Generation and characterization of polarization-shaped femtosecond laser pulses

Phase and polarization changes of pulsed Gaussian beams during focusing and propagation

“…In the next few lines only the expressions giving the ellipse parameters are listed. The details of the derivation of these instantaneous properties described by the x and y linear states can be found in Appendix A.2.1, based on [90,115,125,126]. The instantaneous ellipticity of the ellipse can be calculated as…”

“…The only difference is that while for infinite harmonic waves the amplitudes and relative phases of the perpendicular components are constant, for non-monochromatic waves they are time dependent [115,125,126], they have the same form as (2.3), that is,…”

“…Note that References [90,125,126] and [115], on which the following considerations are based, use an opposite sign convention, +ω 0 t and −ω 0 t, respectively. Here, consistent with other parts of this work, the latter is used, and as a result sign differences may appear from the expressions in the references.…”

“…One method to find the expression is a graphical solution [125], or it can be done in a pure mathematical way [90]. Here a different algebraic approach is presented.…”

“…With a similar logic to that of the graphical solution of [125] one can replace ± with a direct expression, and have (2.17).…”