## Abstract

To expand the spectral bandwidths with high diffraction efficiency of volume phase (VP) gratings, it is important to know the influence of a variety of refractive index distributions (RIDs) inside the recording material on the bandwidths. The influence of various graded types of RIDs on the full width at half the maximum of the spectral bandwidth (${\lambda _{\rm FWHM}}$) and the angular bandwidth (${\theta _{\rm FWHM}}$) is investigated in the Bragg regime. It becomes clear that various graded types of RIDs influence their bandwidths and the characteristics, and the combination of the RIDs and refractive index modulation (${{ n}_m}$) is the most important factor for obtaining the large bandwidths of VP gratings. Theoretically, the ${\lambda _{\rm FWHM}}$ are obtained as the values of 149.7 nm and 257.6 nm (${{ n}_m} = {0.045}$) for the wavelengths of 900 nm and 1550 nm, respectively. Furthermore, I have succeeded in developing the expression for ${\lambda _{\rm FWHM}}$ and ${\theta _{\rm FWHM}}$, using the proportional characteristics of VP gratings investigated in this work. The correlative coupling-length coefficients “G-factors” devised as a variety of RID functions in the previous paper are introduced into them. It is apparent that the derived equations of the bandwidths can be adapted to any graded type of RID that changes continuously from a triangular type to a rectangular type of VP grating, which has not been reported yet. The equations have made it easy to design ${\lambda _{\rm FWHM}}$ and ${\theta _{\rm FWHM}}$ of VP gratings.

© 2019 Optical Society of America

Full Article | PDF Article**OSA Recommended Articles**

K. Nakajima

J. Opt. Soc. Am. A **36**(11) 1861-1870 (2019)

Kun Xue, Emmanuel Boss, Ronghua Ma, and Ming Shen

Appl. Opt. **58**(31) 8549-8564 (2019)

Lina Fan, Kehui Jia, and Junshan Ma

Appl. Opt. **58**(31) 8371-8375 (2019)