Abstract

We report on the development of a compact, easy-to-use terahertz radiation source, which combines a quantum-cascade laser (QCL) operating at 3.1 THz with a compact, low-input-power Stirling cooler. The QCL, which is based on a two-miniband design, has been developed for high output and low electrical pump power. The amount of generated heat complies with the nominal cooling capacity of the Stirling cooler of 7 W at 65 K with 240 W of electrical input power. Special care has been taken to achieve a good thermal coupling between the QCL and the cold finger of the cooler. The whole system weighs less than 15 kg including the cooler and power supplies. The maximum output power is 8 mW at 3.1 THz. With an appropriate optical beam shaping, the emission profile of the laser is fundamental Gaussian. The applicability of the system is demonstrated by imaging and molecular-spectroscopy experiments.

© 2010 OSA

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    [CrossRef]

2010

L. Schrottke, M. Giehler, M. Wienold, R. Hey, and H. T. Grahn, “Compact model for the efficient simulation of the optical gain and transport properties in THz quantum-cascade lasers,” Semicond. Sci. Technol. 25(4), 045025 (2010).
[CrossRef]

H. Richter, S. G. Pavlov, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and H.-W. Hübers, “Sub-megahertz frequency stabilization of a terahertz quantum cascade laser to a molecular absorption line,” Appl. Phys. Lett. 96(7), 071112 (2010).
[CrossRef]

2009

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 17(3), 1159–1168 (2009).
[CrossRef] [PubMed]

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

M. Wienold, L. Schrottke, M. Giehler, R. Hey, W. Anders, and H. T. Grahn, “Low-voltage terahertz quantum-cascade lasers based on LO-phonon-assisted interminiband transitions,” Electron. Lett. 45(20), 1030–1031 (2009).
[CrossRef]

2008

H.-W. Hübers, “Terahertz Heterodyne Receivers,” IEEE J. Sel. Top. Quantum Electron. 14(2), 378–391 (2008).
[CrossRef]

H. Richter, A. D. Semenov, S. Pavlov, L. Mahler, A. Tredicucci, K. 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(14), 141108 (2008).
[CrossRef]

2007

2006

K. L. Nguyen, M. L. Johns, L. F. Gladden, C. H. Worrall, P. Alexander, H. E. Beere, M. Pepper, D. A. Ritchie, J. Alton, S. Barbieri, and E. H. Linfield, “Three-dimensional imaging with a terahertz quantum cascade laser,” Opt. Express 14(6), 2123–2129 (2006).
[CrossRef] [PubMed]

A. W. M. Lee, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320×240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18(13), 1415–1417 (2006).
[CrossRef]

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(14), 141125 (2006).
[CrossRef]

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 a distributed feedback terahertz quantum cascade laser,” Appl. Phys. Lett. 89(6), 061115 (2006).
[CrossRef]

E. Bründermann, M. Havenith, G. Scalari, M. Giovannini, J. Faist, J. Kunsch, L. Mechold, and M. Abraham, “Turn-key compact high temperature terahertz quantum cascade lasers: imaging and room temperature detection,” Opt. Express 14(5), 1829–1841 (2006).
[CrossRef] [PubMed]

2005

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

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(15), 5890–5896 (2005).
[CrossRef] [PubMed]

A. M. Veprik, S. V. Riabzev, G. S. Vilenchik, and N. Pundak, “Ultra-low vibration split Stirling linear cryogenic cooler with a dynamically counterbalanced pneumatically driven expander,” Cryogenics 45(2), 117–122 (2005).
[CrossRef]

L. L. Bonilla and H. T. Grahn, “Nonlinear dynamics of semiconductor superlattices,” Rep. Prog. Phys. 68(3), 577–683 (2005).
[CrossRef]

2004

2002

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]

Abraham, M.

Adam, A. J. L.

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Alexander, P.

Alton, J.

Anders, W.

