The multiwave regime of light diffraction and focusing effect in volume phase gratings

Is it possible to consider a thin hologram as a slide?

“…Therefore, in our case, the continuity conditions of E y and y E z   are used as the boundary conditions. We will solve this problem using perturbation theory [12], which represents the electric field of the wave in the region 0≤z≤d as follows 1 : .…”

“…For a small d, by replacing the sine function in (24) with its argument, we obtain (23) up to a phase factor. Let us check for expressions ( 22) and ( 23) the validity of the electrodynamic reciprocity theorem (Section 2.5 [15]), which, as applied to phase gratings, requires that when the wave vectors of the incident and diffracted waves are interchanged, and the sign of the grating vector is simultaneously changed, the diffraction efficiency does not change [12]. The diffraction efficiency η is given by [16] * 1 11…”

“…A rigorous statement of the boundary-value problem is used, taking into account the transmitted and reflected diffraction orders [9,10]. The wave equation is solved using perturbation theory [11][12][13][14]. We compare the expression for the first diffraction order obtained in the first approximation of the perturbation theory with the corresponding expression obtained in simplified consideration, as the hologram thickness (d) tends to zero.…”

“…To achieve this, both expressions are expanded to a series in d and limited to a linear term. Both expressions are analyzed from the perspective of the fulfillment of the electrodynamic reciprocity theorem [15,12]. For a particular case, the expressions are compared with the results of the two-wave approximation of coupled-wave theory [16].…”