Abstract

This article experimentally demonstrates that the relative intensity noise (RIN) of a mid-infrared quantum cascade laser is insensitive to the optical feedback for feedback ratios up to 31% (−5.1 dB). The RIN of the free-running laser is in the range of −150 dB/Hz to −160 dB/Hz, while the optical feedback induced RIN variation is less than ± 2.0 dB. In addition, the feedback-induced lasing frequency variation is less than 2.0 GHz. Rate equation analyses of the laser are in good agreement with the experimental observations.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

2018 (3)

2017 (6)

P. Bardella, L. Columbo, and M. Gioannini, “Self-generation of optical frequency comb in single section quantum dot Fabry-Perot lasers: a theoretical study,” Opt. Express 25(21), 26234–26252 (2017).
[Crossref]

D. Kazakov, M. Piccardo, Y. Wang, P. Chevalier, T. S. Mansuripur, F. Xie, C.-e. Zah, K. Lascola, A. Belyanin, and F. Capasso, “Self-starting harmonic frequency comb generation in a quantum cascade laser,” Nat. Photonics 11(12), 789–792 (2017).
[Crossref]

I. Sergachev, R. Maulini, T. Gresch, S. Blaser, A. Bismuto, A. Müller, Y. Bidaux, T. Südmeyer, and S. Schilt, “Frequency stability of a dual wavelength quantum cascade laser,” Opt. Express 25(10), 11027–11037 (2017).
[Crossref]

R. Terabayashi, V. Sonnenschein, H. Tomita, N. Hayashi, S. Kato, L. Jin, M. Yamanaka, N. Nishizawa, A. Sato, K. Nozawa, K. Hashizume, T. Oh-hara, and T. Iguchi, “Optical feedback in dfb quantum cascade laser for mid-infrared cavity ring-down spectroscopy,” Hyperfine Interact. 238(1), 10 (2017).
[Crossref]

T. Hagelschuer, M. Wienold, H. Richter, L. Schrottke, H. T. Grahn, and H. W. Hubers, “Real-time gas sensing based on optical feedback in a terahertz quantum-cascade laser,” Opt. Express 25(24), 30203–30213 (2017).
[Crossref]

S. Ferre, L. Jumpertz, M. Carras, R. Ferreira, and F. Grillot, “Beam shaping in high-power broad-area quantum cascade lasers using optical feedback,” Sci. Rep. 7(1), 44284 (2017).
[Crossref]

2016 (4)

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-e. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94(6), 063807 (2016).
[Crossref]

L. Jumpertz, K. Schires, M. Carras, M. Sciamanna, and F. Grillot, “Chaotic light at mid-infrared wavelength,” Light: Sci. Appl. 5(6), e16088 (2016).
[Crossref]

G. Friart, G. Van der Sande, G. Verschaffelt, and T. Erneux, “Analytical stability boundaries for quantum cascade lasers subject to optical feedback,” Phys. Rev. E 93(5), 052201 (2016).
[Crossref]

M. C. Cardilli, M. Dabbicco, F. P. Mezzapesa, and G. Scamarcio, “Linewidth measurement of mid infrared quantum cascade laser by optical feedback interferometry,” Appl. Phys. Lett. 108(3), 031105 (2016).
[Crossref]

2015 (1)

C. Juretzka, H. Simos, A. Bogris, D. Syvridis, W. Elsäßer, and M. Carras, “Intensity Noise Properties of Midinfrared Injection Locked Quantum Cascade Lasers: II. Experiments,” IEEE J. Quantum Electron. 51(1), 1–8 (2015).
[Crossref]

2014 (5)

H. Simos, A. Bogris, D. Syvridis, and W. Elsäßer, “Intensity Noise Properties of Mid-Infrared Injection Locked Quantum Cascade Lasers: I. Modeling,” IEEE J. Quantum Electron. 50(2), 98–105 (2014).
[Crossref]

