Study On The Transmission Properties Of 1D Photonic Crystals Under An Applied Magnetic Field

Photonic crystals are periodic structures by periodically arranged dielectric materials of different refractive indices. The electromagnetic modes of the photonic crystals are in the form of band and gap. The photonic band-gap structure depends on the symmetry of photonic crystals, the dielectric constants of the component materials and the size of the unit cell. For the ordinary photonic crystals, the photonic band-gap remains immutable once they are fabricated. Since the band-gap structure is dependent on the dielectric function, it is possible to control the band-gap structure by changing the dielectric function through some external parameters without changing the structure of the photonic crystal itself. In this paper, we investigate the case of modulating the photonic band-gap structures by an applied external magnetic field.The optical properties of bulk media are described by the dielectric function, which depend on the response of the charged particles to the external field. It is modeled by the Lorentz oscillator in the classical physics. The movement of charged particles can be considered as a forced oscillator in the electromagnetic field, and the dielectric function can be determined by the relation between the polarization and the external field. If an external magnetic field is applied, the Lorentz force acts on the charged particles which make the dielectric function to be a tensor, and a new frequency parameter, cyclotron frequency, appear in the dielectric function. The dielectric tensor depends not only on the frequency, but also on the external magnetic field. Due to the dependence of the dielectric function on the external magnetic field, the optical lengths of the media, which is the product of the refraction and the length, can be modulated by changing the external magnetic field, such that the phase shift of the electromagnetic wave propagated through the media is changed. This will significantly affect the transmission and photonic band structures of the photonic crystals. Based on the electromagnetic field theory and band-gap theory as in the solid state physics, in this thesis we study the light propagation properties of one dimensional photonic crystal under an applied external static magnetic field.For the Voigt effect, the propagation direction of the EM wave is perpendicular to the external magnetic direction. The change in dielectric function does not influence on the TE wave. It influence only on the TM wave. When the external is applied, there is a new resonance region appears around the cyclotron frequency. The dispersion curve of the bulk material and the photonic band-gap structures are drastically changed around the cyclotron frequency. The band is split into a number of narrow bands, and the transmission spectra show complex structures. The photons in the narrow band are strongly localized. The transmission depends sensitively on the external magnetic field in some incident frequency regions and in some incident angle regions.For the Faraday effect, the propagation direction of the EM wave is parallel to the external magnetic field. There are left-handed and right-handed circular polarizations in the photonic crystal. The dielectric functions are modified by the external magnetic field in different manners from that of Voigt configrarion. For the TM wave of the right-handed circular polarization, dielectric function turned to a negative value from a positive value, instantly. The transmission peaks move to the high frequency region. In the low frequency areas,a number of narrow transmission peaks are found. Correspondingly, there are a number of narrow flat bands. But, for the TM wave of the left-handed circular polarization, the effect on dielectric function is weak. The transmission peaks and bands move to the low frequency slightly. Under the applied magnetic field, the distribution of the fields in the narrow bands is quite different from that without the external magnetic field.