Compact optical one-way waveguide isolators for photonic-band-gap microchips

Abstract

In two-dimensional (2D) photonic crystals (PC's), we demonstrate compact optical waveguide isolators in which light can propagate only one way. Waveguides are composed of magneto-optical materials with magnetic domain walls. Magneto-optical effects and magnetic domain walls break time-reversal and space-inversion symmetries, respectively, leading to nonreciprocal waveguides with different group velocities for forward and backward propagating light of a given frequency. When backward light has a zero group velocity, only forward light can be transmitted while backward light stops. Slow leakage of backward light (when the group velocity is not precisely zero) is eliminated by introducing absorption loss in nonreciprocal PC waveguides. Then, absorption of forward light is less than that of backward light. Introducing gain material and signal amplification by current injection, forward light can propagate with no net loss and only backward light is attenuated. We demonstrate that backward light, with nearly zero group velocity, can be eliminated because of absorption over a long effective optical path length. This enables compact on-chip photonic band-gap isolators. The waveguide isolator is assumed to be composed of europium oxide with the Faraday rotation angle of ${\ensuremath{\theta}}_{F}=3.49\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.3em}{0ex}}\mathrm{rad}∕\mathrm{cm}$ at wavelength $\ensuremath{\lambda}=1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ under a magnetic field $0.9\phantom{\rule{0.3em}{0ex}}\text{Tesla}$. In a waveguide isolator with the length of $8.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$, transmittance of backward light is mostly zero at a specific frequency when transmittance of forward light is amplified to 1 by current injection. The usable bandwidth is up to $12\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ centered at $1.5\phantom{\rule{0.3em}{0ex}}\text{micron}$ wavelength as the device length is increased $(L=42.6\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m})$. We demonstrate similar results for an asymmetric nonreciprocal waveguide without a magnetic domain wall. The possibility of compact on-chip photonic band-gap isolators is demonstrated for 2D membrane photonic crystals with finite thickness in the third dimension. Computations are performed using plane wave expansion, finite difference time domain, and optical Wannier function methods.