The core has a side length of 372.6 µm. (b) The emission of sample (1) is strongly blue shifted to 3.2 THz, the devices lases in the second bandgap. Sample (2) shows two lasing modes, one at the K-point at 2.64 THz and another one at 2.52 THz, which can be assigned to the flat band region next to the K-point. The side length of the core is 283.9 µm.

By surrounding the core with a PC, the behavior can be changed strongly. If the modes of the reference cavities lie within the bandgap of the PC, the devices emit in the same frequency range. That is not surprising as the active region provides the highest gain and the mirror works best. For a period of 26.62 µm the bandgap overlaps with the gain maximum for both samples, shown in Fig. 4(b). The same is true for sample (1) with a period of 22.18 µm (Fig. 4(a))and sample (2) with a period of 31.05 µm (Fig. 5(b)). All these devices show modes in the same frequency range as the reference cavities.

But if they don’t overlap, the emission is shifted into the bandgap, where the mirror has the smallest losses. Sample (2) surrounded by a PC with a period of 22.18 µm (Fig. 4(a)) shows a blue shift of the emission. The modes visible in the reference spectrum disappear and a new mode at 2.7 THz appears, which corresponds to 0.2 [fa/c]. The emission is shifted to the lower edge of the bandgap. Especially remarkable is the spectrum obtained from sample (1) surrounded by a PC with a period of 35.49 µm (Fig. 5(b)). It shows a weak lasing mode at 3.2 THz which is far off the gain maximum at 2.8 THz. The reference cavity doesn’t show any hints of lasing at this frequency due to the low gain. This mode corresponds to 0.377 [fa/c], which is in the second bandgap of the PC.

By changing the period it is also possible to obtain lasing at high symmetry points. At these points the band structure shows flat band regions which correspond to a low group velocity and therefore to a high feedback. Sample (1) with a period of 31.05 µm (Fig. 5(a)) and sample (2) with a period of 35.49 µm (Fig. 5(b)) show both lasing at the K-point at 0.31 [fa/c]. The modes of sample (1) are blue shifted to 3 THz and are now outside the gain maximum. Sample (2) is lasing in the frequency region of the gain maximum but only at frequencies which can be assigned to the flat band regions of the PC.

The various periods show nicely how the emission of a THz-QCL can be tuned through the gain region. The strong feedback of the PC with a complete bandgap for TM-modes allows only one period of the PC, corresponding to two rows of pillars, to be used to achieve the desired effect. The modes in all cavities, with and without the PC, can be identified as possible resonator modes of the hexagonally shaped core. The three dominant types of modes in hexagon are: Fabry-Perot, triangular and hexagonal modes. They can be distinguished by the mode position and the spacing. All observed modes can be assigned to one of the possible mode types in the resonator. This means that the PC is not creating new modes but it is working as a frequency selective mirror. The feedback for modes in the bandgap is improved because these modes have lower mirror losses, therefore the lasing of these modes is enhanced. The samples processed with two periods of the PC, corresponding to four rows of pillars, show the same shift in the spectra. The devices don’t show single mode emission in general due to the broad bandgap of the PC and the wide gain region. The agreement between the 2D calculations and measured spectra is excellent. All devices are lasing either in the bandgap or in flat band regions.

4. Conclusion

We have designed and processed THz-QCLs with a PC acting as a frequency selective mirror. The PC has a complete bandgap for TM-modes. Four different periods have been processed. The devices are lasing in the PC bandgap or at the band edges of the band structure. The PC shifts the emission from the maximum gain of the active region to the frequency range where the mirror has the highest reflectivity, i.e. into the bandgap of the PC. Especially remarkable is the spectrum obtained from sample (1) and the PC with a period of 35.49 µm (Fig. 5(b)), which showed lasing far away from the gain maximum in the second bandgap of the PC. For the vertical confinement a double-metal waveguide has been used, therefore no mode leakage into the substrate or scattering losses through the surface is possible. This waveguide also forces the light to propagate through the PC. To achieve the mentioned effects it is enough to surround the core by only one period of PC. The devices have not shown single mode emission in general as the PCs have provided a broad stop band.

This work was partly supported by the Austrian Scientific Fund FWF (SFB-ADLIS), the Austrian nanoinitative project PLATON, the EC (TERANOVA, POISE) and the Society for Microelectronics (GME, Austria).

References and links

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, 1374 (2003). [CrossRef] [PubMed]

2.

