Finite element method analysis of band gap and transmission of two-dimensional metallic photonic crystals at terahertz frequencies

Photonic band gap and transmission characteristics of 2D metallic photonic crystals at THz frequencies have been investigated using finite element method (FEM). Photonic crystals composed of metallic rods in air, in square and triangular lattice arrangements, are considered for transverse electric and transverse magnetic polarizations. The modes and band gap characteristics of metallic photonic crystal structure are investigated by solving the eigenvalue problem over a unit cell of the lattice using periodic boundary conditions. A photonic band gap diagram of dielectric photonic crystal in square lattice array is also considered and compared with well-known plane wave expansion results verifying our FEM approach. The photonic band gap designs for both dielectric and metallic photonic crystals are consistent with previous studies obtained by different methods. Perfect match is obtained between photonic band gap diagrams and transmission spectra of corresponding lattice structure

Realization of a three-dimensional photonic topological insulator

Confining photons in a finite volume is in high demand in modern photonic devices. This motivated decades ago the invention of photonic crystals, featured with a photonic bandgap forbidding light propagation in all directions. Recently, inspired by the discoveries of topological insulators (TIs), the confinement of photons with topological protection has been demonstrated in two-dimensional (2D) photonic structures known as photonic TIs, with promising applications in topological lasers and robust optical delay lines. However, a fully three-dimensional (3D) topological photonic bandgap has never before been achieved. Here, we experimentally demonstrate a 3D photonic TI with an extremely wide (> 25% bandwidth) 3D topological bandgap. The sample consists of split-ring resonators (SRRs) with strong magneto-electric coupling and behaves as a 'weak TI', or a stack of 2D quantum spin Hall insulators. Using direct field measurements, we map out both the gapped bulk bandstructure and the Dirac-like dispersion of the photonic surface states, and demonstrate robust photonic propagation along a non-planar surface. Our work extends the family of 3D TIs from fermions to bosons and paves the way for applications in topological photonic cavities, circuits, and lasers in 3D geometries

Degeneracy analysis for a super cell of a photonic crystal and its application to the creation of band gaps

A method is introduced to analyze the degeneracy properties of the band structure of a photonic crystal making use of the super cells. The band structure associated with a super cell of a photonic crystal has degeneracies at the edge of the Brillouin zone if the photonic crystal has some kind of point group symmetry. Both E-polarization and H-polarization cases have the same degeneracies for a 2-dimensional (2D) photonic crystal. Two theorems are given and proved. These degeneracies can be lifted to create photonic band gaps by changing the transform matrix between the super cell and the smallest unit cell. The existence of the photonic band gaps for many known 2D photonic crystals is explained through the degeneracy analysis.Comment: 19 pages, revtex4, 14 figures, p

Efficient excitation of self-collimated beams and single Bloch modes in planar photonic crystals

Using finite-difference time-domain calculations, we investigate out-of-plane coupling between a square-lattice planar photonic crystal and a conventional waveguide located above the photonic crystal. We couple a waveguide oriented in the GX direction to a photonic crystal mode in the second band and show that anticrossing takes place. In this way, a self-collimated beam is launched in the planar photonic crystal, with full power transfer. Furthermore, we investigate the coupling between a waveguide oriented in the GM direction and a photonic crystal and show that single photonic crystal modes can be selectively excited

Graphene-based photonic crystal

A novel type of photonic crystal formed by embedding a periodic array of constituent stacks of alternating graphene and dielectric discs into a background dielectric medium is proposed. The photonic band structure and transmittance of such photonic crystal are calculated. The graphene-based photonic crystals can be used effectively as the frequency filters and waveguides for the far infrared region of electromagnetic spectrum. Due to substantial suppression of absorption of low-frequency radiation in doped graphene the damping and skin effect in the photonic crystal are also suppressed. The advantages of the graphene-based photonic crystal are discussed.Comment: 4 pages, 3 figure

Photonic Crystal Laser Accelerator Structures

Photonic crystals have great potential for use as laser-driven accelerator structures. A photonic crystal is a dielectric structure arranged in a periodic geometry. Like a crystalline solid with its electronic band structure, the modes of a photonic crystal lie in a set of allowed photonic bands. Similarly, it is possible for a photonic crystal to exhibit one or more photonic band gaps, with frequencies in the gap unable to propagate in the crystal. Thus photonic crystals can confine an optical mode in an all-dielectric structure, eliminating the need for metals and their characteristic losses at optical frequencies. We discuss several geometries of photonic crystal accelerator structures. Photonic crystal fibers (PCFs) are optical fibers which can confine a speed-of-light optical mode in vacuum. Planar structures, both two- and three-dimensional, can also confine such a mode, and have the additional advantage that they can be manufactured using common microfabrication techniques such as those used for integrated circuits. This allows for a variety of possible materials, so that dielectrics with desirable optical and radiation-hardness properties can be chosen. We discuss examples of simulated photonic crystal structures to demonstrate the scaling laws and trade-offs involved, and touch on potential fabrication processes.Comment: 3 pages, 3 figures; Submitted to Particale Accelerator Conference (PAC 2003), May 12-16, 2003, Portland, Oregon (IEEE