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Optical fibres are a true representative of the remarkable advancements and speed of adoption and commercialisation of technology in recent decades. Propelled by the invention of the laser in 1960, these tiny waveguides quickly spread from the scientific laboratories into the everyday life: Internet, medical diagnostics, sensors in food, transport, oil and other industries, decoration. Application of fibres relies on possibility of controlling the propagation of light through them which has initiated invention of a range of accessories and fibre-based devices. This chapter is dedicated to a widely exploited group of fibre devices called long period gratings. In general, grating is a periodic change in the refractive index profile along the fibre. Depending on their periods gratings are divided into: fibre Bragg gratings (FBGs) with periods comparable to the wavelength of the guided light and long period gratings (LPGs) with periods ranging from several tens to several hundreds of microns. The former reflect narrow bandwidths and are therefore used as band rejection filters in transmission or retro reflectors. LPGs were first designed (Vengsarkar et al., 1996) to mend the problem of back reflection in FBGs that appears to be detrimental in some applications, e.g. gain equalizers, (Vengsarkar et al., 1996). Due to the dependence of their spectral bands on external parameters both types of gratings are now widely used in sensing technology. In addition to inherited advantages of fibre sensors such as simplicity of interrogation schemes, compactness, multiplexing capability and non-obtrusive interaction with living tissues, gratings exhibit very high sensitivity and localisation of the parameter change, which makes them suitable for biomedical diagnostics, remote sensing in oil, food and pharmaceutical industry and radioactive environments, as well as build-in sensors in transportation. Advanced laser processing techniques along with mechanical and chemical methods allow for fabrication of LPGs in practically any fibre regardless of its index profile and material composition, Fig. 1a)-c). Therefore, it is not surprising that the major novelty in fibre industry – the photonic crystal fibre (PCF) (Knight et al., 1996; Russell, 2003), was quickly embraced as a new medium for grating fabrication. Different guiding principle of PCFs

Modelling of Long Period Gratings in Photonic Crystal Fibres and Sensors Based on Them