Observation of Defect-Free Surface Modes in Optical Waveguide Arrays

We report on the experimental observation of novel defect-free surface modes predicted theoretically for modulated photonic lattices [I. L. Garanovich et al., Phys. Rev. Lett. 100, 203904 (2008)]. We generate the linear surface modes in truncated arrays of periodically curved optical waveguides created in fused silica by a laser direct-writing technique. Our results demonstrate that the degree of surface wave localization can be controlled by selecting the waveguide bending amplitude.

Figure 1

(a) Periodically curved waveguide array with spacing $d$ and longitudinal bending period $L$. (b) Schematic of the femtosecond laser direct-writing setup. Insert shows waveguide mode profile measured at 633 nm.

Figure 2

(a) Effective model corresponding to the semi-infinite periodically curved waveguide array. (b) Effective coupling in infinite periodically curved array as a function of the bending amplitude. The self-collimation point is marked with a cross. (c) Effective surface defect strength in a semi-infinite periodically curved array as a function of the bending amplitude. (d) Numerically calculated propagation constants of the defect-free surface modes. Pairs of points marked by $a$ and $a^{*}$, $b$ and $b^{*}$, $c$ and $c^{*}$ correspond to Figs. 4a, 4b, 4c, respectively. The gray shading marks the lattice transmission band.

Figure 3

Experimental fluorescent images of light propagation in the straight array. Laser beam is launched into the (a) left edge waveguide of the array, (b)  center waveguide, and (c) right edge waveguide.

Figure 4

(a–d) Light propagation in the four curved arrays with different bending amplitude $A$. In each of the four blocks fluorescent images are shown on the top, and corresponding numerical simulations are shown at the bottom. Light is launched into the left edge waveguide of the array (left), center waveguide (center), and right edge waveguide (right).