Study On Generation And Propagation Of Solitons And Travelling Waves In Metamaterials

Optical soliton is a localized electromagnetic wave stably propagating in nonlinear medium with dispersion or/and diffraction effects.It is always as an important research area of nonlinear optics.Modulation instability(MI)is a very general nonlinear phenomenon in nature.Its occurrence mechanism is closely related to soliton phenomenon.Due to the common physical essence and behavior characteristics of soliton,our study on physical essence and mechanism of optical soliton may help understanding and searching the physical study and physical mechanism of other solitons and promote the development of soliton dynamics study of these solitons.In addition,optical soliton has huge potential applications in the field of Quantum information processing,ultra-long-distance optical communication,optical switch,optical storage,optical trapping,et al.As is well known,the formation of optical soliton is due to the balance between linear and nonlinear processes.In the recent ten years,an artificial-constructed medium,named metamaterials(MMs),becomes hot topic of material science owing to its characteristics which are not found in natural materials.The occurrence of nonlinear MMs arouses the study on propagation of soliton in these MMs.Because the linear and nonlinear electromagnetic characteristics of MMs can be artificially adjusted,they are much richer than ordinary materials.This means that the soliton is easier to form and the approaches of manipulating solitons is more.These contain numerous soliton phenomena and soliton physics.MMs exhibits many new effects.The paper discusses the influence of these new effects on MI and optical soliton propagating in MMs.The study results are expected not only to facilitate the development of optical soliton dynamics,but also to provide the basis for new type of optical devices in future.The main innovative research results are as follows:Firstly,the combination of linear dispersive magnetic permeability and nonlinear polarizability leads to abnormal self-steepen(SS)effect on beam pulses propagation in nonlinear MMs.The interplay between the nonlinearity and supercollimation(SC)of nonlinear photonic crystal(one of MMs)leads to nonlinear diffraction effect on beam pulses propagation near the SC frequency point,and The tunable SC frequency influence the nonlinear diffraction effect.We discover the new occurrence conditions of MI and the influence of abnormal SS,third order and fifth order effects on MI in positive and negative index regions of MMs.We also find the nonlinear diffraction effect and tunable SC frequency lead to new MI in MMs.Secondly,the higher order nonlinear Schrodinger equation(HONSE)in MMs is solved by the Riccati function method,and the bright and dark optical solitons are obtained under various conditions about coefficients of HONSE.The influences of abnormal SS and second-order nonlinear dispersion effects on soliton formation and propagation are detailed discussed.Comparing to only positive refractive region of ordinary medium,MMs possess both positive and negative refractive regions.The sign and magnitude of SS and second-order nonlinear dispersion effects in MMs can be adjustable in any refractive region.We discover the formation conditions of bright and dark optical solitons and the influence of abnormal SS and second second-order nonlinear dispersion effects on bright and dark optical solitons propagation in three group velocity dispersion cases of positive and negative index regions in MMs.In addition,we receive many other travelling wave solutions of HONSE,i.e.hyperbolic type solutions,triangular type periodic solutions,Jacobi elliptical type double periodic solutions and Weierstrass type double periodic solutions.Finally,we research the solitons and travelling wave solutions of short pulse equation(SPE)describing optical pulses propagation in MMs,and obtain their physical condition of occurrence and evolution law.The bounded travelling wave solutions are found only probably in the focusing nonlinearity and impossibly in the defocusing nonlinearity.Under the focusing nonlinearity,the bounded travelling wave solutions are gotten,including two kinds of periodic(or inverted)loop bounded traveling wave solutions and a periodic(or inverted)hump bounded traveling wave solution.It is easy to find that the former two kinds of periodic(or inverted)loop bounded traveling wave solutions can degenerate into one(or inverted)loop solitary wave solution.