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Dipartimento di Fisica - Politecnico di Milano

High-order harmonic generation in crystals

Motivations. Intense mid-IR laser pulses focused in semiconductors may drive charge carrier dynamics in a strongly non-perturbative regime. This condition leads to the promotion of electrons from the valence to the conduction band and then to the emission of coherent radiation due to two mechanisms: (1) nonlinearities in the intraband current through Bloch oscillations, as well as (2) emission from interband polarization that accompanies the decay of the photoexcited electrons to the lower band.

The emitted radiation appears as high-order even and odd harmonics of the fundamental radiation and can be used to study the band structure and the out-of-equilibrium charge carrier dynamics in the material.

Thesis goal. This thesis work aims at the study of high-order harmonic emission driven by mid-IR (2.7-4 micron) intense few-optical-cycle laser pulses in crystalline semiconductors and to the link of this emission to the physical properties of the crystal (electronic band structure, optical properties, charge carrier dynamics).

Methods, thesis activities and perspectives. Mid-IR laser pulses generated by an Optical Parametric Amplifier are focused in crystalline semiconductors. High-order harmonic radiation emerging from the crystal can be detected both in reflection and in transmission as a function of the crystal orientation with respect to the laser polarization direction. A typical case is that of zinc telluride (ZnTe) a semiconductor with a cubic, zinc-blende crystal structure, shown in the figure. The laser is focused perpendicularly to the crystal, that is cut along the <110> plane (yellow plane), and the harmonic spectra are acquired in transmission as a function of the angle that the laser polarization makes with the crystal axes.

The collected spectra are reported in the following logarithmic polar map, where harmonic spectra (harmonic order is along the radial direction) are reported for different angles of the crystal orientation.

Even and odd harmonics show very different behaviors that can be linked to the tridimensional crystal structure.

By bidimensional Fourier transform, one can link the spectral emission to the temporal evolution of the emitted electromagnetic field; the result is reported in the last figure. 

Here two different temporal scales can be seen: a very fast oscillation (period of few fs) related to the optical carrier and a much slower evolution, over tens of fs, that may be ascribed to the interplay of different electron decay paths.

The thesis activities are experimental and may concern:

(i) Studies of high harmonic generation in photoexcited semiconductor crystals using a pump-probe technique both in reflection and in transmission;

(ii) extension of the investigation to organic molecular crystals (e.g. sugar);

(iii) exploitation of high-harmonic generation to the study of nonlinear charge carrier dynamics in semiconductors with reduced dimensionality.

Involvement in the modelling of the semiconductor electron dynamics is also available.