Complete classification and additional saddle-point solutions for high-order above-threshold ionization induced by a strong laser field. III. Two-component fields

The complete classification of the saddle-point solutions for high-order above-threshold ionization, presented in and for a linearly polarized laser field, is generalized to the case of an arbitrary bichromatic elliptically polarized field. We first present the classification of the saddle-point solutions for the case of a monochromatic elliptically polarized driving field, which is the simplest example of the field that has two components, i.e., that evolves in the plane. For a bichromatic laser field whose elliptically polarized components have the frequencies <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>r</a:mi><a:mi>ω</a:mi></a:mrow></a:math> and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>s</b:mi><b:mi>ω</b:mi></b:mrow></b:math> (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>r</c:mi></c:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>s</d:mi></d:math> are integers, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>s</e:mi><e:mo>&gt;</e:mo><e:mi>r</e:mi></e:mrow></e:math>, and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>ω</f:mi></f:math> is the fundamental frequency), the system of the saddle-point equations has <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mn>8</g:mn><g:msup><g:mi>s</g:mi><g:mn>2</g:mn></g:msup></g:mrow></g:math> solutions per optical cycle. One-half of these solutions are the so-called backward-scattering solutions for which the direction of the electron motion is significantly affected by the rescattering. The other half are the forward-scattering solutions for which the electron is only slightly deflected during the rescattering event. For some specific field configurations, the number of saddle-point solutions can be smaller. For example, for a bicircular field, which consists of two counterrotating circularly polarized components, there are <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mn>4</h:mn><h:mi>s</h:mi><h:mo>(</h:mo><h:mi>r</h:mi><h:mo>+</h:mo><h:mi>s</h:mi><h:mo>)</h:mo></h:mrow></h:math> solutions, while for the corotating configuration there are <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mn>4</i:mn><i:msup><i:mi>s</i:mi><i:mn>2</i:mn></i:msup></i:mrow></i:math> solutions. As an application, we have shown that for a monochromatic elliptically polarized laser field, all four threshold anomalies appear in the spectra of the rescattered photoelectrons.