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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 67, Iss. 12 — Dec. 1, 1977
  • pp: 1607–1615

Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power

W. Lukosz and R. E. Kunz  »View Author Affiliations


JOSA, Vol. 67, Issue 12, pp. 1607-1615 (1977)
http://dx.doi.org/10.1364/JOSA.67.001607


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Abstract

Expressions for the total power radiated by magnetic and electric dipoles of arbitrary orientation located in a medium 1 at distance z0 from the interface to a homogeneous or planar stratified medium 2 are derived. A relation between the normalized powers radiated by magnetic and electric dipoles is established. For a homogeneous loss-free medium 2, curves of the normalized powers L(z0)/L ∞ radiated by magnetic and electric dipoles versus the normalized distance z01, are presented for different values of the relative refractive index n = n2/n1, as the only parameter. The computer calculations are compared with analytical expressions derived for small and large distances. For n > 1, the contribution of the evanescent waves to the radiated power is calculated separately. We show that the classical results for the normalized radiated power yield the correct normalized spontaneous emission rates from an excited atomic state for electric and magnetic dipole transitions, respectively. We point out that the results for the electric dipole also give the change of the total power scattered by a small dielectric scattering particle when it is placed close to an interface.

© 1978 Optical Society of America

Citation
W. Lukosz and R. E. Kunz, "Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power," J. Opt. Soc. Am. 67, 1607-1615 (1977)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-67-12-1607


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References

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  20. See, for instance, Ref. 18, p. 18.
  21. This result is a consequence of our choice of the definition of the reflection coefficients. The reflection coefficient r1,2(s) is the ratio of the magnetic field strengths at the interface of, respectively, the reflected and the incident wave. The reflection coefficient r1,2s is defined analogously in the electric field strengths. In part of the literature the definition of the reflection coefficient for p-polarized light differs from ours by a factor (-1).
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  26. Using a different approach Agarwal developed a quantum mechanical theory for electric dipole transitions in Ref. 16. His final expressions for a normalized damping coefficient for atoms in vacuum in front of a homogeneous loss-free dielectric half-space are, for the perpendicular but not for the parallel orientation of the electric dipole moment, equivalent to our results when we insert the Fresnel coefficients into Eqs. (3. 15)-(3. 17) for the electric dipole.
  27. M. Kerker, The Scattering of Light and other Electromagnetic Radiation (Academic, New York, 1969), Chap. 3.2.
  28. For example, we plan to apply Eqs. (3. 15)-(3. 17) to calculate the power radiated by dipoles located close to a planar dielectric waveguide into the modes of the guide.

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