Abstract

We theoretically study a low-threshold band-edge lasing in three-dimensional photonic crystals (PhCs) with a face-centered cubic lattice structure, using a complex-valued permittivity approach combined with the Korringa–Kohn–Rostoker method. We show that the lasing threshold at the low-frequency band edge is smaller than that at the high-frequency band edge for the first-order stop band of the PhC. We also analyze the impact of the number of the PhC’s layers on the frequency of band-edge lasing and the lasing threshold near the first-order stop band in the ΓL direction, and demonstrate a broad tunability of the lasing frequency with change in the emission collection angle. The obtained results are beneficial for the performance enhancement of tunable, PhC-based chip lasers.

© 2013 Optical Society of America

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2012 (1)

M. S. Reddy, R. Vijaya, I. D. Rukhlenko, and M. Premaratne, J. Nanophoton. 6, 063526 (2012).
[CrossRef]

2011 (2)

2010 (2)

S. Kedia, R. Vijaya, A. K. Ray, and S. Sinha, J. Nanophoton. 4, 049506 (2010).
[CrossRef]

S. Kim, S. Yoon, H. Seok, J. Lee, and H. Jeon, Opt. Express 18, 7685 (2010).
[CrossRef]

2009 (1)

2008 (1)

2007 (2)

L. K. Teh, C. C. Wong, H. Y. Yang, S. P. Lau, and S. F. Yu, Appl. Phys. Lett. 91, 161116 (2007).
[CrossRef]

L. A. Dorado and R. A. Depine, Phys. Rev. 75, 241101 (2007).
[CrossRef]

2005 (1)

Q. Yan, Z. Zhou, and X. S. Zhao, Langmuir 21, 3158(2005).
[CrossRef]

2003 (1)

Y. H. Lee, H. Y. Rue, and M. Notomi, Phys. Rev. B 68, 045209 (2003).
[CrossRef]

2002 (1)

M. N. Shkunov, Z. V. Vardeny, M. C. De Long, R. C. Polson, A. A. Zakhidov, and R. H. Baughman, Adv. Funct. Mater. 12, 21 (2002).
[CrossRef]

2000 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

1999 (2)

1998 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

1994 (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

Baughman, R. H.

M. N. Shkunov, Z. V. Vardeny, M. C. De Long, R. C. Polson, A. A. Zakhidov, and R. H. Baughman, Adv. Funct. Mater. 12, 21 (2002).
[CrossRef]

Bloemer, M. J.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

Chen, W.

De Long, M. C.

M. N. Shkunov, Z. V. Vardeny, M. C. De Long, R. C. Polson, A. A. Zakhidov, and R. H. Baughman, Adv. Funct. Mater. 12, 21 (2002).
[CrossRef]

Depine, R. A.

L. A. Dorado and R. A. Depine, Phys. Rev. 75, 241101 (2007).
[CrossRef]

Dorado, L. A.

L. A. Dorado and R. A. Depine, Phys. Rev. 75, 241101 (2007).
[CrossRef]

Dowling, J. P.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

Fu, F.

Hostein, R.

Jeon, H.

Juodkazis, S.

Karle, T. J.

Kedia, S.

S. Kedia, R. Vijaya, A. K. Ray, and S. Sinha, J. Nanophoton. 4, 049506 (2010).
[CrossRef]

M. S. Reddy, S. Kedia, R. Vijaya, A. K. Ray, S. Sinha, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J.5, 4700409(2013).
[CrossRef]

Kim, S.

Lau, S. P.

L. K. Teh, C. C. Wong, H. Y. Yang, S. P. Lau, and S. F. Yu, Appl. Phys. Lett. 91, 161116 (2007).
[CrossRef]

Lee, J.

Lee, Y. H.

Y. H. Lee, H. Y. Rue, and M. Notomi, Phys. Rev. B 68, 045209 (2003).
[CrossRef]

Liu, A.

Lu, T.-C.

Maeda, M.

Minaki, M.

Misawa, H.

Mizeikis, V.

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

Nishijima, Y.

