Abstract

A high-Q photonic crystal (PC) microcavity for TM-like modes, which can be applied to quantum cascade lasers (QCLs), was successfully designed in an air-hole based PC slab with semiconductor cladding layers. In spite of no photonic badgaps for TM-like modes in air-hole based PC slabs, cavity Q reached up to 2,200 by utilizing a graded square lattice PC structure. This is ~18 times higher than those previously reported for PC defect-mode microcavities for QCLs. This large improvement is attributed to a suppression of the coupling between the cavity mode and the leaky modes thanks to the dielectric perturbation in the graded structure. We also predicted a dramatic reduction of the threshold current in the designed cavity down to one-fifteenth of that of a conventional QCL, due to a decreased optical volume.

© 2008 Optical Society of America

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  1. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
    [CrossRef] [PubMed]
  2. L. A. Dunbar, R. Houdre, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, "Small optical volume terahertz emitting microdisk quantum cascade lasers," Appl. Phys. Lett. 90141114 (2007).
    [CrossRef]
  3. S. Hofling, J. Seufert, J. P. Reithmaier, and A. Forchel, "Room temperature operation of ultra-short quantum cascade lasers with deeply etched Bragg mirrors," Electron. Lett. 41, 704-705 (2005).
    [CrossRef]
  4. J. Heinrich, R. Langhans, J. Seufert, S. Hofling, and A. Forchel, "Quantum cascade microlasers with two-dimensional photonic crystal reflectors," IEEE Photon. Technol. Lett. 19, 1937-1939 (2007).
    [CrossRef]
  5. R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
    [CrossRef] [PubMed]
  6. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  7. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
    [CrossRef] [PubMed]
  8. K. Nozaki, S. Kita, and T. Baba, "Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser," Opt. Express 15, 7506-7514 (2007).
    [CrossRef] [PubMed]
  9. M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, "Room temperature continuous-wave lasing in photonic crystal nanocavity," Opt. Express 14, 6308-6315 (2006).
    [CrossRef] [PubMed]
  10. H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
    [CrossRef] [PubMed]
  11. S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
    [CrossRef]
  12. L. C. Andreani and D. Gerace, "Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method," Phys. Rev. B 73, 235114 (2006).
    [CrossRef]
  13. P. Ma, F. Robin, H. Jackel, "Realistic photonic bandgap structures for TM-polarized light for all-optical switching," Opt. Express 14, 12794-12802 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12794.
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. M. Loncar, B. G. Lee, L. Diehl, M. Belkin, F. Capasso, M. Giovannini, J. Faist, and E. Gini, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Opt. Express 15, 4499-4514 (2007),
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    [CrossRef]
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    [CrossRef]
  19. L. Martiardonna, L. Carbone, A. Tandaechanurat, M. Kitamura, S. Iwamoto, L. Manna, M. D. Vittorio, R. Cingolani, and Y. Arakawa, "Two-dimensional photonic crystal resist membrane nanocavity embedding colloidal dot-in-a-rod nanocrystals," Nano Lett. 8, 260-264 (2008).
    [CrossRef]
  20. O. Painter, K. Srinivasan, and P. E. Barclay, "Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals," Phys. Rev. B 68,035214 (2003).
    [CrossRef]
  21. H. Page, C. Becker, A. Robertson, G. Glastre, V. Ortiz, and C. Sirtori, "300 K operation of a GaAs-based quantum-cascade laser at lambda approximate to 9μm," Appl. Phys. Lett. 78, 3529-3531 (2001).
    [CrossRef] [PubMed]
  22. K. Srinivasan and O. Painter, "Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals," Opt. Express 11, 579-593 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-6-579.
    [CrossRef]
  23. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
    [CrossRef] [PubMed]
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    [CrossRef]
  25. T. Herrle, S. Haneder, and W. Wegscheider, "Role of excited states for the material gain and threshold current density in quantum wire intersubband laser structures," Phys. Rev. B 73,205328 (2006).
    [CrossRef]
  26. S. Chakravarty, P. Bhattacharya, J. Topol'ancik, and Z. Wu, "Electrically injected quantum dot photonic crystal microcavity light emitters and microcavity arrays," J. Phys. D Appl. Phys. 40, 2683-2690 (2007).
  27. E. M. Purcell, "Spontaneous Emission probabilities at radio frequencies," Phys. Rev. 69, 681-681 (1946).

