Abstract

Non-uniform lateral current distribution in quantum cascade (QC) lasers is investigated, as a result of stimulated-optical-emission-assisted electron transport, the rate of which depends on the local photon density and is comparable to the longitudinal optical (LO) phonon scattering rate. A microscopic model based on rate equations is built to study the self-consistent process of interaction between local electrons and photons in QC lasers. The non-uniform distribution of lateral current and the corresponding spatial hole burning are simulated from this model. Moreover, multi-transverse-mode operation in QC lasers is also investigated.

© 2014 Optical Society of America

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  1. M. D. Escarra, A. Benz, A. M. Bhatt, A. J. Hoffman, X. Wang, J. Y. Fan, C. Gmachl, “Thermoelectric effect in quantum cascade lasers,” IEEE Photonics J. 2, 500–509 (2010).
    [CrossRef]
  2. A. Lops, V. Spagnolo, G. Scamarcio, “Thermal modeling of GaInAs/AlInAs quantum cascade lasers,” J. Appl. Phys. 100, 043109 (2006).
    [CrossRef]
  3. W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
    [CrossRef]
  4. Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
    [CrossRef]
  5. N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
    [CrossRef] [PubMed]
  6. A. K. Wojcik, N. Yu, L. Diehl, F. Capasso, A. Belyanin, “Self-synchronization of laser modes and multistability in quantum cascade lasers,” Phys. Rev. Lett. 106, 133902 (2011).
    [CrossRef] [PubMed]
  7. Z.-M. S. Li, Y.-Y. Li, G.-P. Ru, “Simulation of quantum cascade lasers,” J. Appl. Phys. 110, 093109 (2011).
    [CrossRef]
  8. C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, “Resonant tunneling in quantum cascade lasers,” IEEE J. Quantum Electron. 34, 1722–1729 (1998).
    [CrossRef]
  9. Y. Yao, Z. Liu, A. J. Hoffman, K. J. Franz, C. F. Gmachl, “Voltage tenability of quantum cascade lasers,” IEEE J. Quantum Electron. 45, 730–736 (2009).
    [CrossRef]
  10. S. Kumar, Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
    [CrossRef]
  11. X. Huang, W. O. Charles, C. Gmachl, “Temperature-insensitive long-wavelength (λ≈ 14μ m) Quantum Cascade lasers with low threshold,” Opt. Express 19, 8297–8302 (2011).
    [CrossRef] [PubMed]
  12. X. Huang, Y. Chiu, W. O. Charles, C. Gmachl, “Ridge-width dependence of the threshold of long wavelength (λ≈ 14μ m) Quantum Cascade lasers with sloped and vertical side walls,” Opt. Express 20, 2539–2547 (2012).
    [CrossRef] [PubMed]
  13. 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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
    [CrossRef]

2012 (2)

Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
[CrossRef]

X. Huang, Y. Chiu, W. O. Charles, C. Gmachl, “Ridge-width dependence of the threshold of long wavelength (λ≈ 14μ m) Quantum Cascade lasers with sloped and vertical side walls,” Opt. Express 20, 2539–2547 (2012).
[CrossRef] [PubMed]

2011 (3)

X. Huang, W. O. Charles, C. Gmachl, “Temperature-insensitive long-wavelength (λ≈ 14μ m) Quantum Cascade lasers with low threshold,” Opt. Express 19, 8297–8302 (2011).
[CrossRef] [PubMed]

A. K. Wojcik, N. Yu, L. Diehl, F. Capasso, A. Belyanin, “Self-synchronization of laser modes and multistability in quantum cascade lasers,” Phys. Rev. Lett. 106, 133902 (2011).
[CrossRef] [PubMed]

Z.-M. S. Li, Y.-Y. Li, G.-P. Ru, “Simulation of quantum cascade lasers,” J. Appl. Phys. 110, 093109 (2011).
[CrossRef]

2010 (1)

M. D. Escarra, A. Benz, A. M. Bhatt, A. J. Hoffman, X. Wang, J. Y. Fan, C. Gmachl, “Thermoelectric effect in quantum cascade lasers,” IEEE Photonics J. 2, 500–509 (2010).
[CrossRef]

2009 (3)

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

Y. Yao, Z. Liu, A. J. Hoffman, K. J. Franz, C. F. Gmachl, “Voltage tenability of quantum cascade lasers,” IEEE J. Quantum Electron. 45, 730–736 (2009).
[CrossRef]

S. Kumar, Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
[CrossRef]

2008 (1)

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

2006 (1)

A. Lops, V. Spagnolo, G. Scamarcio, “Thermal modeling of GaInAs/AlInAs quantum cascade lasers,” J. Appl. Phys. 100, 043109 (2006).
[CrossRef]

2005 (1)

W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
[CrossRef]

1998 (1)

C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, “Resonant tunneling in quantum cascade lasers,” IEEE J. Quantum Electron. 34, 1722–1729 (1998).
[CrossRef]

Aidam, R.

Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
[CrossRef]

Belyanin, A.

A. K. Wojcik, N. Yu, L. Diehl, F. Capasso, A. Belyanin, “Self-synchronization of laser modes and multistability in quantum cascade lasers,” Phys. Rev. Lett. 106, 133902 (2011).
[CrossRef] [PubMed]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Benz, A.

M. D. Escarra, A. Benz, A. M. Bhatt, A. J. Hoffman, X. Wang, J. Y. Fan, C. Gmachl, “Thermoelectric effect in quantum cascade lasers,” IEEE Photonics J. 2, 500–509 (2010).
[CrossRef]

Bewley, W. W.

W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
[CrossRef]

Bhatt, A. M.

M. D. Escarra, A. Benz, A. M. Bhatt, A. J. Hoffman, X. Wang, J. Y. Fan, C. Gmachl, “Thermoelectric effect in quantum cascade lasers,” IEEE Photonics J. 2, 500–509 (2010).
[CrossRef]

Bour, D.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Bronner, W.

Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
[CrossRef]

Capasso, F.

A. K. Wojcik, N. Yu, L. Diehl, F. Capasso, A. Belyanin, “Self-synchronization of laser modes and multistability in quantum cascade lasers,” Phys. Rev. Lett. 106, 133902 (2011).
[CrossRef] [PubMed]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, “Resonant tunneling in quantum cascade lasers,” IEEE J. Quantum Electron. 34, 1722–1729 (1998).
[CrossRef]

Charles, W. O.

Chiu, Y.

Cho, A. Y.

C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, “Resonant tunneling in quantum cascade lasers,” IEEE J. Quantum Electron. 34, 1722–1729 (1998).
[CrossRef]

Corzine, S.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Crozier, K. B.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

Cubukcu, E.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

Diehl, L.

A. K. Wojcik, N. Yu, L. Diehl, F. Capasso, A. Belyanin, “Self-synchronization of laser modes and multistability in quantum cascade lasers,” Phys. Rev. Lett. 106, 133902 (2011).
[CrossRef] [PubMed]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Escarra, M. D.

M. D. Escarra, A. Benz, A. M. Bhatt, A. J. Hoffman, X. Wang, J. Y. Fan, C. Gmachl, “Thermoelectric effect in quantum cascade lasers,” IEEE Photonics J. 2, 500–509 (2010).
[CrossRef]

Evans, A. J.

W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
[CrossRef]

Faist, J.

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, “Resonant tunneling in quantum cascade lasers,” IEEE J. Quantum Electron. 34, 1722–1729 (1998).
[CrossRef]

Fan, J. Y.

M. D. Escarra, A. Benz, A. M. Bhatt, A. J. Hoffman, X. Wang, J. Y. Fan, C. Gmachl, “Thermoelectric effect in quantum cascade lasers,” IEEE Photonics J. 2, 500–509 (2010).
[CrossRef]

Franz, K. J.

Y. Yao, Z. Liu, A. J. Hoffman, K. J. Franz, C. F. Gmachl, “Voltage tenability of quantum cascade lasers,” IEEE J. Quantum Electron. 45, 730–736 (2009).
[CrossRef]

Fuchs, F.

Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
[CrossRef]

Gmachl, C.

Gmachl, C. F.

Y. Yao, Z. Liu, A. J. Hoffman, K. J. Franz, C. F. Gmachl, “Voltage tenability of quantum cascade lasers,” IEEE J. Quantum Electron. 45, 730–736 (2009).
[CrossRef]

Gordon, A.

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Hföler, G.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

Hinkov, B.

Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
[CrossRef]

Hoffman, A. J.