S. Schartner, S. Golka, C. Pflügl, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, “Band structure mapping of photonic crystal intersubband detectors,” Appl. Phys. Lett. 89, 151107 (2006). [CrossRef]

3.

J. C. Knight, T. A. Birks, P. S. J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547 (1996). [CrossRef] [PubMed]

4.

T. A. Birks, Y. D. West, and P. S. J. Russel, “Endlessly single mode photonic crystal fiber,” Opt. Lett. 22, 961 (1997). [CrossRef] [PubMed]

5.

J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Lasers,” Science 264, 553 (1994). [CrossRef] [PubMed]

6.

R. Köhler, A. Tredicucci, H. E. Beere, E. H. Lienfield, A. G. Davis, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature (London) 417, 156 (2002). [CrossRef]

7.

G. Scalari, C. Walther, H. Beere, D. Ritchie, and J. Faist, “Laser emission at 830 and 960 GHz from quantum cascade lasers,” presented at the 9th International Conference on Intersubband Transition in Quantum Wells, Ambleside, Cumbria, U.K., 9-14 September 2007.

8.

G. Scalari, S. Blaser, J. Faist, H. Beere, E. Linfield, and D. Ritchie, “Terahertz Emission from Quantum Cascade Lasers in the Quantum Hall Regime: Evidence of Many Body Resonances and Localization Effects,” Phys. Rev. Lett. 93, 237403 (2004). [CrossRef] [PubMed]

9.

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express 13, 3331 (2004). [CrossRef]

10.

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

11.

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, 091113 (2007). [CrossRef]

12.

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

13.

G. Fasching, V. Tamosiunas, A. Benz, A. M. Andrews, K. Unterrainer, R. Zobl, T. Roch, W. Schrenk, and G. Strasser, “Sub-wavelength microdisk and microring terahertz quantum-cascade lasers,” IEEE J. Quantum Elect. (to be published).

14.

H.-W. Hübers, S. G. Pavlov, A. D. Semenov, R. Köhler, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and E. H. Linfield, “Terahertz quantum cascade laser as local oscillator in a heterodyne receiver,” Opt. Express 13, 5890 (2005). [CrossRef] [PubMed]

15.

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshev, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Terahertz heterodyne receiver based on a quantum cascade laser and a superconducting bolometer,” Appl. Phys. Lett. 86, 244104 (2005). [CrossRef]

16.

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Real-time terahertz imaging over a standoff distance (>25 meters),” Appl. Phys. Lett. 89, 141125 (2006). [CrossRef]

17.

H.-W. Hübers, S. G. Pavlov, H. Richter, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, and D. A. Ritchie, “High-resolution gas phase spectroscopy with distributed feedback terahertz quantum cascade lasers,” Appl. Phys. Lett. 89, 061115 (2006). [CrossRef]

18.

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. Exp. 15, 5948 (2007). [CrossRef]

19.

D. M. Tennant, R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, F. Capasso, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Fabrication methods for a quantum cascade photonic crystal surface emitting laser,” J. Vac. Sci. Technol. B 21, 2907 (2003). [CrossRef]

20.

K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” Appl. Phys. Lett. 84, 4146 (2004). [CrossRef]

21.

G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101, 081726 (2007). [CrossRef]

22.

L. A. Dunbar, V. Moreau, R. Ferrini, R. Houdr, 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, 8960 (2005). [CrossRef] [PubMed]

23.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751 (1999). [CrossRef]

24.

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

25.

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, 211112 (2005). [CrossRef]

26.

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82, 1015 (2002). [CrossRef]

27.

A. Benz, G. Fasching, A. M. Andrews, M. Martl, K. Unterrainer, T. Roch, W. Schrenk, S. Golka, and G. Strasser, “The influence of doping on the performance of terahertz quantum-cascade lasers,” Appl. Phys. Lett. 90, 101107 (2007). [CrossRef]

OCIS Codes
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: July 17, 2007
Revised Manuscript: August 17, 2007
Manuscript Accepted: August 17, 2007
Published: September 14, 2007

Citation
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, 12418-12424 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-19-12418


