Omnidirectional reflection from finite periodic and Fibonacci quasi-periodic multilayers of alternating isotropic and birefringent thin films

Omnidirectional reflection from periodic and Fibonacci quasi-periodic multilayers that are embedded in an isotropic medium is further analyzed. Besides the isotropic structures, birefringent structures are considered that comprise uniaxial layers in the principal-axis system, alternating with isotropic layers so that the refractive index of isotropic layers is equal to the principal extraordinary refractive index of the uniaxial layers. The transfer-matrix method is applied, and the same formalism is used forboth the isotropic and the uniaxial media in the principal-axis system. Simple and original relations are obtained for the invariant of the one-dimensional Fibonacci sequences at oblique incidence. Numerical examples are given comparatively for the isotropic and the birefringent structures in the case of periodic and Fibonacci quasi-periodic sequences at different values of the refractive indices.