Light diffusion and localization in three-dimensional nonlinear disordered media

By using a three-dimensional finite-difference time-domain parallel code, the linear and nonlinear propagation of light pulses in a disordered assembly of scatterers, generated by a molecular dynamics code, is simulated. We calculate the static and dynamical light diffusion constant and the transmission in the presence of localized states. We numerically demonstrate the “modulational instability random laser”: at high input peak power, energy is transferred to localized states from the input pulse, resulting in a power-dependent nonexponential time decay of the transmitted pulse.

Figure 1

(Color online) Top panels (a)–(c): electric field in the middle of the output face of the sample at low input peak power $(P_{\mathrm{in}}=1\mathrm{nW})$, for three different particle diameters $(\sigma =250,350,400\mathrm{nm})$. The insets show the particle distribution in the $yz$ (top) and $xz$ (bottom) middle section of the sample. Bottom panel (d): normalized local intensity in logarithmic scale (the peak intensity is scaled to unity). The inset shows the calculated speckle pattern.

Figure 2

(Color online) (a) Tail of the normalized transmitted pulse (the flux of the $z$ component of the Poynting vector at the output face) for various particle diameters; the normalization is such that the transmission peak is scaled to unity. The dashed line is the input pulse profile. The inset shows the transmitted pulse in linear scale, the gray region is the input pulse. (b) Calculated diffusion constant for various filling fractions. The continuous line is a best-fit by an inverse power law. The inset shows the dynamical diffusivity for two values of the particle diameters.

Figure 3

(a) Time dynamics of the scaled local intensity for two different input peak powers (the peak intensity is scaled to unity); the inset shows the corresponding autocorrelation functions versus the delay $\tau$; (b) transmitted (the peak transmission is scaled to unity) signal for various input peak powers; the inset shows the calculated instantaneous diffusivity.

Figure 4

(Color online) (a) Spectral emission for increasing peak power; (b) spectrogram displaying the time evolution of the spectra for $P=3\mathrm{kW}$; (c) normalized transmission (the peak transmission is scaled to unity) of a low power pulse at $\lambda =300\mathrm{nm}$ and $\sigma =400\mathrm{nm}$ displaying a nonexponential tail; the inset shows the field distribution for $\sigma =400\mathrm{nm}$ at high power $(P=2.5\mathrm{kW})$ at $t=4\mathrm{ps}$ in the $xz$ middle section of the sample; (d) density of states (in arbitrary units) and $Q$-factor distribution for $\sigma =400\mathrm{nm}$.