PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 39 > pp. 299-339

Finite Difference Time Domain Modeling of Light Amplification in Active Photonic Band Gap Structures

By A. D'Orazio, V. De Palo, M. De Sario, V. Petruzzelli, and F. Prudenzano

Full Article PDF (2,385 KB)

Abstract:
Abstract-The paper deals with the modeling, based on the Finite Difference Time Domain method, of active one- and twodimensional photonic crystals. The onset of laser oscillation is observed by simulating the active substance as having a negative frequency-dependent Lorentzian-shaped conductivity so including into Maxwell's equations an electric current density. Particular attention is devoted to the implementation of uniaxial perfectly matched layer absorbing boundary conditions for the simulation of infinitely extending structures having gain features. Laser behaviour is simulated as a function of various parameters; the threshold wavelengthand conductivity are evaluated as the wavelengthand conductivity where the transmittance diverges. Moreover, the properties of the active two-dimensional photonic band gap structures are given in terms of a Q quality factor which increases by increasing the crystal size and strongly depends on the lattice shape. For the square lattice, when the crystal size increases from N = 2 to N = 8 the Q-factor increases by about an order of magnitude (from 0.027 to 0.110) for TE polarization while for TM polarization it decreases from 0.025 to 0.022. At last the Q-factor pertaining to the chess-board lattice, to parity of other parameters, assumes greater values and already for N = 4, it reaches the values obtained for the 16×8 square lattice, for bothTE and TM polarizations.

Citation:
A. D'Orazio, V. De Palo, M. De Sario, V. Petruzzelli, and F. Prudenzano, "Finite difference time domain modeling of light amplification in active photonic band gap structures," Progress In Electromagnetics Research, Vol. 39, 299-339, 2003.
doi:10.2528/PIER02112501
http://www.jpier.org/pier/pier.php?paper=0211251

References:
1. Yablonovitch, E., "Inhibited spontaneous emission in solid state physics and electronics," Phys. Rev. Letters, Vol. 5D, 2059-2062, 1987.
doi:10.1103/PhysRevLett.58.2059

2. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Letters, Vol. 58, 2486-2489, 1987.
doi:10.1103/PhysRevLett.58.2486

3. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Crystals. Molding the Flow of Light, Princeton University Press, 1995., 1995.

4. D'Orazio, A., M. De Sario, V. Petruzzelli, and F. Prudenzano, "Numerical modeling of photonic band gap waveguiding structures," Recent Research Developments in Optics, 2002.

5. Sakoda, K., "Enhanced light amplification due to groupvelocity anomaly peculiar to two-and three-dimensional photonic crystals," Optics Express, Vol. 4, No. 5, 167-176, 1999.

6. Dowling, J. P., M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: A new approach to gain enhancement," J. Appl. Phys., Vol. 75, 1896-1899, 1994.
doi:10.1063/1.356336

7. Ohtaka, K., "Density of states of slab photonic crystals and the laser oscillation in photonic crystals," Journal of Lightwave Technology, Vol. 17, No. 11, 2161-2169, 1999.
doi:10.1109/50.803007

8. Vlasov, Yu. A., K. Luterova, I. Pelant, B. Honerlage, and V. N. Astratov, "Enhancement of optical gain semiconductors embedded in three-dimensional photonic crystals," Appl. Phys. Lett., Vol. 71, No. 12, 1616-1618, 1997.
doi:10.1063/1.119995

9. Kopp, V. I., B. Fan, and H. K. M. Vithana, "and A. Z. Genack Lowthreshold lasing at the edge of a photonic stop band in cholesteric liquid crystal," Opt. Letters, Vol. 23 No. 21, No. Vol. 23 21, 1707-1709, 1998.

10. Villeneuve, P. R., S. Fan, and J. D. Joannoupoulos, "Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency," Phys. Rev. B, Vol. 54, 7837-7842, 1996.
doi:10.1103/PhysRevB.54.7837

11. Kuzmiak, V. and A. A. Maradudin, "Localized defect modes in a two-dimensional triangular photonic crystal," Phys. Rev. B, Vol. 57, 15242-15249, 1998.
doi:10.1103/PhysRevB.57.15242

12. Pottier, P., C. Seassal, X. Letartre, J. L. Leclercq, P. Viktorovitch, D. Cassagne, and J. Jouanin, "Triangular and hexagonal high Q-factor 2-D photonic band gap cavities on III-V suspended membranes," J. Lightwave Technology, Vol. 17, 2058-2062, 1999.
doi:10.1109/50.802995

13. Qiu, M. and S. He, "Numerical method for computing defect modes in two-dimensional photonic crystals with dielectric or metallic inclusions," Physics Review B, Vol. 61, 12871-12876, 2000.
doi:10.1103/PhysRevB.61.12871

14. Ripin, D. J., K. Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski, "One-dimensional photonic bandgap microcavities for strong optical confinement in GaAs and GaAs/AlxOy semiconductor waveguides," J. Lightwave Technology, Vol. 17, 2152-2160, 1999.
doi:10.1109/50.803006

15. Villeneuve, P. R., S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: Mode symmetry, tunability and coupling efficiency," Physics Review B, Vol. 54, 7837-7842, 1996.
doi:10.1103/PhysRevB.54.7837

16. Smith, D. R., R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, and P. M. Platzman, "Photonic band structure and defects in one and two dimensions," J. Optical Society of America B, Vol. 10, 314-321, 1993.

17. Inoue, K., M. Sasada, J. Kawamata, K. Sakoda, and J. W. Haus, "A two-dimensional photonic crystal laser," Jpn. J. Appl. Phys., Vol. 38, No. 2B, 157, 1999.
doi:10.1143/JJAP.38.L157

18. Imada, M., S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, "Coherent two-dimensional lasing action in surfaceemitting laser withtriangular-lattice photonic crystal structure," Applied Phys. Letters, Vol. 75, No. 3, 316-318, 1999.
doi:10.1063/1.124361

19. Taflove, A., Advances in Computational Electrodynamics — The Finite-Difference Time-Domain Method, ArtechHouse, 1998.

20. Yariv, A., Quantum Electronics, Wiley, New York, 1967.

21. Nojima, S., "Enhancement of optical gain in two-dimensional photonic crystals with active lattice points," Jpn. J. Applied Physics 2, Vol. 37, 565, 1998.
doi:10.1143/JJAP.37.L565

22. Bell, P. M., J. B. Pendry, L. Martin Moreno, and A. J. Ward, Comput. Phys. Commun., Vol. 85, 306, Vol. 85, 1995., 1995.


© Copyright 2014 EMW Publishing. All Rights Reserved