Phenomenological Treatment of Small-Scale Light Trapping

The calculation of filament diameter is based on the wave equation involving field-dependent electric permittivity for light frequencies expanded up to sixth power of electric field vector. With reasonable assumptions a diameter of 4–6 μ has been obtained. For increasing power fed into the beam two or more filaments may be formed simultaneously. It is believed that there exist relaxation processes inside the filament somewhat diminishing nonlinear terms of electric permittivity. Thus, the solution of the wave equation becomes divergent resulting in filament vanishing. As a result, new filaments occur sequentially, forming an apparent light channel.