Applied Math Seminar
                      2-3pm, April 17, Thursday
                     Mathematics Conference Room



	      Stable vortex and dipole optical solitons 
		 in a saturable nonlinear medium


			  Prof. Jianke Yang 
  	    Department of Mathematics and Statistics, UVM


Abstract: 

Optical laser beams in a nonlinear waveguide have drawn a lot
of theoretical and experimental studies these days. Many novel 
nonlinear phenomena such as beam self-focusing and coupling
have been predicted and observed. In this talk, we discuss
vortex and dipole optical solitons (beams) in a saturable 
nonlinear medium (such as photorefractive materials) in 2+1 
dimensions. Such solitons have been reported both numerically and 
experimentally in the literature. But some controversy arose
on whether vortex solitons with small vortex components are 
stable or not. In addition, it was claimed previously that
unstable vortex solitons always break up into dipole solitons, 
which may be erroneous. 

In this talk, the above issues are resolved. We show both 
analytically and numerically that vortex solitons with 
small vortex components are stable, while vortex solitons
with large vortex components are unstable. This implies that 
vortex solitons with small vortex components should be observable 
in experiments. We also show that an unstable vortex soliton can 
break up into two rotating fundamental solitons in addition to a 
rotating dipole soliton. Experimental confirmation of these 
theoretical results are been considered by experimentalists.