Propagation of high-power tightly focused laser beams and self-depolarization effect

Electromagnetic aspects of localized action of high-power laser field on transparent solids

“…Bearing in mind symmetry properties of nonlinear susceptibility tensor [14], one can deduce the following dependence of nonlinear material response on electric field: PNLIE, (2) where E* denotes complex conjugated. Coefficients a and f3 are proportional to nonlinear-susceptibility tensor components and connected with linear n0 and nonlinear n2 parts of refractive index [11,12] in esu units.…”

“…The first term of(6) satisfies the following linear equation: LtE10+k2E10=O (7) to which linear boundary conditions are attached [11,12]. To describe nonlinear depolarization effect one should take into account the first nonlinear approximation m=1 that satisfies the following equations for quasi-monochromatic waves x1 +k2E1 =_4irk2a[ExoEo2 +aE;1Ej…”

“…E(x,y,z) = e' qm pm_n Umn (x,y,z) = e(u00 +u + qpu + qu11 +...), (11) (11) and (12) are of order of 1 then the second and the third terms in those series are of order of 0.01, the fourth terms are an order of 0.0001. Thus, in case of self-focusing absence, described by presented asymptotical expansions, cubic nonlinear terms show influence of the same order as linear diffraction terms while nonlinear gradient terms are an order of magnitude less than linear diffraction terms.…”

“…(17) Significant advantage of paraxial approximation is that corresponding equations can be integrated analytically [11]. Rather long analytical calculations of polarization parameters for expansions (15) - (16) show that they can be represented in the following form [11,12]: R=x.yf(r) and O1=O(r),…”