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Invariant formulation of the reflection of long waves by interfaces

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  • Lekner, John

Abstract

A theory which calculates reflection amplitudes as perturbation series about a reference profile must obtain results for observables which are invariant to the positioning of the reference profile. We construct a manifestly invariant theory for electromagnetic s and p waves, to second order in the ratio of interface thickness to wavelength. The results are expressed in terms of “integral invariants”: combinations of integrals over the difference between the reference and the actual dielectric functions, which are invariant to their relative positioning. To second order in the interface thickness, |rs|2 is characterized by one second order invariant (i2), while |rp|2 and rp/rs are each characterized by a first order invariant (I1) and two second order invariants (i2 and j2).

Suggested Citation

  • Lekner, John, 1984. "Invariant formulation of the reflection of long waves by interfaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 229-252.
    • Handle: RePEc:eee:phsmap:v:128:y:1984:i:1:p:229-252
    DOI: 10.1016/0378-4371(84)90089-X
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