## Lateral distributed-feedback gratings for single-mode, high-power terahertz quantum-cascade lasers |

Optics Express, Vol. 20, Issue 10, pp. 11207-11217 (2012)

http://dx.doi.org/10.1364/OE.20.011207

Acrobat PDF (1235 KB)

### Abstract

We report on terahertz quantum-cascade lasers (THz QCLs) based on first-order lateral distributed-feedback (lDFB) gratings, which exhibit continuous-wave operation, high output powers (>8 mW), and single-mode emission at 3.3–3.4 THz. A general method is presented to determine the coupling coefficients of lateral gratings in terms of the coupled-mode theory, which demonstrates that large coupling strengths are obtained in the presence of corrugated metal layers. The experimental spectra are in agreement with simulations of the lDFB cavities, which take into account the reflective end facets.

© 2012 OSA

## 1. Introduction

1. 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**, 5890–5896 (2005). [CrossRef] [PubMed]

5. Y. Ren, J. N. Hovenier, R. Higgins, J. R. Gao, T. M. Klapwijk, S. C. Shi, B. Klein, T.-Y. Kao, Q. Hu, and J. L. Reno, “High-resolution heterodyne spectroscopy using a tunable quantum cascade laser around 3.5 THz,” Appl. Phys. Lett. **98**, 231109 (2011). [CrossRef]

6. H. Richter, M. Greiner-Bär, S. G. Pavlov, A. D. Semenov, M. Wienold, L. Schrottke, M. Giehler, R. Hey, H. T. Grahn, and H.-W. Hübers, “A compact, continuous-wave terahertz source based on a quantum-cascade laser and a miniature cryocooler,” Opt. Express **18**, 10177–10187 (2010). [CrossRef] [PubMed]

7. J. Faist, C. Gmachl, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “Distributed feedback quantum cascade lasers,” Appl. Phys. Lett. **70**, 2670–2672 (1997). [CrossRef]

8. G. P. Luo, C. Peng, H. Q. Le, S. S. Pei, W.-Y. Hwang, B. Ishaug, J. Um, J. N. Baillargeon, and C.-H. Lin, “Grating-tuned external-cavity quantum-cascade semiconductor lasers,” Appl. Phys. Lett. **78**, 2834–2636 (2001). [CrossRef]

9. J. Xu, J. M. Hensley, D. B. Fenner, R. P. Green, L. Mahler, A. Tredicucci, M. G. Allen, F. Beltram, H. E. Beere, and D. A. Ritchie, “Tunable terahertz quantum cascade lasers with an external cavity,” Appl. Phys. Lett. **91**, 121104 (2007). [CrossRef]

10. L. Mahler, A. Tredicucci, R. Köhler, F. Beltram, H. E. Beere, E. H. Linfield, and D. A. Ritchie, “High-performance operation of single-mode terahertz quantum cascade lasers with metallic gratings,” Appl. Phys. Lett. **87**, 181101 (2005). [CrossRef]

13. D. G. Allen, T. Hargett, J. L. Reno, A. A. Zinn, and M. C. Wanke, “Index tuning for precise frequency selection of terahertz quantum cascade lasers,” IEEE Photon. Technol. Lett. **23**, 30–32 (2011). [CrossRef]

14. S. Golka, C. Pflügl, W. Schrenk, and G. Strasser, “Quantum cascade lasers with lateral double-sided distributed feedback grating,” Appl. Phys. Lett. **86**, 111103 (2005). [CrossRef]

16. M. I. Amanti, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Low divergence Terahertz photonic-wire laser,” Opt. Express **18**, 6390–6395 (2010). [CrossRef] [PubMed]

15. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Distributed-feedback terahertz quantum-cascade lasers with laterally corrugated metal waveguides,” Opt. Lett. **30**, 2909–2911 (2005). [CrossRef] [PubMed]

17. 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 (London) **417**, 156–159 (2002). [CrossRef]

18. M. Rochat, A. Lassaad, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. **81**, 1381–1383 (2002). [CrossRef]

*n*-doped layer underneath the active region. Fabry-Pérot lasers based on this type of waveguide have shown to be beneficial over metal-metal waveguides with respect to output power and beam quality [19

