Wave propagation and optical properties in slabs with light-induced free charge carriers

A theoretical analysis on wave propagation and optical properties of slabs with light-induced free charge carriers within a Fabry-Pérot framework is presented. The key of the analysis is to attack the wave propagation problem in terms of the time-averaged Poynting vector modulus within the medium through an alternative approach. This fact allows coupling the microscopic (free charge rate) and macroscopic (electromagnetic field evolution) equations self-consistently by means of the nonlinear permittivity and conductivity, which, in turn, depend on the time-averaged Poynting vector modulus. Thereby, the transmittance, reflectance, and absorptive power are derived as functions of the pump intensity and medium thickness. Bistable behavior is found at relatively high excitation intensity for positive values of the nonlinear permittivity coefficient. The bistability enhances for increasing values of such coefficient and weakens for increasing values of nonlinear photoconductivity coefficient. On the contrary, for negative nonlinear permittivity coefficient, bistability does not appear possessing these media mirrorlike behavior. Some possible applications are suggested.

Figure 1

(a) A harmonic plane wave of amplitude $E_0$, impinges on a parallel-plane-faces medium surrounded by vacuum. The wave is reflected and transmitted with coefficients $r$ and $t$, respectively, without changes in its polarization. Note that, $\tilde{z}=k_{0}z$ is the dimensionless propagation coordinate. (b) Schematic representation of the intrinsic interband transitions problem. Electrons are excited from the valence band to form an electron-hole pair.

Figure 2

(Color online) Transmittance, reflectance, absorptive power, and spatially averaged generalized relative permittivity as function of the dimensionless excitation parameter for several $(n_0\gamma ,n_0\delta )$ values as indicated in each graph. All figures with ${ϵ}_1=2.25$ and $\tilde{d}=2\pi$.

Figure 3

(Color online) Transmittance, reflectance, absorptive power, and spatially averaged generalized relative permittivity as function of the dimensionless thickness for several $(n_0\gamma ,n_0\delta )$ values as indicated in each graph. All figures with ${ϵ}_1=2.25$ and ${\ln }_{10}\xi =-5.5$.

Figure 4

(Color online) Ratio among the diffusion and recombination terms as a function of the dimensionless spatial coordinate for $n_0\gamma =0$, $n_0\gamma >0$, and $n_0\gamma <0$, as indicated in the figure, with ${ϵ}_1=2.25$, $n_0\delta ={10}^{-4}$, $\xi ={10}^9$ and $\tilde{d}=2\pi$.

Figure 5

Schematic representation of the extrinsic $n$-type transitions problem. Electrons are excited from donors centers $N_D$ to begin a free carrier electron.