M. D. Escarra, A. Benz, A. M. Bhatt, A. J. Hoffman, X. Wang, J. Y. Fan, C. Gmachl, “Thermoelectric effect in quantum cascade lasers,” IEEE Photonics J. 2, 500–509 (2010).
[CrossRef]

Y. Yao, Z. Liu, A. J. Hoffman, K. J. Franz, C. F. Gmachl, “Voltage tenability of quantum cascade lasers,” IEEE J. Quantum Electron. 45, 730–736 (2009).
[CrossRef]

Höfler, G.

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Hu, Q.

S. Kumar, Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
[CrossRef]

Huang, X.

Hugger, S.

Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
[CrossRef]

Hutchinson, A. L.

C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, “Resonant tunneling in quantum cascade lasers,” IEEE J. Quantum Electron. 34, 1722–1729 (1998).
[CrossRef]

Kärtner, F. X.

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Kim, C. S.

W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
[CrossRef]

Kinzer, M.

Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
[CrossRef]

Kumar, S.

S. Kumar, Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
[CrossRef]

Li, Y.-Y.

Z.-M. S. Li, Y.-Y. Li, G.-P. Ru, “Simulation of quantum cascade lasers,” J. Appl. Phys. 110, 093109 (2011).
[CrossRef]

Li, Z.-M. S.

Z.-M. S. Li, Y.-Y. Li, G.-P. Ru, “Simulation of quantum cascade lasers,” J. Appl. Phys. 110, 093109 (2011).
[CrossRef]

Lindle, J. R.

W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
[CrossRef]

Liu, H. C.

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Liu, Z.

Y. Yao, Z. Liu, A. J. Hoffman, K. J. Franz, C. F. Gmachl, “Voltage tenability of quantum cascade lasers,” IEEE J. Quantum Electron. 45, 730–736 (2009).
[CrossRef]

Lops, A.

A. Lops, V. Spagnolo, G. Scamarcio, “Thermal modeling of GaInAs/AlInAs quantum cascade lasers,” J. Appl. Phys. 100, 043109 (2006).
[CrossRef]

Lösch, R.

Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
[CrossRef]

Maier, T.

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Meyer, J. R.

W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
[CrossRef]

Razeghi, M.

W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
[CrossRef]

Ru, G.-P.

Z.-M. S. Li, Y.-Y. Li, G.-P. Ru, “Simulation of quantum cascade lasers,” J. Appl. Phys. 110, 093109 (2011).
[CrossRef]

Scamarcio, G.

A. Lops, V. Spagnolo, G. Scamarcio, “Thermal modeling of GaInAs/AlInAs quantum cascade lasers,” J. Appl. Phys. 100, 043109 (2006).
[CrossRef]

Schneider, H.

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Sirtori, C.

C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, “Resonant tunneling in quantum cascade lasers,” IEEE J. Quantum Electron. 34, 1722–1729 (1998).
[CrossRef]

Sivco, D. L.

C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, “Resonant tunneling in quantum cascade lasers,” IEEE J. Quantum Electron. 34, 1722–1729 (1998).
[CrossRef]

Slivken, S.

W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
[CrossRef]

Spagnolo, V.

A. Lops, V. Spagnolo, G. Scamarcio, “Thermal modeling of GaInAs/AlInAs quantum cascade lasers,” J. Appl. Phys. 100, 043109 (2006).
[CrossRef]

Troccoli, M.

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Vurgaftman, I.

W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
[CrossRef]

Wagner, J.

Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
[CrossRef]

Wang, C. Y.

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Wang, X.

M. D. Escarra, A. Benz, A. M. Bhatt, A. J. Hoffman, X. Wang, J. Y. Fan, C. Gmachl, “Thermoelectric effect in quantum cascade lasers,” IEEE Photonics J. 2, 500–509 (2010).
[CrossRef]

Wojcik, A. K.

A. K. Wojcik, N. Yu, L. Diehl, F. Capasso, A. Belyanin, “Self-synchronization of laser modes and multistability in quantum cascade lasers,” Phys. Rev. Lett. 106, 133902 (2011).
[CrossRef] [PubMed]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

Yang, Q.

Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
[CrossRef]

Yao, Y.

Y. Yao, Z. Liu, A. J. Hoffman, K. J. Franz, C. F. Gmachl, “Voltage tenability of quantum cascade lasers,” IEEE J. Quantum Electron. 45, 730–736 (2009).
[CrossRef]

Yu, J. S.

W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
[CrossRef]

Yu, N.