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

20. H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. **43**, 2327–2335 (1972). [CrossRef]

## 2. Modeling of lateral gratings

*z*), where in the following Δ

*ε*(

*z*) denotes the modulation of the dielectric function with respect to a reference waveguide. In Fig. 1(a), a schematic diagram of an lDFB QCL with its two end facets is shown. The grating period Λ corresponds to the vacuum Bragg wavelength of

*λ*= 2Λ

_{B}*n/m*, where

*n*denotes the real part of the effective refractive index of the waveguide (

*n*

_{eff}=

*n*+

*ik*) and

*m*the grating order. Figure 1(b) depicts an lDFB mesa after dry etching.

*m*th-order grating are usually determined by two-dimensional integrals of the

*m*th Fourier components of Δ

*ε*weighted by the modal intensity profile of the corresponding reference waveguide (cf. Ref. [21]). For the integration, the change of the modal intensity profile between the two grating sections is assumed to be negligibly small. There are in general two complex coupling coefficients for the coupling of forward with backward and of backward with forward traveling waves. Here, only symmetric gratings are considered, for which the origin in the ridge direction

*z*can be chosen such that Δ

*ε*(

*z*) = Δ

*ε*(−

*z*). In this case, the two complex coupling coefficients can be subsumed into a single complex coupling coefficient

*K*+

*iK*, where the index coupling coefficient

_{g}*K*is positive and the gain coupling coefficient

*K*can be positive or negative due to a possible phase difference of 0 or

_{g}*π*between index and gain coupling.

22. A. Laakso, M. Dumitrescu, J. Viheriälä, J. Karinen, M. Suominen, and M. Pessa, “Optical modeling of laterally-corrugated ridge-waveguide gratings,” Opt. Quant. Electron. **40**, 907–920 (2008). [CrossRef]

*n*=

_{g}*n*), the expression for

*K*becomes a very simple analytic one: where Δ

*ε*= 2

*n*Δ

*n*denotes the difference of the dielectric constant between the sections. Equation (3) can be easily derived from the general Eqs. (1) and (2) cited in [22

22. A. Laakso, M. Dumitrescu, J. Viheriälä, J. Karinen, M. Suominen, and M. Pessa, “Optical modeling of laterally-corrugated ridge-waveguide gratings,” Opt. Quant. Electron. **40**, 907–920 (2008). [CrossRef]

15. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Distributed-feedback terahertz quantum-cascade lasers with laterally corrugated metal waveguides,” Opt. Lett. **30**, 2909–2911 (2005). [CrossRef] [PubMed]

22. A. Laakso, M. Dumitrescu, J. Viheriälä, J. Karinen, M. Suominen, and M. Pessa, “Optical modeling of laterally-corrugated ridge-waveguide gratings,” Opt. Quant. Electron. **40**, 907–920 (2008). [CrossRef]

*μ*m, Δ

*ε*= 0.2, and

*n*= 3.584, Eq. (3) results in

*K*= 6.23 cm

^{−1}. This is exactly the same value as obtained via the numerical determination of

*ω*

_{−}and

*ω*

_{+}for the corresponding one-dimensional photonic crystal, which confirms the validity of the photonic-crystal approach. Since a stack of homogeneous slabs is considered here, the numerical result for

*K*does not depend on the lateral and vertical dimensions of the simulated unit cell.

*x*= 0 (vanishing tangential magnetic or electric field, respectively). The grating period is 12.5

*μ*m, and the full width of the ridge is 120 and 107

*μ*m in the wide- and narrow-ridge section, respectively. The THz dielectric constants used in the simulations are basically the same as in Ref. [23

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

*Ga*

_{x}_{1−x}As, we take into account the contribution of bulk phonons, and we neglect free-carrier absorption in the active region. The different panels in Fig. 2(b) show the two perpendicular projections of the modal intensity for the

*ω*

_{−}and

*ω*

_{+}modes with the fundamental TM

_{00}symmetry. The

*ω*

_{+}mode is localized in the narrow-ridge section of the grating, and the mode profile is basically that of a Fabry-Pérot single-plasmon waveguide. The

*ω*

_{−}mode is localized mainly in the wide-ridge section, and the mode profile is significantly altered as compared to the

*ω*

_{+}mode. The intensity distribution exhibits features of a surface plasmon bound to a metal film of finite width [24

24. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B **61**, 10484–10503 (2000). [CrossRef]

*ω*

_{−}mode appears to couple weakly to the bottom contact metallization.

