Abstract
The propagation characteristics of a subwavelength plasmonic crystal are studied based on its complex Bloch band structure. Photonic crystal bands are generated with an alternative 2D Finite Element Method formulation in which the Bloch wave problem is reduced to a quadratic eigenvalue system for the Bloch wavevector amplitude k. This method constitutes an efficient and convenient alternative to nonlinear search methods normally employed in the calculation of photonic bands when dispersive materials are involved. The method yields complex wavevector Bloch modes that determine the wave-scattering characteristics of finite crystals. This is evidenced in a comparison between the band structure of the square-lattice plasmonic crystal and scattering transfer-functions from a corresponding finite crystal slab. We report on a wave interference effect that leads to transmission resonances similar to Fano resonances, as well as on the isotropy of the crystal's negative index band. Our results indicate that effective propagation constants obtained from scattering simulations may not always be directly related to individual crystal Bloch bands.
Highlights
The study of the optical properties of Photonic Crystals (PCs) has relied on the generation of Bloch-mode photonic band structures
We derive the Finite Element Method (FEM) formulation for the plasmonic crystal eigenvalue problem following similar steps as [4]. This formulation is implemented in a simple way with the COMSOL Finite Elements package [11] and used to produce the photonic bands presented in Sec. 3, for a square-lattice Subwavelength Plasmonic Crystals (SPCs) displaying a negative refraction band [5, 6]
The Finite-Element formulation presented in Section 2 is convenient for the calculation o photonic band structures of periodic metamaterials composed of dispersive materials
Summary
The study of the optical properties of Photonic Crystals (PCs) has relied on the generation of Bloch-mode photonic band structures. Tonic bandgap frequencies and play an important role in representing the evanescent field inside a finite or semi-infinite PC slab under external excitation This has been suggested in [10], in which an equivalent formulation to that presented here, based on the plane-wave expansion method [3], was used to calculate imaginary k bandgap modes in PCs composed of nondispersive, purely dielectric materials. This formulation is implemented in a simple way with the COMSOL Finite Elements package [11] and used to produce the photonic bands presented in Sec. 3, for a square-lattice SPC displaying a negative refraction band [5, 6].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
