Abstract

Time-resolved transmission spectroscopy of a mid-infrared quantum cascade laser emitting at 11.7μm allows us to iteratively retrieve the effective refractive index and the extinction coefficient of the gain medium in a broad spectral range with an accuracy of ±7×103. Besides a 3% slowdown of the group velocity we find a large induced group-velocity dispersion with changing signs in the vicinity of the gain maximum, disclosing implications for self-pulse formation in quantum-cascade lasers. Additionally we measured the temperature in the active region by exploiting the thermo-optic effect. A linear behavior with respect to the current and the duty cycle was observed.

© 2009 Optical Society of America

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  2. M. Austerer, C. Pflügl, S. Golka, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, Appl. Phys. Lett. 88, 121104 (2006).
    [CrossRef]
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    [CrossRef]
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2008 (2)

E. Peter, S. Laurent, C. Sirtori, M. Carras, J. A. Robbo, M. Garcia, and X. Marcadet, Appl. Phys. Lett. 92, 021103 (2008).
[CrossRef]

W. Parz, T. Müller, J. Darmo, K. Unterrainer, M. Austerer, G. Strasser, L. R. Wilson, J. W. Cockburn, A. B. Krysa, and J. S. Roberts, Appl. Phys. Lett. 93, 091105 (2008).
[CrossRef]

2007 (8)

I. Pupeza, R. Wilk, and M. Koch, Opt. Express 15, 4335 (2007).
[CrossRef] [PubMed]

Y. Logvin, V. P. Kalosha, and H. Anis, Opt. Express 15, 985 (2007).
[CrossRef] [PubMed]

M. S. Vitiello, G. Scamarcio, V. Spagnolo, A. Lops, Q. Yang, C. Manz, and J. Wagner, Appl. Phys. Lett. 90, 121109 (2007).
[CrossRef]

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, Nat. Photonics 1, 288 (2007).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, Phys. Rev. A 75, 031802 (2007).
[CrossRef]

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

J. Kröll, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, Nature 449, 698 (2007).
[CrossRef] [PubMed]

J. Kröll, J. Darmo, K. Unterrainer, S. S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, Appl. Phys. Lett. 91, 161108 (2007).
[CrossRef]

2006 (2)

M. Austerer, C. Pflügl, S. Golka, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, Appl. Phys. Lett. 88, 121104 (2006).
[CrossRef]

R. Herda, A. Isomaki, and O. Okhotnikov, Electron. Lett. 42, 1025 (2006).
[CrossRef]

2005 (1)

2004 (1)

2002 (1)

C. Gmachl, A. Soibel, R. Colombelli, D. Sivco, F. Capasso, and A. Cho, IEEE Photon. Technol. Lett. 14, 1671 (2002).
[CrossRef]

2000 (3)

H. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, D. Sivco, J. Baillargeon, A. Hutchinson, A. Cho, and H. Liu, Science 290, 1739 (2000).
[CrossRef] [PubMed]

R. Huber, A. Brodschelm, F. Tauser, and A. Leitenstorfer, Appl. Phys. Lett. 76, 3191 (2000).
[CrossRef]

1999 (1)

1996 (2)

L. Duvillaret, F. Garet, and J.-L. Coutaz, IEEE J. Sel. Top. Quantum Electron. 2, 739 (1996).
[CrossRef]

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 68, 1604 (1996).
[CrossRef]

1993 (1)

1989 (1)

E. Kesler and M. P. Ippen, Electron. Lett. 25, 640 (1989).
[CrossRef]

1975 (1)

B. W. Hakki and T. L. Paoli, J. Appl. Phys. 46, 1299 (1975).
[CrossRef]

Andrews, A. M.

M. Austerer, C. Pflügl, S. Golka, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, Appl. Phys. Lett. 88, 121104 (2006).
[CrossRef]

Anis, H.

Austerer, M.

W. Parz, T. Müller, J. Darmo, K. Unterrainer, M. Austerer, G. Strasser, L. R. Wilson, J. W. Cockburn, A. B. Krysa, and J. S. Roberts, Appl. Phys. Lett. 93, 091105 (2008).
[CrossRef]

M. Austerer, C. Pflügl, S. Golka, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, Appl. Phys. Lett. 88, 121104 (2006).
[CrossRef]

Baillargeon, J.

R. Paiella, F. Capasso, C. Gmachl, D. Sivco, J. Baillargeon, A. Hutchinson, A. Cho, and H. Liu, Science 290, 1739 (2000).
[CrossRef] [PubMed]

Belkin, M. A.

