Non-reciprocal Electromagnetic Phenomenon In A Linear Array Of Ferrite Cylinders

Due to the time-reversal symmetry breaking of ferrite material under a bias DC magnetic field,the permeability of ferrite material has an asymmetric tensor form,which leads to non-reciprocal propagation characteristics.Using magnetic photonic crystals to manipulate photons has attracted extensive research recently.The introduction of ferrite material into photonic crystals results in non-reciprocal propagation,such as the unidirectional surface states based on the magnetic surface polaritons and the chiral edge states which is similar to the quantum Hall effect.Breaking the time reversal symmetry and parity reversal symmetry at the same time while maintaining the parity-time symmetry,such a photonic crystal can support bulk one-way propagating modes.These non-reciprocal studies can be used to design devices such as isolators,circulators and unidirectional waveguides.Due to higher requirements for miniaturization and integration of devices to realize system on chip,recent years,magnetic photonic crystals with lower profile,or even one dimensional magnetic linear array arouses people's great interest.In this paper,we study the non-reciprocal electromagnetic propagation by a linear array of ferrite cylinders from simulation and experiments.At the same time,we study the non-reciprocal Goos-Hanchen shift in a linear array of ferrite cylinders.Specific tasks include:1.Study on the non-reciprocal electromagnetic wave propagation controlled by a linear array of ferrite cylinders.We explain the non-reciprocal characteristics from the point of view of single ferrite cylinder's scattering.Considering the ferrite array as a grating,we use the finite element method to calculate the diffraction coefficients of different order of the array.In experiment,using a set of small cylinders to replace the big one,which can reduce the demagnetizing factor greatly,we construct the test sample and demonstrate the non-reciprocal wave propagation by a linear array of ferrite cylinders from transmission experiments.Furthermore,by using permanent ferrite to provide bias magnetic field for ferrite cylinders,we can directly observe the non-reciprocal propagation of electromagnetic wave by using the field mapping technique.2.Study on the non-reciprocal Goos-Hanchen shift in a linear array of ferrite cylinders.We calculate the reflected and transmitted phase change of the ferrite array and find the frequency where negative Goos-Hanchen shift exists according to the stationary phase method.We can directly observe the negative Goos-Hanchen shift through simulation.The shift is about two times of wavelength,which can be observed in experiment.Changing the direction of the bias magnetic field,we find that the Goos-Hanchen shift in this structure if non-reciprocal.Furthermore,by changing the structure's periodic constant,the value of external magnetic field and the form of periodic unit,we discuss the influence of these parameters on the Goos-Hanchen shift of the linear array of ferrite cylinders.