Abstract
We present a novel computational approach for calculating spontaneous emission in the presence of a surface of a material slab. The only requirement on the material is that it should have periodicity parallel to the surface. The spontaneous emission rate is calculated using Fermi’s golden rule, which can be described in terms of the classical Density of States (DOS). The DOS can in turn be expressed in terms of the Green’s function. We calculate the Green’s function for light of a specific frequency and a specific incident direction and distance with respect to the surface and then integrate over all incident directions. The only information required from the material, is the reflection coefficients for plane waves at the surface. With our method we reproduce results of an analytical calculation for a semi-infinite homogeneous dielectric. We also present new results for a slab of cylindrical dielectric rods embedded in air on a square lattice.
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Yablonovitch, E., Gmitter, T.J. and Bhat, R., (1988)Inhibited and enhanced spontaneous emission from optically thin AlGaAs/GaAs double hetero structure s Phys. Rev. Lett. 61, 2546–2549.
Leung, K.M. and Liu, Y.F. (1990)Full vector wave calculation of photonic band structures in Face-Centered-Cubic dielectric mediaPhys. Rev. Lett. 65, 2646- 2649.
Zhang, Z. and Satpathy, S. (1990)Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations Phys. Rev. Lett. 65, 2650–2653.
Ho, K.M., Chan, C.T. and Soukoulis, C.M. (1990)Existence of a photonic gap in periodic dielectric structures Phys. Rev. Lett. 65, 3152–3155.
Yablonovitch, E., Gmitter, T.J. and Leung, K.M. (1991)Photonic band structure: the Face-Centered-Cubic case employing nonspherical atoms Phys. Rev. Lett. 67, 2295–2298.
Snoeks, E., Lagendijk, A. and Polman, A. (1995)Measuring and modifying the spontaneous emission rate of Erbium near an interface Phys. Rev. Lett. 74, 2459–2462.
Khosravi, H. and Loudon, R. (1991)Vacuum field fluctuations and spontaneous emission in the vicinity of a dielectric surface Pro. R. Soc. Lond. A 433, 337–353.
Khosravi, H. and Loudon, R. (1992)Vacuum field fluctuations and spontaneous emission in a dielectric slab Pro. R. Soc. Lond. A 436, 373–389.
Joannopoulus, J.D. (1995)Minding the gap Nature 375, 278.
Lagendijk, A. and van Tiggelen, B.A.Resonant Multiple Scattering of Light to appear in Physics Reports.
Sprik, R., Lagendijk, A. and van Tiggelen, B.A.Photonic band structures for atomic latticesto appear in Proceedings NATO Conference “Photonic Band Gap Materials”, June 1995, Crete, Greece.
Economou, E.N. (1983)Green’s Functions in Quantum Physics, Springer Berlin.
Pendry, J.B. and MacKinnon, A. (1992)Calculation of photon dispersion relations Phys. Rev. Lett. 69, 2772–2774.
Pendry, J.B. (1994)Photonic band structures J. Mod. Opt. 41, 209–229.
Bell, P.M., Pendry, J.B., Martin Moreno, L., and Ward, A.J. (1995)A program for calculating photonic band structures and transmission coefficients of complex structures Comp. Phys. Comm. 85, 306–322.
Loudon, R. (1983)The Quantum Theory of Light, Clarendon Press, Oxford.
Collin, R.E. (1991)Field Theory of Guided Waves, IEEE Press, New York.
Robertson, W.M., Arjavalingam, G., Meade, R.D., Brommer, K.D., Rappe, A.M. and Joannopoulus, J.D. (1992)Measurement of photonic band structure in a two- dimensional periodic dieletric array Phys. Rev. Lett. 68, 2023–2026.
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© 1996 Kluwer Academic Publishers
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Wijnands, F., Pendry, J.B., Roberts, P.J., Bell, P.M., Moreno, L.M., Garcia-Vidal, F.J. (1996). Numerical method for calculating spontaneous emission rate near a surface using Green’s functions. In: Rarity, J., Weisbuch, C. (eds) Microcavities and Photonic Bandgaps: Physics and Applications. NATO ASI Series, vol 324. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0313-5_27
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DOI: https://doi.org/10.1007/978-94-009-0313-5_27
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6626-6
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