2008

L. Martiardonna, L. Carbone, A. Tandaechanurat, M. Kitamura, S. Iwamoto, L. Manna, M. D. Vittorio, R. Cingolani, and Y. Arakawa, "Two-dimensional photonic crystal resist membrane nanocavity embedding colloidal dot-in-a-rod nanocrystals," Nano Lett. 8, 260-264 (2008).
[CrossRef]

A. Tandaechanurat, S. Iwamoto, M. Nomura, N. Kumagai, and Y. Arakawa, "Increase of Q-factor in photonic crystal H1-defect nanocavities after closing of photonic bandgap with optimal slab thickness," Opt. Express 16,448-455, (2008), http://oe.osa.org/abstract.cfm?URI=oe-16-1-448.
[CrossRef]

2007

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, and O. Painter, "Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap," Opt. Express 15, 5948-5965 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-10-5948.
[CrossRef] [PubMed]

K. Nozaki, S. Kita, and T. Baba, "Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser," Opt. Express 15, 7506-7514 (2007).
[CrossRef] [PubMed]

M. Loncar, B. G. Lee, L. Diehl, M. Belkin, F. Capasso, M. Giovannini, J. Faist, and E. Gini, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Opt. Express 15, 4499-4514 (2007),
[CrossRef] [PubMed]

S. Chakravarty, P. Bhattacharya, J. Topol'ancik, and Z. Wu, "Electrically injected quantum dot photonic crystal microcavity light emitters and microcavity arrays," J. Phys. D Appl. Phys. 40, 2683-2690 (2007).

L. A. Dunbar, R. Houdre, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, "Small optical volume terahertz emitting microdisk quantum cascade lasers," Appl. Phys. Lett. 90141114 (2007).
[CrossRef]

J. Heinrich, R. Langhans, J. Seufert, S. Hofling, and A. Forchel, "Quantum cascade microlasers with two-dimensional photonic crystal reflectors," IEEE Photon. Technol. Lett. 19, 1937-1939 (2007).
[CrossRef]

2006

L. C. Andreani and D. Gerace, "Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method," Phys. Rev. B 73, 235114 (2006).
[CrossRef]

T. Herrle, S. Haneder, and W. Wegscheider, "Role of excited states for the material gain and threshold current density in quantum wire intersubband laser structures," Phys. Rev. B 73,205328 (2006).
[CrossRef]

M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, "Room temperature continuous-wave lasing in photonic crystal nanocavity," Opt. Express 14, 6308-6315 (2006).
[CrossRef] [PubMed]

P. Ma, F. Robin, H. Jackel, "Realistic photonic bandgap structures for TM-polarized light for all-optical switching," Opt. Express 14, 12794-12802 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12794.
[CrossRef] [PubMed]

2005

S. Hofling, J. Seufert, J. P. Reithmaier, and A. Forchel, "Room temperature operation of ultra-short quantum cascade lasers with deeply etched Bragg mirrors," Electron. Lett. 41, 704-705 (2005).
[CrossRef]

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

2004

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

2003

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

K. Srinivasan, P. E. Barclay, O. Painter, J. X. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

O. Painter, K. Srinivasan, and P. E. Barclay, "Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals," Phys. Rev. B 68,035214 (2003).
[CrossRef]

K. Srinivasan and O. Painter, "Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals," Opt. Express 11, 579-593 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-6-579.
[CrossRef]

2002

2001

H. Page, C. Becker, A. Robertson, G. Glastre, V. Ortiz, and C. Sirtori, "300 K operation of a GaAs-based quantum-cascade laser at lambda approximate to 9μm," Appl. Phys. Lett. 78, 3529-3531 (2001).
[CrossRef] [PubMed]

1999

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

1994

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

1987

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

1966

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
[CrossRef] [PubMed]

1946

E. M. Purcell, "Spontaneous Emission probabilities at radio frequencies," Phys. Rev. 69, 681-681 (1946).

Andreani, L. C.

