  In the present article we consider an accurate modeling of spectrograph with
cascade of volume-phase holographic gratings. The proposed optical scheme
allows to detect spectra in an extended wavelength range without gaps providing
relatively high spectral resolution and high throughput. However, modeling and
minimization of possible cross-talks between gratings and stray light in such a
scheme represents a separate task. We use analytical equations of coupled wave
theory together with rigorous coupled wave analysis to optimize the gratings
parameters and further apply the latter together with non-sequential raytracing
algorithm to model propagation of beams through the spectrograph. The results
show relatively high throughput up to 53% and absence of any significant
cross-talks or ghost images even for ordinary holograms recorded on dichromated
gelatin.
