Abstract

We demonstrate how the lasing threshold of a two dimensional photonic crystal containing a four-level gain medium is modified, as a result of the interplay between the group velocity and the modal reflectivity at the interface between the cavity and the exterior. Depending on their relative strength and the optical density of states, we show how the lasing threshold may be dramatically altered inside a band or, most importantly, close to the band edge. The idea is realized via self-consistent calculations based on a finite-difference time-domain method. The simulations are in good agreement with theoretical predictions.

© 2014 Optical Society of America

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    [CrossRef]
  2. J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
    [CrossRef]
  3. M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
    [CrossRef] [PubMed]
  4. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7 (1999).
    [CrossRef]
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    [CrossRef]
  6. S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77(15), 2310–2312 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013

2012

2010

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12(2), 024013 (2010).
[CrossRef]

2009

Y. Pinhasi, A. Yalalom, and G. A. Pinhasi, “Propagation analysis of ultrashort pulses in resonant dielectric media,” J. Opt. Soc. Am. B 26(12), 2404–2413 (2009).
[CrossRef]

D. Luo, X. W. Sun, H. T. Dai, Y. J. Liu, H. Z. Yang, and W. Ji, “Two-directional lasing from a dye-doped two-dimensional hexagonal photonic crystal made of holographic polymer-dispersed liquid crystals,” Appl. Phys. Lett. 95(15), 151115 (2009).
[CrossRef]

2008

X. Hu, J. Cao, M. Li, Z. Ye, M. Miyawaki, and K.-M. Ho, “Modeling of three-dimensional photonic crystal lasers in a frequency domain: A scattering matrix solution,” Phys. Rev. B 77(20), 205104 (2008).
[CrossRef]

2007

S. V. Zhukovsky and D. N. Chigrin, “Numerical modelling of lasing in microstructures,” Phys. Status Solidi 244(10), 3515–3527 (2007).
[CrossRef]

C. Karnutsch, M. Stroisch, M. Punke, U. Lemmer, J. Wang, and T. Weimann, “Laser diode-pumped organic semiconductor lasers utilizing two-dimensional photonic crystal resonators,” Phot. Tech. Lett. 19(10), 741–743 (2007).
[CrossRef]

2006

P. Bermel, E. Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Phys. Rev. B 73(16), 165125 (2006).
[CrossRef]

2005

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj, and A. Levenson, “Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes,” Appl. Phys. Lett. 86(1), 011116 (2005).
[CrossRef]

2004

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85(17), 3657–3659 (2004).
[CrossRef]

2003

S.-H. Kwon, H.-Y. Ryu, G.-H. Kim, Y.-H. Lee, and S.-B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B 68(4), 045209 (2003).
[CrossRef]

2002

H.-Y. Ryu, S.-H. Kwon, Y.-J. Lee, Y.-H. Lee, and J.-S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80(19), 3476–3478 (2002).
[CrossRef]

W. Cao, A. Muñoz, P. Palffy-Muhoray, and B. Taheri, “Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II,” Nat. Mater. 1(2), 111–113 (2002).
[CrossRef] [PubMed]

L. Florescu, K. Busch, and S. John, “Semiclassical theory of lasing in photonic crystals,” J. Opt. Soc. Am. B 19(9), 2215–2223 (2002).
[CrossRef]

2001

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[CrossRef]

N. Susa, “Threshold gain and gain-enhancement due to distributed-feedback in two-dimensional photonic-crystal lasers,” J. Appl. Phys. 89(2), 815–823 (2001).
[CrossRef]

2000

S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77(15), 2310–2312 (2000).
[CrossRef]

1999

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7 (1999).
[CrossRef]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316 (1999).
[CrossRef]

K. Sakoda, “Enhanced light amplification due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals,” Opt. Express 4(5), 167–176 (1999).
[CrossRef] [PubMed]

1998

1996

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[CrossRef] [PubMed]

1994

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

1971

H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971).H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

Bermel, P.

P. Bermel, E. Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Phys. Rev. B 73(16), 165125 (2006).
[CrossRef]

Bloemer, M. J.