M. Wienold, L. Schrottke, M. Giehler, R. Hey, W. Anders, and H. T. Grahn, “Low-voltage terahertz quantum-cascade lasers based on LO-phonon-assisted interminiband transitions,” Electron. Lett. 45(20), 1030–1031 (2009).
[CrossRef]

Barbieri, S.

Baryshev, A.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

Baryshew, A.

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Baselmans, J. J. A.

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Beck, M.

Beere, H. E.

H. Richter, S. G. Pavlov, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and H.-W. Hübers, “Sub-megahertz frequency stabilization of a terahertz quantum cascade laser to a molecular absorption line,” Appl. Phys. Lett. 96(7), 071112 (2010).
[CrossRef]

K. L. Nguyen, M. L. Johns, L. F. Gladden, C. H. Worrall, P. Alexander, H. E. Beere, M. Pepper, D. A. Ritchie, J. Alton, S. Barbieri, and E. H. Linfield, “Three-dimensional imaging with a terahertz quantum cascade laser,” Opt. Express 14(6), 2123–2129 (2006).
[CrossRef] [PubMed]

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 a distributed feedback terahertz quantum cascade laser,” Appl. Phys. Lett. 89(6), 061115 (2006).
[CrossRef]

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(15), 5890–5896 (2005).
[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]

Bonilla, L. L.

L. L. Bonilla and H. T. Grahn, “Nonlinear dynamics of semiconductor superlattices,” Rep. Prog. Phys. 68(3), 577–683 (2005).
[CrossRef]

Bründermann, E.

Darmo, J.

Davies, A. G.

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]

Debbage, P.

Faist, J.

Fasching, G.

Fischer, M.

Gao, J. R.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Giehler, M.

L. Schrottke, M. Giehler, M. Wienold, R. Hey, and H. T. Grahn, “Compact model for the efficient simulation of the optical gain and transport properties in THz quantum-cascade lasers,” Semicond. Sci. Technol. 25(4), 045025 (2010).
[CrossRef]

M. Wienold, L. Schrottke, M. Giehler, R. Hey, W. Anders, and H. T. Grahn, “Low-voltage terahertz quantum-cascade lasers based on LO-phonon-assisted interminiband transitions,” Electron. Lett. 45(20), 1030–1031 (2009).
[CrossRef]

Giovannini, M.

Gladden, L. F.

Graf, U. U.

Grahn, H. T.

L. Schrottke, M. Giehler, M. Wienold, R. Hey, and H. T. Grahn, “Compact model for the efficient simulation of the optical gain and transport properties in THz quantum-cascade lasers,” Semicond. Sci. Technol. 25(4), 045025 (2010).
[CrossRef]

M. Wienold, L. Schrottke, M. Giehler, R. Hey, W. Anders, and H. T. Grahn, “Low-voltage terahertz quantum-cascade lasers based on LO-phonon-assisted interminiband transitions,” Electron. Lett. 45(20), 1030–1031 (2009).
[CrossRef]

L. L. Bonilla and H. T. Grahn, “Nonlinear dynamics of semiconductor superlattices,” Rep. Prog. Phys. 68(3), 577–683 (2005).
[CrossRef]

Hajenius, M.

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Hart, R. A.

Havenith, M.

Henschke, R.

Hesler, J. L.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

Hey, R.

L. Schrottke, M. Giehler, M. Wienold, R. Hey, and H. T. Grahn, “Compact model for the efficient simulation of the optical gain and transport properties in THz quantum-cascade lasers,” Semicond. Sci. Technol. 25(4), 045025 (2010).
[CrossRef]

M. Wienold, L. Schrottke, M. Giehler, R. Hey, W. Anders, and H. T. Grahn, “Low-voltage terahertz quantum-cascade lasers based on LO-phonon-assisted interminiband transitions,” Electron. Lett. 45(20), 1030–1031 (2009).
[CrossRef]

Hovenier, J. N.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Hu, Q.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

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(14), 141125 (2006).
[CrossRef]

A. W. M. Lee, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320×240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18(13), 1415–1417 (2006).
[CrossRef]

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Hübers, H.-W.