L. Jumpertz, M. Carras, K. Schires, and F. Grillot, “Regimes of external optical feedback in 5.6 µm distributed feedback mid-infrared quantum cascade lasers,” Appl. Phys. Lett. 105(13), 131112 (2014).
[Crossref]

L. L. Columbo and M. Brambilla, “Multimode regimes in quantum cascade lasers with optical feedback,” Opt. Express 22(9), 10105–10118 (2014).
[Crossref]

J. Jágerská, P. Jouy, A. Hugi, B. Tuzson, H. Looser, M. Mangold, M. Beck, L. Emmenegger, and J. Faist, “Dual-wavelength quantum cascade laser for trace gas spectroscopy,” Appl. Phys. Lett. 105(16), 161109 (2014).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104(4), 041112 (2014).
[Crossref]

2013 (3)

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
[Crossref]

T. Inoue, S. Mori, K. Tsushima, and K. Kasahara, “Quantum cascade laser intensity noise under external feedback conditions estimated from self-mixing method,” Electron. Lett. 49(6), 407–409 (2013).
[Crossref]

C. Juretzka, M. Carras, F. Schad, L. Drzewietzki, S. Breuer, and W. Elsäßer, “9.5 dB relative intensity noise reduction in quantum cascade laser by detuned loading,” Electron. Lett. 49(24), 1548–1550 (2013).
[Crossref]

2012 (3)

A. Hugi, G. Villares, S. Blaser, H. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref]

J. C. Zhang, F. Q. Liu, S. Tan, D. Y. Yao, L. J. Wang, L. Li, J. Q. Liu, and Z. G. Wang, “High-performance uncooled distributed-feedback quantum cascade laser without lateral regrowth,” Appl. Phys. Lett. 100(11), 112105 (2012).
[Crossref]

C. Otto, B. Globisch, K. Lüdge, E. Schöll, and T. Erneux, “Complex dynamics of semiconductor quantum dot lasers subject to delayed optical feedback,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 22(10), 1250246 (2012).
[Crossref]

2010 (1)

2009 (1)

F.-Q. Liu, L. Li, L. Wang, J. Liu, W. Zhang, Q. Zhang, W. Liu, Q. Lu, and Z. Wang, “Solid source MBE growth of quantum cascade lasers,” Appl. Phys. A 97(3), 527–532 (2009).
[Crossref]

2008 (3)

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

A. Kosterev, G. Wysocki, Y. Bakhirkin, S. So, R. Lewicki, M. Fraser, F. Tittel, and R. Curl, “Application of quantum cascade lasers to trace gas analysis,” Appl. Phys. B 90(2), 165–176 (2008).
[Crossref]

Y. Takagi, N. Kumazaki, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Relative intensity noise measurements of 5 µm quantum cascade laser and 1.55 µm semiconductor laser,” Electron. Lett. 44(14), 860–861 (2008).
[Crossref]

2007 (1)

2006 (1)

2005 (1)

2002 (1)

F. Rana and R. J. Ram, “Current noise and photon noise in quantum cascade lasers,” Phys. Rev. B 65(12), 125313 (2002).
[Crossref]

1994 (1)

H. Kakiuchida and J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30(9), 2087–2097 (1994).
[Crossref]

1990 (1)

J. Helms and K. Petermann, “A simple analytic expression for the stable operation range of laser diode with optical feedback,” IEEE J. Quantum Electron. 26(5), 833–836 (1990).
[Crossref]

1988 (1)

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24(7), 1242–1247 (1988).
[Crossref]

1985 (1)

D. Lenstra, B. Verbeek, and A. D. Boef, “Coherence collapse in singlemode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985).
[Crossref]

1980 (1)

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

Akikusa, N.

Y. Takagi, N. Kumazaki, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Relative intensity noise measurements of 5 µm quantum cascade laser and 1.55 µm semiconductor laser,” Electron. Lett. 44(14), 860–861 (2008).
[Crossref]

Aoust, G.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-e. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94(6), 063807 (2016).
[Crossref]

Bakhirkin, Y.

