Observation of Dynamic Localization in Periodically Curved Waveguide Arrays

We report on a direct experimental observation of dynamic localization (DL) of light in sinusoidally-curved lithium-niobate waveguide arrays which provides the optical analog of DL for electrons in periodic potentials subjected to ac electric fields as originally proposed by Dunlap and Kenkre [Phys. Rev. B 34, 3625 (1986)]. The theoretical condition for DL in a sinusoidal field is experimentally demonstrated.

Figure 1

Left: Schematic of the first manufactured sample showing the three waveguide arrays: the straight array (1), the sinusoidally curved array with short period (2), and the semicycle sinusoidal array (3). Right: Microscope image showing a particular of the straight and short-period curved arrays.

Figure 2

Left: 2D output intensity pattern recorded on the IR camera for single waveguide excitation at $\lambda =1610\mathrm{nm}$ of the straight array, and corresponding intensity profile cross section. The points show the waveguide intensity distribution $|c_n{|}^2=|J_n(2\Delta L){|}^2$ predicted by the coupled-mode Eqs. (3) for $\Delta =3{\mathrm{cm}}^{-1}$. Right: beam evolution (top view) predicted by numerical simulations for the straight array.

Figure 3

Left: 2D output intensity patterns recorded on the IR camera for a single waveguide excitation of the short-period curved array at different wavelengths, and corresponding intensity profile cross sections (solid curves). In the figures the dashed curves are the numerically predicted intensity profiles. Right: corresponding beam evolution (top view) predicted by numerical simulations of Eq. (1).

Figure 4

Same as Fig. 3, but for the semicycle curved array.

Figure 5

Measured 2D output intensity patterns and corresponding cross sections for an astigmatic Gaussian beam excitation of array (3) with (a) $w_x\sim 24.7\mu \mathrm{m}$, and (b) $w_x\sim 37.4\mu \mathrm{m}$. The dashed curves are the input Gaussian beam profiles in the $x$ direction.

Figure 6

Measured number of excited waveguides $\sqrt{⟨n^2⟩}$ versus $\Gamma$ (dots) for 7 waveguide arrays with increasing values of $\Lambda$, and corresponding theoretical behavior (solid curve). The recorded 2D output intensity profiles are also shown.