Attosecond pulse trains with elliptical polarization from an orthogonally polarized two-color field
D. Habibović, W. Becker, D. B. Milošević
Abstract
Generation of an elliptically polarized attosecond pulse train by an orthogonally polarized two-color (OTC) laser field is investigated theoretically and simulated numerically. The OTC field consists of two linearly polarized fields with orthogonal polarizations and frequencies that are integer multiples of the fundamental frequency <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ω</mml:mi> </mml:math> . For the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ω</mml:mi> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> <mml:mi>ω</mml:mi> </mml:math> OTC field, the emitted harmonics are elliptically polarized so that they may form an elliptically polarized attosecond pulse train provided that a group of harmonics is phase-locked. This is the case if only one quantum orbit generates the corresponding part of the harmonic spectrum. If so, then two attosecond pulses are emitted per optical cycle due to the dynamical symmetry of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ω</mml:mi> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> <mml:mi>ω</mml:mi> </mml:math> OTC field. Atomic targets with an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>s</mml:mi> </mml:math> ground state only generate attosecond pulses with almost linear polarization. Using, however, targets with a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>p</mml:mi> </mml:math> ground state, attosecond pulses with substantial ellipticity can be produced because ground states with opposite magnetic quantum numbers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:math> produce harmonics with opposite helicities at different rates. In this case, the harmonic intensity and harmonic ellipticity are different for the ground states with the magnetic quantum number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> </mml:math> . These differences are the source of the attosecond pulse ellipticity and can be controlled using the relative phase as a control parameter. In addition, by choosing a particular group of harmonics, one can select the desired ellipticity of the attosecond pulse train.