H. Richter, S. G. Pavlov, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and H.-W. Hübers, “Sub-megahertz frequency stabilization of a terahertz quantum cascade laser to a molecular absorption line,” Appl. Phys. Lett. 96(7), 071112 (2010).
[CrossRef]

H. Richter, A. D. Semenov, S. Pavlov, L. Mahler, A. Tredicucci, K. 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(14), 141108 (2008).
[CrossRef]

H.-W. Hübers, “Terahertz Heterodyne Receivers,” IEEE J. Sel. Top. Quantum Electron. 14(2), 378–391 (2008).
[CrossRef]

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 a distributed feedback terahertz quantum cascade laser,” Appl. Phys. Lett. 89(6), 061115 (2006).
[CrossRef]

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(15), 5890–5896 (2005).
[CrossRef] [PubMed]

Il’in, K.

H. Richter, A. D. Semenov, S. Pavlov, L. Mahler, A. Tredicucci, K. 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(14), 141108 (2008).
[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]

Jellema, W.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

Johns, M. L.

Kennedy, J.

Khosropanah, P.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

Klaassen, T. O.

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Klapwijk, T. M.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Klein, B.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

Köhler, R.

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(15), 5890–5896 (2005).
[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]

Kremser, C.

Kröll, J.

Kumar, S.

A. W. M. Lee, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320×240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18(13), 1415–1417 (2006).
[CrossRef]

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(14), 141125 (2006).
[CrossRef]

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Kunsch, J.

Laughman, L. M.

Lee, A. W. M.

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(14), 141125 (2006).
[CrossRef]

A. W. M. Lee, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320×240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18(13), 1415–1417 (2006).
[CrossRef]

Linfield, E. H.

Mahler, L.

H. Richter, S. G. Pavlov, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and H.-W. Hübers, “Sub-megahertz frequency stabilization of a terahertz quantum cascade laser to a molecular absorption line,” Appl. Phys. Lett. 96(7), 071112 (2010).
[CrossRef]

H. Richter, A. D. Semenov, S. Pavlov, L. Mahler, A. Tredicucci, K. 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(14), 141108 (2008).
[CrossRef]

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 a distributed feedback terahertz quantum cascade laser,” Appl. Phys. Lett. 89(6), 061115 (2006).
[CrossRef]

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(15), 5890–5896 (2005).
[CrossRef] [PubMed]

Mechold, L.

Mueller, E. R.

Newman, L. A.

Nguyen, K. L.

Paveliev, D. G.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

Pavlov, S.

H. Richter, A. D. Semenov, S. Pavlov, L. Mahler, A. Tredicucci, K. 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(14), 141108 (2008).
[CrossRef]

Pavlov, S. G.

H. Richter, S. G. Pavlov, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and H.-W. Hübers, “Sub-megahertz frequency stabilization of a terahertz quantum cascade laser to a molecular absorption line,” Appl. Phys. Lett. 96(7), 071112 (2010).
[CrossRef]

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 a distributed feedback terahertz quantum cascade laser,” Appl. Phys. Lett. 89(6), 061115 (2006).
[CrossRef]

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(15), 5890–5896 (2005).
[CrossRef] [PubMed]

Pepper, M.

Philipp, M.

Pickett, H. M.

Pundak, N.

A. M. Veprik, S. V. Riabzev, G. S. Vilenchik, and N. Pundak, “Ultra-low vibration split Stirling linear cryogenic cooler with a dynamically counterbalanced pneumatically driven expander,” Cryogenics 45(2), 117–122 (2005).
[CrossRef]

Qin, Q.

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(14), 141125 (2006).
[CrossRef]

Rabanus, D.