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, Nat. Photonics 1, 288 (2007).
[CrossRef]

Belyanin, A.

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, Nat. Photonics 1, 288 (2007).
[CrossRef]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Bour, D.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, Phys. Rev. A 75, 031802 (2007).
[CrossRef]

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

Brodschelm, A.

R. Huber, A. Brodschelm, F. Tauser, and A. Leitenstorfer, Appl. Phys. Lett. 76, 3191 (2000).
[CrossRef]

Calligaro, M.

J. Kröll, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, Nature 449, 698 (2007).
[CrossRef] [PubMed]

J. Kröll, J. Darmo, K. Unterrainer, S. S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, Appl. Phys. Lett. 91, 161108 (2007).
[CrossRef]

Capasso, F.

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, Phys. Rev. A 75, 031802 (2007).
[CrossRef]

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, Nat. Photonics 1, 288 (2007).
[CrossRef]

C. Gmachl, A. Soibel, R. Colombelli, D. Sivco, F. Capasso, and A. Cho, IEEE Photon. Technol. Lett. 14, 1671 (2002).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, D. Sivco, J. Baillargeon, A. Hutchinson, A. Cho, and H. Liu, Science 290, 1739 (2000).
[CrossRef] [PubMed]

Carras, M.

E. Peter, S. Laurent, C. Sirtori, M. Carras, J. A. Robbo, M. Garcia, and X. Marcadet, Appl. Phys. Lett. 92, 021103 (2008).
[CrossRef]

Cho, A.

C. Gmachl, A. Soibel, R. Colombelli, D. Sivco, F. Capasso, and A. Cho, IEEE Photon. Technol. Lett. 14, 1671 (2002).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, D. Sivco, J. Baillargeon, A. Hutchinson, A. Cho, and H. Liu, Science 290, 1739 (2000).
[CrossRef] [PubMed]

Cho, A. Y.

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, Nat. Photonics 1, 288 (2007).
[CrossRef]

Choi, H.

Cleaver, J. R. A.

Cockburn, J. W.

W. Parz, T. Müller, J. Darmo, K. Unterrainer, M. Austerer, G. Strasser, L. R. Wilson, J. W. Cockburn, A. B. Krysa, and J. S. Roberts, Appl. Phys. Lett. 93, 091105 (2008).
[CrossRef]

Colombelli, R.

C. Gmachl, A. Soibel, R. Colombelli, D. Sivco, F. Capasso, and A. Cho, IEEE Photon. Technol. Lett. 14, 1671 (2002).
[CrossRef]

Corzine, S.

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Coutaz, J.-L.

L. Duvillaret, F. Garet, and J.-L. Coutaz, Appl. Opt. 38, 409 (1999).
[CrossRef]

L. Duvillaret, F. Garet, and J.-L. Coutaz, IEEE J. Sel. Top. Quantum Electron. 2, 739 (1996).
[CrossRef]

Darmo, J.

W. Parz, T. Müller, J. Darmo, K. Unterrainer, M. Austerer, G. Strasser, L. R. Wilson, J. W. Cockburn, A. B. Krysa, and J. S. Roberts, Appl. Phys. Lett. 93, 091105 (2008).
[CrossRef]

J. Kröll, J. Darmo, K. Unterrainer, S. S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, Appl. Phys. Lett. 91, 161108 (2007).
[CrossRef]

Dhillon, S. S.

J. Kröll, J. Darmo, K. Unterrainer, S. S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, Appl. Phys. Lett. 91, 161108 (2007).
[CrossRef]

J. Kröll, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, Nature 449, 698 (2007).
[CrossRef] [PubMed]

Diehl, L.

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, Opt. Express 15, 15898 (2007).
[CrossRef] [PubMed]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Duvillaret, L.

L. Duvillaret, F. Garet, and J.-L. Coutaz, Appl. Opt. 38, 409 (1999).
[CrossRef]

L. Duvillaret, F. Garet, and J.-L. Coutaz, IEEE J. Sel. Top. Quantum Electron. 2, 739 (1996).
[CrossRef]

Faist, J.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Fischer, B.

Garcia, M.

E. Peter, S. Laurent, C. Sirtori, M. Carras, J. A. Robbo, M. Garcia, and X. Marcadet, Appl. Phys. Lett. 92, 021103 (2008).
[CrossRef]

Garet, F.

