The Internal Oscillation And The Propagation Properties Of Spatial Solitons In Photoisomerization System

Internal oscillations and interactions of optical soliton are investigated. Internal modes and internal oscillations of vector solitons in photoisomerization polymer and necklace solitons in Bessel photonic lattices, three-dimensional Bessel solitary wave and interaction of one-dimensional solitons are studied in detail. The contents and achievements are as follows:1. Internal mode and internal oscillations of vector solitons ossociated with photoisomerizationVector solitons in photoisomerization polymer are studied. When the vector solitons are perturbed, internal modes will be aroused. Internal modes of vector spatial solitons are obtained for the first time. It is found that the perturbation eigenvalue of photoisomerization vector solitons are real numbers, which indicates that such vector solitons are stable, and the corresponding perturbation eigenfunctions are internal modes of the vector solitons. We also find the internal modes have only real parts. The simulation to the propagation of the vector solitons shows that the vector solitons keep their shapes and amplitude unchanged when no perturbation is presented; when the vector solitons are perturbed by its internal modes, quazi-periodic oscillation of the amplitude of the vector solitons appears, however no collapse of solitons are observed; the amplitude of the vector solitons jitter when a white noise is added, however no collapse occurs either when the white noise is not large enough. The stability of the vector solitons is thus confirmed.2. Stability, internal model and internal oscillationof necklace solitons in Bessel latticesStability, internal model and internal oscillation of necklace soliton in Bessel lattice are studied, taking ten-pearled necklaces for example. Afer the numerical solutions of necklace solitons are obtained, the linear stability analysis on the solutions is provided. It is found that perturbation eigenvalues of the necklace solitons are complex numbers, but with the increase of propagation constant b, several zero windows emerge from the maxima of the real part of eigenvalue. Zero-windows correspond to the stable regions of the necklace solitons; non-zero windows correspond to the non-stable regions. In the stable region, we obtain internal modes of necklace soliton for the first time to our knowledge. Simulation results indicates that when the vector solitons are perturbed by the internal modes, quasi-periodic oscillations of the necklace soliton in the stable area occurs, however on collapse occurs. On the other hand the necklace solitons in the unstable area collapse when propagating. The necklace soliton studied here are different with the previously investigated multi-pole solitons in Bessel lattices. When the propagation constant b tends to zero, the energy of multi-pole solitons divrges while the energy of necklace solitons studied here converges.3. Three-dimensional Bessel soltion clusters in the nonlinear mediaApproximate soliton solutions to nonlinear Schrodinger equation under cylindrical coordinates and spherical coordinates are obtained when the radius of the cylinder and the sphere tend to infinity. We find that the soliton solution in the cylindrical coordinates meets the m-order Bessel function. The solitons split into both 2m discrete solitons in the azimuthal direction and ldiscrete solitons in the axial direction. There are many different quantum states of the Bessel solitons clusters in the cylinder. On the other hand, the spatial optical solitons in the sphere meet m-order spherical Bessel function. The spatial optical soliton split into 2m discrete solitons in the azimuthal direction. There are many different quantum states in the form of the spherical Bessel solitons clusters. The spatial optical solitons experience a small deflection angle because of the nonlinear effects, that is, the phenomenon of phase shift accurs.4. The propagation and interaction of the one-dimensional temporal solitonsThe effects of gain or loss on the propagation of a bright solitons and a dark soliton are studied firstly in one-dimensional integrable system. It is found that the soliton amplitude attenuated and the width increased in the loss media however the amplitude enlarged and the width decreased in the gain media. And then by analysing the collision between two bright solitons or two dark solitons, the conclusion is obtained that the interaction between the bright solitons dependeds on the phase difference however the interaction between the dark solitons was independent on the phase difference on the contrary. Finally, using numerical simulation of the bright and dark solitons in the external potential field, it is found that the bright and dark solitons were acted upon by attractive force in the potential well, so solitons oscillate back and forth near the equilibrium position. On the contrary, the bright and dark solitons were affected by the repulsive force in the potential barrier, whch lead to their departure from the potential barrier center. The faster the transverse velocity of solitons is, the greater the amplitude of oscillation is.