Generalized Exact Dynamic Localization in Curved Coupled Optical Waveguide Arrays

We observed exact dynamic localization in its general case in strongly coupled curved waveguide arrays with periodic, nonsquare-wave curvatures. We achieved a six times change in the dynamic localization bandwidth by changing a design parameter in our deviated-square-wave curvature. By analyzing the relation between the bandwidth and curvature profile, we offer a general method to control the localization bandwidth.

Figure 1

(a) Schematic of a CCOW. The waveguides are terminated at a slab. The curvature profile and the beam profile for two different optical wavelengths at various positions along the array for (b) constant, (c) piecewise constant, and (d) a varying curvature for different wavelengths.

Figure 2

The radius of curvature, $R(v)$ (thick, red line), and the Bloch vector, $k(v)$ (thin, blue line), for ${\kappa }_o=-\pi /d$ when $\lambda ={\lambda }_R$ for (a) $a=0$, (b) $a=0.52$, and (c) when $\lambda ={\lambda }_R/0.9$ for $a=0.52$. The BZ shown in the right axes spans from $-1$ to 1. The horizontal dashed lines mark a wave vector ${\kappa }_1$, which is set to zero for clarity. The circles indicate the $R\mathbf{(}{v}_{jm}({\kappa }_1)\mathbf{)}$ which contribute to $W({\kappa }_1)$. (d) $W(\kappa )$ for several values of $a$ when $\lambda ={\lambda }_R/0.9$.

Figure 3

Spatially resolved spectra of (a) DSW-EDL with $a=-0.52$, (b) EDL with $a=0$, and (c) DSW-EDL with $a=+0.52$. (d) Measured (symbols) and simulated (dashed lines) transmission spectrum of the center waveguide for the three structures.