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The inverse problem in optics of stratified media with discontinuous parameters

Analytical properties of spectral coefficients of a non-absorbing stratified medium with discontinuous parameters are studied. Explicit formulae establishing one-to-one correspondence between the spectral coefficients' phases and amplitudes are derived. Conditions under which these formulae can be applied are discussed. The uniqueness of the determination of the discontinuous refractive index from the amplitude reflection coefficient is proved under practically sensible conditions.