We propose a particular analytical representation (ansatz) for analytical solution of Maxwell’s equations with one-dimensional potential. The resulting expressions are presented as self-consistent equations for the calculation of x-ray reflection and transmission coefficients at the interfaces with an arbitrary potential profile. The reported approach is testified for typical model potentials, and the convergence of the successive iterations for improvement of solution accuracy is demonstrated. The equations derived in the paper can be used for the solution of the inverse problem in x-ray reflectometry.

• Received 23 January 2003

DOI:https://doi.org/10.1103/PhysRevB.67.235417