Abstract

We explain the origin of voltage variations due to self-mixing in a terahertz (THz) frequency quantum cascade laser (QCL) using an extended density matrix (DM) approach. Our DM model allows calculation of both the current–voltage (IV) and optical power characteristics of the QCL under optical feedback by changing the cavity loss, to which the gain of the active region is clamped. The variation of intra-cavity field strength necessary to achieve gain clamping, and the corresponding change in bias required to maintain a constant current density through the heterostructure is then calculated. Strong enhancement of the self-mixing voltage signal due to non-linearity of the (IV) characteristics is predicted and confirmed experimentally in an exemplar 2.6 THz bound-to-continuum QCL.

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References

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2015 (3)

2014 (2)

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett 50(2), 309–311 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

2013 (4)

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21(19), 22194–22205 (2013).
[Crossref]

2012 (2)

2011 (1)

2010 (1)

2007 (1)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. photonics 1, 97–105 (2007).
[Crossref]

2005 (1)

H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005).
[Crossref]

1994 (1)

R. Juškaitis, N. Rea, and T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt 33, 578–584 (1994).
[Crossref]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quant. Electron. 16(3), 347–355 (1980).
[Crossref]

Alhathlool, R.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

Ban, D.

Bertling, K.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photon. 7(3), 570–631 (2015).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21(19), 22194–22205 (2013).
[Crossref]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Bosch, T.

Burnett, A. D.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

Callebaut, H.

H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005).
[Crossref]

Chan, C.

Chen, L.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett 50(2), 309–311 (2014).
[Crossref]

Chowdhury, S.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

Davies, A. G.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett 50(2), 309–311 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21(19), 22194–22205 (2013).
[Crossref]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[Crossref] [PubMed]

Davies, A. Giles

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

Davies, G.

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

De Chatellus, H. G.

Dean, P.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett 50(2), 309–311 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21(19), 22194–22205 (2013).
[Crossref]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[Crossref] [PubMed]

Dinh, T. V.

T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonić, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85(23), 235427 (2012).
[Crossref]

Dupont, E.

Faist, J.

Fathololoumi, S.

Franckié, M.

Freeman, J.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett 50(2), 309–311 (2014).
[Crossref]

Harrison, P.

Hofling, S.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Hu, Q.

Hugon, O.

Ikonic, Z.

Indjin, D.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21(19), 22194–22205 (2013).
[Crossref]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[Crossref] [PubMed]

Jacquin, O.

Jirauschek, C.

Juškaitis, R.

R. Juškaitis, N. Rea, and T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt 33, 578–584 (1994).
[Crossref]

Kamp, M.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Kane, D.

D. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback E ffects on Semiconductor Lasers (John Wiley & Sons, 2005).
[Crossref]

Keeley, J.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

Kelsall, R. W.

T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonić, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85(23), 235427 (2012).
[Crossref]

Khanna, S.

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

Khanna, S. P.

Kliese, R.

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[Crossref] [PubMed]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quant. Electron. 16(3), 347–355 (1980).
[Crossref]

Koeth, J.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Lachab, M.

Lacot, E.

Laframboise, S.

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quant. Electron. 16(3), 347–355 (1980).
[Crossref]

Lee, Y.

Y. Lee, Principles of terahertz science and technology (Springer Science & Business Media, 2009).

LengLim, Y.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

Lever, L. J. M.

T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonić, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85(23), 235427 (2012).
[Crossref]

Li, L.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett 50(2), 309–311 (2014).
[Crossref]

Li, L. H.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

Lim, Y. L.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photon. 7(3), 570–631 (2015).
[Crossref]

J. A. Roumy, J. Perchoux, Y. L. Lim, T. Taimre, A. D. Rakić, and T. Bosch, “Effect of injection current and temperature on signal strength in a laser diode optical feedback interferometer,” Appl. Opt. 54(2), 312–318 (2015).
[Crossref] [PubMed]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21(19), 22194–22205 (2013).
[Crossref]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[Crossref] [PubMed]

Linfield, E.

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

Linfield, E. H.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett 50(2), 309–311 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21(19), 22194–22205 (2013).
[Crossref]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[Crossref] [PubMed]

Liu, H. C.

Liverini, V.

Mátyás, A.

Nikolic, M.

Perchoux, J.

Rakic, A.

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

Rakic, A. D.

J. A. Roumy, J. Perchoux, Y. L. Lim, T. Taimre, A. D. Rakić, and T. Bosch, “Effect of injection current and temperature on signal strength in a laser diode optical feedback interferometer,” Appl. Opt. 54(2), 312–318 (2015).
[Crossref] [PubMed]

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photon. 7(3), 570–631 (2015).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21(19), 22194–22205 (2013).
[Crossref]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[Crossref] [PubMed]

Rea, N.

R. Juškaitis, N. Rea, and T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt 33, 578–584 (1994).
[Crossref]

Roumy, J. A.

Roussely, G.

Shore, K. A.

D. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback E ffects on Semiconductor Lasers (John Wiley & Sons, 2005).
[Crossref]

Taimre, T.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photon. 7(3), 570–631 (2015).
[Crossref]

J. A. Roumy, J. Perchoux, Y. L. Lim, T. Taimre, A. D. Rakić, and T. Bosch, “Effect of injection current and temperature on signal strength in a laser diode optical feedback interferometer,” Appl. Opt. 54(2), 312–318 (2015).
[Crossref] [PubMed]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21(19), 22194–22205 (2013).
[Crossref]

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. photonics 1, 97–105 (2007).
[Crossref]

Trinité, V.

