  We describe a dispersive unit consisting of cascaded volume-phase holographic
gratings for spectroscopic applications. Each of the gratings provides high
diffractive efficiency in a relatively narrow wavelength range and transmits
the rest of the radiation to the 0th order of diffraction. The spectral lines
formed by different gratings are centered in the longitudal direction and
separated in the transverse direction due to tilt of the gratings around two
axes. We consider a technique of design and optimization of such a scheme. It
allows to define modulation of index of refraction and thickness of the
holographic layer for each of the gratings as well as their fringes frequencies
and inclination angles. At the first stage the gratings parameters are found
approximately using analytical expressions of Kogelnik's coupled wave theory.
Then each of the grating starting from the longwave sub-range is optimized
separately by using of numerical optimization procedure and rigorous coupled
wave analysis to achieve a high diffraction efficiency profile with a steep
shortwave edge. In parallel such targets as ray aiming and linear dispersion
maintenance are controlled by means of ray tracing. We demonstrate this
technique on example of a small-sized spectrograph for astronomical
applications. It works in the range of 500-650 nm and uses three gratings
covering 50 nm each. It has spectral resolution of 6130 - 12548. Obtaining of
the asymmetrical efficiency curve is shown with use of dichromated gelatin and
a photopolymer. Change of the curve shape allows to increase filling
coefficient for the target sub-range up to 2.3 times.