A. Kosterev, G. Wysocki, Y. Bakhirkin, S. So, R. Lewicki, M. Fraser, F. Tittel, and R. Curl, “Application of quantum cascade lasers to trace gas analysis,” Appl. Phys. B 90(2), 165–176 (2008).
[Crossref]

Bardella, P.

Beck, M.

J. Jágerská, P. Jouy, A. Hugi, B. Tuzson, H. Looser, M. Mangold, M. Beck, L. Emmenegger, and J. Faist, “Dual-wavelength quantum cascade laser for trace gas spectroscopy,” Appl. Phys. Lett. 105(16), 161109 (2014).
[Crossref]

Beere, H. E.

Belyanin, A.

D. Kazakov, M. Piccardo, Y. Wang, P. Chevalier, T. S. Mansuripur, F. Xie, C.-e. Zah, K. Lascola, A. Belyanin, and F. Capasso, “Self-starting harmonic frequency comb generation in a quantum cascade laser,” Nat. Photonics 11(12), 789–792 (2017).
[Crossref]

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-e. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94(6), 063807 (2016).
[Crossref]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Bidaux, Y.

Bismuto, A.

Blaser, S.

Boef, A. D.

D. Lenstra, B. Verbeek, and A. D. Boef, “Coherence collapse in singlemode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985).
[Crossref]

Bogris, A.

C. Juretzka, H. Simos, A. Bogris, D. Syvridis, W. Elsäßer, and M. Carras, “Intensity Noise Properties of Midinfrared Injection Locked Quantum Cascade Lasers: II. Experiments,” IEEE J. Quantum Electron. 51(1), 1–8 (2015).
[Crossref]

H. Simos, A. Bogris, D. Syvridis, and W. Elsäßer, “Intensity Noise Properties of Mid-Infrared Injection Locked Quantum Cascade Lasers: I. Modeling,” IEEE J. Quantum Electron. 50(2), 98–105 (2014).
[Crossref]

Borri, S.

Bour, D.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Brambilla, M.

Breuer, S.

C. Juretzka, M. Carras, F. Schad, L. Drzewietzki, S. Breuer, and W. Elsäßer, “9.5 dB relative intensity noise reduction in quantum cascade laser by detuned loading,” Electron. Lett. 49(24), 1548–1550 (2013).
[Crossref]

Caffey, D. P.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-e. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94(6), 063807 (2016).
[Crossref]

Caneau, C.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-e. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94(6), 063807 (2016).
[Crossref]

Capasso, F.

D. Kazakov, M. Piccardo, Y. Wang, P. Chevalier, T. S. Mansuripur, F. Xie, C.-e. Zah, K. Lascola, A. Belyanin, and F. Capasso, “Self-starting harmonic frequency comb generation in a quantum cascade laser,” Nat. Photonics 11(12), 789–792 (2017).
[Crossref]

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-e. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94(6), 063807 (2016).
[Crossref]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008).
[Crossref]

Carbajo, P. G.

Cardilli, M. C.

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H. Simos, A. Bogris, D. Syvridis, and W. Elsäßer, “Intensity Noise Properties of Mid-Infrared Injection Locked Quantum Cascade Lasers: I. Modeling,” IEEE J. Quantum Electron. 50(2), 98–105 (2014).
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C. Juretzka, H. Simos, A. Bogris, D. Syvridis, W. Elsäßer, and M. Carras, “Intensity Noise Properties of Midinfrared Injection Locked Quantum Cascade Lasers: II. Experiments,” IEEE J. Quantum Electron. 51(1), 1–8 (2015).
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H. Simos, A. Bogris, D. Syvridis, and W. Elsäßer, “Intensity Noise Properties of Mid-Infrared Injection Locked Quantum Cascade Lasers: I. Modeling,” IEEE J. Quantum Electron. 50(2), 98–105 (2014).
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A. Kosterev, G. Wysocki, Y. Bakhirkin, S. So, R. Lewicki, M. Fraser, F. Tittel, and R. Curl, “Application of quantum cascade lasers to trace gas analysis,” Appl. Phys. B 90(2), 165–176 (2008).
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T. Inoue, S. Mori, K. Tsushima, and K. Kasahara, “Quantum cascade laser intensity noise under external feedback conditions estimated from self-mixing method,” Electron. Lett. 49(6), 407–409 (2013).
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F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
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F.-Q. Liu, L. Li, L. Wang, J. Liu, W. Zhang, Q. Zhang, W. Liu, Q. Lu, and Z. Wang, “Solid source MBE growth of quantum cascade lasers,” Appl. Phys. A 97(3), 527–532 (2009).
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[Crossref]