Valavanis, A.

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett 50(2), 309–311 (2014).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21(19), 22194–22205 (2013).
[Crossref]

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonić, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85(23), 235427 (2012).
[Crossref]

P. Dean, Y. L. Lim, A. Valavanis, R. Kliese, M. Nikolić, S. P. Khanna, M. Lachab, D. Indjin, Z. Ikonić, P. Harrison, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging through self-mixing in a quantum cascade laser,” Opt. Lett. 36(13), 2587–2589 (2011).
[Crossref] [PubMed]

von Edlinger, M.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Wacker, A.

Wasilewski, Z.

Weih, R.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Wilson, S.

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

Wilson, S. J.

A. D. Rakić, T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, Z. Ikonić, P. Harrison, A. Valavanis, S. P. Khanna, M. Lachab, S. J. Wilson, E. H. Linfield, and A. G. Davies, “Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis,” Opt. Express 21(19), 22194–22205 (2013).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

Wilson, T.

R. Juškaitis, N. Rea, and T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt 33, 578–584 (1994).
[Crossref]

Winge, D. O.

Wolf, J.

Zhu, J.

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett 50(2), 309–311 (2014).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt (1)

R. Juškaitis, N. Rea, and T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt 33, 578–584 (1994).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Hofling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. LengLim, R. Alhathlool, S. Chowdhury, T. Taimre, L. H. Li, D. Indjin, S. J. Wilson, A. D. Rakić, E. H. Linfield, and A. Giles Davies, “Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser,” Appl. Phys. Lett. 103, 181112 (2013).
[Crossref]

Electron. Lett (1)

L. Li, L. Chen, J. Zhu, J. Freeman, P. Dean, A. Valavanis, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with >1 W output powers,” Electron. Lett 50(2), 309–311 (2014).
[Crossref]

IEEE J. Quant. Electron. (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quant. Electron. 16(3), 347–355 (1980).
[Crossref]

IEEE Sensors J. (1)

A. Valavanis, P. Dean, Y. L. Lim, R. Alhathlool, M. Nikolic, R. Kliese, S. Khanna, D. Indjin, S. Wilson, A. Rakić, E. Linfield, and G. Davies, “Self-mixing interferometry with terahertz quantum cascade lasers,” IEEE Sensors J. 13(1), 37–43 (2013).
[Crossref]

J. Appl. Phys. (1)

H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Phys. D: Appl. Phys. (1)

P. Dean, A. Valavanis, J. Keeley, K. Bertling, Y. L. Lim, R. Alhathlool, A. D. Burnett, L. H. Li, S. P. Khanna, D. Indjin, T. Taimre, A. D. Rakić, E. H. Linfield, and A. G. Davies, “Terahertz imaging using quantum cascade lasers–a review of systems and applications,” J. Phys. D: Appl. Phys. 47(37), 374008 (2014).
[Crossref]

Nat. photonics (1)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. photonics 1, 97–105 (2007).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

T. V. Dinh, A. Valavanis, L. J. M. Lever, Z. Ikonić, and R. W. Kelsall, “Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers,” Phys. Rev. B 85(23), 235427 (2012).
[Crossref]

Other (3)

A. Grier, “Data associated with Origin of terminal voltage variations due to self-mixing in terahertz frequency quantum cascade lasers,” University of Leeds data repository (2016) http://doi.org/10.5518/77 .

Y. Lee, Principles of terahertz science and technology (Springer Science & Business Media, 2009).

D. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback E ffects on Semiconductor Lasers (John Wiley & Sons, 2005).
[Crossref]

Supplementary Material (1)

NameDescription
» Dataset 1       Data associated with 'Origin of terminal voltage variations due to self-mixing in terahertz frequency quantum cascade lasers'

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Figures (4)

Figure 1
Figure 1

Comparison of calculated and experimental PI and VI curves for a heat sink temperature of 35 K. A contact resistance of 1.57 Ω is applied to the density matrix IV data simulated for a lattice temperature of 50 K.

Figure 2
Figure 2

(a) Calculated current density and (b) optical power for QCL under lasing operation for a lattice temperature of 50 K. Changing cavity loss changes the threshold gain and lasing power which varies the photon driven current.

Figure 3
Figure 3

Comparison of peak SM terminal voltage signal calculated with an inverse interpolation of the density matrix model output, and experimental SM measurement.

Figure 4
Figure 4

Comparison of experimental and “hybrid” VSM results with a constant current–loss response of dI/dL = 1.5 × 10−4 kA/cm.

Equations (7)

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

V SM Δ P .
H i , j = z i , j A 0 e i ω 0 t ,
ρ i , j = ρ i , j + exp ( i ω 0 t ) + ρ i , j DC + ρ i , j exp ( i ω 0 t ) .
J = e i [ H , z ] ,
P = c n w h ϵ 0 2 | A 0 | 2 ,
V SM ( I ) = | V ( I , L FR ) V ( I , L FR + Δ L ) | ,
V SM ( I ) = ( d V FR d I ( I ) d I d L ) Δ L ,

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