*ϕ*[cf. Fig. 1(a)]. In the case of cleaved facets, these are not known

_{F}*a priori*due to the limited accuracy of the cleaving process. This causes an uncertainty of the frequency values, which is approximately equal to the mode spacing of the corresponding Fabry-Pérot cavity.

## 3. Experimental results and discussion

_{0.25}Ga

_{0.75}As heterostructure reported as sample B in Ref. [25

25. M. Wienold, L. Schrottke, M. Giehler, R. Hey, W. Anders, and H. T. Grahn, “Low-threshold terahertz quantum-cascade lasers based on GaAs/Al_{0.25}Ga_{0.75}As heterostructures,” Appl. Phys. Lett. **97**, 071113 (2010). [CrossRef]

*μ*m. These are also the parameters, which we used for the simulations (neglecting a small technological gap of about 1

*μ*m between the top metallization and the etch mask).

*μ*m and as-cleaved facets are discussed. The corresponding Bragg frequencies fall within the emission range of 3.15–3.45 THz found for Fabry-Pérot lasers of the same wafer. Since the three laser stripes are located on the same die, they have all the same ridge length (1.454 mm). Figure 3(a) shows the light-current-voltage (

*L*-

*I*-

*V*) characteristics of the three lasers for driving currents up to 0.75 A (455 A cm

^{−2}). In this range, the emission of the lasers is dominated by a single spectral mode. Due to the large dissipated electrical power, only temperatures above 20 K can be maintained over the whole range of driving currents. The three lasers exhibit similar

*L*-

*I*-

*V*characteristics with threshold current densities

*J*

_{th}of 290, 290, and 270 A cm

^{−2}at 30 K for Λ = 12.4, 12.5, and 12.6

*μ*m, respectively. The maximum operating temperature is about 55 K for Λ = 12.4 and 12.5

*μ*m and about 60 K for Λ = 12.6

*μ*m. The slope efficiency at threshold (30 K) is approximately 30 mW/A for all three lasers. The output powers at a driving current of 0.75 A are 8.7, 8.0, and 8.7 mW at 30 K and 3.6, 3.3, and 4.8 mW at 50 K for Λ = 12.4, 12.5, and 12.6

*μ*m, respectively. For comparison, a Fabry-Pérot laser ridge of the same wafer with similar dimensions (0.10

*×*1.52 mm

^{2}) operated in cw mode up to 55 K. For this laser, values for the threshold current density, slope efficiency, and maximum cw output power at 30 K are 320 A cm

^{−2}, 20 mW/A, and 6.5 mW, respectively. The smaller threshold current densities of the lDFB QCLs in comparison with Fabry-Pérot QCLs are qualitatively explained by a smaller threshold gain as a consequence of the feedback provided by the grating in addition to the feedback of the reflective end facets. However, the effect is stronger than expected. While the levels of cw output power are comparable for lDFB and Fabry-Pérot laser ridges, the spectral power density for the lDFB QCLs is much higher due to single-mode operation.

