Accurate theoretical analysis of photonic band-gap materials

Two improvements for the solution of Maxwell’s equations in periodic dielectric media are introduced, abandoning the plane-wave cutoff and interpolating the dielectric function. These improvements permit the accurate study of previously inaccessible systems. Example calculations are discussed, employing a basis of ∼${10}^6$ plane waves for which these two improvements reduce both the memory and central processing unit requirements by ∼${10}^4$.