We use transfer matrix formalism to investigate periodic multilayer structures including uniaxial anisotropic materials in the specific case where the optical z axis is normal to the layer interfaces. Having decoupled the problem into two independent states of polarization, we first derive a universal transfer matrix for the unit cell of an arbitrary bilayer (z uniaxial–z uniaxial or z uniaxial–isotropic), and then determine the effective indices in the long-wavelength limit through a homogenization procedure. A graphic representation illustrates the analytical results in terms of generalized filling factors. The procedure is also generalized to n-ary stacks.
© 2008 Optical Society of America
Original Manuscript: December 17, 2007
Manuscript Accepted: January 28, 2008
Published: April 25, 2008
Yann G. Boucher, Judikaël Le Rouzo, Isabelle Ribet-Mohamed, and Riad Haïdar, "Modified form birefringence in periodic multilayer structures including uniaxial anisotropic materials," J. Opt. Soc. Am. B 25, 777-784 (2008)