Holographic spectroscopy: analysis of convergent phase development

Abstract

A real-number representation of wave amplitudes and phases inside the photosensitive medium with holographic elementary grating is deduced from coupled-wave equations by choosing a separation ansatz. Using numerical simulations, we show that so-called in-Bragg and off-Bragg cases are closely tied to the phase relationship between the reference and signal waves. Since the formulation is, as a whole, performed in the real number space, the results allow a strong intuitive interpretation. Asymptotic convergence to constant boundary values of the phase difference (in-Bragg) and to linear functions with slope (off-Bragg case) are discussed and unambiguously attributed to the type of recorded grating (pure index, mixed, or pure absorption grating). Finally, an analytical examination of the real amplitudes dependent on the waves' phase parameters is derived. All results are discussed in the framework of energy transfer between two waves coupled at a recorded holographic grating.