Kink Solitons and Breathers during Twist of Liquid Crystals under External Field

Author:Li Zuo

Supervisor:hou chun feng


Degree Year:2019





Liquid crystal(LC)is a kind of important optical material which has been widely used in the fields of photoelectric display,optical switch,information storage and so on.There are a variety of nonlinear phenomena in LCs.Solitons are among them.The solitary phenomena in LCs,especially the spatial optical solitons in LCs have been studied widely and verified in experiments.In addition to the spatial optical soliton,the arrangement or structural change of the LC under the external fields will also generate solitary phenomena.Combining the interaction of LC with electric and magnetic fields,we systematically study the kink solitons and breathers generated during the twist of nematic liquid crystals(NLCs)with different material properties,so as to continue to explore the nonlinear effects of LCs and provide a theoretical basis for practical applications.Firstly,considering the general NLC molecules under external electric field as the research object,the twist molecular kinematic model is given and the Sine-Gordon equation containing the term sin 2u satisfied by the twist motion is derived.We predict the existence of solitons and breathers during the twsit of NLC molecules under electric field by the soliton and breather solution of the equation.By analyzing the changes of the shape of double kink solitons and breathers under different parameters,we think the causes of these changes are mainly the effects of electric field and the twist elastic coefficient of LC.It is thus concluded that the soliton shape can be adjusted by changing the electric field and the twist elastic coefficient.Secondly,considering the general NLC molecules and strong polar NLC molecules under electric and magnetic fields as the research object respectively,we study the kink solitons generated during their twist process.For general NLC molecules,the coefficients of the term sin 2u of Sine-Gordon equation are modulated by electric and magnetic fields,but the influence of the magnetic field is much smaller than the electric field.Therefore,the distribution of the kink solitons and breathers does not change significantly comparing the situation under the electric field.For strong polar NLC molecules,its twist motion satisfies the double Sine-Gordon equation.According to the parameters’ relationship related to electric and magnetic fields,the equation is solved in three cases and the double kink soliton solutions in two cases are obtained,and the velocity expression of the soliton is given.The external fields and the twist elastic coefficient have an effect on the shape and velocity of kink solitons.Thirdly,from the perspective of increasing the magnetic properties of LCs,the NLC molecules with magnetic groups are considered.The twist motion of magnetic LC molecules under the control of magnetic field is analyzed.The kinematic equation is proved to be Sine-Gordon equation containing the term sinu.The double kink soliton and breather solutions are derived and we predict kink solitons and breathers can be generated during the twist process under the control of magnetic field.The influence of the control of the magnetic field and the twist elastic coefficient on the deflection angle of the magnetic LC molecules and the shape of the soliton is discussed.Finally,taking the LC under the continuum model as the research object,the twist motion of the magnetic LC under the control of the magnetic field and the twist motion of the NLC under the electric field are studied respectively.Considering the relationship between the torque generated by the mechanical properties of the LC during the twist motion and the one generated by the external field,the kinematic equations of the two cases are derived by the law of rotation.The results show that they are all Sine-Gordon equations.The double kink soliton solution and the breather solution are given.The conclusion is the same with the situation when the discrete molecules are studied.It is indicated that for LCs,whether it is regarded as discrete molecules or a continuous medium,solitons and breathers can be generated during the twist motion under certain condition.