Local normal-mode coupling and energy band splitting in elliptically birefringent one-dimensional magnetophotonic crystals

Abstract

An analysis is presented of wave-vector dispersion in elliptically birefringent stratified magneto-optic media having one-dimensional periodicity. It is found that local normal-mode polarization-state differences between adjacent layers lead to mode coupling and impact the wave-vector dispersion and the character of the Bloch states of the system. This coupling produces extra terms in the dispersion relation not present in uniform circularly birefringent magneto-optic stratified media. Normal mode coupling lifts the degeneracy at frequency band cross-over points under certain conditions and induces a magnetization-dependent optical band gap. This study examines the conditions for band gap formation in the system. It shows that such a frequency-split can be characterized by a simple coupling parameter that depends on the relation between polarization states of local normal modes in adjacent layers. The character of the Bloch states and conditions for maximizing the strength of the band splitting in these systems are analyzed.

Elliptical normal modes and stop band reconfiguration in multimode birefringent one-dimensional magnetophotonic crystals

“…The electromagnetic wave equation in a birefringent magneto-optic medium is given by ( ) [17,20] where E 0 is the plane wave amplitude, kk is a dyadic product of the wave vector, I is the 3×3 identity matrix, and …”

“…Elliptically-polarized normal modes A transfer matrix formulation can be built based on this model to calculate the transmittance of the stack, as described in [17,19,20]. This transfer matrix approach…”

“…Levy and coworkers reported on flat-top response in multiple resonator one-dimensional magnetophotonic crystals [13] and large polarization rotations in waveguide nonreciprocal Bragg systems [14][15][16]. They also studied band gap formation, local normal mode coupling and Bloch states in birefringent magneto-photonic periodic stacks [17][18][19][20]. Degenerate band gap periodic magneto-optic systems were analyzed in [21], while applications of magneto-photonic waveguide Bragg structures to sensors and switches were reported in [22,23].…”

“…Elliptical birefringence arises naturally in magneto-optic waveguides due to the combined effects of magneto-optic gyrotropy and shape anisotropy [14,15,17,19,20]. Stress birefringence, due to lattice mismatch between waveguide film and substrate also contributes to the effect.…”

“…Generally the above conditions lead to different diagonal components in the relative permittivity matrix and semi-major axes of the elliptical modes aligning with the directions of transverse electric and transverse magnetic polarizations [17,20].…”