Effects of grating period and mode order on the growth and sensitivity of the resonant peaks of long period gratings

A general analytical expression for describing the growth of the resonant peak wavelengths of long period gratings is derived. The theoretical calculations explain the shift of peak loss wavelengths in the direction of either shorter or longer wavelengths as the induced index change of grating increases. We have calculated and experimentally verified the sensitivity of the resonant peak wavelengths with respect to an overlay index for various grating periods. It is shown that the center wavelength shift of the claddding modes depends strongly on the grating period and the claddding mode order.