L. C. Andreani and D. Gerace, "Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method," Phys. Rev. B 73, 235114 (2006).
[CrossRef]

Arakawa, Y.

Asano, T.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Baba, T.

Baek, J. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Bahriz, M.

Barclay, P. E.

K. Srinivasan, P. E. Barclay, O. Painter, J. X. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

O. Painter, K. Srinivasan, and P. E. Barclay, "Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals," Phys. Rev. B 68,035214 (2003).
[CrossRef]

Becker, C.

H. Page, C. Becker, A. Robertson, G. Glastre, V. Ortiz, and C. Sirtori, "300 K operation of a GaAs-based quantum-cascade laser at lambda approximate to 9μm," Appl. Phys. Lett. 78, 3529-3531 (2001).
[CrossRef] [PubMed]

Belkin, M.

M. Loncar, B. G. Lee, L. Diehl, M. Belkin, F. Capasso, M. Giovannini, J. Faist, and E. Gini, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Opt. Express 15, 4499-4514 (2007),
[CrossRef] [PubMed]

Bhattacharya, P.

S. Chakravarty, P. Bhattacharya, J. Topol'ancik, and Z. Wu, "Electrically injected quantum dot photonic crystal microcavity light emitters and microcavity arrays," J. Phys. D Appl. Phys. 40, 2683-2690 (2007).

Capasso, F.

M. Loncar, B. G. Lee, L. Diehl, M. Belkin, F. Capasso, M. Giovannini, J. Faist, and E. Gini, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Opt. Express 15, 4499-4514 (2007),
[CrossRef] [PubMed]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Carbone, L.

L. Martiardonna, L. Carbone, A. Tandaechanurat, M. Kitamura, S. Iwamoto, L. Manna, M. D. Vittorio, R. Cingolani, and Y. Arakawa, "Two-dimensional photonic crystal resist membrane nanocavity embedding colloidal dot-in-a-rod nanocrystals," Nano Lett. 8, 260-264 (2008).
[CrossRef]

Chakravarty, S.

S. Chakravarty, P. Bhattacharya, J. Topol'ancik, and Z. Wu, "Electrically injected quantum dot photonic crystal microcavity light emitters and microcavity arrays," J. Phys. D Appl. Phys. 40, 2683-2690 (2007).

Chen, J. X.

K. Srinivasan, P. E. Barclay, O. Painter, J. X. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Cho, A. Y.

K. Srinivasan, P. E. Barclay, O. Painter, J. X. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Cingolani, R.

L. Martiardonna, L. Carbone, A. Tandaechanurat, M. Kitamura, S. Iwamoto, L. Manna, M. D. Vittorio, R. Cingolani, and Y. Arakawa, "Two-dimensional photonic crystal resist membrane nanocavity embedding colloidal dot-in-a-rod nanocrystals," Nano Lett. 8, 260-264 (2008).
[CrossRef]

Colombelli, R.

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, and O. Painter, "Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap," Opt. Express 15, 5948-5965 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-10-5948.
[CrossRef] [PubMed]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

Crisafulli, O.

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Diehl, L.

M. Loncar, B. G. Lee, L. Diehl, M. Belkin, F. Capasso, M. Giovannini, J. Faist, and E. Gini, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Opt. Express 15, 4499-4514 (2007),
[CrossRef] [PubMed]

Dunbar, L. A.

L. A. Dunbar, R. Houdre, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, "Small optical volume terahertz emitting microdisk quantum cascade lasers," Appl. Phys. Lett. 90141114 (2007).
[CrossRef]

Faist, J.

