Design of compact long-period gratings imprinted in optimized photonic crystal fibers

To imprint a long-period grating (LPG) in a photonic crystal fiber (PCF) with an optimum response, first the parameters of the PCF should be optimized. In this paper, by using a semi-analytical enhanced improved vectorial effective index method, the optimized PCF parameters are determined by dividing the single-mode operation of the PCF into two regions in terms of air-hole spacing Λ (Λ>3 μm and Λ≤3 μm). For each region appropriate expressions are suggested to evaluate the PCF parameters. By calculating the effective refractive index difference between the optimized core and cladding of the PCF under a phase-matching condition, the optimum grating period in terms of the PCF parameters is obtained.