L. Duvillaret, F. Garet, and J.-L. Coutaz, Appl. Opt. 38, 409 (1999).
[CrossRef]

L. Duvillaret, F. Garet, and J.-L. Coutaz, IEEE J. Sel. Top. Quantum Electron. 2, 739 (1996).
[CrossRef]

Gmachl, C.

C. Gmachl, A. Soibel, R. Colombelli, D. Sivco, F. Capasso, and A. Cho, IEEE Photon. Technol. Lett. 14, 1671 (2002).
[CrossRef]

R. Paiella, F. Capasso, C. Gmachl, D. Sivco, J. Baillargeon, A. Hutchinson, A. Cho, and H. Liu, Science 290, 1739 (2000).
[CrossRef] [PubMed]

Golka, S.

M. Austerer, C. Pflügl, S. Golka, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, Appl. Phys. Lett. 88, 121104 (2006).
[CrossRef]

Gordon, A.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Gordon, R.

Hakki, B. W.

B. W. Hakki and T. L. Paoli, J. Appl. Phys. 46, 1299 (1975).
[CrossRef]

Haus, H.

H. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

Heberle, A. P.

Herda, R.

R. Herda, A. Isomaki, and O. Okhotnikov, Electron. Lett. 42, 1025 (2006).
[CrossRef]

Hickernell, R. K.

Hofler, G.

Höfler, G.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Horiguchi, M.

Huber, R.

R. Huber, A. Brodschelm, F. Tauser, and A. Leitenstorfer, Appl. Phys. Lett. 76, 3191 (2000).
[CrossRef]

Hutchinson, A.

R. Paiella, F. Capasso, C. Gmachl, D. Sivco, J. Baillargeon, A. Hutchinson, A. Cho, and H. Liu, Science 290, 1739 (2000).
[CrossRef] [PubMed]

Ippen, M. P.

E. Kesler and M. P. Ippen, Electron. Lett. 25, 640 (1989).
[CrossRef]

Isomaki, A.

R. Herda, A. Isomaki, and O. Okhotnikov, Electron. Lett. 42, 1025 (2006).
[CrossRef]

Jepsen, P. U.

Jirauschek, C.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Kalosha, V. P.

Kärtner, F. X.

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, Phys. Rev. A 75, 031802 (2007).
[CrossRef]

Kesler, E.

E. Kesler and M. P. Ippen, Electron. Lett. 25, 640 (1989).
[CrossRef]

Koch, M.

Kröll, J.

J. Kröll, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, Nature 449, 698 (2007).
[CrossRef] [PubMed]

J. Kröll, J. Darmo, K. Unterrainer, S. S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, Appl. Phys. Lett. 91, 161108 (2007).
[CrossRef]

Krysa, A. B.

W. Parz, T. Müller, J. Darmo, K. Unterrainer, M. Austerer, G. Strasser, L. R. Wilson, J. W. Cockburn, A. B. Krysa, and J. S. Roberts, Appl. Phys. Lett. 93, 091105 (2008).
[CrossRef]

Laurent, S.

E. Peter, S. Laurent, C. Sirtori, M. Carras, J. A. Robbo, M. Garcia, and X. Marcadet, Appl. Phys. Lett. 92, 021103 (2008).
[CrossRef]

Leitenstorfer, A.

R. Huber, A. Brodschelm, F. Tauser, and A. Leitenstorfer, Appl. Phys. Lett. 76, 3191 (2000).
[CrossRef]

Liu, H.

R. Paiella, F. Capasso, C. Gmachl, D. Sivco, J. Baillargeon, A. Hutchinson, A. Cho, and H. Liu, Science 290, 1739 (2000).
[CrossRef] [PubMed]

Logvin, Y.

Lops, A.

M. S. Vitiello, G. Scamarcio, V. Spagnolo, A. Lops, Q. Yang, C. Manz, and J. Wagner, Appl. Phys. Lett. 90, 121109 (2007).
[CrossRef]

Manz, C.

M. S. Vitiello, G. Scamarcio, V. Spagnolo, A. Lops, Q. Yang, C. Manz, and J. Wagner, Appl. Phys. Lett. 90, 121109 (2007).
[CrossRef]

Marcadet, X.