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References

  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, 1374 (2003). [CrossRef] [PubMed]
  2. S. Schartner, S. Golka, C. Pfl¨ugl,W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, "Band structure mapping of photonic crystal intersubband detectors," Appl. Phys. Lett. 89, 151107 (2006). [CrossRef]
  3. J. C. Knight, T. A. Birks, P. S. J. Russel, and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt. Lett. 21, 1547 (1996). [CrossRef] [PubMed]
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  5. J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, "Quantum Cascade Lasers," Science 264, 553 (1994). [CrossRef] [PubMed]
  6. R. K¨ohler, A. Tredicucci, H. E. Beere, E. H. Lienfield, A. G. Davis, D. A. Ritchie, R. C. Iotti, and F. Rossi, "Terahertz semiconductor-heterostructure laser," Nature (London) 417, 156 (2002).Q1 [CrossRef]
  7. G. Scalari, C. Walther, H. Beere, D. Ritchie, and J. Faist, "Laser emission at 830 and 960 GHz from quantum cascade lasers," presented at the 9th International Conference on Intersubband Transition in Quantum Wells, Ambleside, Cumbria, U.K., 9-14 September 2007.
  8. G. Scalari, S. Blaser, J. Faist, H. Beere, E. Linfield, and D. Ritchie, "Terahertz Emission from Quantum Cascade Lasers in the Quantum Hall Regime: Evidence of Many Body Resonances and Localization Effects," Phys. Rev. Lett. 93, 237403 (2004). [CrossRef] [PubMed]
  9. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode," Opt. Express 13, 3331 (2004). [CrossRef]
  10. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "High-power terahertz quantum-cascade lasers," Electron. Lett. 42, 89 (2006). [CrossRef]
  11. 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, 091113 (2007). [CrossRef]
  12. L. A. Dunbar, R. Houdr, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, "Small optical volume terahertz emitting microdisk quantum cascade lasers," Appl. Phys. Lett. 90, 141114 (2007). [CrossRef]
  13. G. Fasching, V. Tamosiunas, A. Benz, A. M. Andrews, K. Unterrainer, R. Zobl, T. Roch, W. Schrenk, and G. Strasser, "Sub-wavelength microdisk and microring terahertz quantum-cascade lasers," IEEE J. Quantum Elect. (to be published).Q2
  14. H.-W. H¨ubers, S. G. Pavlov, A. D. Semenov, R. K¨ohler, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and E. H. Linfield, "Terahertz quantum cascade laser as local oscillator in a heterodyne receiver," Opt. Express 13, 5890 (2005).Q3 [CrossRef] [PubMed]
  15. J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshev, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Terahertz heterodyne receiver based on a quantum cascade laser and a superconducting bolometer," Appl. Phys. Lett. 86, 244104 (2005). [CrossRef]
  16. A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, "Real-time terahertz imaging over a standoff distance (>25 meters)," Appl. Phys. Lett. 89, 141125 (2006). [CrossRef]
  17. H.-W. H¨ubers, S. G. Pavlov, H. Richter, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, and D. A. Ritchie, "High-resolution gas phase spectroscopy with distributed feedback terahertz quantum cascade lasers," Appl. Phys. Lett. 89, 061115 (2006).Q4 [CrossRef]
  18. 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. Exp. 15, 5948 (2007).Q5 [CrossRef]
  19. D. M. Tennant, R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, F. Capasso, A. M. Sergent, D. L. Sivco, and A. Y. Cho, "Fabrication methods for a quantum cascade photonic crystal surface emitting laser," J. Vac. Sci. Technol. B 21, 2907 (2003). [CrossRef]
  20. K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, M. Troccoli, and F. Capasso, "Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser," Appl. Phys. Lett. 84, 4146 (2004). [CrossRef]
  21. G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, "Multi-wavelength operation and vertical emission in THz quantum-cascade lasers," J. Appl. Phys. 101, 081726 (2007). [CrossRef]
  22. L. A. Dunbar, V. Moreau, R. Ferrini, R. Houdr, 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, 8960 (2005). [CrossRef] [PubMed]
  23. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751 (1999). [CrossRef]
  24. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173 (2001). [CrossRef] [PubMed]
  25. 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, 211112 (2005). [CrossRef]
  26. B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, "3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation," Appl. Phys. Lett. 82, 1015 (2002). [CrossRef]
  27. A. Benz, G. Fasching, A. M. Andrews, M. Martl, K. Unterrainer, T. Roch, W. Schrenk, S. Golka, and G. Strasser, "The influence of doping on the performance of terahertz quantum-cascade lasers," Appl. Phys. Lett. 90, 101107 (2007). [CrossRef]

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