Studies On Propagation Properties Of Autosolitons In Nonlinear Metamaterials

Metamaterials(MMs)are a kind of synthetic materials composed of microscopic units whose sizes are much smaller than the wavelength of electromagnetic waves.And the various permittivity and permeability can be achieved through engineering the shapes and sizes of the unis.In recent years,with the development of MMs from microwave frequencies,millimeter wave frequencies to visible light frequencies,and from linear MMs to nonlinear MMs,as well as gain MMs,the investigation of the electromagnetic waves propagation in MMs have rapidly attracted the interests of researchers both at home and abroad,which is a research hotspot in the field of MMs.In this paper,we consider the nonlinear Schr?dinger equation which describes the electromagnetic wave propagation in nonlinear MMs with gain,and abtain two different types of autosoliton solutions using the ansatz method and Hirota method,respectively.Then we investigate the formation conditions,existence regions and propagation properties of the two types of autosolitons in detail.Different from the autosolitons in conventional materials,autosolitons in nonlinear MMs possess wider existence regions,and its electromagnetic properties can also be controlled flexibly.This research results provide a theoretical evidence for exploring the propagation of electromagnetic waves in nonlinear MMs in the presence of gain.The particular research contents are as follows:(1)The research backgrounds,current status,wide application prospect of MMs and the optical solitons in MMs are brifly introduced.(2)On the basis of the nonlinear Schr?dinger equation which describes the electromagnetic wave propagation in nonlinear MMs,the Sech-type autosoliton solutions with a nonlinear chirp are presented via the ansatz method.The results indicate that this type of autosoliton can exist in the nonlinear MMs under the balance of nonlinear loss and linear gain.In different nonlinear polarization MMs,the changes of the amplitude,beam width and initial chirp with the normalized frequency and the gain coefficient are also different.Meanwhile,numerical simulations confirm the existence of the Sech-type autosoliton solutions in nonlinear MMs.The results indicate that the propagation properties of the autosolitons can be controlled through adjusting the incident wavefrequencies or choosing the nonlinear MMs with different polarization and gain.(3)Based on the same theoretical model in(2),we obtain the exponential type autosoliton solutions using the Hirota method.The research shows that comparing with the autosolitons in(2),this type of autosoliton solutions not only possesses a different form,but also exists in different regions of the nonlinear MMs and presents different propagation properties.Besides,we analyze the peak amplitude,full width at half maximum and initial frequency chirps in different regions of the nonlinear MMs in detail.The results disclose that the properties of the autosolitons can also be controlled through changing the incident wave frequencies or choosing appropriate nonlinear MMs.Finally,we numerically confirm that this exponential type autosolitons can exist in the nonlinear MMs.(4)We summarize the main contents of this paper,look into the prospects of the electromagnetic waves propagation in nonlinear MMs and point out some open problems in the future.