Disordered resonant media: Self-induced transparency versus light localization

We propose a concept of disordered resonant media, which are characterized by random variations of their parameters along the light propagation direction. In particular, a simple model of disorder considered in the paper implies random change of the density of active particles (two-level atoms). Within this model, the effect of disorder on self-induced transparency (SIT) is analyzed using numerical simulations of light pulse propagation through the medium. The transition from the SIT to localization regime is revealed as well as its dependence on the disorder level, atom density, medium thickness, and period of random variations.

Figure 1

The system considered in the paper: active (two-level) atoms (e.g., quantum dots) dispersed over the volume of the background dielectric. The density of active particles randomly changes along the direction of light pulse propagation with the period $\delta L$.

Figure 2

Profiles of transmitted intensity for different values of the disorder parameter $r$ averaged over 100 realizations. Other parameters: $L=1000\lambda$, ${\omega }_L^0={10}^{12}{\mathrm{s}}^{-1},\delta L=\lambda /4$. The inset shows the profile of the incident $3\pi$ pulse.

Figure 3

Profiles of reflected intensity for different values of the disorder parameter $r$ averaged over 100 realizations. Other parameters are the same as in Fig. 2.

Figure 4

Average output energy of transmitted (T) and reflected (R) light as well as their sum (S), depending on the disorder parameter $r$. Energy averaged over 100 realizations was calculated for the time intervals (a) $300t_p$ and (b) $500t_p$ and was normalized on the input energy. The parameters are the same as in Fig. 2. The error bars in panel (b) show the unbiased standard deviations for the corresponding average values.

Figure 5

[(a)–(d)] Distribution of population difference along the medium for different realizations and disorder parameters: (a) $r=0.7,T=0.297$, $R=0.309$; (b) $r=0.7,T=0.086,R=0.358$; (c) $r=0.8$, $T=0.059,R=0.360$; and (d) $r=1,T=0.050,R=0.375$. The distributions are plotted for the time instants [(a), (b)] $350t_p$ and [(c), (d)] $300t_p$. (e) The examples of transmitted pulse for different realizations at $r=0.7$. The parameters are the same as in Fig. 2.

Figure 6

Output energy of transmitted (T) and reflected (R) light as well as their sum (S), depending on the medium thickness $L$. The parameters used are $r=1,{\omega }_L^0={10}^{12}{\mathrm{s}}^{-1}$, $\delta L=\lambda /4$. Energy averaged over 100 realizations was calculated for the time interval $300t_p$ and was normalized on the input energy.

Figure 7

Output energy of transmitted (T) and reflected (R) light as well as their sum (S) depending on the average light-matter coupling ${\omega }_L^0$. The parameters used are $r=1,L=1000\lambda {\mathrm{s}}^{-1},\delta L=\lambda /4$. Energy averaged over 100 realizations was calculated for the time interval $300t_p$ and was normalized on the input energy.

Figure 8

Output energy of transmitted (T) and reflected (R) light as well as their sum (S) depending on the period of random variations $\delta L$. The parameters used are $r=1,L=1000\lambda {\mathrm{s}}^{-1},{\omega }_L^0={10}^{12}{\mathrm{s}}^{-1}$. Energy averaged over 100 realizations was calculated for the time interval $300t_p$ and was normalized on the input energy.