Reno, J. L.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

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(14), 141125 (2006).
[CrossRef]

A. W. M. Lee, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320×240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18(13), 1415–1417 (2006).
[CrossRef]

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Riabzev, S. V.

A. M. Veprik, S. V. Riabzev, G. S. Vilenchik, and N. Pundak, “Ultra-low vibration split Stirling linear cryogenic cooler with a dynamically counterbalanced pneumatically driven expander,” Cryogenics 45(2), 117–122 (2005).
[CrossRef]

Richter, H.

H. Richter, S. G. Pavlov, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and H.-W. Hübers, “Sub-megahertz frequency stabilization of a terahertz quantum cascade laser to a molecular absorption line,” Appl. Phys. Lett. 96(7), 071112 (2010).
[CrossRef]

H. Richter, A. D. Semenov, S. Pavlov, L. Mahler, A. Tredicucci, K. 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(14), 141108 (2008).
[CrossRef]

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 a distributed feedback terahertz quantum cascade laser,” Appl. Phys. Lett. 89(6), 061115 (2006).
[CrossRef]

Ricken, O.

Ritchie, D. A.

H. Richter, S. G. Pavlov, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and H.-W. Hübers, “Sub-megahertz frequency stabilization of a terahertz quantum cascade laser to a molecular absorption line,” Appl. Phys. Lett. 96(7), 071112 (2010).
[CrossRef]

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 a distributed feedback terahertz quantum cascade laser,” Appl. Phys. Lett. 89(6), 061115 (2006).
[CrossRef]

K. L. Nguyen, M. L. Johns, L. F. Gladden, C. H. Worrall, P. Alexander, H. E. Beere, M. Pepper, D. A. Ritchie, J. Alton, S. Barbieri, and E. H. Linfield, “Three-dimensional imaging with a terahertz quantum cascade laser,” Opt. Express 14(6), 2123–2129 (2006).
[CrossRef] [PubMed]

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(15), 5890–5896 (2005).
[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]

Robotham, W. E.

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]

Scalari, G.

Schrottke, L.

L. Schrottke, M. Giehler, M. Wienold, R. Hey, and H. T. Grahn, “Compact model for the efficient simulation of the optical gain and transport properties in THz quantum-cascade lasers,” Semicond. Sci. Technol. 25(4), 045025 (2010).
[CrossRef]

M. Wienold, L. Schrottke, M. Giehler, R. Hey, W. Anders, and H. T. Grahn, “Low-voltage terahertz quantum-cascade lasers based on LO-phonon-assisted interminiband transitions,” Electron. Lett. 45(20), 1030–1031 (2009).
[CrossRef]

Semenov, A. D.

H. Richter, S. G. Pavlov, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and H.-W. Hübers, “Sub-megahertz frequency stabilization of a terahertz quantum cascade laser to a molecular absorption line,” Appl. Phys. Lett. 96(7), 071112 (2010).
[CrossRef]

H. Richter, A. D. Semenov, S. Pavlov, L. Mahler, A. Tredicucci, K. 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(14), 141108 (2008).
[CrossRef]

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 a distributed feedback terahertz quantum cascade laser,” Appl. Phys. Lett. 89(6), 061115 (2006).
[CrossRef]

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(15), 5890–5896 (2005).
[CrossRef] [PubMed]

Siegel, M.

H. Richter, A. D. Semenov, S. Pavlov, L. Mahler, A. Tredicucci, K. 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(14), 141108 (2008).
[CrossRef]

Stutzki, J.

Tamosiunas, V.

Tredicucci, A.

H. Richter, S. G. Pavlov, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and H.-W. Hübers, “Sub-megahertz frequency stabilization of a terahertz quantum cascade laser to a molecular absorption line,” Appl. Phys. Lett. 96(7), 071112 (2010).
[CrossRef]

H. Richter, A. D. Semenov, S. Pavlov, L. Mahler, A. Tredicucci, K. 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(14), 141108 (2008).
[CrossRef]

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 a distributed feedback terahertz quantum cascade laser,” Appl. Phys. Lett. 89(6), 061115 (2006).
[CrossRef]

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(15), 5890–5896 (2005).
[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]

Unterrainer, K.

