Dressed-band theory for semiconductors in a high-intensity infrared laser field

Under the illumination of intense off-resonant laser light, the electronic states of semiconductors are strongly modified, or dressed, by the oscillating electric field. We present a framework using linear combination of atomic orbital band theory to calculate the dressed band structure and optical absorption spectrum of covalent semiconductors in an intense off-resonant laser field. The interaction with the laser field is taken into account exactly from the beginning of the band calculation. It is shown that the irradiation of an intense infrared laser gives rise to a blueshift of the absorption edge as well as the emergence of a new absorption band below the edge, in agreement with recent experimental data for GaAs crystals.

Figure 1

Energy band structure of GaAs calculated by the tight-binding model.

Figure 2

Feynman diagram for the density matrix $\rho (t,\Omega )$.

Figure 3

Dressed bands for $E_0=0.5\times {10}^9\mathrm{V}∕\mathrm{m}$, $\hslash \omega =0.28\mathrm{eV}$ and the polarization of the pump light in the [111] direction. The other parameter values are the same as Fig. 1. The dashed lines correspond to the original bands.

Figure 4

(a) Dependence of the differential absorption coefficient on the intensity of the pump laser light. The energy of the pump light is $\hslash \omega =0.14\mathrm{eV}$ with the polarization in the [111] direction. the other parameter values are the same as Fig. 1. The lines correspond to the electric amplitude of the pump laser light $E_0=1.0\times {10}^8\mathrm{V}∕\mathrm{m}$ (solid line), $E_0=0.75\times {10}^8\mathrm{V}∕\mathrm{m}$ (dashed line), $E_0=0.5\times {10}^8\mathrm{V}∕\mathrm{m}$ (dash-dotted line), and $E_0=0.25\times {10}^8\mathrm{V}∕\mathrm{m}$ (dotted line). $E_g=1.42$ corresponds to the unperturbed band gap energy. (b) Differential transmission normalized by the transmission without pump laser field. The width of the sample is $3.5\mu \mathrm{m}$. The parameter values are the same as the corresponding lines of (a).

Figure 5

(a) Dependence of the differential absorption coefficient on the photon energy of the pump laser light. The field intensity of the pump laser light is $E_0=1.0\times {10}^8\mathrm{V}∕\mathrm{m}$ with the polarization in the [111] direction. The other parameter values are the same as Fig. 1. The lines correspond to the photon energy of the pump laser light $\hslash \omega =0.14\mathrm{eV}$ ($\lambda \approx 9\mu \mathrm{m}$, solid line), $\hslash \omega =0.21\mathrm{eV}$ ($\lambda \approx 6\mu \mathrm{m}$, dashed line), $\hslash \omega =0.28\mathrm{eV}$ ($\lambda \approx 4.5\mu \mathrm{m}$, dotted line). (b) Differential transmission normalized by the transmission without pump laser field. The width of the sample is $3.5\mu \mathrm{m}$. The parameter values are the same as the corresponding lines of (a).

Figure 6

Dependence of the differential absorption coefficient on the polarization of the probe laser light. The parameter values are $E_0=1.0\times {10}^8\mathrm{V}∕\mathrm{m}$, $\hslash \omega =0.14\mathrm{eV}$, and the polarization of the pump laser light is in the [111] direction. The other parameter values are the same as Fig. 1. The lines correspond to the polarization of probe laser light [111] (0°) (solid line), [201] (45°) (dashed line), $\left[1\overline{1}0\right]$ (90°) (dotted line).