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

2. Temporal optical differentiators (ODs) realized by using a LPG　　

3. 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

4.  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 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

5. Optical pulse shaper realized by using a LPG