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[CrossRef] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

Bowden, C. M.

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[CrossRef] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

Brien, J.

Busch, K.

Cao, H.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85(17), 3657–3659 (2004).
[CrossRef]

Cao, J.

X. Hu, J. Cao, M. Li, Z. Ye, M. Miyawaki, and K.-M. Ho, “Modeling of three-dimensional photonic crystal lasers in a frequency domain: A scattering matrix solution,” Phys. Rev. B 77(20), 205104 (2008).
[CrossRef]

Cao, W.

W. Cao, A. Muñoz, P. Palffy-Muhoray, and B. Taheri, “Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II,” Nat. Mater. 1(2), 111–113 (2002).
[CrossRef] [PubMed]

Chang, R. P. H.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85(17), 3657–3659 (2004).
[CrossRef]

Chigrin, D. N.

S. V. Zhukovsky and D. N. Chigrin, “Numerical modelling of lasing in microstructures,” Phys. Status Solidi 244(10), 3515–3527 (2007).
[CrossRef]

Chutinan, A.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316 (1999).
[CrossRef]

D’Urso, B.

Dai, H. T.

D. Luo, X. W. Sun, H. T. Dai, Y. J. Liu, H. Z. Yang, and W. Ji, “Two-directional lasing from a dye-doped two-dimensional hexagonal photonic crystal made of holographic polymer-dispersed liquid crystals,” Appl. Phys. Lett. 95(15), 151115 (2009).
[CrossRef]

Dodabalapur, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7 (1999).
[CrossRef]

Dowling, J. P.

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[CrossRef] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

Dravid, V. P.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85(17), 3657–3659 (2004).
[CrossRef]

Fang, A.

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12(2), 024013 (2010).
[CrossRef]

Feldmann, J.

S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77(15), 2310–2312 (2000).
[CrossRef]

Fietz, C.

Fink, Y.

P. Bermel, E. Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Phys. Rev. B 73(16), 165125 (2006).
[CrossRef]

Florescu, L.

Gombert, A.

S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77(15), 2310–2312 (2000).
[CrossRef]

Ho, K.-M.

X. Hu, J. Cao, M. Li, Z. Ye, M. Miyawaki, and K.-M. Ho, “Modeling of three-dimensional photonic crystal lasers in a frequency domain: A scattering matrix solution,” Phys. Rev. B 77(20), 205104 (2008).
[CrossRef]

Hu, X.

X. Hu, J. Cao, M. Li, Z. Ye, M. Miyawaki, and K.-M. Ho, “Modeling of three-dimensional photonic crystal lasers in a frequency domain: A scattering matrix solution,” Phys. Rev. B 77(20), 205104 (2008).
[CrossRef]

Imada, M.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316 (1999).
[CrossRef]

Ji, W.

D. Luo, X. W. Sun, H. T. Dai, Y. J. Liu, H. Z. Yang, and W. Ji, “Two-directional lasing from a dye-doped two-dimensional hexagonal photonic crystal made of holographic polymer-dispersed liquid crystals,” Appl. Phys. Lett. 95(15), 151115 (2009).
[CrossRef]

Joannopoulos, J.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7 (1999).
[CrossRef]

Joannopoulos, J. D.

P. Bermel, E. Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Phys. Rev. B 73(16), 165125 (2006).
[CrossRef]

John, S.

Kallinger, C.

S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77(15), 2310–2312 (2000).
[CrossRef]

Karnutsch, C.

C. Karnutsch, M. Stroisch, M. Punke, U. Lemmer, J. Wang, and T. Weimann, “Laser diode-pumped organic semiconductor lasers utilizing two-dimensional photonic crystal resonators,” Phot. Tech. Lett. 19(10), 741–743 (2007).
[CrossRef]

Kim, G.-H.

S.-H. Kwon, H.-Y. Ryu, G.-H. Kim, Y.-H. Lee, and S.-B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

Kim, J.-S.