L. A. Dunbar, R. Houdre, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, "Small optical volume terahertz emitting microdisk quantum cascade lasers," Appl. Phys. Lett. 90141114 (2007).
[CrossRef]

M. Loncar, B. G. Lee, L. Diehl, M. Belkin, F. Capasso, M. Giovannini, J. Faist, and E. Gini, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Opt. Express 15, 4499-4514 (2007),
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Forchel, A.

J. Heinrich, R. Langhans, J. Seufert, S. Hofling, and A. Forchel, "Quantum cascade microlasers with two-dimensional photonic crystal reflectors," IEEE Photon. Technol. Lett. 19, 1937-1939 (2007).
[CrossRef]

S. Hofling, J. Seufert, J. P. Reithmaier, and A. Forchel, "Room temperature operation of ultra-short quantum cascade lasers with deeply etched Bragg mirrors," Electron. Lett. 41, 704-705 (2005).
[CrossRef]

Gerace, D.

L. C. Andreani and D. Gerace, "Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method," Phys. Rev. B 73, 235114 (2006).
[CrossRef]

Gini, E.

M. Loncar, B. G. Lee, L. Diehl, M. Belkin, F. Capasso, M. Giovannini, J. Faist, and E. Gini, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Opt. Express 15, 4499-4514 (2007),
[CrossRef] [PubMed]

Giovannini, M.

M. Loncar, B. G. Lee, L. Diehl, M. Belkin, F. Capasso, M. Giovannini, J. Faist, and E. Gini, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Opt. Express 15, 4499-4514 (2007),
[CrossRef] [PubMed]

L. A. Dunbar, R. Houdre, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, "Small optical volume terahertz emitting microdisk quantum cascade lasers," Appl. Phys. Lett. 90141114 (2007).
[CrossRef]

Glastre, G.

H. Page, C. Becker, A. Robertson, G. Glastre, V. Ortiz, and C. Sirtori, "300 K operation of a GaAs-based quantum-cascade laser at lambda approximate to 9μm," Appl. Phys. Lett. 78, 3529-3531 (2001).
[CrossRef] [PubMed]

Gmachl, C.

K. Srinivasan, P. E. Barclay, O. Painter, J. X. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Gmachl, C. F.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

Haneder, S.

T. Herrle, S. Haneder, and W. Wegscheider, "Role of excited states for the material gain and threshold current density in quantum wire intersubband laser structures," Phys. Rev. B 73,205328 (2006).
[CrossRef]

Heinrich, J.

J. Heinrich, R. Langhans, J. Seufert, S. Hofling, and A. Forchel, "Quantum cascade microlasers with two-dimensional photonic crystal reflectors," IEEE Photon. Technol. Lett. 19, 1937-1939 (2007).
[CrossRef]

Herrle, T.

T. Herrle, S. Haneder, and W. Wegscheider, "Role of excited states for the material gain and threshold current density in quantum wire intersubband laser structures," Phys. Rev. B 73,205328 (2006).
[CrossRef]

Hofling, S.

J. Heinrich, R. Langhans, J. Seufert, S. Hofling, and A. Forchel, "Quantum cascade microlasers with two-dimensional photonic crystal reflectors," IEEE Photon. Technol. Lett. 19, 1937-1939 (2007).
[CrossRef]

S. Hofling, J. Seufert, J. P. Reithmaier, and A. Forchel, "Room temperature operation of ultra-short quantum cascade lasers with deeply etched Bragg mirrors," Electron. Lett. 41, 704-705 (2005).
[CrossRef]

Houdre, R.

L. A. Dunbar, R. Houdre, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, "Small optical volume terahertz emitting microdisk quantum cascade lasers," Appl. Phys. Lett. 90141114 (2007).
[CrossRef]

Hutchinson, A. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Ishida, S.

Iwamoto, S.

Jackel, H.