Notomi, M.

Y. H. Lee, H. Y. Rue, and M. Notomi, Phys. Rev. B 68, 045209 (2003).
[CrossRef]

Ohtaka, K.

Polson, R. C.

M. N. Shkunov, Z. V. Vardeny, M. C. De Long, R. C. Polson, A. A. Zakhidov, and R. H. Baughman, Adv. Funct. Mater. 12, 21 (2002).
[CrossRef]

Premaratne, M.

M. S. Reddy, R. Vijaya, I. D. Rukhlenko, and M. Premaratne, J. Nanophoton. 6, 063526 (2012).
[CrossRef]

M. S. Reddy, S. Kedia, R. Vijaya, A. K. Ray, S. Sinha, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J.5, 4700409(2013).
[CrossRef]

Qi, A.

Raineri, F.

Ray, A. K.

S. Kedia, R. Vijaya, A. K. Ray, and S. Sinha, J. Nanophoton. 4, 049506 (2010).
[CrossRef]

M. S. Reddy, S. Kedia, R. Vijaya, A. K. Ray, S. Sinha, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J.5, 4700409(2013).
[CrossRef]

Reddy, M. S.

M. S. Reddy, R. Vijaya, I. D. Rukhlenko, and M. Premaratne, J. Nanophoton. 6, 063526 (2012).
[CrossRef]

M. S. Reddy, S. Kedia, R. Vijaya, A. K. Ray, S. Sinha, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J.5, 4700409(2013).
[CrossRef]

Rue, H. Y.

Y. H. Lee, H. Y. Rue, and M. Notomi, Phys. Rev. B 68, 045209 (2003).
[CrossRef]

Rukhlenko, I. D.

M. S. Reddy, R. Vijaya, I. D. Rukhlenko, and M. Premaratne, J. Nanophoton. 6, 063526 (2012).
[CrossRef]

M. S. Reddy, S. Kedia, R. Vijaya, A. K. Ray, S. Sinha, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J.5, 4700409(2013).
[CrossRef]

Sakoda, K.

Scalora, M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

Seok, H.

Shkunov, M. N.

M. N. Shkunov, Z. V. Vardeny, M. C. De Long, R. C. Polson, A. A. Zakhidov, and R. H. Baughman, Adv. Funct. Mater. 12, 21 (2002).
[CrossRef]

Sinha, S.

S. Kedia, R. Vijaya, A. K. Ray, and S. Sinha, J. Nanophoton. 4, 049506 (2010).
[CrossRef]

M. S. Reddy, S. Kedia, R. Vijaya, A. K. Ray, S. Sinha, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J.5, 4700409(2013).
[CrossRef]

Stefanou, N.

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

Teh, L. K.

L. K. Teh, C. C. Wong, H. Y. Yang, S. P. Lau, and S. F. Yu, Appl. Phys. Lett. 91, 161116 (2007).
[CrossRef]

Ueno, K.

Ueta, T.

Vardeny, Z. V.

M. N. Shkunov, Z. V. Vardeny, M. C. De Long, R. C. Polson, A. A. Zakhidov, and R. H. Baughman, Adv. Funct. Mater. 12, 21 (2002).
[CrossRef]

Vijaya, R.

M. S. Reddy, R. Vijaya, I. D. Rukhlenko, and M. Premaratne, J. Nanophoton. 6, 063526 (2012).
[CrossRef]

S. Kedia, R. Vijaya, A. K. Ray, and S. Sinha, J. Nanophoton. 4, 049506 (2010).
[CrossRef]

M. S. Reddy, S. Kedia, R. Vijaya, A. K. Ray, S. Sinha, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J.5, 4700409(2013).
[CrossRef]

Wang, H.

Wang, S.-C.

Wang, Y.

Weng, P.

Wong, C. C.

L. K. Teh, C. C. Wong, H. Y. Yang, S. P. Lau, and S. F. Yu, Appl. Phys. Lett. 91, 161116 (2007).
[CrossRef]

Wu, T.-T.

Yacomotti, A. M.

