Figure 1

(a) and (b) Frequency dependence of the imaginary and real parts of the effective linear susceptibility of the TLS ensemble if the pump field is applied in advance, ${\chi }^{″}\left(\nu \right)$ and ${\chi }^{\prime }\left(\nu \right)$ (bold lines), and if not, ${\chi }_0^{″}\left(\nu \right)$ and ${\chi }_0^{\prime }\left(\nu \right)$ (thin lines). Both plots are normalized to ${\chi }_0^{″}\left(0\right)$. The frequency scale is in units of the homogeneous half width, $\nu ∕\Gamma$.Reuse & Permissions

Figure 2

Excitation scheme of a thin slab by the pump $E_{\text{pump}}$ and probe $E_{\mathrm{prob}}$ fields. The length of the slab is $l$ and its thickness is $d(l⪢d)$.Reuse & Permissions

Figure 3

(a) Comparison of the analytical solution $E_{pA}(l,t)$, for the output probe pulse, Eq. (22), shown by the thick line, with the field of the probe that would travel the same distance in free space, shown by the thin solid line. Here for $E_{\mathrm{prob}}(0,t)$ we take $z=0$ and the distance $l$, which the probe would travel in free space, is taken only in the local time $t$, i.e., $t-l∕c$. (b) Comparison of the analytical approximation $E_{pA}(l,t)$ (solid line) with the numerical calculation of the envelope of the output probe pulse, $E_{\mathrm{prob}}(l,t)$ (dots), given by Eq. (17) where $A\left(\nu \right)$ is not approximated but taken from Eq. (16). All plots are normalized to the amplitude $E_0$. Time is in units ${\Delta }_{\mathrm{in}}t$, where $t$ is the local time $t-l∕c$. The parameters are ${\Gamma }_{\mathrm{inh}}=9.5\mathrm{GHz}$, $\Gamma =353.7\mathrm{kHz}$, $\gamma =38\mathrm{Hz}$, ${\Omega }_{\text{pump}}=500\mathrm{kHz}$, ${\Delta }_{\mathrm{in}}=30\mathrm{MHz}$, and $\alpha l∕2=15$.Reuse & Permissions

Figure 4

(a) Excitation scheme for the persistent hole burning. $g,e$, and $t$ are the ground, excited, and trapping states. The pump field is shown by the bold arrow. ${\Gamma }_{\text{fast}}$ is a fast nonradiative process shown by the bold arrow with the white strip. For a dye molecule in a polymer, this can be a photoinduced transformation of the molecule. $\gamma$ is the decay rate of the trapping state. The decay process is shown by the dashed arrow. The lifetime $T_1$ of the trapping state tends to infinity for the molecule. For ${\mathrm{Cr}}^{3+}$ this is a radiative lifetime, which is long because of the small dipole matrix element for this transition. The open circle shows a “hole” in the population of the ground state. The filled circle in state $t$ shows population trapping. (b) Excitation scheme for EIT. $g,e$, and $m$ are the ground, excited, and metastable states. The thin arrow shows the excitation by the probe. The bold arrow shows the interaction with the coupling field. The filled circle shows the population of the ground state. (c) The same excitation scheme as in (b) but in the basis of dark $d$ and bright $b$ states. The continuous arrow shows the effective coupling of the bright and excited states. The strength of the effective coupling is defined as a particular combination of the Rabi frequencies of the probe and coupling fields. The dashed arrow shows the radiative decay from $e$ to $d$. The open circle shows a hole in the population of the bright state. The filled circle shows population trapping in the dark state.Reuse & Permissions