The relation between optical beam propagation in free space and in strongly nonlocal nonlinear mediaDaquan Lu, Wei Hu and Qi Guo
Laboratory of Photonic Information Technology, South China Normal University - Guangzhou 510631, China
received 9 January 2009; accepted in final form 27 April 2009; published May 2009
published online 27 May 2009
The relation between optical beam propagation in strongly nonlocal nonlinear (SNN) media and propagation in free space is demonstrated using the technique of variable transformation. The governing equation, integral and analytical solutions, and propagation properties in free space can be directly transferred to their counterparts in SNN media through a one-to-one correspondence. The one-to-one correspondence together with the Huygens-Fresnel integral yields an efficient numerical method to describe SNN propagation. The existence conditions and possible structures of solitons and breathers in SNN media are described in a unified manner by comparing propagation properties in SNN media with those in free space. The results can be employed in other contexts in which the governing equation for the evolution of waves is equivalent to that in SNN media, such as for quadratic graded-index media, or for harmonically trapped Bose-Einstein condensates in the noninteracting limit.
42.65.Jx - Beam trapping, self-focusing and defocusing; self-phase modulation.
42.65.Tg - Optical solitons; nonlinear guided waves.
42.25.Fx - Diffraction and scattering.
© EPLA 2009