Ju, Y. G.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Kim, S. B.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Kim, S. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Kita, S.

Kitagawa, H.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Kitamura, M.

L. Martiardonna, L. Carbone, A. Tandaechanurat, M. Kitamura, S. Iwamoto, L. Manna, M. D. Vittorio, R. Cingolani, and Y. Arakawa, "Two-dimensional photonic crystal resist membrane nanocavity embedding colloidal dot-in-a-rod nanocrystals," Nano Lett. 8, 260-264 (2008).
[CrossRef]

Kumagai, N.

Kwon, S. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Langhans, R.

J. Heinrich, R. Langhans, J. Seufert, S. Hofling, and A. Forchel, "Quantum cascade microlasers with two-dimensional photonic crystal reflectors," IEEE Photon. Technol. Lett. 19, 1937-1939 (2007).
[CrossRef]

Lee, B. G.

M. Loncar, B. G. Lee, L. Diehl, M. Belkin, F. Capasso, M. Giovannini, J. Faist, and E. Gini, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Opt. Express 15, 4499-4514 (2007),
[CrossRef] [PubMed]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Lee, Y. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Loncar, M.

M. Loncar, B. G. Lee, L. Diehl, M. Belkin, F. Capasso, M. Giovannini, J. Faist, and E. Gini, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Opt. Express 15, 4499-4514 (2007),
[CrossRef] [PubMed]

Ma, P.

Manna, L.

L. Martiardonna, L. Carbone, A. Tandaechanurat, M. Kitamura, S. Iwamoto, L. Manna, M. D. Vittorio, R. Cingolani, and Y. Arakawa, "Two-dimensional photonic crystal resist membrane nanocavity embedding colloidal dot-in-a-rod nanocrystals," Nano Lett. 8, 260-264 (2008).
[CrossRef]

Martiardonna, L.

L. Martiardonna, L. Carbone, A. Tandaechanurat, M. Kitamura, S. Iwamoto, L. Manna, M. D. Vittorio, R. Cingolani, and Y. Arakawa, "Two-dimensional photonic crystal resist membrane nanocavity embedding colloidal dot-in-a-rod nanocrystals," Nano Lett. 8, 260-264 (2008).
[CrossRef]

Moreau, V.

Nakata, Y.

Noda, S.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Nomura, M.

Nozaki, K.

O'Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Ortiz, V.

H. Page, C. Becker, A. Robertson, G. Glastre, V. Ortiz, and C. Sirtori, "300 K operation of a GaAs-based quantum-cascade laser at lambda approximate to 9μm," Appl. Phys. Lett. 78, 3529-3531 (2001).
[CrossRef] [PubMed]

Page, H.

H. Page, C. Becker, A. Robertson, G. Glastre, V. Ortiz, and C. Sirtori, "300 K operation of a GaAs-based quantum-cascade laser at lambda approximate to 9μm," Appl. Phys. Lett. 78, 3529-3531 (2001).
[CrossRef] [PubMed]

Painter, O.

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, and O. Painter, "Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap," Opt. Express 15, 5948-5965 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-10-5948.
[CrossRef] [PubMed]

K. Srinivasan, P. E. Barclay, O. Painter, J. X. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

O. Painter, K. Srinivasan, and P. E. Barclay, "Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals," Phys. Rev. B 68,035214 (2003).
[CrossRef]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

K. Srinivasan and O. Painter, "Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals," Opt. Express 11, 579-593 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-6-579.
[CrossRef]

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-15-670.
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Park, H. G.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Purcell, E. M.

E. M. Purcell, "Spontaneous Emission probabilities at radio frequencies," Phys. Rev. 69, 681-681 (1946).

Reithmaier, J. P.

S. Hofling, J. Seufert, J. P. Reithmaier, and A. Forchel, "Room temperature operation of ultra-short quantum cascade lasers with deeply etched Bragg mirrors," Electron. Lett. 41, 704-705 (2005).
[CrossRef]

Robertson, A.