6. H. Richter, M. Greiner-Bär, S. G. Pavlov, A. D. Semenov, M. Wienold, L. Schrottke, M. Giehler, R. Hey, H. T. Grahn, and H.-W. Hübers, “A compact, continuous-wave terahertz source based on a quantum-cascade laser and a miniature cryocooler,” Opt. Express **18**, 10177–10187 (2010). [CrossRef] [PubMed]

*μ*m laser consists mainly of a single lobe, covering approximately 80% of the power, for which we estimate a full width at half maximum divergence of about 24° in both, the lateral and the vertical, directions. The beam divergence appears to be comparable to the one of third-order DFB QCLs, for which values of 15 to 30° have been reported [16

16. M. I. Amanti, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Low divergence Terahertz photonic-wire laser,” Opt. Express **18**, 6390–6395 (2010). [CrossRef] [PubMed]

_{00}mode is plotted versus the frequency eigenvalues for the three lDFB QCLs with Λ = 12.4, 12.5, and 12.6

*μ*m. We have performed simulations either for a complex coupling coefficient or for a real coupling coefficient (

*K*= 0). The experimentally observed single-mode emission and the calculated longitudinal modes with the lowest threshold gain occur at almost the same frequencies, where the quantitative agreement appears to be better for the simulations with a real coupling coefficient. In this case, an agreement better than 9 GHz is found for all three lasers, while in the case of a complex coupling coefficient the calculated mode with the second lowest threshold gain coincides with the lasing frequency for Λ = 12.6

_{g}*μ*m. While the Bragg frequency (depicted as dashed lines in Fig. 5) decreases with increasing grating period, the finite facet reflectance and the different facet phases cause lasing in the longitudinal mode below the Bragg frequency for Λ = 12.4 and 12.6

*μ*m and above the Bragg frequency for Λ = 12.5

*μ*m. The differences in the calculated threshold gain explain the different experimentally observed threshold current densities. However, the calculation predicts the lowest threshold gain for Λ = 12.5

*μ*m, while experimentally the lowest value of

*J*

_{th}is found for Λ = 12.6

*μ*m [cf. Fig. 3(a)]. Differences between the experimental and simulated results are likely due to the uncertainty of the involved parameters such as the coupling coefficients. For instance, the occurrence of a small displacement between the etch mask and the metallization mask might result in a phase difference between the index and gain coupling, which has been neglected in the simulations.

_{00}mode, the situation becomes more complex for the multi-mode emission regime. In Fig. 4(b), the emission of a second mode at 3.40 THz for the laser with Λ = 12.5

*μ*m can be understood by the Stark shift of the gain with increasing bias, since the emission frequency agrees with the calculated frequency of the mode with the second lowest threshold gain. However, the multi-mode emission pattern for the highest driving current seems to exhibit a stop band between 3.40 and 3.50 THz. This cannot be explained by the spectral position and threshold gain of the longitudinal modes with TM

_{00}symmetry. A likely explanation is the presence of higher-order lateral modes such as TM

_{01}and TM

_{02}, for which the coupling coefficient is much larger and the Bragg frequency is increased due to the smaller effective index of these modes. For lasing of higher-order lateral modes in favor of the fundamental TM

_{00}mode, the threshold gain has to be smaller as compared to the TM

_{00}mode, i.e. the larger coupling coefficient has to compensate the higher waveguide losses.

## 4. Summary and conclusions

## 5. Appendix

*A*(

*z*) and

*B*(

*z*) denote the amplitudes of the forward and backward propagating wave, respectively.

*K*and

_{ab}*K*refer to the coupling coefficients of the forward and backward propagating mode, respectively, and Δ

_{ba}*β*=

*β*

_{0}−

*β*corresponds to the difference of the propagation constant

_{B}*β*

_{0}=

*ωn*

_{eff}

*/c*and the Bragg wavevector

*β*=

_{B}*π*/Λ. The coupled-mode equations in Eq. (4) are formally solved by with The latter equation is the dispersion relation for the coupled system of forward and backward propagating waves of a uniform grating of infinite length. The propagation constant of the coupled system are given by

*β*=

_{±}*π/*Λ

*± q*, while

*β*

_{0}and Δ

*β*refer to the reference waveguide. Note that

*q*,

*β*

_{0}, and Δ

*β*are complex quantities in the current notation due to the presence of gain and losses, while the frequency

*ω*is a real quantity.