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L. Weicker, D. Wolfersberger, and M. Sciamanna, “Stability analysis of a quantum cascade laser subject to phase-conjugate feedback,” Phys. Rev. E 98(1), 012214 (2018).
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[Crossref]

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[Crossref]

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D. Kazakov, M. Piccardo, Y. Wang, P. Chevalier, T. S. Mansuripur, F. Xie, C.-e. Zah, K. Lascola, A. Belyanin, and F. Capasso, “Self-starting harmonic frequency comb generation in a quantum cascade laser,” Nat. Photonics 11(12), 789–792 (2017).
[Crossref]

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[Crossref]

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R. Terabayashi, V. Sonnenschein, H. Tomita, N. Hayashi, S. Kato, L. Jin, M. Yamanaka, N. Nishizawa, A. Sato, K. Nozawa, K. Hashizume, T. Oh-hara, and T. Iguchi, “Optical feedback in dfb quantum cascade laser for mid-infrared cavity ring-down spectroscopy,” Hyperfine Interact. 238(1), 10 (2017).
[Crossref]

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J. C. Zhang, F. Q. Liu, S. Tan, D. Y. Yao, L. J. Wang, L. Li, J. Q. Liu, and Z. G. Wang, “High-performance uncooled distributed-feedback quantum cascade laser without lateral regrowth,” Appl. Phys. Lett. 100(11), 112105 (2012).
[Crossref]

Zah, C.-e.

D. Kazakov, M. Piccardo, Y. Wang, P. Chevalier, T. S. Mansuripur, F. Xie, C.-e. Zah, K. Lascola, A. Belyanin, and F. Capasso, “Self-starting harmonic frequency comb generation in a quantum cascade laser,” Nat. Photonics 11(12), 789–792 (2017).
[Crossref]

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-e. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94(6), 063807 (2016).
[Crossref]

Zhang, J. C.

J. C. Zhang, F. Q. Liu, S. Tan, D. Y. Yao, L. J. Wang, L. Li, J. Q. Liu, and Z. G. Wang, “High-performance uncooled distributed-feedback quantum cascade laser without lateral regrowth,” Appl. Phys. Lett. 100(11), 112105 (2012).
[Crossref]

Zhang, Q.

F.-Q. Liu, L. Li, L. Wang, J. Liu, W. Zhang, Q. Zhang, W. Liu, Q. Lu, and Z. Wang, “Solid source MBE growth of quantum cascade lasers,” Appl. Phys. A 97(3), 527–532 (2009).
[Crossref]

Zhang, W.

F.-Q. Liu, L. Li, L. Wang, J. Liu, W. Zhang, Q. Zhang, W. Liu, Q. Lu, and Z. Wang, “Solid source MBE growth of quantum cascade lasers,” Appl. Phys. A 97(3), 527–532 (2009).
[Crossref]

Zhao, B.-B.