H.-Y. Ryu, S.-H. Kwon, Y.-J. Lee, Y.-H. Lee, and J.-S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80(19), 3476–3478 (2002).
[CrossRef]

Kim, S.-B.

S.-H. Kwon, H.-Y. Ryu, G.-H. Kim, Y.-H. Lee, and S.-B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

Kogelnik, H.

H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971).H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

Koschny, T.

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12(2), 024013 (2010).
[CrossRef]

Kwon, S.-H.

S.-H. Kwon, H.-Y. Ryu, G.-H. Kim, Y.-H. Lee, and S.-B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

H.-Y. Ryu, S.-H. Kwon, Y.-J. Lee, Y.-H. Lee, and J.-S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80(19), 3476–3478 (2002).
[CrossRef]

Lee, Y.-H.

S.-H. Kwon, H.-Y. Ryu, G.-H. Kim, Y.-H. Lee, and S.-B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B 68(4), 045209 (2003).
[CrossRef]

H.-Y. Ryu, S.-H. Kwon, Y.-J. Lee, Y.-H. Lee, and J.-S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80(19), 3476–3478 (2002).
[CrossRef]

Lee, Y.-J.

H.-Y. Ryu, S.-H. Kwon, Y.-J. Lee, Y.-H. Lee, and J.-S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80(19), 3476–3478 (2002).
[CrossRef]

Lemmer, U.

C. Karnutsch, M. Stroisch, M. Punke, U. Lemmer, J. Wang, and T. Weimann, “Laser diode-pumped organic semiconductor lasers utilizing two-dimensional photonic crystal resonators,” Phot. Tech. Lett. 19(10), 741–743 (2007).
[CrossRef]

S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77(15), 2310–2312 (2000).
[CrossRef]

Levenson, A.

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj, and A. Levenson, “Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes,” Appl. Phys. Lett. 86(1), 011116 (2005).
[CrossRef]

Li, M.

X. Hu, J. Cao, M. Li, Z. Ye, M. Miyawaki, and K.-M. Ho, “Modeling of three-dimensional photonic crystal lasers in a frequency domain: A scattering matrix solution,” Phys. Rev. B 77(20), 205104 (2008).
[CrossRef]

Li, S.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85(17), 3657–3659 (2004).
[CrossRef]

Lidorikis, E.

P. Bermel, E. Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Phys. Rev. B 73(16), 165125 (2006).
[CrossRef]

Liu, X.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85(17), 3657–3659 (2004).
[CrossRef]

Liu, Y. J.

D. Luo, X. W. Sun, H. T. Dai, Y. J. Liu, H. Z. Yang, and W. Ji, “Two-directional lasing from a dye-doped two-dimensional hexagonal photonic crystal made of holographic polymer-dispersed liquid crystals,” Appl. Phys. Lett. 95(15), 151115 (2009).
[CrossRef]

Luo, D.

D. Luo, X. W. Sun, H. T. Dai, Y. J. Liu, H. Z. Yang, and W. Ji, “Two-directional lasing from a dye-doped two-dimensional hexagonal photonic crystal made of holographic polymer-dispersed liquid crystals,” Appl. Phys. Lett. 95(15), 151115 (2009).
[CrossRef]

Meier, M.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7 (1999).
[CrossRef]

Mekis, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7 (1999).
[CrossRef]

Miyawaki, M.

X. Hu, J. Cao, M. Li, Z. Ye, M. Miyawaki, and K.-M. Ho, “Modeling of three-dimensional photonic crystal lasers in a frequency domain: A scattering matrix solution,” Phys. Rev. B 77(20), 205104 (2008).
[CrossRef]

Muñoz, A.

W. Cao, A. Muñoz, P. Palffy-Muhoray, and B. Taheri, “Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II,” Nat. Mater. 1(2), 111–113 (2002).
[CrossRef] [PubMed]

Murata, M.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316 (1999).
[CrossRef]

Nalamasu, O.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7 (1999).
[CrossRef]

Noda, S.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316 (1999).
[CrossRef]

Nojima, S.

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[CrossRef]

Notomi, M.