*K*=

_{ab}*K*+

*iK*exp(

_{g}*iϕ*) and

_{g}*K*=

_{ba}*K*+

*iK*exp(−

_{g}*iϕ*) with

_{g}*K*denoting the index coupling coefficient,

*K*the gain coupling coefficient, and

_{g}*ϕ*the phase difference between index and gain coupling. We obtain the relation Here, only symmetric gratings are considered, for which the origin in the ridge direction

_{g}*z*can be chosen such that Δ

*ε*(

*z*) = Δ

*ε*(−

*z*). The only possible values for

*ϕ*are 0 and

_{g}*π*,

*K*= (

_{ab}K_{ba}*K ± iK*)

_{g}^{2}, where we chose the plus sign in the following by allowing for negative amplitudes

*K*. We rewrite Eq. (6) using

_{g}*ω*=

*β*

_{0}

*c/n*

_{eff}=

*β*

_{0}

*c/*(

*n*+

*ik*): In the following, the wavevector

*π*/Λ

*± q*is treated as a real quantity, which causes

*β*

_{0}and Δ

*β*to be real, while the frequency

*ω*becomes complex. The case

*q*= 0 correspond to the eigenfrequencies of a one-dimensional photonic crystal at the edge of the Brillouin zone. Assuming a symmetric grating with

*K*= (

_{ab}K_{ba}*K*+

*iK*)

_{g}^{2}, the complex frequencies of the two eigenmodes at

*q*= 0 are given by Eq. (1).

## Acknowledgments

## References and links

1. | 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 |

2. | H. Richter, A. D. Semenov, S. G. Pavlov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, K. S. Il’in, M. Siegel, and H.-W. Hübers, “Terahertz heterodyne receiver with quantum cascade laser and hot electron bolometer mixer in a pulse tube cooler,” Appl. Phys. Lett. |

3. | P. Khosropanah, W. Zhang, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, M. I. Amanti, G. Scalari, and J. Faist, “3.4 THz heterodyne receiver using a hot electron bolometer and a distributed feedback quantum cascade laser,” J. Appl. Phys. |

4. | D. Rabanus, U. U. Graf, M. Philipp, O. Ricken, J. Stutzki, B. Vowinkel, M. C. Wiedner, C. Walther, M. Fischer, and J. Faist, “Phase locking of a 1.5 Terahertz quantum cascade laser and use as a local oscillator in a heterodyne HEB receiver,” Opt. Express |

5. | Y. Ren, J. N. Hovenier, R. Higgins, J. R. Gao, T. M. Klapwijk, S. C. Shi, B. Klein, T.-Y. Kao, Q. Hu, and J. L. Reno, “High-resolution heterodyne spectroscopy using a tunable quantum cascade laser around 3.5 THz,” Appl. Phys. Lett. |

6. | H. Richter, M. Greiner-Bär, S. G. Pavlov, A. D. Semenov, M. Wienold, L. Schrottke, M. Giehler, R. Hey, H. T. Grahn, and H.-W. Hübers, “A compact, continuous-wave terahertz source based on a quantum-cascade laser and a miniature cryocooler,” Opt. Express |

7. | J. Faist, C. Gmachl, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “Distributed feedback quantum cascade lasers,” Appl. Phys. Lett. |

8. | G. P. Luo, C. Peng, H. Q. Le, S. S. Pei, W.-Y. Hwang, B. Ishaug, J. Um, J. N. Baillargeon, and C.-H. Lin, “Grating-tuned external-cavity quantum-cascade semiconductor lasers,” Appl. Phys. Lett. |

9. | J. Xu, J. M. Hensley, D. B. Fenner, R. P. Green, L. Mahler, A. Tredicucci, M. G. Allen, F. Beltram, H. E. Beere, and D. A. Ritchie, “Tunable terahertz quantum cascade lasers with an external cavity,” Appl. Phys. Lett. |

10. | L. Mahler, A. Tredicucci, R. Köhler, F. Beltram, H. E. Beere, E. H. Linfield, and D. A. Ritchie, “High-performance operation of single-mode terahertz quantum cascade lasers with metallic gratings,” Appl. Phys. Lett. |

11. | M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics |

12. | L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, and D. A. Ritchie, “High-power surface emission from terahertz distributed feedback lasers with a dual-slit unit cell,” Appl. Phys. Lett. |

