Optical Soliton In PT-symmetric Waveguide And Collective Excitation In Chains Of Solitons

Recently, the concept of parity-time-symmetry has been a subject of intense interest in the field of quantum mechanics because there can also exist real eigenvalue in the parity-time-symmetric system, which changes the requirement for Hermitian operator of measurable quantity. Then, the concept of parity-time-symmetry has been extended in optical field for the reason of similarities between paraxial optical wave equation and wave mechanics equation in quantum mechanics. A necessary condition for parity-time-symmetric system is that real and imaginary parts of potential are even and odd functions, respectively, which can be realized by designing even refractive-index and balanced gain/loss profiles in optical waveguides. One can demonstrate that parity-time-symmetric systems possess real eigenvalues using optical experiments. Also, the unexpected properties of power oscillations and non-reciprocal optical wave propagation may be applied to optical devices designing and optical beams controlling. Beyond that, the concept of parity-time-symmetry is also studied in nonlinear optical waveguides which expands the studying of regular soliton.In this paper, we focus on the existence of optical solitons in nonlinear PT-symmetric waveguides and propagations, which involves three parts:1. Based on the model of PT-symmetric nonlinear waveguide with Gaussian and super-Gaussian potentials, we obtain numerically soliton solutions and analyse the effect of input power on the merging and bifurcating of eigenvalue spectra. Comparing with the linear case, we find that the merging points and bifurcation points of eigenvalues are no longer coalesce due to the existence of nonlinearity. Also, we analyse nonlinear modes and the corresponding phase distributions, the results reveal that the symmetric forms of nonlinear modes and phase are the key factor for the forming of stationary solitons. We also show the relations between eigenvalue spectra and system paramaters which can be used to confirm the number of solitons and the minimum power of ground state soliton in system. The numerical results are in accordance with the qualitative analysis of variation method.2. We discuss asymmetric solitons in PT-symmetric potential. With increasing of input power, the eigenvalue spectra of asymmetric solitons are separated from the symmetric one and form a pitchfork structure. Different from Hermitian case, this asymmetric soliton can be found in a special type of PT-symmetric potential. The effect of potential parameters on the bifurcation of eigenvalue spectra and stability of soliton are analyzed, the results show that stable symmetric soliton begin to turn into unstable region when the asymmetric soliton arise in system. We also consider 2-dimentional case and obtain the symmetric and asymmetric 2-dimentional solitons with different propagation constants.3. Based on nonlinear optical coupler, we study the collective excitation of solitons. Supersolitons can be produced by particle-like interaction of soliton in the soliton array constructed with stable symmetric and asymmetric solitons, as well as PT-symmetric solitons. Essentially, supersoliton is a kind of collective excitation mode produced by soliton elastic collisions. Also, we study the initial excite condition to form stable supersoliton, as well as their interactions between supersolitons.