Signatures of Anderson localization excited by an optical frequency comb

We investigate Anderson localization of light as occurring in ultrashort excitations. A theory based on time dependent coupled-mode equations predicts universal features in the spectrum of the transmitted pulse. In particular, the process of strong localization of light is shown to correspond to the formation of peaks in both the amplitude and in the group delay of the transmitted pulse. Parallel ab initio simulations made with finite-difference time-domain codes and molecular dynamics confirm theoretical predictions, while showing that there exists an optimal degree of disorder for the strong localization.

Figure 1

(Color online) Localization couplings and energy propagation scheme in the TDCMT.

Figure 2

(Color online) ${\text{TiO}}_2$ refractive index $n$ vs frequency, as obtained from the Sellmeier equation after Devore (Ref. 30). The filled area corresponds to the frequency-comb spectrum. The inset shows the input pulse.

Figure 3

(Color online) Slices $\left(x,z\right)$ (in the middle of $y$ axis) of the electromagnetic energy $\mathcal{E}$, resulting from dispersive simulations of (a) ${\text{SiO}}_2$ and (b) ${\text{TiO}}_2$. Corresponding FROG signal of the transmitted pulse $\left(E_y\right)$ for (c) ${\text{SiO}}_2$ and for (d) ${\text{TiO}}_2$.

Figure 4

(Color online) Squared modulus of the Fourier transform of $E_y$ (dashed line, left axis) and group delay (continuous line, right axis) for (a) ${\text{SiO}}_2$ and (b) ${\text{TiO}}_2$. The vertical axis of the group delay is shifted such that the zero corresponds to the exit time of the low frequency side of the input spectrum.

Figure 5

(Color online) (Top panels) Spectral response (squared modulus, left scale, dashed line, and group delay, right scale, continuous line) for different filling fractions for ${\text{TiO}}_2$. (Bottom) Maximum attained group delay versus filling fraction; the insets show the material distribution, corresponding to the top panels.