Veprik, A. M.

A. M. Veprik, S. V. Riabzev, G. S. Vilenchik, and N. Pundak, “Ultra-low vibration split Stirling linear cryogenic cooler with a dynamically counterbalanced pneumatically driven expander,” Cryogenics 45(2), 117–122 (2005).
[CrossRef]

Vilenchik, G. S.

A. M. Veprik, S. V. Riabzev, G. S. Vilenchik, and N. Pundak, “Ultra-low vibration split Stirling linear cryogenic cooler with a dynamically counterbalanced pneumatically driven expander,” Cryogenics 45(2), 117–122 (2005).
[CrossRef]

Vowinkel, B.

Walther, C.

Wiedner, M. C.

Wienold, M.

L. Schrottke, M. Giehler, M. Wienold, R. Hey, and H. T. Grahn, “Compact model for the efficient simulation of the optical gain and transport properties in THz quantum-cascade lasers,” Semicond. Sci. Technol. 25(4), 045025 (2010).
[CrossRef]

M. Wienold, L. Schrottke, M. Giehler, R. Hey, W. Anders, and H. T. Grahn, “Low-voltage terahertz quantum-cascade lasers based on LO-phonon-assisted interminiband transitions,” Electron. Lett. 45(20), 1030–1031 (2009).
[CrossRef]

Williams, B. S.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

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

A. W. M. Lee, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320×240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18(13), 1415–1417 (2006).
[CrossRef]

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(14), 141125 (2006).
[CrossRef]

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Worrall, C. H.

Yang, Z. Q.

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

Zhang, W.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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(14), 141125 (2006).
[CrossRef]

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 a distributed feedback terahertz quantum cascade laser,” Appl. Phys. Lett. 89(6), 061115 (2006).
[CrossRef]

H. Richter, A. D. Semenov, S. Pavlov, L. Mahler, A. Tredicucci, K. 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(14), 141108 (2008).
[CrossRef]

J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshew, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, 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(24), 244104 (2005).
[CrossRef]

H. Richter, S. G. Pavlov, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and H.-W. Hübers, “Sub-megahertz frequency stabilization of a terahertz quantum cascade laser to a molecular absorption line,” Appl. Phys. Lett. 96(7), 071112 (2010).
[CrossRef]

Cryogenics

A. M. Veprik, S. V. Riabzev, G. S. Vilenchik, and N. Pundak, “Ultra-low vibration split Stirling linear cryogenic cooler with a dynamically counterbalanced pneumatically driven expander,” Cryogenics 45(2), 117–122 (2005).
[CrossRef]

Electron. Lett.

M. Wienold, L. Schrottke, M. Giehler, R. Hey, W. Anders, and H. T. Grahn, “Low-voltage terahertz quantum-cascade lasers based on LO-phonon-assisted interminiband transitions,” Electron. Lett. 45(20), 1030–1031 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

H.-W. Hübers, “Terahertz Heterodyne Receivers,” IEEE J. Sel. Top. Quantum Electron. 14(2), 378–391 (2008).
[CrossRef]

IEEE Photon. Technol. Lett.

A. W. M. Lee, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Real-time imaging using a 4.3-THz quantum cascade laser and a 320×240 microbolometer focal-plane array,” IEEE Photon. Technol. Lett. 18(13), 1415–1417 (2006).
[CrossRef]

Nat. Photonics

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

Nature

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]

Opt. Express

Opt. Lett.

P. Khosropanah, A. Baryshev, W. Zhang, W. Jellema, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, D. G. Paveliev, B. S. Williams, Q. Hu, J. L. Reno, B. Klein, and J. L. Hesler, “Phase locking of a 2.7 THz quantum cascade laser to a microwave reference,” Opt. Lett. 19(34), 2958–2960 (2009).
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Rep. Prog. Phys.