Appl. Opt. (1)

Appl. Phys. A (1)

F.-Q. Liu, L. Li, L. Wang, J. Liu, W. Zhang, Q. Zhang, W. Liu, Q. Lu, and Z. Wang, “Solid source MBE growth of quantum cascade lasers,” Appl. Phys. A 97(3), 527–532 (2009).
[Crossref]

Appl. Phys. B (1)

A. Kosterev, G. Wysocki, Y. Bakhirkin, S. So, R. Lewicki, M. Fraser, F. Tittel, and R. Curl, “Application of quantum cascade lasers to trace gas analysis,” Appl. Phys. B 90(2), 165–176 (2008).
[Crossref]

Appl. Phys. Lett. (5)

L. Jumpertz, M. Carras, K. Schires, and F. Grillot, “Regimes of external optical feedback in 5.6 µm distributed feedback mid-infrared quantum cascade lasers,” Appl. Phys. Lett. 105(13), 131112 (2014).
[Crossref]

M. C. Cardilli, M. Dabbicco, F. P. Mezzapesa, and G. Scamarcio, “Linewidth measurement of mid infrared quantum cascade laser by optical feedback interferometry,” Appl. Phys. Lett. 108(3), 031105 (2016).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104(4), 041112 (2014).
[Crossref]

J. C. Zhang, F. Q. Liu, S. Tan, D. Y. Yao, L. J. Wang, L. Li, J. Q. Liu, and Z. G. Wang, “High-performance uncooled distributed-feedback quantum cascade laser without lateral regrowth,” Appl. Phys. Lett. 100(11), 112105 (2012).
[Crossref]

J. Jágerská, P. Jouy, A. Hugi, B. Tuzson, H. Looser, M. Mangold, M. Beck, L. Emmenegger, and J. Faist, “Dual-wavelength quantum cascade laser for trace gas spectroscopy,” Appl. Phys. Lett. 105(16), 161109 (2014).
[Crossref]

Electron. Lett. (3)

Y. Takagi, N. Kumazaki, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Relative intensity noise measurements of 5 µm quantum cascade laser and 1.55 µm semiconductor laser,” Electron. Lett. 44(14), 860–861 (2008).
[Crossref]

T. Inoue, S. Mori, K. Tsushima, and K. Kasahara, “Quantum cascade laser intensity noise under external feedback conditions estimated from self-mixing method,” Electron. Lett. 49(6), 407–409 (2013).
[Crossref]

C. Juretzka, M. Carras, F. Schad, L. Drzewietzki, S. Breuer, and W. Elsäßer, “9.5 dB relative intensity noise reduction in quantum cascade laser by detuned loading,” Electron. Lett. 49(24), 1548–1550 (2013).
[Crossref]

Hyperfine Interact. (1)

R. Terabayashi, V. Sonnenschein, H. Tomita, N. Hayashi, S. Kato, L. Jin, M. Yamanaka, N. Nishizawa, A. Sato, K. Nozawa, K. Hashizume, T. Oh-hara, and T. Iguchi, “Optical feedback in dfb quantum cascade laser for mid-infrared cavity ring-down spectroscopy,” Hyperfine Interact. 238(1), 10 (2017).
[Crossref]

IEEE J. Quantum Electron. (7)

H. Simos, A. Bogris, D. Syvridis, and W. Elsäßer, “Intensity Noise Properties of Mid-Infrared Injection Locked Quantum Cascade Lasers: I. Modeling,” IEEE J. Quantum Electron. 50(2), 98–105 (2014).
[Crossref]

C. Juretzka, H. Simos, A. Bogris, D. Syvridis, W. Elsäßer, and M. Carras, “Intensity Noise Properties of Midinfrared Injection Locked Quantum Cascade Lasers: II. Experiments,” IEEE J. Quantum Electron. 51(1), 1–8 (2015).
[Crossref]

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J. Ohtsubo, Semiconductor Lasers Stability, Instability and Chaos, Springer Series in Optical Sciences (Springer, 2012).

