Research On The Casimir Force Between Sandwich Structure Containing Special Optical Materials

In 1948 Casimir proposed the theory of the existence of gravitational forces between two neutral ideal parallel conductors in vacuum.It is a macroscopic quantum effect caused by vacuum fluctuation.It plays an important role in physics,especially in the recent development of micro-and nano-electromechanical system.Casimir force has become a significant factor affecting the performance of nano-electromechanical devices,while Casimir attraction will cause micro-and nano-electromechanical devices bonding,so recently the focus has been on the possibility of developing the Casimir repulsion and restoring forces.In recent years,with the development of metamaterials and magneto-optical materials,it has been possible to fabricate materials with a strong magnetic response in certain electromagnetic bands,especially in the optical band,which provides favorable conditions for the production of Casimir repulsive forces.In this paper,two kinds of special optical materials(Metamaterials and Magneto-optical materials)are inserted into the general two-layer structure to form the sandwich structure.We mainly study the Casimir force between two kinds of sandwich structures and how to generate Casimir repulsive and restoring force.The main research work in this paper and the conclusions are as follows:Firstly,by using the calculation method of the Casimir force between the real media plates and base on the Lifshiftz theory and Maxwell stress tensor method,we deduce the formula for calculating the Casimir force between the media plane plates with metamaterials.However,the Casimir force calculation expression relates to the calculation of the reflection coefficient of the plate,on this issue,we derive the transfer matrix of the three-dimensional electromagnetic model,then we calculate the reflection coefficient of the sandwich structure by the transfer matrix method,finally,we obtain the expression of the Casimir force between sandwich structures.Secondly,we study the Casimir effect between sandwich structures containing dispersive metamaterials.we analyze the influence of magnetic plasma frequency,magnetic resonance frequency and permittivity of dielectric plate on the magnitude and direction of Casimir force.The results show that with the increase of the magnetic plasma frequency,the decrease of the magnetic resonance frequency and the decrease of the permittivity of the dielectric plate substrate,the sandwich structure can produce strong Casimir repulsive force.In addition,we also find that when the distance between plates increases further,the sandwich structure can show the Casimir restoring force by adjusting the filling factor and the thickness of the metamaterials plate.Lastly,we study the Casimir effect of the sandwich structure with magneto-optical material.The results show that by inserting the magneto-optical material between the two plates,the Casimir attraction between the two plates can be transformed into the repulsive force,and by changing the characteristic parameters of the magneto-optical materials,thickness,and the distance between the middle layer can control the size of Caimir repulsive force and produce the Casimir restoring force.In a word,the realization of the Casimir repulsion and restoring force between the sandwich structures provides a new solution to the problem of stability of the micro-and nano-electromechanical system.