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B 68(4), 045209 (2003).
[CrossRef]

Painter, O.

Palffy-Muhoray, P.

W. Cao, A. Muñoz, P. Palffy-Muhoray, and B. Taheri, “Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II,” Nat. Mater. 1(2), 111–113 (2002).
[CrossRef] [PubMed]

Pinhasi, G. A.

Pinhasi, Y.

Punke, M.

C. Karnutsch, M. Stroisch, M. Punke, U. Lemmer, J. Wang, and T. Weimann, “Laser diode-pumped organic semiconductor lasers utilizing two-dimensional photonic crystal resonators,” Phot. Tech. Lett. 19(10), 741–743 (2007).
[CrossRef]

Raineri, F.

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj, and A. Levenson, “Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes,” Appl. Phys. Lett. 86(1), 011116 (2005).
[CrossRef]

Raj, R.

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj, and A. Levenson, “Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes,” Appl. Phys. Lett. 86(1), 011116 (2005).
[CrossRef]

Riechel, S.

S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77(15), 2310–2312 (2000).
[CrossRef]

Ryu, H.-Y.

S.-H. Kwon, H.-Y. Ryu, G.-H. Kim, Y.-H. Lee, and S.-B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B 68(4), 045209 (2003).
[CrossRef]

H.-Y. Ryu, S.-H. Kwon, Y.-J. Lee, Y.-H. Lee, and J.-S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80(19), 3476–3478 (2002).
[CrossRef]

Sakoda, K.

Sasaki, G.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316 (1999).
[CrossRef]

Scalora, M.

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[CrossRef] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

Scherer, A.

Scherf, U.

S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77(15), 2310–2312 (2000).
[CrossRef]

Seassal, C.

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj, and A. Levenson, “Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes,” Appl. Phys. Lett. 86(1), 011116 (2005).
[CrossRef]

Shank, C. V.

H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971).H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

Slusher, R.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7 (1999).
[CrossRef]

Soukoulis, C. M.

C. Fietz and C. M. Soukoulis, “Finite element simulation of microphotonic lasing system,” Opt. Express 20(10), 11548–11560 (2012).
[CrossRef] [PubMed]

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12(2), 024013 (2010).
[CrossRef]

Stroisch, M.

C. Karnutsch, M. Stroisch, M. Punke, U. Lemmer, J. Wang, and T. Weimann, “Laser diode-pumped organic semiconductor lasers utilizing two-dimensional photonic crystal resonators,” Phot. Tech. Lett. 19(10), 741–743 (2007).
[CrossRef]

Sun, X. W.

D. Luo, X. W. Sun, H. T. Dai, Y. J. Liu, H. Z. Yang, and W. Ji, “Two-directional lasing from a dye-doped two-dimensional hexagonal photonic crystal made of holographic polymer-dispersed liquid crystals,” Appl. Phys. Lett. 95(15), 151115 (2009).
[CrossRef]

Susa, N.

N. Susa, “Threshold gain and gain-enhancement due to distributed-feedback in two-dimensional photonic-crystal lasers,” J. Appl. Phys. 89(2), 815–823 (2001).
[CrossRef]

Taheri, B.

W. Cao, A. Muñoz, P. Palffy-Muhoray, and B. Taheri, “Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II,” Nat. Mater. 1(2), 111–113 (2002).
[CrossRef] [PubMed]

Timko, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7 (1999).
[CrossRef]

Tocci, M. D.

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[CrossRef] [PubMed]

Tokuda, T.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316 (1999).
[CrossRef]

Tombrello, T.

Vecchi, G.

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj, and A. Levenson, “Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes,” Appl. Phys. Lett. 86(1), 011116 (2005).
[CrossRef]

Viktorovitch, P.

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj, and A. Levenson, “Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes,” Appl. Phys. Lett. 86(1), 011116 (2005).
[CrossRef]

Wang, J.

