The Dynamatic Of Solitons In PT Symmetric Kerr Medium

The concept of parity-time-symmetry derives from quantum mechanics.Due to the existence of the full real eigenvalue of PT symmetric system,the requirement of measurable quantity has been changed,and it leads to a lot of research hotspots.In optics,the paraxial transmission equation of beam is similar with the nonlinear Schrodinger equation in mathematical mechanics,which makes researchers naturally introduce the concept of PT symmetry to optics.In quantum mechanics,the condition of PT symmetric system is that the real and imaginary part of potential should be even and odd function respectively.For an optic system,the only thing to realize PT symmetry is designing even refractive-index and balanced gain/loss profiles in optic medium.The introduction of PT symmetry into the optical field brings new possibilities to control beam propagation and the design new optical devices.In addition,because of the nonlinear effect of medium,researchers have extended the concept of PT symmetry to the field of soliton research,which has expanded the studying of regular solitons.In this paper,we focus on the effect of the introduction of PT on the propagation of beam in the medium by numerical simulation,which involves two parts:1.Beam U =sech(x)is the soliton solution of the nonlinear Kerr medium.We introduce the PT symmetric Gauss barrier and the PT symmetric periodic barrier into the medium.We studied the propagation characteristics of the beam after going through the barrier.The beam will have deflection and energy gain after going through the PT symmetric Gauss barrier and the PT symmetric periodic barrier.These phenomenon is the effect of the gain/loss coefficient,the barrier depth and the longitudinal width of the barrier.The energy gain and deflection angle of the beam become bigger as the increase of the gain loss coefficient of the potential barrier.However,as the barrier depth and the longitudinal width of barrier increase,the energy gain and deflection angle of the beam will fluctuate first.However,if the period of PT symmetric periodic barrier is small,the beam will cross several periods of the barrier.The gain/loss and the refractive index cancel out each other,which eliminate the energy gain and deflection.2.The PT symmetry is introduced into the self-focusing Kerr nonlinear medium,while the form of PT symmetry is still the Gauss type and the periodic type.We get the soliton solutions of each potential energy distributions by numerical iteration.Fundamental solitons,dipole solitons and tripolar solitons is found in the self-focusing PT symmetric Gauss potential energy.While in the self-focusing PT symmetric periodic potential energy,we only get fundamental solitons are found.We also analysis the stability of these solitons by adding perturbation and found that fundamental soliton are steady in self-focusing PT symmetric Gauss potential while the dipole solitons and the tripole soliton with large propagation constant are not steady.