H. Page, C. Becker, A. Robertson, G. Glastre, V. Ortiz, and C. Sirtori, "300 K operation of a GaAs-based quantum-cascade laser at lambda approximate to 9μm," Appl. Phys. Lett. 78, 3529-3531 (2001).
[CrossRef] [PubMed]

Robin, F.

Scalari, G.

L. A. Dunbar, R. Houdre, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, "Small optical volume terahertz emitting microdisk quantum cascade lasers," Appl. Phys. Lett. 90141114 (2007).
[CrossRef]

Scherer, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Sergent, A. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

Seufert, J.

J. Heinrich, R. Langhans, J. Seufert, S. Hofling, and A. Forchel, "Quantum cascade microlasers with two-dimensional photonic crystal reflectors," IEEE Photon. Technol. Lett. 19, 1937-1939 (2007).
[CrossRef]

S. Hofling, J. Seufert, J. P. Reithmaier, and A. Forchel, "Room temperature operation of ultra-short quantum cascade lasers with deeply etched Bragg mirrors," Electron. Lett. 41, 704-705 (2005).
[CrossRef]

Sirigu, L.

L. A. Dunbar, R. Houdre, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, "Small optical volume terahertz emitting microdisk quantum cascade lasers," Appl. Phys. Lett. 90141114 (2007).
[CrossRef]

Sirtori, C.

H. Page, C. Becker, A. Robertson, G. Glastre, V. Ortiz, and C. Sirtori, "300 K operation of a GaAs-based quantum-cascade laser at lambda approximate to 9μm," Appl. Phys. Lett. 78, 3529-3531 (2001).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Sivco, D. L.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Srinivasan, K.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

O. Painter, K. Srinivasan, and P. E. Barclay, "Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals," Phys. Rev. B 68,035214 (2003).
[CrossRef]

K. Srinivasan and O. Painter, "Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals," Opt. Express 11, 579-593 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-6-579.
[CrossRef]

K. Srinivasan, P. E. Barclay, O. Painter, J. X. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-15-670.
[CrossRef]

Takayama, S.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Tanaka, Y.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Tandaechanurat, A.

A. Tandaechanurat, S. Iwamoto, M. Nomura, N. Kumagai, and Y. Arakawa, "Increase of Q-factor in photonic crystal H1-defect nanocavities after closing of photonic bandgap with optimal slab thickness," Opt. Express 16,448-455, (2008), http://oe.osa.org/abstract.cfm?URI=oe-16-1-448.
[CrossRef]

L. Martiardonna, L. Carbone, A. Tandaechanurat, M. Kitamura, S. Iwamoto, L. Manna, M. D. Vittorio, R. Cingolani, and Y. Arakawa, "Two-dimensional photonic crystal resist membrane nanocavity embedding colloidal dot-in-a-rod nanocrystals," Nano Lett. 8, 260-264 (2008).
[CrossRef]

Tennant, D. M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

Topol'ancik, J.

S. Chakravarty, P. Bhattacharya, J. Topol'ancik, and Z. Wu, "Electrically injected quantum dot photonic crystal microcavity light emitters and microcavity arrays," J. Phys. D Appl. Phys. 40, 2683-2690 (2007).

Troccoli, M.

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

Vittorio, M. D.

L. Martiardonna, L. Carbone, A. Tandaechanurat, M. Kitamura, S. Iwamoto, L. Manna, M. D. Vittorio, R. Cingolani, and Y. Arakawa, "Two-dimensional photonic crystal resist membrane nanocavity embedding colloidal dot-in-a-rod nanocrystals," Nano Lett. 8, 260-264 (2008).
[CrossRef]

Watanabe, K.

Wegscheider, W.

T. Herrle, S. Haneder, and W. Wegscheider, "Role of excited states for the material gain and threshold current density in quantum wire intersubband laser structures," Phys. Rev. B 73,205328 (2006).
[CrossRef]

Wu, Z.

