Light field distributions in one-dimensional photonic crystal fibers

摘要

It is shown that the light field distribution in a bandgap within periodic structures for one-dimensional (1D) photonic crystal fibers is described by a decaying factor multiplied by a periodical function that has the same period length as the one of the medium or has double the period length of the medium, depending on the sign of the trace of eigenvalue matrix. This fundamental property is applicable to any 1D planar periodic structures, no matter how many layers a unit cell has, what the contrast of refractive indices is, and whether the dielectric parameters in individual layers are homogeneous or inhomogeneous; it plays a significant role in the understanding of numerical results in a number of previously published research works. It is also shown that, similar to the refractive index guidance in conventional optical fibers, the photonic bandgap guidance is also a form of total internal reflection.