Long period fiber grating and its application to all-optical pulse shaping

Temporal optical differentiators (ODs) realized by using a LPG　　

OD definition Transfer function of an ideal Nth-order (N =1, 2, 3,---) OD [Ngo et. al. [1][3]]: An Nth-order OD performs Nth temporal differentiation of complex field envelop of optical input signal x(t) to yield an output signal y(t): 3

 OD = notch filter with a  phase jump at signal’s central frequency. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Optics Express, vol. 14, no. 22, pp. 1069910707, October 2006.  Spectral response of a 1st-order (N = 1) OD based on a uniform long-period grating (LPG).  S1: 2.6 cm long LPG with 19 nm bandwidth. S3: 8.9 cm long LPG with 5.5 nm bandwidth  OD = notch filter with a  phase jump at signal’s central frequency. 4

Optical pulse shaper realized by using a LPG