Enhanced light amplification due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals

doi:10.1364/OE.4.000167

Enhanced light amplification due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals

Kazuaki Sakoda »View Author Affiliations

Optics Express, Vol. 4, Issue 5, pp. 167-176 (1999)
http://dx.doi.org/10.1364/OE.4.000167

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Abstract

An analytical expression was derived for light amplification by stimulated emission in arbitrary photonic crystals, which showed an enhancement due to small group velocity. This enhancement was evaluated quantitatively for a two-dimensional crystal with a finite thickness, and an extremely large enhancement due to group-velocity anomaly peculiar to two- and three-dimensional crystals was found even for quite a thin crystal.

[Optical Society of America ]

OCIS Codes
(250.4480) Optoelectronics : Optical amplifiers
(260.2110) Physical optics : Electromagnetic optics
(350.3950) Other areas of optics : Micro-optics

ToC Category:
Research Papers

History
Original Manuscript: January 26, 1999
Published: March 1, 1999

Citation
Kazuaki Sakoda, "Enhanced light amplification due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals," Opt. Express 4, 167-176 (1999)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-4-5-167

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References

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, 1995).
C. M. Soukoulis, ed., Photonic Band Gaps and Localization (Plenum, New York, 1993).
C. M. Soukoulis, ed., Photonic Band Gap Materials (Kluwer, Dordrecht, 1996). [CrossRef]
K. Sakoda, "Photonic crystals," in Optical Properties of Low-Dimensional Materials, Vol. 2, T. Ogawa and Y. Kanemitsu, ed. (World Scientific, Singapore, 1998). [CrossRef]
E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
S. John and J. Wang, "Quantum optics of localized light in a photonic band gap," Phys. Rev. B 43, 12772-12789 (1991). [CrossRef]
S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, "Microwave propagation in two-dimensional dielectric lattices," Phys. Rev. Lett. 67, 2017-2020 (1991). [CrossRef] [PubMed]
E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, "Donor and acceptor modes in photonic band structure," Phys. Rev. Lett. 67, 3380-3383 (1991). [CrossRef] [PubMed]
K. Sakoda and H. Shiroma, "Numerical method for localized defect modes in photonic lattices," Phys. Rev. B 56, 4830-4835 (1997). [CrossRef]
K. Sakoda, T. Ueta, and K. Ohtaka, "Numerical analysis of eigenmodes localized at line defects in photonic lattices," Phys. Rev. B 56, 14905-14908 (1997). [CrossRef]
K. Sakoda, "Numerical study on localized defect modes in two-dimensional triangular photonic crystals," J. Appl. Phys. 84, 1210-1214 (1998). [CrossRef]
T. Ueta, K. Ohtaka, N. Kawai, and K. Sakoda, "Limits on quality factors of localized defect modes in photonic crystals due to dielectric loss," J. Appl. Phys. 84, 6299-6304 (1998). [CrossRef]
D. L. Mills and S. E. Trullinger, "Gap solitons in nonlinear periodic structures," Phys. Rev. B 36, 947-952 (1987). [CrossRef]
S. John and N. Akozbek, "Nonlinear optical solitary waves in a photonic band gap," Phys. Rev. Lett. 71, 1168-1171 (1993). [CrossRef] [PubMed]
S. John and T. Quang, "Spontaneous emission near the edge of a photonic band gap," Phys. Rev. A 50, 1764-1769 (1994). [CrossRef] [PubMed]
S. John and T. Quang, "Localization of superradiance near a photonic band gap," Phys. Rev. Lett. 74, 3419-3422 (1995). [CrossRef] [PubMed]
K. Sakoda and K. Ohtaka, "Optical response of three-dimensional photonic lattices: Solutions of inhomogeneous Maxwell's equations and their applications," Phys. Rev. B 54, 5732-5741 (1996). [CrossRef]
K. Sakoda and K. Ohtaka, "Sum-frequency generation in a two-dimensional photonic lattice," Phys. Rev. B 54, 5742-5749 (1996). [CrossRef]
M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991). [CrossRef]
W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023-2026 (1992). [CrossRef] [PubMed]
K. Sakoda, "Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices," Phys. Rev. B 52, 7982-7986 (1995). [CrossRef]
K. Sakoda, "Group-theoretical classification of eigenmodes in three-dimensional photonic lattices," Phys. Rev. B 55, 15345-15348 (1997). [CrossRef]
K. Ohtaka and Y. Tanabe, "Photonic bands using vector spherical waves. III. Group-theoretical treatment," J. Phys. Soc. Jpn. 65, 2670-2684 (1996). [CrossRef]
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, 1896-1899 (1994). [CrossRef]
S. Nojima, "Enhancement of optical gain in two-dimensional photonic crystals with active lattice points," Jpn. J. Appl. Phys. 2, Lett. 37 L565-L567 (1998). [CrossRef]
K. Sakoda, "Enhanced stimulated emission in a two-dimensional photonic crystal," Proc. 1998 Int. Conf. Appl. Phot. Tech., Applications of Photonic Technology 3, Vol. SPIE 3491, edited by G. A. Lampropoulos and R. A. Lessard (SPIE, Washington, D.C., 1998) 248-253.
H. C. Casey, Jr. and M. B. Panish, Heterostructure Lasers: Part A, Fundamental Principles (Academic, New York, 1978), Sec. 2.10.
P. Yeh, "Electromagnetic propagation in birefringent layered media," J. Opt. Soc. Am. 69, 742-756 (1979). [CrossRef]
K. Sakoda, "Optical transmittance of a two-dimensional triangular photonic lattice," Phys. Rev. B 51, 4672-4675 (1995). [CrossRef]
K. Sakoda, "Transmittance and Bragg reflectivity of two-dimensional photonic lattices," Phys. Rev. B 52, 8992-9002 (1995). [CrossRef]
K. Sakoda, "Numerical analysis of the interference patterns in the optical transmission spectra of a square photonic lattice," J. Opt. Soc. Am. B 14, 1961-1966 (1997). [CrossRef]

