Scaling property and multi-resonance of PCF-based long period gratings

In a long period grating (LPG) made on a silica-based single material photonic crystal fibre (PCF), the effect of material dispersion on the resonance wavelength of the LPG is negligible. The resonance wavelength, the period and length of the LPG, and the diameter and pitch of the air-hole lattice of the PCF are found to obey a scaling law that is derived from the scaling property of the Maxwell's Equations. Simulations show that the resonance wavelength has a non-monotonic dependence on the grating period and, for a particular grating period, there could exist multiple resonance wavelengths and hence multiple transmission dips due to phase matching between the fundamental core mode and a cladding mode simultaneously at multiple wavelengths.