Abstract

We present a theoretical analysis of lasing action in photonic crystal surface-emitting lasers (PCSELs). The semiclassical laser equations for such structures are simulated with three different theoretical techniques: exact finite-difference time-domain calculations, an steady-state ab-initio laser theory and a semi-analytical coupled-mode formalism. Our simulations show that, for an exemplary four-level gain model, the excitation of dark Fano resonances featuring arbitrarily large quality factors can lead to a significant reduction of the lasing threshold of PCSELs with respect to conventional vertical-cavity surface-emitting lasers. Our calculations also suggest that at the onset of lasing action, most of the laser power generated by finite-size PCSELs is emitted in the photonic crystal plane rather than the vertical direction. In addition to their fundamental interest, these findings may affect further engineering of active devices based on photonic crystal slabs.

© 2011 OSA

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2010 (4)

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics 4, 447–450 (2010).
[CrossRef]

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4, 395–399 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 81, 687–702 (2010).
[CrossRef]

J. Bravo-Abad, A. W. Rodriguez, J. D. Joannopoulos, P. T. Rakich, S. G. Johnson, M. Soljac̆ić, “Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing,” Appl. Phys. Lett. 96, 101110 (2010).
[CrossRef]

2009 (4)

J. Bravo-Abad, E. P. Ippen, M. Soljac̆ić, “Ultrafast photodetection in an all-silicon chip enabled by two-photon absorption,” Appl. Phys. Lett. 94, 241103 (2009).
[CrossRef]

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljac̆ić, S. G. Johnson, “Nonlinear harmonic generation and devices in doubly-resonant Kerr cavities,” Phys. Rev. A 79, 013812 (2009).
[CrossRef]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629 (2009).
[CrossRef] [PubMed]

2008 (7)

H. E. Türeci, L. Ge, S. Rotter, A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[CrossRef] [PubMed]

H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic crystal surface-emitting laser at blue-violet wavelengths,” Science 319, 445–447 (2008).
[CrossRef]

S. Gottardo, R. Sapienza, P. D. García, A. Blanco, D. S. Wiersma, C. López, “Resonance-driven random lasing,” Nat. Photonics 2, 429–432 (2008).
[CrossRef]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

T. Lu, C. Kao, H. Kuo, G. Huang, S. Wang, “CW lasing of current injection blue GaN-based vertical cavity surface emitting laser,” Appl. Phys. Lett. 92, 141102 (2008).
[CrossRef]

L. Ge, R. Tandy, A. D. Stone, H. E. Türeci, “Quantitative Verification of Ab Initio Self-Consistent Laser Theory,” Opt. Express 16, 16895 (2008).
[CrossRef] [PubMed]

R. E. Hamam, M. Ibanescu, E. J. Reed, P. Bermel, S. G. Johnson, E. Ippen, J. D. Joannopoulos, M. Soljac̆ić, “Purcell effect in nonlinear photonic structures: A coupled mode theory analysis,” Opt. Express 16, 12523–12537 (2008).
[CrossRef] [PubMed]

2007 (3)

J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, M. Soljac̆ić, “Enhanced non-linear optics in photonic-crystal microcavities,” Opt. Express 15, 16161–16176 (2007).
[CrossRef] [PubMed]

M. T. Hill, Y. -S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. -H. Kwon, Y.- H. Lee, R. Notzel, M. K. Smit, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 1, 589–594 (2007).
[CrossRef]

S. Noda, M. Fujita, T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (2007).
[CrossRef]

2006 (4)

P. Bermel, E. Lidorikis, Y. Fink, J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Phys. Rev. B 73, 165125 (2006).
[CrossRef]

H. E. Türeci, A. D. Stone, B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[CrossRef]

B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Cioccio, J. Fedeli, “Surface-emitting micro-laser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

H. Altug, D. Englund, J. Vuckovic, “Ultra-fast photonic-crystal nanolasers,” Nat. Phys. 2, 485–488 (2006).
[CrossRef]

2004 (4)

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

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, F. Koyama, “Observation of fast spontaneous emission decay in GaInAsP photonic crystal point defect nanocavity at room temperature,” Appl. Phys. Lett. 85, 3889–3891 (2004).
[CrossRef]

H. Y. Ryu, M. Notomi, E. Kuramochi, T. Segawa, “Large spontaneous emission factor (> 0.1) in the photonic crystal monopole-mode laser,” Appl. Phys. Lett. 84, 1067–1069 (2004).
[CrossRef]

W. Suh, Z. Wang, S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
[CrossRef]

2003 (2)

D. J. Bergman, M. L. Stockman, “Surface Plasmon Amplification by Stimulated Emission of Radiation: Quantum Generation of Coherent Surface Plasmons in Nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

X. Duan, Y. Huang, R. Agarwal, C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature 421, 241–245 (2003).
[CrossRef] [PubMed]

2002 (4)

M. Imada, A. Chutinan, S. Noda, M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65, 195306 (2002).
[CrossRef]

J. C. Johnson, H.- J. Choi, K. P. Knutsen, R. D. Schaller, P. Yang, R. J. Saykally, “Single gallium nitride nanowire lasers,” Nat. Mater. 1, 106–110 (2002).
[CrossRef]

S. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

M. Soljac̆ić, M. Ibanescu, S. G. Johnson, Y. Fink, J. D. Joannopoulos, “Optimal bistable switching in non-linear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

2001 (4)

T. Ochiai, K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[CrossRef] [PubMed]

H. Cao, Y. Ling, J. Y. Xu, C. Q. Cao, P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86, 4524–4527 (2001).
[CrossRef] [PubMed]

2000 (1)

X. Jiang, C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
[CrossRef] [PubMed]

1999 (1)

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

1998 (2)

A. S. Nagra, R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[CrossRef]

C. Gmachl, F. Capasso, E.E. Narimanov, J.U. Nöckel, A. D. Stone, J. Faist, D. Sivco, A. Cho, “High power directional emission from lasers with chaotic resonators,” Science 280, 1556–64 (1998).
[CrossRef] [PubMed]

1996 (2)

D. S. Wiersma, A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[CrossRef]

S. D. Glauber, “An anisotropic perfectly matched layer absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

1994 (1)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[CrossRef]

1992 (1)

H. Yokoyama, “Physics and device applications of optical microcavities,” Science 256, 66–70 (1992).
[CrossRef] [PubMed]

1989 (1)

S. Haroche, D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42, 24–30 (1989).
[CrossRef]

1987 (1)

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

1966 (1)

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

1960 (1)

T. H. Maiman, “Stimulated optical radiation in ruby,” Nature 187, 493–494 (1960).
[CrossRef]

Agarwal, R.

X. Duan, Y. Huang, R. Agarwal, C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature 421, 241–245 (2003).
[CrossRef] [PubMed]

Altug, H.

H. Altug, D. Englund, J. Vuckovic, “Ultra-fast photonic-crystal nanolasers,” Nat. Phys. 2, 485–488 (2006).
[CrossRef]

Asano, T.

S. Noda, M. Fujita, T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449–458 (2007).
[CrossRef]

Baba, T.

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, F. Koyama, “Observation of fast spontaneous emission decay in GaInAsP photonic crystal point defect nanocavity at room temperature,” Appl. Phys. Lett. 85, 3889–3891 (2004).
[CrossRef]

Baek, J.- H.

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

Bakir, B.

B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Cioccio, J. Fedeli, “Surface-emitting micro-laser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Balachandran, R. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[CrossRef]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629 (2009).
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Li Ge, D. Y. Chong, A. D. Stone, “Steady-state Ab Initio Laser Theory: Generalizations and Analytic Results,” arxiv:1008.0628.

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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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W. Suh, Z. Wang, S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

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H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic crystal surface-emitting laser at blue-violet wavelengths,” Science 319, 445–447 (2008).
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L. Ge, R. Tandy, A. D. Stone, H. E. Türeci, “Quantitative Verification of Ab Initio Self-Consistent Laser Theory,” Opt. Express 16, 16895 (2008).
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L. Ge, R. Tandy, A. D. Stone, H. E. Türeci, “Quantitative Verification of Ab Initio Self-Consistent Laser Theory,” Opt. Express 16, 16895 (2008).
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H. E. Türeci, L. Ge, S. Rotter, A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
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H. E. Türeci, A. D. Stone, B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
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M. T. Hill, Y. -S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. -H. Kwon, Y.- H. Lee, R. Notzel, M. K. Smit, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 1, 589–594 (2007).
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M. T. Hill, Y. -S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. -H. Kwon, Y.- H. Lee, R. Notzel, M. K. Smit, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 1, 589–594 (2007).
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M. T. Hill, Y. -S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. -H. Kwon, Y.- H. Lee, R. Notzel, M. K. Smit, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 1, 589–594 (2007).
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W. Suh, Z. Wang, S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
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S. Gottardo, R. Sapienza, P. D. García, A. Blanco, D. S. Wiersma, C. López, “Resonance-driven random lasing,” Nat. Photonics 2, 429–432 (2008).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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S. Noda, M. Yokoyama, M. Imada, A. Chutinan, M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
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A. S. Nagra, R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
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H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, S. Noda, “GaN photonic crystal surface-emitting laser at blue-violet wavelengths,” Science 319, 445–447 (2008).
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R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629 (2009).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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M. T. Hill, Y. -S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. -H. Kwon, Y.- H. Lee, R. Notzel, M. K. Smit, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 1, 589–594 (2007).
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B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Cioccio, J. Fedeli, “Surface-emitting micro-laser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
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M. T. Hill, Y. -S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. -H. Kwon, Y.- H. Lee, R. Notzel, M. K. Smit, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 1, 589–594 (2007).
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H. Altug, D. Englund, J. Vuckovic, “Ultra-fast photonic-crystal nanolasers,” Nat. Phys. 2, 485–488 (2006).
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[CrossRef] [PubMed]

H.- G. Park, S.- H. Kim, S.- H. Kwon, Y. -G. Ju, J.- K. Yang, J.- H. Baek, S. -B. Kim, Y.- H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
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Li Ge, D. Y. Chong, A. D. Stone, “Steady-state Ab Initio Laser Theory: Generalizations and Analytic Results,” arxiv:1008.0628.

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