L. L. Bonilla and H. T. Grahn, “Nonlinear dynamics of semiconductor superlattices,” Rep. Prog. Phys. 68(3), 577–683 (2005).
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Semicond. Sci. Technol.

L. Schrottke, M. Giehler, M. Wienold, R. Hey, and H. T. Grahn, “Compact model for the efficient simulation of the optical gain and transport properties in THz quantum-cascade lasers,” Semicond. Sci. Technol. 25(4), 045025 (2010).
[CrossRef]

Other

U. U. Graf, S. Heyminck, R. Güsten, P. Hartogh, H.-W. Hübers, K. Jacobs, M. Philipp, D. Rabanus, H.-P. Röser, J. Stutzki, P. Van der Wal, and A. Wagner-Gentner, “GREAT: the German first light heterodyne instrument for SOFIA,” in Proc. Conf. on Millimeter and Submillimeter Detectors for Astronomy III, vol. SPIE 6275, Orlando, 2006, pp. 62750K–1-62750K–7.

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Figures (9)

Fig. 1
Fig. 1

Voltage and output power of the QCL as a function of current with a starting temperature of 54 K and an end temperature of 58 K. The steps in the output power are probably caused by electric-field domains.

Fig. 2
Fig. 2

Cw laser output signal as a function of temperature for several driving currents.

Fig. 3
Fig. 3

Electrical input power at lasing threshold of the QCL (blue curve) and cooling power available from the Stirling cooler (black curve) as a function of temperature. The step at 54 K occurs because the internal temperature stabilization of the cooler does not function below this temperature. Across the whole range, the electrical input power at the temperature threshold is much less than the available cooling power. The red ellipse indicates the region of maximum output power.

Fig. 4
Fig. 4

Beam profiles of the QCL. (a) Beam profile measured at 2.5 cm distance from the QCL. Two emission maxima (red) can be distinguished. One originates directly from the laser ridge, and the other one comes from the substrate. (b) Beam profile at the position of the minimum waist created by a lens in front of the QCL. (c) Residual of the measured beam profile from (b) and a fitted Gaussian profile normalized to the peak intensity. The deviation is between + 4.5% and −8.8% (cf. legend on the right side).

Fig. 5
Fig. 5

Emission spectra of the QCL measured with a Fourier transform spectrometer for 400, 480, and 600 mA at 39, 44, and 52 K, respectively. The spectral resolution is approximately 10 GHz. The spectra are shifted for clarity. Several longitudinal modes of the Fabry-Pérot laser cavity separated by 28 GHz appear. Only the four strongest modes are labeled with their frequency. The frequency coverage is approximately 250 GHz.

Fig. 6
Fig. 6

Measurement of the beam profile at the position of the minimum waist by scanning a sharp metal blade in steps of 0.1 mm across the beam. The black squares are measured data points and the red curve is a fit to Eq. (1). The width is 700 µm.

Fig. 7
Fig. 7

a) Simplified scheme of the imaging setup: The sample is raster-scanned at the position of the minimum beam waist created by the TPX lens. b) THz image of a sugar bag and the electronic components of a music greeting card inside an envelope. The envelope was raster-scanned in steps of 1 mm through the position of the minimum waist. The legend shows the intensity of the transmitted signal (in arbitrary units).

Fig. 8
Fig. 8

Experimental set-up for gas-phase spectroscopy.

Fig. 9
Fig. 9

Absorption signal of 12CH3OH as a function of laser current at 53 K for 4.4 hPa (red curve) and below 0.01 hPa (black curve). The black curve is shifted by −0.3 for clarity. Each scan took only 320 ms. The maximum signal-to-noise ratio is 1500.

Equations (1)

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I(x)=I012[1+erf(2ln2xxcd)],

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