Order-N photonic band structures for metals and other dispersive materials

We show how to calculate photonic band structures for idealized metals and other dispersive systems using an efficient order-N scheme. That is to say, we use a scheme where the calculation time scales linearly with the system size. The inverse dielectric function is treated as a simple pole. The method is applied to two simple periodic idealized metallic systems where it gives results in close agreement with calculations made with other techniques. Further, the approach demonstrates excellent numerical stability within the limits we give. By generalizing to an inverse dielectric function expanded as a series of poles, our method opens the way for efficient calculations on complex structures containing a whole different class of material.