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Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
Published on: April 4, 2016
Stochastic theory of an optical vortex in nonlinear media
1Faculty of Science and Engineering, Ritsumeikan University-BKC, Noji-Hill, Kusatsu City, 525-8577, Japan. kra@se.ritsumei.ac.jp
Abstract:
A stochastic theory is given of an optical vortex occurring in nonlinear Kerr media. This is carried out by starting from the nonlinear Schrödinger type equation which accommodates vortex solution. By using the action functional method, the evolution equation of vortex center is derived. Then the Langevin equation is introduced in the presence of random fluctuations, which leads to the Fokker-Planck equation for the distribution function of the vortex center coordinate by using a functional integral. The Fokker-Planck equation is analyzed for a specific form of pinning potential by taking into account an interplay between the strength of the pinning potential and the random parameters, diffusion and dissipation constants. This procedure is performed by several approximate schemes.
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