Electron heating in the conduction band of insulators irradiated by ultrashort laser pulses

H. Bachau, A. N. Belsky, P. Martin, A. N. Vasil’ev, and B. N. Yatsenko

Phys. Rev. B 74, 235215 – Published 26 December 2006

Abstract

We investigate the theoretical problem of electron heating in the conduction band of wide band gap insulators and semiconductors induced by intense femto-second Ti:Sapphire laser pulses. We analyze in detail the heating mechanism due to the sequence of direct interbranch transitions in the conduction band, which has been shown to be of crucial importance in previous work. This analysis is fulfilled by resolving the time dependant Schrödinger equation (TDSE) in a basis of Bloch functions for the CsI crystal. The field is represented semiclassically and the laser-electron interaction is treated in the dipole approximation. The presented approaches are based on a one-active electron approximation. First the TDSE is solved in a basis of Bloch functions, in one dimension, the influence of laser and crystal parameters on the electron spectra is studied. The electron transfer from the lower conduction band to the higher one is already effective at intensity of $3 \times 10^{12} W ∕ {cm}^{2}$ . Then the problem is solved in three dimension. The electron spectra is consistent with the experimental results, we note in particular the presence of a large plateau at intensities of the order of the terawatt per square centimeter.

Received 3 April 2006

DOI:https://doi.org/10.1103/PhysRevB.74.235215

Authors & Affiliations

H. Bachau¹, A. N. Belsky¹, P. Martin¹, A. N. Vasil’ev^2,*, and B. N. Yatsenko^1,3

¹Centre des Lasers Intenses et Applications, UMR5107 CNRS-Université de Bordeaux I-CEA, Université de Bordeaux I, 33405 Talence Cedex, France
²Physics Department, Moscow State University, Vorob’evy Gory, Moscow 119992, Russia
³Scobeltsyn Institute of Nuclear Physics, Moscow State University, Vorob’evy Gory, Moscow 119992, Russia

^*Corresponding author. Electronic address: anv@ibrae.ac.ru

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Vol. 74, Iss. 23 — 15 December 2006

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Figure 1
The conduction band structure in the first Brillouin zone for the one-dimensional case and a nearly free electron model (lattice constant and $U_{g}$ correspond to CsI crystal). One-, two-, three-, and four-photon $(ℏ ω = 1.55 eV)$ transitions are marked out by arrows.Reuse & Permissions
Figure 2
Dependence of the population of the second lowest band (probability of multi-photon transitions) after the interaction versus the wave-vector (lattice constant and $U_{g}$ correspond to CsI crystal), for excitation intensities of $0.05 TW ∕ {cm}^{2}$ , $0.5 TW ∕ {cm}^{2}$ , $3 TW ∕ {cm}^{2}$ , and $10 TW ∕ {cm}^{2}$ and for a pulse duration of $T = 40 fs$ , the photon energy is $ℏ ω = 1.55 eV$ .Reuse & Permissions
Figure 3
Dependence of the population of the second lowest band (probability of direct multiphoton transitions) after the interaction versus the wave vector (lattice constant and $U_{g}$ correspond to CsI crystal), for pulse durations of $20 fs$ , $40 fs$ , and $70 fs$ . The peak laser intensity is $I_{0} = 3 TW ∕ {cm}^{2}$ and the photon energy is $ℏ ω = 1.55 eV$ .Reuse & Permissions
Figure 4
Dependence of the transition probability to the upper bands (probability of escape) for an electron, initially located on the lowest band, after the interaction with the laser pulse. Top panel: Influence of $U_{g} : U_{g}$ equals to one half of $U_{g}$ corresponding to CsI crystal (1), $U_{g}$ corresponds to CsI crystal (2), and twice of this $U_{g}$ (3); intensity of $3 TW ∕ {cm}^{2}$ , pulse duration is of $40 fs$ ; Middle panel: Influence on pulse duration: $20 fs$ (1), $40 fs$ (2), and $80 fs$ (3); intensity of $3 TW ∕ {cm}^{2}$ , $U_{g}$ corresponds to CsI crystal; Bottom panel: Influence on pulse intensity: intensities of $1 TW ∕ {cm}^{2}$ (1), $3 TW ∕ {cm}^{2}$ (2) and $10 TW ∕ {cm}^{2}$ (3); pulse duration is $40 fs$ and $U_{g}$ corresponds to CsI crystal. For all curves the photon energy is $1.55 eV$ and the lattice constant corresponds to CsI crystal.Reuse & Permissions
Figure 5
Spectra of electrons in the conduction band after interaction with laser pulse. Top panel: Influence of $U_{g} : U_{g}$ equals to one half of $U_{g}$ corresponding to CsI crystal (1), $U_{g}$ corresponds to CsI crystal (2), and twice of this $U_{g}$ (3); intensity of $3 TW ∕ {cm}^{2}$ , pulse duration is of $40 fs$ ; Middle panel: Influence on pulse duration: $20 fs$ (1), $40 fs$ (2), and $80 fs$ (3); intensity of $3 TW ∕ {cm}^{2}$ , $U_{g}$ corresponds to CsI crystal; Bottom panel: Influence on pulse intensity: intensities of $1 TW ∕ {cm}^{2}$ (1), $3 TW ∕ {cm}^{2}$ (2) and $10 TW ∕ {cm}^{2}$ (3); pulse duration is $40 fs$ and $U_{g}$ corresponds to CsI crystal. For all curves the photon energy is $1.55 eV$ and the lattice constant correspond to CsI crystal. Dotted and solid curves (2) correspond to calculations with different numbers of sampling points (doubled number in the case of dotted line). Vertical grid has step equal to photon energy $(1.55 eV)$ .Reuse & Permissions

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