A. K. Wojcik, N. Yu, L. Diehl, F. Capasso, A. Belyanin, “Self-synchronization of laser modes and multistability in quantum cascade lasers,” Phys. Rev. Lett. 106, 133902 (2011).
[CrossRef] [PubMed]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (3)

W. W. Bewley, J. R. Lindle, C. S. Kim, I. Vurgaftman, J. R. Meyer, A. J. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41, 833–841 (2005).
[CrossRef]

C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, “Resonant tunneling in quantum cascade lasers,” IEEE J. Quantum Electron. 34, 1722–1729 (1998).
[CrossRef]

Y. Yao, Z. Liu, A. J. Hoffman, K. J. Franz, C. F. Gmachl, “Voltage tenability of quantum cascade lasers,” IEEE J. Quantum Electron. 45, 730–736 (2009).
[CrossRef]

IEEE Photonics J. (1)

M. D. Escarra, A. Benz, A. M. Bhatt, A. J. Hoffman, X. Wang, J. Y. Fan, C. Gmachl, “Thermoelectric effect in quantum cascade lasers,” IEEE Photonics J. 2, 500–509 (2010).
[CrossRef]

J. Appl. Phys. (2)

A. Lops, V. Spagnolo, G. Scamarcio, “Thermal modeling of GaInAs/AlInAs quantum cascade lasers,” J. Appl. Phys. 100, 043109 (2006).
[CrossRef]

Z.-M. S. Li, Y.-Y. Li, G.-P. Ru, “Simulation of quantum cascade lasers,” J. Appl. Phys. 110, 093109 (2011).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (1)

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, F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[CrossRef]

Phys. Rev. B (1)

S. Kumar, Q. Hu, “Coherence of resonant-tunneling transport in terahertz quantum-cascade lasers,” Phys. Rev. B 80, 245316 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Hföler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102, 013901 (2009).
[CrossRef] [PubMed]

A. K. Wojcik, N. Yu, L. Diehl, F. Capasso, A. Belyanin, “Self-synchronization of laser modes and multistability in quantum cascade lasers,” Phys. Rev. Lett. 106, 133902 (2011).
[CrossRef] [PubMed]

Phys. Status Solidi C (1)

Q. Yang, M. Kinzer, F. Fuchs, S. Hugger, B. Hinkov, W. Bronner, R. Lösch, R. Aidam, J. Wagner, “Beam steering and lateral hole burning in mid-infrared quantum-cascade lasers,” Phys. Status Solidi C 9, 302–305 (2012).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

2D mode simulation for the fundamental transverse mode of a dry-etched QC laser emitting at ∼ 14 μm, with a ridge width of 14 μm. The active core is equally divided into 135 (9 × 15) regions. The two white lines are used to denote the center region along the vertical direction, which is studied in more detail.

Fig. 2
Fig. 2

Current density map of the cross section of the active core, with the QC laser at 3 times threshold.

Fig. 3
Fig. 3

(a) The total effective depletion rate, including LO phonon scattering and depletion by stimulated optical emission, of the upper laser level in different regions between the two white lines in Fig. 1. (b) Electron density of the upper laser level versus applied current in different regions.

Fig. 4
Fig. 4

Lateral current distribution with different injected current ranging from threshold current to 9 times threshold current. Also displayed is the lateral mode profile.

Fig. 5
Fig. 5

Gain map of the cross section of the active core, with the QC laser at 3 times threshold.

Fig. 6
Fig. 6

(a) Lateral hole burning simulation results. (a) Lateral hole burning with different injected current. Also displayed is the lateral mode profile. (b) Comparison of lateral spatial hole burning modeling, with uniform current density assumption and non-uniform current density due to stimulated optical emission, respectively.

Fig. 7
Fig. 7

2D simulation results of the first higher-order mode in the same QC structure as depicted in Fig. 1. The active core is also equally divided into 135 (9 × 15) regions. The two white lines denoted the center region in the vertical direction.

Fig. 8
Fig. 8

QC laser operation with the fundamental mode and the first higher-order mode. Simulations were conducted in two ways. One is based on the assumption that the current distribution in the active core is uniform, and the other is based on the self-consistent process of electron-photon interaction which leads to non-uniform current density.

Fig. 9
Fig. 9

Local current densities with different injected current ranging from threshold current to 9 times threshold current. Also displayed are the lateral mode profiles of the fundamental mode and the first higher-order mode. The first higher-order mode starts to lase at 3.3 times the threshold of the fundamental mode.

