TY - UNPB

T1 - "Cartesian light": unconventional propagation of light in a 3D superlattice of coupled cavities within a 3D photonic band gap

AU - Hack, Sjoerd Arthur

AU - van der Vegt, Jacobus J.W.

AU - Vos, Willem L.

PY - 2018/12/11

Y1 - 2018/12/11

N2 - We explore the unconventional propagation of light in a three-dimensional (3D) superlattice of coupled resonant cavities in a 3D photonic band gap crystal. Such a 3D cavity superlattice is the photonic analogue of the Anderson model for spins and electrons in the limit of zero disorder. Using the plane-wave expansion method, we calculate the dispersion relations of the 3D cavity superlattice with the cubic inverse woodpile structure that reveal five coupled-cavity bands, typical of quadrupole-like resonances. For three out of five bands, we observe that the dispersion bandwidth is significantly larger in the ($k_x$,$k_z$)-diagonal directions than in other directions. To explain the directionality of the dispersion bandwidth, we employ the tight-binding method from which we derive coupling coefficients in 3D. For all converged coupled-cavity bands, we find that light hops predominantly in a few high-symmetry directions including the Cartesian (x,y,z) directions, therefore we propose the name "Cartesian light". Such 3D Cartesian hopping of light in a band gap yields propagation as superlattice Bloch modes that differ fundamentally from the conventional 3D spatially-extended Bloch wave propagation in crystals, from light tunneling through a band gap, from coupled-resonator optical waveguiding, and also from light diffusing at the edge of a gap.

AB - We explore the unconventional propagation of light in a three-dimensional (3D) superlattice of coupled resonant cavities in a 3D photonic band gap crystal. Such a 3D cavity superlattice is the photonic analogue of the Anderson model for spins and electrons in the limit of zero disorder. Using the plane-wave expansion method, we calculate the dispersion relations of the 3D cavity superlattice with the cubic inverse woodpile structure that reveal five coupled-cavity bands, typical of quadrupole-like resonances. For three out of five bands, we observe that the dispersion bandwidth is significantly larger in the ($k_x$,$k_z$)-diagonal directions than in other directions. To explain the directionality of the dispersion bandwidth, we employ the tight-binding method from which we derive coupling coefficients in 3D. For all converged coupled-cavity bands, we find that light hops predominantly in a few high-symmetry directions including the Cartesian (x,y,z) directions, therefore we propose the name "Cartesian light". Such 3D Cartesian hopping of light in a band gap yields propagation as superlattice Bloch modes that differ fundamentally from the conventional 3D spatially-extended Bloch wave propagation in crystals, from light tunneling through a band gap, from coupled-resonator optical waveguiding, and also from light diffusing at the edge of a gap.

M3 - Working paper

T3 - Arxiv.org

BT - "Cartesian light": unconventional propagation of light in a 3D superlattice of coupled cavities within a 3D photonic band gap

ER -