Tailoring the transmission spectrum of the long period gratings by variation in the length of the grating

In this paper we have presented a mathematical treatment for tailoring the Transmission Spectrum of the Long Period Gratings by variation in the length of the grating. Our results show that the transmission spectra show a rather varied behavior depending on the length of the grating. We have formulated generalized expressions for finding positions of maxima and minima as well as power retained by the core mode at these positions in the transmission spectrum of the grating. This facilitates the designing of gratings to be used as in line loss elements in applications like gain flattening, gain equalization etc.