C. Karnutsch, M. Stroisch, M. Punke, U. Lemmer, J. Wang, and T. Weimann, “Laser diode-pumped organic semiconductor lasers utilizing two-dimensional photonic crystal resonators,” Phot. Tech. Lett. 19(10), 741–743 (2007).
[CrossRef]

Weimann, T.

C. Karnutsch, M. Stroisch, M. Punke, U. Lemmer, J. Wang, and T. Weimann, “Laser diode-pumped organic semiconductor lasers utilizing two-dimensional photonic crystal resonators,” Phot. Tech. Lett. 19(10), 741–743 (2007).
[CrossRef]

Wittwer, V.

S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77(15), 2310–2312 (2000).
[CrossRef]

Wu, X.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85(17), 3657–3659 (2004).
[CrossRef]

Yacomotti, A. M.

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj, and A. Levenson, “Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes,” Appl. Phys. Lett. 86(1), 011116 (2005).
[CrossRef]

Yalalom, A.

Yamilov, A.

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85(17), 3657–3659 (2004).
[CrossRef]

Yang, H. Z.

D. Luo, X. W. Sun, H. T. Dai, Y. J. Liu, H. Z. Yang, and W. Ji, “Two-directional lasing from a dye-doped two-dimensional hexagonal photonic crystal made of holographic polymer-dispersed liquid crystals,” Appl. Phys. Lett. 95(15), 151115 (2009).
[CrossRef]

Yariv, A.

Ye, Z.

X. Hu, J. Cao, M. Li, Z. Ye, M. Miyawaki, and K.-M. Ho, “Modeling of three-dimensional photonic crystal lasers in a frequency domain: A scattering matrix solution,” Phys. Rev. B 77(20), 205104 (2008).
[CrossRef]

Zhukovsky, S. V.

S. V. Zhukovsky and D. N. Chigrin, “Numerical modelling of lasing in microstructures,” Phys. Status Solidi 244(10), 3515–3527 (2007).
[CrossRef]

Appl. Phys. Lett.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. Slusher, J. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7 (1999).
[CrossRef]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316 (1999).
[CrossRef]

S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77(15), 2310–2312 (2000).
[CrossRef]

H.-Y. Ryu, S.-H. Kwon, Y.-J. Lee, Y.-H. Lee, and J.-S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80(19), 3476–3478 (2002).
[CrossRef]

S.-H. Kwon, H.-Y. Ryu, G.-H. Kim, Y.-H. Lee, and S.-B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

X. Wu, A. Yamilov, X. Liu, S. Li, V. P. Dravid, R. P. H. Chang, and H. Cao, “Ultraviolet photonic crystal laser,” Appl. Phys. Lett. 85(17), 3657–3659 (2004).
[CrossRef]

F. Raineri, G. Vecchi, A. M. Yacomotti, C. Seassal, P. Viktorovitch, R. Raj, and A. Levenson, “Doubly resonant photonic crystal for efficient laser operation: Pumping and lasing at low group velocity photonic modes,” Appl. Phys. Lett. 86(1), 011116 (2005).
[CrossRef]

H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971).H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

D. Luo, X. W. Sun, H. T. Dai, Y. J. Liu, H. Z. Yang, and W. Ji, “Two-directional lasing from a dye-doped two-dimensional hexagonal photonic crystal made of holographic polymer-dispersed liquid crystals,” Appl. Phys. Lett. 95(15), 151115 (2009).
[CrossRef]

J. Appl. Phys.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[CrossRef]

S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001).
[CrossRef]

N. Susa, “Threshold gain and gain-enhancement due to distributed-feedback in two-dimensional photonic-crystal lasers,” J. Appl. Phys. 89(2), 815–823 (2001).
[CrossRef]

J. Opt.

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12(2), 024013 (2010).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Mater.

W. Cao, A. Muñoz, P. Palffy-Muhoray, and B. Taheri, “Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II,” Nat. Mater. 1(2), 111–113 (2002).
[CrossRef] [PubMed]

Opt. Express

Phot. Tech. Lett.

