Nonlinear optics in photonic crystal fibers

Photonic crystal fibers (PCFs) are very similar to normal optical fibers in that they consist of a core surrounded by cladding, such that light is guided within the core of the fiber. The primary difference between PCF and standard optical fibers is that PCFs feature an air–silica cross-section, whereas standard optical fibers have an all-glass cross-section. An electron micrograph of a typical PCF is shown in Fig. 1. The air holes extend along the axis of the fiber for its entire length and the core of the fiber is formed by a defect, or missing hole, in the periodic structure. The core is formed of solid glass, whose refractive index is that of pure silica (or whatever other glass is chosen), and the cladding is formed by the air–glass mixture, whose effective refractive index depends on the ratio of air-to-glass, also known as the air-fill fraction, that comprises the structure. The resulting effective-index of the cladding will be lower compared with that of the core and, as such, will provide the refractive index variation necessary to support total internal reflection at the core-cladding boundary, and guide light in a manner similar to that of standard optical fibers. The fiber design (i.e., size, shape, and the air-fill fraction) dictates solutions to Maxwell’s equations for light propagating within the fiber. Valid solutions are referred to as ‘modes’ which propagate along the fiber in a known manner, and have a well-defined shape in the transverse direction (i.e., they have a well-defined....