13. | D. G. Allen, T. Hargett, J. L. Reno, A. A. Zinn, and M. C. Wanke, “Index tuning for precise frequency selection of terahertz quantum cascade lasers,” IEEE Photon. Technol. Lett. |

14. | S. Golka, C. Pflügl, W. Schrenk, and G. Strasser, “Quantum cascade lasers with lateral double-sided distributed feedback grating,” Appl. Phys. Lett. |

15. | B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Distributed-feedback terahertz quantum-cascade lasers with laterally corrugated metal waveguides,” Opt. Lett. |

16. | M. I. Amanti, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Low divergence Terahertz photonic-wire laser,” Opt. Express |

17. | 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 (London) |

18. | M. Rochat, A. Lassaad, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. |

19. | B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics |

20. | H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. |

21. | S. L. Chuang, |

22. | A. Laakso, M. Dumitrescu, J. Viheriälä, J. Karinen, M. Suominen, and M. Pessa, “Optical modeling of laterally-corrugated ridge-waveguide gratings,” Opt. Quant. Electron. |

23. | S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. |

24. | P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B |

25. | M. Wienold, L. Schrottke, M. Giehler, R. Hey, W. Anders, and H. T. Grahn, “Low-threshold terahertz quantum-cascade lasers based on GaAs/Al |

26. | A. Barkan, F. K. Tittel, D. M. Mittleman, R. Dengler, P. H. Siegel, G. Scalari, L. Ajili, J. Faist, H. E. Beere, E. H. Linfield, A. G. Davies, and D. A. Ritchie, “Linewidth and tuning characteristics of terahertz quantum cascade lasers,” Opt. Lett. |

**OCIS Codes**

(140.3070) Lasers and laser optics : Infrared and far-infrared lasers

(140.3490) Lasers and laser optics : Lasers, distributed-feedback

(140.5965) Lasers and laser optics : Semiconductor lasers, quantum cascade

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: December 15, 2011

Revised Manuscript: March 4, 2012

Manuscript Accepted: April 10, 2012

Published: May 1, 2012

**Citation**

M. Wienold, A. Tahraoui, L. Schrottke, R. Sharma, X. Lü, K. Biermann, R. Hey, and H. T. Grahn, "Lateral distributed-feedback gratings for single-mode, high-power terahertz quantum-cascade lasers," Opt. Express **20**, 11207-11217 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11207

