Quasi-normal-modes description of transmission properties for photonic bandgap structures

Journal of the Optical Society of America B: Optical Physics

Volumn 26, Issue 4, 2009, Pages 876-891

  Settimi, A ^a   Severini, S ^b   Hoenders, B J ^c  

^a ISTITUTO NAZIONALE DI GEOFISICA E VULCANOLOGIA   (Italy)

^b Centro Inteiforze Studi per le Applicazioni Militari   (Italy)

^c UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY GAP; SPONTANEOUS EMISSION;

COUNTERPROPAGATING; DIRECT METHOD; DYNAMICAL VARIABLES; INITIAL CONDITIONS; INTERFERENCE EFFECTS; OPTICAL CAVITIES; PHOTONIC BAND-GAP STRUCTURES; TRANSMISSION PROPERTY;

ELECTROMAGNETIC FIELD EFFECTS;

EID: 65249130651     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.26.000876     Document Type: Article

References (35)

1. K. Sakoda, Optical Properties of Photonic Crystals (Springer Verlag, 2001).
2. J. Maddox, "Photonic band-gaps bite the dust," Nature 348, 481-481 (1990).
3. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
4. S. John, "Electromagnetic absorption in a disordered medium near a photon mobility edge," Phys. Rev. Lett. 53, 2169-2172 (1984).
5. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
6. M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
7. J. E. Sipe, L. Poladian, and C. Martijn de Sterke, "Propagation through nonuniform grating structures," J. Opt. Soc. Am. A 4, 1307-1320 (1994).
8. E. S. C. Ching, P. T. Leung, and K. Young, "Optical processes in microcavities - the role of quasi-normal modes," in Optical Processes in Microcavities, R. K. Chang and A. J. Campillo, eds. (World Scientific, 1996), pp. 1-75.
9. P. T. Leung, S. Y Liu, and K. Young, "Completeness and orthogonality of quasinormal modes in leaky optical cavities," Phys. Rev. A 49, 3057-3067 (1994).
10. P. T. Leung, S. S. Tong, and K. Young, "Two-component eigenfunction expansion for open systems described by the wave equation I: completeness of expansion," J. Phys. A 30, 2139-2151 (1997).
11. P. T. Leung, S. S. Tong, and K. Young, "Two-component eigenfunction expansion for open systems described by the wave equation II: linear space structure," J. Phys. A 30, 2153-2162 (1997).
12. E. S. C. Ching, P. T. Leung, A. Maassen van den Brink, W. M. Suen, S. S. Tong, and K. Young, "Quasinormal-mode expansion for waves in open systems," Rev. Mod. Phys. 70, 1545-1554 (1998).
13. P. T. Leung, W. M. Suen, C. P. Sun, and K. Young, "Waves in open systems via a biorthogonal basis," Phys. Rev. E 57, 6101-6104 (1998).
14. K. C. Ho, P. T. Leung, A. Maassen van den Brink, and K. Young, "Second quantization of open systems using quasinormal modes," Phys. Rev. E 58, 2965-2978 (1998).
15. A. Maassen van den Brink and K. Young, "Jordan blocks and generalized bi-orthogonal bases: realizations in open wave systems," J. Phys. A 34, 2607-2624 (2001).
16. B. J. Hoenders, "On the decomposition of the electromagnetic field into its natural modes," in Proceedings of the 4th International Conference on Coherence and. Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, 1978), pp. 221-233.
17. B. J. Hoenders and H. A. Ferwerda, "On a new proposal concerning the calculation of the derivatives of a function subject to errors," Optik (Jena) 40, 14-17 (1974).
18. B. J. Hoenders, "Completeness of a set of modes connected with the electromagnetic field of a homogeneous sphere embedded in an infinite medium," J. Math. Phys. 11, 1815-1832 (1978).
19. B. J. Hoenders, "On the completeness of the natural modes for quantum mechanical potential scattering," J. Math. Phys. 20, 329-335 (1979).
20. M. Bertolotti, "Linear one-dimensional resonant cavities," in Microresonators as Building Blocks for VLSI Photonics of AIP Conference Proceedings, F. Michelotti, A. Driessen, and M. Bertolotti, eds. (AIP, 2004), Vol. 709, pp. 19-47.
21. B. J. Hoenders and M. Bertolotti, "The (quasi)normal natural mode description of the scattering process by dispersive photonic crystals," Proc. SPIE 6182, 61821F-6182G (2006).
22. M. Maksimovic, M. Hammer, and E. van Groesen, "Field representation for optical defect resonances in multilayer microcavities using quasi-normal modes," Opt. Lett. 281, 1401-1411 (2008).
23. S. Severini, A. Settimi, N. Mattiucci, C. Sibilia, M. Centini, G. D'Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, "Quasi normal modes description of waves in 1D photonic crystals," Proc. SPIE 5036, 392-401 (2003).
24. A. Settimi, S. Severini, N. Mattiucci, C. Sibilia, M. Centini, G. D'Aguanno, M. Bertolotti, M. Scalora, M. Bloemer, and C. M. Bowden, "Quasinormal-mode description of waves in one-dimensional photonic crystals," Phys. Rev. E 68, 026614 (2003).
25. S. Severini, A. Settimi, C. Sibilia, M. Bertolotti, A. Napoli, and A. Messina, "Quasi-normal frequencies in open cavities: an application to photonic crystals," Acta Phys. Hung. B 23, 135-142 (2005).
26. S. Severini, A. Settimi, C. Sibilia, M. Bertolotti, A. Napoli, and A. Messina, "Quantum counterpropagation in open optical cavities via the quasi-normal-mode approach," Laser Phys. 16, 911-920 (2006).
27. M. Born and E. Wolf, Principles of Optics (Macmillan, 1964).
28. G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a Complex Variable - Theory and Technique (McGraw-Hill, 1983).
29. E. N. Economou, Green's Functions in Quantum Physics (Springer-Verlag, 1979).
30. A. Bachelot and A. Motet-Bachelot, "Les résonances d'un trou noir de Schwarzschild," Ann. Inst. Henri Poincaré, Sect. A 59, 3-68 (1993).
31. D. W. L. Sprung, H. Wu, and J. Martorell, "Scattering by a finite periodic potential," Am. J. Phys. 61, 1118-1124 (1993).
32. M. G. Rozman, P. Raineken, and R. Tehver, "Scattering by locally periodic one-dimensional potentials," Phys. Lett. A 187, 127-131 (1994).
33. J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996).
34. J. P. Dowling, "Parity, time-reversal and group delay for inhomogeneous dielectric slabs: Application to pulse propagation in finite, one-dimensional, photonic bandgap structures," in Proceedings of IEEE-Optoelctronics (IEEE, 1998), Vol. 145, pp. 420-435.
35. A. Sopahaluwakan, "Characterization and simulation of localized states in periodic structures," Ph.D. dissertation (University of Twente, 2006).