Asymmetric Light Propagation Based On Complex Graded Photonic Crystals

Asymmetrically molding light propagation is of great importance, in particular, in optical region due to its fundamental interest and potential applications in compact photonic integrated circuits. All dielectric photonic crystals have the advantages of linear control, low loss and easy acquisition. In this paper, we demonstrate an asymmetric light propagation by designing two dimensional all-dielectric complex graded photonic crystals (GPCs) consisting of rod dimers with rotational gradient layer by layer. The GPC enables beam splitting for the left-hand side incidence, while for the right-hand side incidence beam focusing is observed due to the breaking of spatial inversion symmetry. In the first chapter of the dissertation, we introduce the background and the concept of photonic crystals. Meanwhile, the related properties and some of the current applications are presented briefly. Finally, we present the basic framework of this dissertation.In chapter two, we introduce some historical literatures on asymmetric transmission of electromagnetic waves. The use of chiral metal micro structure arrays and magnetic metamaterials can achieve one-way transmission of electromagnetic waves. A band mismatch photonic crystal heterostructure can also be used to achieve one-way transmission of electromagnetic waves. Besides, the closely related works that use GPCs to realize the beam splitting on one side and focusing on the opposite side are also presented. However, due to the loss issue or the low efficiency, these methods or materials might not suitable for the integrated photonic devices production.In chapter three, we present the theoretical approach employed in the dissertation. The behavior of photons in the dielectric medium of a photonic crystal can be described by the use of Maxwell’s equations, namely, by solving the Helmholtz equation with certain boundary conditions. For two-dimensional system consisting of cylinders, we take the cylindrical vector wave functions as a base to expand the field. We first use the Mie scattering theory to derive the scattering coefficient of a single cylinder, and then use the multiple scattering theory to derive the scattering characteristics of a system with a group of cylinders. Accordingly, we can get the photonic band characteristics of the system, field patterns and the transmittance.In the fourth chapter, we demonstrate an asymmetric light propagation by designing two dimensional all-dielectric GPCs consisting of rod dimers with rotational gradient layer by layer. Due to spatial-inversion-symmetry breaking characteristics, for the leftward incidence the Gaussian beam is split, while for the opposite rightward incidence a beam focusing is observed. We analyze the physical mechanism behind the phenomenon from the perspective of band diagrams and isofrequency contours. By tuning the azimuthal angle at the first layer and the rotational gradient, we find the functionality is operable both in near field range at subwavelength scale and in the far field range with a relatively larger configuration. Both the transmission efficiency are higher than the previous work. In addition, it can be used to implement unidirectional transmission as well through the introduction of the radius gradient.Finally, we sum summarize the results of the present work. An outlook is also presented for the promising applications of the complex GPC.