Strongly Localized State of a Photon at the Intersection of the Phase Slips in 2D Photonic Crystal with Low Contrast of Dielectric Constant

Details Strongly Localized State of a Photon at the Intersection of the Phase Slips in 2D Photonic Crystal with Low Contrast of Dielectric Constant Strongly Localized State of a Photon at the Intersection of the Phase Slips in 2D Photonic Crystal with Low Contrast of Dielectric Constant

2002-09-28

arxiv.org/abs/cond-mat/0209657v1

Phys. Rev. Lett. 90, 253901 (2003)

Physics

Condensed Matter

6 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.90.253901

Two-dimensional photonic crystal with a rectangular symmetry and low contrast (< 1) of the dielectric constant is considered. We demonstrate that, despite the {\em absence} of a bandgap, strong localization of a photon can be achieved for certain ``magic'' geometries of a unit cell by introducing two $\pi/2$ phase slips along the major axes. Long-living photon mode is bound to the intersection of the phase slips. We calculate analytically the lifetime of this mode for the simplest geometry -- a square lattice of cylinders of a radius, $r$. We find the magic radius, $r_c$, of a cylinder to be 43.10 percent of the lattice constant. For this value of $r$, the quality factor of the bound mode exceeds $10^6$. Small ($\sim 1%$) deviation of $r$ from $r_c$ results in a drastic damping of the bound mode.

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