## Detailed analysis of transmission spectra and Bragg-reflection spectra of a two-dimensional photonic crystal with a lattice constant of 1.15 µm

JOSA B, Vol. 16, Issue 3, pp. 361-365 (1999)

http://dx.doi.org/10.1364/JOSAB.16.000361

Acrobat PDF (229 KB)

### Abstract

We investigated the transmission spectra and the Bragg-reflection spectra of a two-dimensional photonic crystal composed of a triangular array of circular air rods formed in PbO glass, for which the laser oscillation peculiar to the two-dimensional photonic band structure was observed recently. The sample parameters, i.e., the lattice constant, the radius of the air rods, and the dielectric constant of the host PbO glass, were evaluated from the observation angle of the Bragg reflection and by comparison of observed with calculated band gaps. The transmission spectra and the Bragg-reflection spectra were calculated with the plane-wave expansion method, and a good agreement with both the dispersion relation and the observed Bragg-reflection spectra was shown.

© 1999 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(050.1950) Diffraction and gratings : Diffraction gratings

(050.2770) Diffraction and gratings : Gratings

(120.5700) Instrumentation, measurement, and metrology : Reflection

(220.4000) Optical design and fabrication : Microstructure fabrication

(260.2110) Physical optics : Electromagnetic optics

**Citation**

Kazuaki Sakoda, Michihide Sasada, Tetsuya Fukushima, Akio Yamanaka, Noriko Kawai, and Kuon Inoue, "Detailed analysis of transmission spectra and Bragg-reflection spectra of a two-dimensional photonic crystal with a lattice constant of 1.15 µm," J. Opt. Soc. Am. B **16**, 361-365 (1999)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-16-3-361

Sort: Year | Journal | Reset

### References

- For fundamental ideas and properties of photonic crystals see J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University, Princeton, N.J. 1995); C. M. Soukoulis, ed., Photonic Band Gaps and Localization (Plenum, New York, 1993); C. M. Soukoulis, ed., Photonic Band Gap Materials (Kluwer Academic, Dordrecht, The Netherlands, 1996).
- E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987).
- G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269 (1988).
- S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418 (1990); “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12, 772 (1991).
- 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 (1991).
- 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 (1991).
- D. L. Mills and S. E. Trullinger, “Gap solitons in nonlinear periodic structures,” Phys. Rev. B 36, 947 (1987).
- S. John and N. Aközbek, “Nonlinear optical solitary waves in a photonic band gap,” Phys. Rev. Lett. 71, 1168 (1993).
- S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764 (1994); “Localization of superradiance near a photonic band gap,” Phys. Rev. Lett. 74, 3419 (1995).
- 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 (1996); “Sum-frequency generation in a two-dimensional photonic lattice,” Phys. Rev. B 54, 5742 (1996).
- 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 (1994).
- K. Sakoda, “Enhanced stimulated emission in a two-dimensional photonic crystal,” in Proceedings of the 1998 International Conference on Application of Photonic Technology (Institute of Electrical and Electronics Engineers, Piscataway, N.J., to be published).
- M. Sasada, A. Yamanaka, K. Sakoda, K. Inoue, and J. W. Haus, “Laser oscillation from dye molecules in a two-dimensional photonic crystal,” in Proceedings of the Conference on Lasers and Electro-Optics/Pacific Rim (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1997), p. 42.
- K. Inoue, M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, “Laser action characteristic of a two-dimensional photonic lattice,” in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 47.
- M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565 (1991).
- K. Inoue, M. Wada, K. Sakoda, M. Hayashi, T. Fukushima, and A. Yamanaka, “Near-infrared photonic band gap of two-dimensional triangular air-rod lattice as revealed by transmittance measurement,” Phys. Rev. B 53, 1010 (1996).
- K. Inoue, M. Wada, K. Sakoda, A. Yamanaka, M. Hayashi, and J. W. Haus, “Fabrication of two-dimensional photonic band structure with near-infrared band gap,” Jpn. J. Appl. Phys., Part 2 33, L1463 (1994).
- K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51, 4672 (1995); “Transmittance and Bragg reflectivity of a two-dimensional photonic lattices,” Phys. Rev. B 52, 8992 (1995); “Numerical analysis of the interference patterns in the optical transmission spectra of a square photonic lattice,” J. Opt. Soc. Am. B JOBPDE 14, 1961 (1997).
- K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52, 7982 (1995).
- 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 (1992); “Measurement of the photon dispersion relation in two-dimensional ordered dielectric arrays,” J. Opt. Soc. Am. B 10, 322 (1993).
- K. Ohtaka and Y. Tanabe, “Photonic bands using vector spherical waves III: group-theoretical treatment,” J. Phys. Soc. Jpn. 65, 2670 (1996).
- K. Sakoda, “Group-theoretical classification of eigenmodes in three-dimensional photonic lattices,” Phys. Rev. B 55, 15, 345 (1997).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

OSA is a member of CrossRef.