Yan, Q.

Q. Yan, Z. Zhou, and X. S. Zhao, Langmuir 21, 3158(2005).
[CrossRef]

Yang, H. Y.

L. K. Teh, C. C. Wong, H. Y. Yang, S. P. Lau, and S. F. Yu, Appl. Phys. Lett. 91, 161116 (2007).
[CrossRef]

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

Yoon, S.

Yu, S. F.

L. K. Teh, C. C. Wong, H. Y. Yang, S. P. Lau, and S. F. Yu, Appl. Phys. Lett. 91, 161116 (2007).
[CrossRef]

Zakhidov, A. A.

M. N. Shkunov, Z. V. Vardeny, M. C. De Long, R. C. Polson, A. A. Zakhidov, and R. H. Baughman, Adv. Funct. Mater. 12, 21 (2002).
[CrossRef]

Zhao, X. S.

Q. Yan, Z. Zhou, and X. S. Zhao, Langmuir 21, 3158(2005).
[CrossRef]

Zheng, W.

Zhou, W.

Zhou, Z.

Q. Yan, Z. Zhou, and X. S. Zhao, Langmuir 21, 3158(2005).
[CrossRef]

Adv. Funct. Mater. (1)

M. N. Shkunov, Z. V. Vardeny, M. C. De Long, R. C. Polson, A. A. Zakhidov, and R. H. Baughman, Adv. Funct. Mater. 12, 21 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

L. K. Teh, C. C. Wong, H. Y. Yang, S. P. Lau, and S. F. Yu, Appl. Phys. Lett. 91, 161116 (2007).
[CrossRef]

Comput. Phys. Commun. (2)

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

J. Appl. Phys. (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

J. Nanophoton. (2)

S. Kedia, R. Vijaya, A. K. Ray, and S. Sinha, J. Nanophoton. 4, 049506 (2010).
[CrossRef]

M. S. Reddy, R. Vijaya, I. D. Rukhlenko, and M. Premaratne, J. Nanophoton. 6, 063526 (2012).
[CrossRef]

Langmuir (1)

Q. Yan, Z. Zhou, and X. S. Zhao, Langmuir 21, 3158(2005).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. (1)

L. A. Dorado and R. A. Depine, Phys. Rev. 75, 241101 (2007).
[CrossRef]

Phys. Rev. B (1)

Y. H. Lee, H. Y. Rue, and M. Notomi, Phys. Rev. B 68, 045209 (2003).
[CrossRef]

Other (1)

M. S. Reddy, S. Kedia, R. Vijaya, A. K. Ray, S. Sinha, I. D. Rukhlenko, and M. Premaratne, IEEE Photonics J.5, 4700409(2013).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Reflectance (in logarithmic scale) in the ΓL direction from PhC with fcc structure as a function of normalized frequency and ε. The PhC is made of polystyrene spheres (ε=2.5281) surrounded by air. The reflectance is seen to diverge near the band edges of the first-order PhC stop band, which is bounded by vertical lines.

Fig. 2.
Fig. 2.

(a) Dispersion of a 3D PhC with fcc structure and (b) lasing thresholds (solid circles) for different PhC modes, and the corresponding group velocities (open circles). Note that the lasing thresholds are given in terms of the imaginary part of permittivity ε=εiε. The material parameters are the same as in Fig. 1.

Fig. 3.
Fig. 3.

(a) Normalized frequency (red curves) of lasing modes near the edges of the first-order stop band as a function of number of PhC layers. Blue curves show the stop band edges calculated with KKR method. Shaded in light blue is the stop band of infinite PhC. (b) Lasing threshold for frequencies near the first-order band edges. The parameters of the PhC are the same as in Fig. 2.

Fig. 4.
Fig. 4.

(a) Lasing frequency (wine color curves) near the edges of the first-order stop band of a 30-layer PhC versus collection angle measured from the ΓL direction. Green curve is the central frequency of the stop band calculated using Bragg’s law. (b) Lasing threshold for frequencies near the first-order band edges as function of the collection angle.

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