Other

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, 1995).
C. M. Soukoulis, ed., Photonic Band Gaps and Localization (Plenum, New York, 1993).
C. M. Soukoulis, ed., Photonic Band Gap Materials (Kluwer, Dordrecht, 1996). [CrossRef]
K. Sakoda, "Photonic crystals," in Optical Properties of Low-Dimensional Materials, Vol. 2, T. Ogawa and Y. Kanemitsu, ed. (World Scientific, Singapore, 1998). [CrossRef]
E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
S. John and J. Wang, "Quantum optics of localized light in a photonic band gap," Phys. Rev. B 43, 12772-12789 (1991). [CrossRef]
S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, "Microwave propagation in two-dimensional dielectric lattices," Phys. Rev. Lett. 67, 2017-2020 (1991). [CrossRef] [PubMed]
E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, "Donor and acceptor modes in photonic band structure," Phys. Rev. Lett. 67, 3380-3383 (1991). [CrossRef] [PubMed]
K. Sakoda and H. Shiroma, "Numerical method for localized defect modes in photonic lattices," Phys. Rev. B 56, 4830-4835 (1997). [CrossRef]
K. Sakoda, T. Ueta, and K. Ohtaka, "Numerical analysis of eigenmodes localized at line defects in photonic lattices," Phys. Rev. B 56, 14905-14908 (1997). [CrossRef]
K. Sakoda, "Numerical study on localized defect modes in two-dimensional triangular photonic crystals," J. Appl. Phys. 84, 1210-1214 (1998). [CrossRef]
T. Ueta, K. Ohtaka, N. Kawai, and K. Sakoda, "Limits on quality factors of localized defect modes in photonic crystals due to dielectric loss," J. Appl. Phys. 84, 6299-6304 (1998). [CrossRef]
D. L. Mills and S. E. Trullinger, "Gap solitons in nonlinear periodic structures," Phys. Rev. B 36, 947-952 (1987). [CrossRef]
S. John and N. Akozbek, "Nonlinear optical solitary waves in a photonic band gap," Phys. Rev. Lett. 71, 1168-1171 (1993). [CrossRef] [PubMed]
S. John and T. Quang, "Spontaneous emission near the edge of a photonic band gap," Phys. Rev. A 50, 1764-1769 (1994). [CrossRef] [PubMed]
S. John and T. Quang, "Localization of superradiance near a photonic band gap," Phys. Rev. Lett. 74, 3419-3422 (1995). [CrossRef] [PubMed]
K. Sakoda and K. Ohtaka, "Optical response of three-dimensional photonic lattices: Solutions of inhomogeneous Maxwell's equations and their applications," Phys. Rev. B 54, 5732-5741 (1996). [CrossRef]
K. Sakoda and K. Ohtaka, "Sum-frequency generation in a two-dimensional photonic lattice," Phys. Rev. B 54, 5742-5749 (1996). [CrossRef]
M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991). [CrossRef]
W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023-2026 (1992). [CrossRef] [PubMed]
K. Sakoda, "Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices," Phys. Rev. B 52, 7982-7986 (1995). [CrossRef]
K. Sakoda, "Group-theoretical classification of eigenmodes in three-dimensional photonic lattices," Phys. Rev. B 55, 15345-15348 (1997). [CrossRef]
K. Ohtaka and Y. Tanabe, "Photonic bands using vector spherical waves. III. Group-theoretical treatment," J. Phys. Soc. Jpn. 65, 2670-2684 (1996). [CrossRef]
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, 1896-1899 (1994). [CrossRef]
S. Nojima, "Enhancement of optical gain in two-dimensional photonic crystals with active lattice points," Jpn. J. Appl. Phys. 2, Lett. 37 L565-L567 (1998). [CrossRef]
K. Sakoda, "Enhanced stimulated emission in a two-dimensional photonic crystal," Proc. 1998 Int. Conf. Appl. Phot. Tech., Applications of Photonic Technology 3, Vol. SPIE 3491, edited by G. A. Lampropoulos and R. A. Lessard (SPIE, Washington, D.C., 1998) 248-253.
H. C. Casey, Jr. and M. B. Panish, Heterostructure Lasers: Part A, Fundamental Principles (Academic, New York, 1978), Sec. 2.10.
P. Yeh, "Electromagnetic propagation in birefringent layered media," J. Opt. Soc. Am. 69, 742-756 (1979). [CrossRef]
K. Sakoda, "Optical transmittance of a two-dimensional triangular photonic lattice," Phys. Rev. B 51, 4672-4675 (1995). [CrossRef]
K. Sakoda, "Transmittance and Bragg reflectivity of two-dimensional photonic lattices," Phys. Rev. B 52, 8992-9002 (1995). [CrossRef]
K. Sakoda, "Numerical analysis of the interference patterns in the optical transmission spectra of a square photonic lattice," J. Opt. Soc. Am. B 14, 1961-1966 (1997). [CrossRef]

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