E. Peter, S. Laurent, C. Sirtori, M. Carras, J. A. Robbo, M. Garcia, and X. Marcadet, Appl. Phys. Lett. 92, 021103 (2008).
[CrossRef]

J. Kröll, S. S. Dhillon, X. Marcadet, M. Calligaro, C. Sirtori, and K. Unterrainer, Nature 449, 698 (2007).
[CrossRef] [PubMed]

J. Kröll, J. Darmo, K. Unterrainer, S. S. Dhillon, C. Sirtori, X. Marcadet, and M. Calligaro, Appl. Phys. Lett. 91, 161108 (2007).
[CrossRef]

Müller, T.

W. Parz, T. Müller, J. Darmo, K. Unterrainer, M. Austerer, G. Strasser, L. R. Wilson, J. W. Cockburn, A. B. Krysa, and J. S. Roberts, Appl. Phys. Lett. 93, 091105 (2008).
[CrossRef]

Norris, T. B.

Oakley, D. C.

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, Nat. Photonics 1, 288 (2007).
[CrossRef]

Okhotnikov, O.

R. Herda, A. Isomaki, and O. Okhotnikov, Electron. Lett. 42, 1025 (2006).
[CrossRef]

Paiella, R.

R. Paiella, F. Capasso, C. Gmachl, D. Sivco, J. Baillargeon, A. Hutchinson, A. Cho, and H. Liu, Science 290, 1739 (2000).
[CrossRef] [PubMed]

Paoli, T. L.

B. W. Hakki and T. L. Paoli, J. Appl. Phys. 46, 1299 (1975).
[CrossRef]

Parz, W.

W. Parz, T. Müller, J. Darmo, K. Unterrainer, M. Austerer, G. Strasser, L. R. Wilson, J. W. Cockburn, A. B. Krysa, and J. S. Roberts, Appl. Phys. Lett. 93, 091105 (2008).
[CrossRef]

Peter, E.

E. Peter, S. Laurent, C. Sirtori, M. Carras, J. A. Robbo, M. Garcia, and X. Marcadet, Appl. Phys. Lett. 92, 021103 (2008).
[CrossRef]

Pflügl, C.

M. Austerer, C. Pflügl, S. Golka, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, Appl. Phys. Lett. 88, 121104 (2006).
[CrossRef]

Pupeza, I.

Robbo, J. A.

E. Peter, S. Laurent, C. Sirtori, M. Carras, J. A. Robbo, M. Garcia, and X. Marcadet, Appl. Phys. Lett. 92, 021103 (2008).
[CrossRef]

Roberts, J. S.

W. Parz, T. Müller, J. Darmo, K. Unterrainer, M. Austerer, G. Strasser, L. R. Wilson, J. W. Cockburn, A. B. Krysa, and J. S. Roberts, Appl. Phys. Lett. 93, 091105 (2008).
[CrossRef]

Roch, T.

M. Austerer, C. Pflügl, S. Golka, W. Schrenk, A. M. Andrews, T. Roch, and G. Strasser, Appl. Phys. Lett. 88, 121104 (2006).
[CrossRef]

Scamarcio, G.

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Figures (4)

Fig. 1
Fig. 1

(a) Setup for the generation of ultrashort mid-infrared pulses with subsequent measurement of the time-resolved electric field after transmission through a QCL. (b) Optical configuration for self-consistent calculation of the complex refractive index.

Fig. 2
Fig. 2

Spectrally resolved transmission through the QCL in (a) phase and (b) amplitude at different bias currents. The symbols mark measured values, while the solid curves are simulation results. All measurements are done for bias currents of 0% (triangles down), 40% (triangles up), 80% (circles), and 100% (squares) of the threshold current. The inset shows the emission spectrum above the lasing threshold.

Fig. 3
Fig. 3

Refractive index and dispersion in a biased QCL. The refractive index n eff j κ , the group refractive index n group , and the GVD are plotted. (a)–(d) show the total values, while (e)–(h) display the gain-induced part. The symbols mark measured values, while the solid curves are simulation results. All measurements are done for bias currents of 0% (triangles down), 40% (triangles up), 80% (circles), and 100% (squares) of the threshold current. The error bars are plotted on the right side of the graphs.

Fig. 4
Fig. 4

(a) Temperature-induced change of the refractive index. Crosses mark measured data, and the solid curve is a quadratic least square fit. (b) Average temperatures in the QCL in dependence of different bias current densities at a duty cycle of 100% (circles) and 50% (triangles). The solid curves are linear least square fits.

Equations (2)

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T = 4 n j κ ( n + 1 j κ ) exp ( j 2 π f c 0 ( n j κ ) d ) ,
Δ n ( T ) = 3.89 × 10 7 K 2 T 2 + 5 × 10 5 K 1 T .

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