S. Chakravarty, P. Bhattacharya, J. Topol'ancik, and Z. Wu, "Electrically injected quantum dot photonic crystal microcavity light emitters and microcavity arrays," J. Phys. D Appl. Phys. 40, 2683-2690 (2007).

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yang, J. K.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Yee, K. S.

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
[CrossRef] [PubMed]

Appl. Phys. Lett.

L. A. Dunbar, R. Houdre, G. Scalari, L. Sirigu, M. Giovannini, and J. Faist, "Small optical volume terahertz emitting microdisk quantum cascade lasers," Appl. Phys. Lett. 90141114 (2007).
[CrossRef]

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

K. Srinivasan, P. E. Barclay, O. Painter, J. X. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

H. Page, C. Becker, A. Robertson, G. Glastre, V. Ortiz, and C. Sirtori, "300 K operation of a GaAs-based quantum-cascade laser at lambda approximate to 9μm," Appl. Phys. Lett. 78, 3529-3531 (2001).
[CrossRef] [PubMed]

Electron. Lett.

S. Hofling, J. Seufert, J. P. Reithmaier, and A. Forchel, "Room temperature operation of ultra-short quantum cascade lasers with deeply etched Bragg mirrors," Electron. Lett. 41, 704-705 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

J. Heinrich, R. Langhans, J. Seufert, S. Hofling, and A. Forchel, "Quantum cascade microlasers with two-dimensional photonic crystal reflectors," IEEE Photon. Technol. Lett. 19, 1937-1939 (2007).
[CrossRef]

IEEE Trans. Antennas Propag.

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
[CrossRef] [PubMed]

J. Phys. D Appl. Phys.

S. Chakravarty, P. Bhattacharya, J. Topol'ancik, and Z. Wu, "Electrically injected quantum dot photonic crystal microcavity light emitters and microcavity arrays," J. Phys. D Appl. Phys. 40, 2683-2690 (2007).

Nano Lett.

L. Martiardonna, L. Carbone, A. Tandaechanurat, M. Kitamura, S. Iwamoto, L. Manna, M. D. Vittorio, R. Cingolani, and Y. Arakawa, "Two-dimensional photonic crystal resist membrane nanocavity embedding colloidal dot-in-a-rod nanocrystals," Nano Lett. 8, 260-264 (2008).
[CrossRef]

Opt. Express

M. Loncar, B. G. Lee, L. Diehl, M. Belkin, F. Capasso, M. Giovannini, J. Faist, and E. Gini, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Opt. Express 15, 4499-4514 (2007),
[CrossRef] [PubMed]

Opt. Express

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-15-670.
[CrossRef]

K. Srinivasan and O. Painter, "Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals," Opt. Express 11, 579-593 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-6-579.
[CrossRef]

M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, "Room temperature continuous-wave lasing in photonic crystal nanocavity," Opt. Express 14, 6308-6315 (2006).
[CrossRef] [PubMed]

P. Ma, F. Robin, H. Jackel, "Realistic photonic bandgap structures for TM-polarized light for all-optical switching," Opt. Express 14, 12794-12802 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12794.
[CrossRef] [PubMed]

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, and O. Painter, "Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap," Opt. Express 15, 5948-5965 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-10-5948.
[CrossRef] [PubMed]

K. Nozaki, S. Kita, and T. Baba, "Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser," Opt. Express 15, 7506-7514 (2007).
[CrossRef] [PubMed]

A. Tandaechanurat, S. Iwamoto, M. Nomura, N. Kumagai, and Y. Arakawa, "Increase of Q-factor in photonic crystal H1-defect nanocavities after closing of photonic bandgap with optimal slab thickness," Opt. Express 16,448-455, (2008), http://oe.osa.org/abstract.cfm?URI=oe-16-1-448.
[CrossRef]

Phys. Rev.