Fig. 10
Fig. 10

Spatial hole burning with different injected current. Also displayed are the lateral mode profiles of the fundamental mode and the first higher-order mode.

Equations (18)

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d N 3 , l , m d t = J l , m e N 3 , l , m τ 3 σ 32 φ p l , m ( N 3 , l , m N 2 , l , m ) ,
d N 2 , l , m d t = N 3 , l , m τ 32 + σ 32 φ p l , m ( N 3 , l , m N 2 , l , m ) N 2 , l , m τ 2 ,
d φ d t = c n φ { Γ σ 32 l = 1 L m = 1 M [ p l , m ( N 3 , l , m N 2 , l , m ) ] L p Σ l , m p l , m α } ,
N 3 , l , m , k = [ J l , m , k e N 3 , l , m , k 1 τ 3 σ 32 φ k 1 p l , m ( N 3 , l , m , k 1 N 2 , l , m , k 1 ) ] Δ t + N 3 , l , m , k 1 ,
N 2 , l , m , k = [ N 2 , l , m , k 1 τ 32 + σ 32 φ k 1 p l , m ( N 3 , l , m , k 1 N 2 , l , m , k 1 ) N 2 , l , m , k 1 τ 2 ] Δ t + N 2 , l , m , k 1 ,
φ k = { c n φ k 1 [ Γ σ 32 l = 1 L m = 1 M [ p l , m ( N 3 , l , m , k N 2 , l , m , k ) ] L p Σ l , m p l , m α ] } Δ t + φ k 1 ,
1 τ 3 , l , m , k eff = 1 τ 3 + 1 τ 3 , l , m , k ST .
τ 3 , l , m , k eff = N 3 , l , m , k N 3 , l , m , k τ 3 + σ 32 φ k p l , m ( N 3 , l , m , k N 2 , l , m , k ) .
J l , m , k + 1 = N 3 , l , m , k / τ 3 , l , m , k eff m = 1 M N 3 , l , m , k / τ 3 , l , m , k eff I / A ,
d N 3 , l , m d t = J l , m e N 3 , l , m τ 3 σ 32 ( φ p l , m + φ ' p l , m ' ) ( N 3 , l , m N 2 , l , m ) ,
d N 2 , l , m d t = N 3 , l , m τ 32 + σ 32 ( φ p l , m + φ ' p l , m ' ) ( N 3 , l , m N 2 , l , m ) N 2 , l , m τ 2 ,
d φ d t = c n φ { Γ σ 32 l = 1 L m = 1 M [ p l , m ( N 3 , l , m N 2 , l , m ) ] L p Σ l , m p l , m α } ,
d φ ' d t = c n φ ' { Γ ' σ 32 l = 1 L m = 1 M [ p l , m ' ( N 3 , l , m N 2 , l , m ) ] L p Σ l , m p l , m α ' }
N 3 , l , m , k = [ J l , m , k e N 3 , l , m , k 1 τ 3 σ 32 ( φ k 1 p l , m + φ k 1 ' p l , m ' ) ( N 3 , l , m , k 1 N 2 , l , m , k 1 ) ] Δ t + N 3 , l , m , k 1 ,
N 2 , l , m , k = [ N 3 , l , m , k 1 τ 32 + σ 32 ( φ k 1 p l , m + φ k 1 ' p l , m ' ) ( N 3 , l , m , k 1 N 2 , l , m , k 1 ) N 2 , l , m , k 1 τ 2 ] Δ t + N 2 , l , m , k 1 ,
φ k = { c n φ k 1 [ Γ σ 32 l = 1 L m = 1 M [ p l , m ( N 3 , l , m , k N 2 , l , m , k ) ] L p Σ l , m p l , m α ] } Δ t + φ k 1 ,
φ k ' = { c n φ k 1 ' [ Γ σ 32 l = 1 L m = 1 M [ p l , m ' ( N 3 , l , m , k N 2 , l , m , k ) ] L p Σ l , m p l , m ' α ' ] } Δ t + φ k 1 ' ,
τ 3 , l , m , k eff = N 3 , l , m , k N 3 , l , m , k τ 3 + σ 32 ( φ k p l , m + φ k ' p l , m ' ) ( N 3 , l , m , k N 2 , l , m , k ) .

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