C. Karnutsch, M. Stroisch, M. Punke, U. Lemmer, J. Wang, and T. Weimann, “Laser diode-pumped organic semiconductor lasers utilizing two-dimensional photonic crystal resonators,” Phot. Tech. Lett. 19(10), 741–743 (2007).
[CrossRef]

Phys. Rev. A

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[CrossRef] [PubMed]

Phys. Rev. B

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B 68(4), 045209 (2003).
[CrossRef]

P. Bermel, E. Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Phys. Rev. B 73(16), 165125 (2006).
[CrossRef]

X. Hu, J. Cao, M. Li, Z. Ye, M. Miyawaki, and K.-M. Ho, “Modeling of three-dimensional photonic crystal lasers in a frequency domain: A scattering matrix solution,” Phys. Rev. B 77(20), 205104 (2008).
[CrossRef]

Phys. Status Solidi

S. V. Zhukovsky and D. N. Chigrin, “Numerical modelling of lasing in microstructures,” Phys. Status Solidi 244(10), 3515–3527 (2007).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of the 2D PC consisting of 10 layers (top) and the respective slab of uniform gain and same length (bottom). The red areas denote the host dielectric of εr = 11.7, which is homogeneously embedded with the four level gain material. Both systems are infinite in the yz plane and confined in the x direction, along which the emitted wave propagates. (b) Unit cell of the 2D PC (c) Calculated band structure for the TE polarization of the infinite version of the 2D PC. The shaded zone denotes the full bandgap.

Fig. 2
Fig. 2

Schematic of the recirculating pulse approach. The pulse travels with group velocity v g inside the cavity and bounces back and forth at the boundary with each semi-infinite exterior space. r ij is the reflectivity of the electric field travelling in area i that bounces at the interface with area j.

Fig. 3
Fig. 3

(a) Lasing power of a gain slab with L = 10a at successive Fabry-Perot resonances and for different pump rates. Each set of connected points is an iso-pump line. The red points inside the dotted box are reproduced partly in (b) on the red line. (b) Lasing power at ω = ωFP = ωa = 2π 99.19THz for different pump rates. Three gain slabs are analyzed, all with the same material properties, but with different lengths, namely L1 = 10a (red), L2 = 20a (green) and L3 = 30a (blue), where a = 840nm. The lasing threshold is reduced with increasing slab length, as expected.

Fig. 4
Fig. 4

Calculations for the passive photonic crystal pictured in Fig. 1. (a) Dispersion curve along the ΓX direction of the infinite system. (b) Normalized group velocity v g /c and interface reflectivities | r 21 |=| r 23 | of the Bloch modes. (c) Q envelope (white line) from semi-analytical Eq. (1) normalized with number of layers n = L/a and overlapped with simulated Q/n for the three finite systems of length L1 = 10a (red), L2 = 20a (green) and L3 = 30a (blue). For clarity these are shown unnormalized separately in (d), (e) and (f).

Fig. 5
Fig. 5

(a) Lasing threshold for the system of length L1 = 10a. (b) Simulated Q factor (open circles) overlapped with the semi-analytical Q factor envelope (solid line). (c) Lasing power for different pump rates above and (d) below the 1st bandgap, for the three 2DPC’s of length L1 = 10a (red), L2 = 20a (green) and L3 = 30a (blue). Notice that the thresholds in (c) are 1 order of magnitude lower than in (d). In all cases the lasing threshold varies consistently with Q.

Fig. 6
Fig. 6

Calculated reflectivities | r 21 |,| r 23 | and their product that determines Q for (a) the original system of n = 10 layers and (b), (c) its modified versions (see inset for unit cell). (d) Calculated lasing threshold and (e) Q factor at the edges of the 1st and 2nd band in log scale. In (e) the semi-analytical Q envelope as calculated with the data from (a), (b) and (c) is also shown as solid line. The dotted lines in (d) are shown for easier comparison among calculated points and do not imply a piece-wise monotonic change in the pump rate threshold. Also, the color code denotes the unit cell structure and should not be confused with the previous figures.

Equations (1)

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Q= ωL v g ln( | r 21 || r 23 |( 1p ) )

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