Abstract
We have developed a rigorous self-consistent approach for the quantization of electromagnetic field in inhomogeneous structures. The approach is based on utilization of the scattering matrix of the system. Instead of the use of standard periodic Born-Karman boundary conditions, we use the quantization condition implying equating eigenvalues of the scattering matrix (S-matrix) of the system to unity (S-quantization). In the trivial case of uniform medium boundary condition for S-quantization is nothing but periodic boundary condition. S-quantization allows calculating modification of the spontaneous emission rate for arbitrary inhomogeneous structure and direction of the emitted radiation. S-quantization solves the long-standing problem coupled to normalization of the quasi-stationary electromagnetic modes. Examples of application of S-quantization for the calculation of spontaneous emission rate for the cases of Bragg reflector and microcavity are demonstrated.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Loudon, Quantum Theory of Light (Oxford Univ. Press, Oxford, 2000), p. 28.
L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, Cambridge, 1995), p. 465.
J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, Princeton, 2008), p. 10.
R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, IEEE Proc. Optoelectron. 145, 391 (1998).
M. A. Kaliteevski, K. A. Ivanov, G. Pozina, and A. J. Gallant, Sci. Rep. 4, 5444 (2014).
E. M. Purcell, Phys. Rev. 69, 681 (1946).
M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, and V. V. Nikolaev, Phys. Rev. B 73, 033106 (2006).
L. A. Weinstein, Open Resonators and Open Waveguides (Golem, Boulder, 1969).
R. M. More, Phys. Rev. A 4, 1782 (1971).
R. M. More and E. Gerjuoy, Phys. Rev. A 7, 1288 (1973).
R. Olshansky, Rev. Mod. Phys. 51, 341 (1979).
S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, Phys. Rev. A 49, 3068 (1994).
P. T. Leung and K. M. Pang, J. Opt. Soc. Am. B 13, 805 (1996).
E. A. Muljarov, W. Langbein, and R. Zimmermann, Europhys. Lett. 92, 50010 (2010).
M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 85, 023835 (2012).
T. G. Philbin, New J. Phys. 12, 123008 (2010).
L. G. Suttorp, J. Phys. A: Math. Theor. 40, 3697 (2007).
M. A. Kaliteevski, K. A. Ivanov, V. A. Mazlin, and A. R. Gubaydullin, to be submitted.
F. de Martini, M. Marrocco, P. Mataloni, L. Crescentini, and R. Loudon, Phys. Rev. A 43, 2480 (1991).
M. A. Kaliteevski, V. A. Mazlin, K. A. Ivanov, and A. R. Gubaydullin, Opt. Spectrosc. 119, 832 (2015).
M. Ley and R. Loudon, J. Mod. Opt. 34, 227 (1987).
E. Yablonovitch, T. J. Gmitter, and K. M. Leung, Phys. Rev. Lett. 67, 2295 (1991).
V. P. Bykov, Sov. Phys. JETP 62, 505 (1972).
H. Kogelnik and C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
A. Askitopoulos, L. Mouchliadis, I. Iorsh, G. Christmann, J. J. Baumberg, M. A. Kaliteevski, Z. Hatzopoulos, and P. G. Savvidis, Phys. Rev. Lett. 106, 076401 (2011).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Russian in Optika i Spektroskopiya, 2016, Vol. 121, No. 3, pp. 446–456.
The article was translated by the authors.
Rights and permissions
About this article
Cite this article
Kaliteevski, M.A., Gubaydullin, A.R., Ivanov, K.A. et al. Quantization of electromagnetic field and analysis of Purcell effect based on formalism of scattering matrix. Opt. Spectrosc. 121, 410–419 (2016). https://doi.org/10.1134/S0030400X16090095
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0030400X16090095