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### References

- 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. Express13, 5890–5896 (2005). [CrossRef] [PubMed]
- H. Richter, A. D. Semenov, S. G. Pavlov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, K. S. Il’in, M. Siegel, and H.-W. Hübers, “Terahertz heterodyne receiver with quantum cascade laser and hot electron bolometer mixer in a pulse tube cooler,” Appl. Phys. Lett.93, 141108 (2008). [CrossRef]
- P. Khosropanah, W. Zhang, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, M. I. Amanti, G. Scalari, and J. Faist, “3.4 THz heterodyne receiver using a hot electron bolometer and a distributed feedback quantum cascade laser,” J. Appl. Phys.104, 113106 (2008). [CrossRef]
- D. Rabanus, U. U. Graf, M. Philipp, O. Ricken, J. Stutzki, B. Vowinkel, M. C. Wiedner, C. Walther, M. Fischer, and J. Faist, “Phase locking of a 1.5 Terahertz quantum cascade laser and use as a local oscillator in a heterodyne HEB receiver,” Opt. Express17, 1159–1168 (2009). [CrossRef] [PubMed]
- Y. Ren, J. N. Hovenier, R. Higgins, J. R. Gao, T. M. Klapwijk, S. C. Shi, B. Klein, T.-Y. Kao, Q. Hu, and J. L. Reno, “High-resolution heterodyne spectroscopy using a tunable quantum cascade laser around 3.5 THz,” Appl. Phys. Lett.98, 231109 (2011). [CrossRef]
- H. Richter, M. Greiner-Bär, S. G. Pavlov, A. D. Semenov, M. Wienold, L. Schrottke, M. Giehler, R. Hey, H. T. Grahn, and H.-W. Hübers, “A compact, continuous-wave terahertz source based on a quantum-cascade laser and a miniature cryocooler,” Opt. Express18, 10177–10187 (2010). [CrossRef] [PubMed]
- J. Faist, C. Gmachl, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “Distributed feedback quantum cascade lasers,” Appl. Phys. Lett.70, 2670–2672 (1997). [CrossRef]
- G. P. Luo, C. Peng, H. Q. Le, S. S. Pei, W.-Y. Hwang, B. Ishaug, J. Um, J. N. Baillargeon, and C.-H. Lin, “Grating-tuned external-cavity quantum-cascade semiconductor lasers,” Appl. Phys. Lett.78, 2834–2636 (2001). [CrossRef]
- J. Xu, J. M. Hensley, D. B. Fenner, R. P. Green, L. Mahler, A. Tredicucci, M. G. Allen, F. Beltram, H. E. Beere, and D. A. Ritchie, “Tunable terahertz quantum cascade lasers with an external cavity,” Appl. Phys. Lett.91, 121104 (2007). [CrossRef]
- L. Mahler, A. Tredicucci, R. Köhler, F. Beltram, H. E. Beere, E. H. Linfield, and D. A. Ritchie, “High-performance operation of single-mode terahertz quantum cascade lasers with metallic gratings,” Appl. Phys. Lett.87, 181101 (2005). [CrossRef]
- M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics3, 586–590 (2009). [CrossRef]
- L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, and D. A. Ritchie, “High-power surface emission from terahertz distributed feedback lasers with a dual-slit unit cell,” Appl. Phys. Lett.96, 191109 (2010). [CrossRef]
- D. G. Allen, T. Hargett, J. L. Reno, A. A. Zinn, and M. C. Wanke, “Index tuning for precise frequency selection of terahertz quantum cascade lasers,” IEEE Photon. Technol. Lett.23, 30–32 (2011). [CrossRef]
- S. Golka, C. Pflügl, W. Schrenk, and G. Strasser, “Quantum cascade lasers with lateral double-sided distributed feedback grating,” Appl. Phys. Lett.86, 111103 (2005). [CrossRef]
- B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Distributed-feedback terahertz quantum-cascade lasers with laterally corrugated metal waveguides,” Opt. Lett.30, 2909–2911 (2005). [CrossRef] [PubMed]
- M. I. Amanti, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Low divergence Terahertz photonic-wire laser,” Opt. Express18, 6390–6395 (2010). [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 (London)417, 156–159 (2002). [CrossRef]
- M. Rochat, A. Lassaad, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett.81, 1381–1383 (2002). [CrossRef]
- B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics1, 517–525 (2007). [CrossRef]
- H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys.43, 2327–2335 (1972). [CrossRef]
- S. L. Chuang, Physics of Photonic Devices (Wiley, New York, 2009), 2nd ed.
- A. Laakso, M. Dumitrescu, J. Viheriälä, J. Karinen, M. Suominen, and M. Pessa, “Optical modeling of laterally-corrugated ridge-waveguide gratings,” Opt. Quant. Electron.40, 907–920 (2008). [CrossRef]
- S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys.97, 053106 (2005). [CrossRef]
- P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B61, 10484–10503 (2000). [CrossRef]
- M. Wienold, L. Schrottke, M. Giehler, R. Hey, W. Anders, and H. T. Grahn, “Low-threshold terahertz quantum-cascade lasers based on GaAs/Al0.25Ga0.75As heterostructures,” Appl. Phys. Lett.97, 071113 (2010). [CrossRef]
- A. Barkan, F. K. Tittel, D. M. Mittleman, R. Dengler, P. H. Siegel, G. Scalari, L. Ajili, J. Faist, H. E. Beere, E. H. Linfield, A. G. Davies, and D. A. Ritchie, “Linewidth and tuning characteristics of terahertz quantum cascade lasers,” Opt. Lett.29, 575–577 (2004). [CrossRef] [PubMed]

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