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Figures (8)

Fig. 1.
Fig. 1. Experimental setup. BS1, BS2: Beam splitter, P1,2: Polarizer, FTIR: Fourier transform infrared spectrometer, PD: Photodiode, AMP: Preamplifier, and ESA: Electrical spectrum analyzer.
Fig. 2.
Fig. 2. (a) L-I-V curve of the free-running QCL. (b) Optical spectra at several pump currents. The QCL becomes dual modes above 420 mA.
Fig. 3.
Fig. 3. Optical feedback effects on (a) the L-I curve, (b) the optical spectra at 340 mA, and (c) the optical spectra at 380 mA. The arrows indicate shift trend of the lasing peak.
Fig. 4.
Fig. 4. Optical feedback effects on the wavenumber shift of the QCL.
Fig. 5.
Fig. 5. (a) Measured RIN spectra of the free-running QCL. (b) RINs averaged over 100-300 MHz. The dashed line indicates the onset of dual-mode lasing.
Fig. 6.
Fig. 6. Optical feedback effects on (a) the RIN spectra at 340 mA, and (b) the difference of the average RIN over 100-300 MHz with respect to the free-running value.
Fig. 7.
Fig. 7. Simulated intrinsic RIN spectra with optical feedback for (a) ϕ0=0 and for (b) ϕ0=π. (c) Low-frequency RIN difference with respect to the free-running case. The pump current is 1.2×Ith, the feedback delay time is τext=0.5 ns, and the LBF is αH=0.5. The dashed line in (c) indicates the minimum RIN at a certain feedback ratio.
Fig. 8.
Fig. 8. Low-frequency RIN difference with optical feedback for (a) αH=0.5, ϕ0=0; (b) αH=0.5, ϕ0=π; (c) αH=2.0, ϕ0=0; and (d) αH=2.0, ϕ0=π. The pump current of the QCL is fixed at 1.2×Ith.

Equations (7)

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d N 3 d t = η I q N 3 τ 32 N 3 τ 31 G 0 Δ N S + F 3 ( t ) .
d N 2 d t = N 3 τ 32 N 2 τ 21 + G 0 Δ N S + F 2 ( t ) .
d N 1 d t = N 3 τ 31 + N 2 τ 21 N 1 τ o u t + F 1 ( t ) .
d S d t = ( m G 0 Δ N 1 / τ p ) S + m β N 3 τ s p + 2 k c r e x t S ( t τ e x t ) S ( t ) cos Δ ϕ + F S ( t ) .
d ϕ d t = α H 2 ( m G 0 Δ N 1 / τ p ) k c r e x t S ( t τ e x t ) S ( t ) sin Δ ϕ + F ϕ ( t ) .
[ j ω + γ 11 γ 12 γ 13 0 γ 21 j ω + γ 22 γ 23 0 γ 31 γ 32 j ω γ 33 γ 34 γ 41 γ 42 γ 43 j ω + γ 44 ] [ δ N 3 ( ω ) δ N 2 ( ω ) δ S ( ω ) δ ϕ ( ω ) ] = [ F 3 F 2 F S F ϕ ]
γ 11 = τ 32 1 + τ 31 1 + G 0 S , γ 12 = G 0 S , γ 13 = G 0 Δ N , γ 21 = τ 32 1 + G 0 S , γ 22 = τ 21 1 + G 0 S γ 23 = G 0 Δ N , γ 31 = m ( β τ s p 1 + G 0 S ) , γ 32 = m G 0 S γ 33 = m G 0 Δ N τ p 1 + k c r e x t ( 1 + e j ω τ e x t ) cos ( ϕ 0 + Δ ω s τ e x t ) γ 34 = 2 k c r e x t ( 1 e j ω τ e x t ) sin ( ϕ 0 + Δ ω s τ e x t ) S , γ 41 = α H 2 m G 0 , γ 42 = α H 2 m G 0 γ 43 = k c r e x t 2 S ( 1 e j ω τ e x t ) sin ( ϕ 0 + Δ ω s τ e x t ) , γ 44 = k c r e x t ( 1 e j ω τ e x t ) cos ( ϕ 0 + Δ ω s τ e x t )

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