Volume Phase Holographic Gratings: Polarization Properties and Diffraction Efficiency

We discuss the polarization properties and first-order diffraction efficiencies of volume phase holographic (VPH) transmission gratings, which can be exploited to improve the throughput of modern spectrographs. The wavelength of peak efficiency can be tuned by adjustment of the incidence angle. We show that the variation of the Kogelnik efficiency versus Bragg angle depends only on one parameter, given by $P_{tune} = (\Delta n d)/(n \Lambda)$, where: $\Delta n$ is semi-amplitude of the refractive index modulation; $n$ is the average index; $d$ is the thickness of the active layer; and $\Lambda$ is the grating period. The efficiency has a well defined dependence on polarization. In particular, it is possible to obtain theoretical 100% diffraction efficiency with one linear polarization at any angle or to obtain 100% efficiency with unpolarized light at specific angles. In the latter case, high efficiency is the result of aligning the peaks of the s- and p-polarization efficiency-versus-thickness curves. The first of these `s-p-phased gratings' for astronomy is in use with the 6dF spectrograph. Consideration of polarization is particularly important for high spectral resolution, which requires large incidence angles. We also discuss the possibility of separating polarization states for improved throughput along the entire optical train of a spectrograph.