Uniqueness of wave-plate measurements in determining the tensor components of second-order surface nonlinearities

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Abstract
The relative amplitude and phase of the components of the second-order susceptibility tensors for second-harmonic generation from a chiral surface can be determined by making measurements of the second-harmonic intensity. The intensity of the p and s components of the reflected or transmitted second-harmonic wave must be measured, but the measurements need not be calibrated nor even be on the same relative intensity scale. However, these intensity measurements must be made as functions of the polarization state of the fundamental radiation. We prove that it is sufficient to make these measurements at a single angle of incidence provided that a wave plate of any retardation other than half wave is used to manipulate the polarization state of the fundamental radiation. Quarter-wave retardation is a good choice. We derive explicit formulas to determine the susceptibility components from the parameters found to describe the intensity measurements, where the electric dipole approximation is made in the description of the nonlinearity.