Band Structure Graph of Metallic Photonic Crystals: a Plane Wave Expansion Approach

Photonic crystals are artificial periodic structures. Their unique properties are one of the most extensively studied topics in the past 20 years. Researchers believe that this structure can overcome the challenge that we are facing nowadays in the nano-optics related research field. One of the most important parameters that exhibits the characteristic or properties of photonic crystals is the photonic band structure graph. A plane wave equation (PWE) has been used to calculate the photonic band structure of photonic crystals. Unfortunately, the PWE numerical method is limited to frequency-independent dielectric materials. Therefore a new equation for the dielectric materials containing metallic components (frequency- dependent materials) has been derived. This equation is much more general compared to the previous studies by other researchers. By utilizing this new calculation, the plane wave expansion method is used to calculate the photonic band structure of photonic crystals containing dielectric rods in metallic media frequency-dependent materials). Thus a new equation is derived.