E. M. Purcell, "Spontaneous Emission probabilities at radio frequencies," Phys. Rev. 69, 681-681 (1946).

Phys. Rev. B

T. Herrle, S. Haneder, and W. Wegscheider, "Role of excited states for the material gain and threshold current density in quantum wire intersubband laser structures," Phys. Rev. B 73,205328 (2006).
[CrossRef]

O. Painter, K. Srinivasan, and P. E. Barclay, "Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals," Phys. Rev. B 68,035214 (2003).
[CrossRef]

L. C. Andreani and D. Gerace, "Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method," Phys. Rev. B 73, 235114 (2006).
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Science

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, "Quantum cascade surface-emitting photonic crystal laser," Science 302, 1374-1377 (2003).
[CrossRef] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Other

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Figures (8)

Fig. 1.
Fig. 1.

Graded lattice PC structure and mechanism of mode coupling of a cavity mode with leaky modes in the structure. (a) Schematic illustration of a 2D graded PC structure. Air hole radii are modulated gradually outwards over two periods. (b), (c) Distributions of the dielectric perturbation in real space and momentum space. (d) Schematic illustration of mode distributions of cavity, radiation, and waveguide modes in momentum space.

Fig. 2.
Fig. 2.

Schematics of a PC QC microcavity and its layer structure. The active region is sandwiched by low-doped GaAs layers to reduce absorption loss caused by high-doped cladding layers. The doping density and thickness of active and cladding layers are the same as in Ref. [20].

Fig. 3.
Fig. 3.

Investigated graded lattice PC pattern, where grey region is high index material and white circles are air holes. Air holes radii are increased quadratically outwards over six periods from r=0.20 a to 0.34 a and the modulated area is surrounded by nine periods of PC lattice with a fixed air hole radius of 0.4 a.

Fig. 4.
Fig. 4.

Cavity characteristics for a graded lattice PC microcavity (A) and a conventional PC microcavity (B). (a), (e) Photonic crystal patterns with gradually modulated r/a and fixed r/a, respectively. (b), (c), (f), (g) Calculated mode distributions of vertical directional electric field component (E z ) at d/a=5 in the xy plane (z=0) ((b), (f)) and in the xz plane (y=-a/2) ((c), (g)). 1D mode plot along z-direction (x=0, y=-a/2) is inserted. (d), (h) Fourier transformed vertical directional electric field component profile ( E Z ˜ ) in the xy plane (z=0). Solid and broken lines represent a light line of cladding layer and that of substrate, respectively.

Fig. 5.
Fig. 5.

Photonic band structure for TM-like modes, calculated by 3D FDTD method, in which r/a=0.4 (radius rate of the outermost air holes), and d/a=5. The broken red line is the frequency of the fundamental cavity mode in a graded PC lattice. The green and yarrow circles indicate the coupling of the cavity mode with the waveguide modes, and dominant component of the cavity mode, respectively.

Fig. 6.
Fig. 6.

Dielectric perturbation profiles in the momentum space of PC cavities (a) with the gradually modulated r/a and (b) with the fixed r/a. (c) Illustration showing the mode coupling between a cavity mode and leaky modes in momentum space. (d) Comparison between dielectric perturbations scanned from point “a” to “b” in (a) and (b).

Fig. 7.
Fig. 7.

Q-factor dependence on d/a. Q-factor is divided into vertical directional Q and lateral directional Q components. The red line is the normalized frequency (a/λ)

Fig. 8.
Fig. 8.

Q-factor dependence on d/a. Total Q-factor (Q total) is divided into passive Q (Q pass) and material Q (Q mat) components.

Tables (1)

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Table 1. Comparison of characteristics of a Fabry-Perot cavity and a PC cavity.

Equations (4)

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1 Q mat = 1 Q total 1 Q pass ,
g Γ = 2 e E 32 Z 32 2 N p ħ c ε 0 n eff L p γ 32 η in τ 3 ( 1 τ 21 τ 32 ) J . Γ ,
Q = 2 π n eff λ α ,
I th = 2 π n eff 2 λ Q g 0 Γ × S ,

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