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Reflection of long waves by interfaces

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  • Lekner, John

Abstract

We derive comparison identities for waves satisfying the equation d2Ψ/dz2+q2(z)Ψ=0. One of these identities is used to show that to second order in the product (wavenumber component normal to interface) × (interface thickness), the reflection amplitude is given by r=(1−2q1q2l2)(q1−q2)(q1+q2), where l is a legnth determined by the deviation of the interface profile from a step, and q1, q2 are the normal components of the wave numbers in media 1 and 2 on either side of the interface. For the continuous interfaces discussed, l is about two-fifths of the 10–90 interface thickness. The corresponding formula for the transmission amplitude is t=(1+12(q1−q2)2l2)2q1(q1+q2).

Suggested Citation

  • Lekner, John, 1982. "Reflection of long waves by interfaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 544-556.
    • Handle: RePEc:eee:phsmap:v:112:y:1982:i:3:p:544-556
    DOI: 10.1016/0378-4371(82)90195-9
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