Power penalty due to the amplitude and phase response ripple of a dispersion compensating fiber Bragg grating for chirped optical signals

A concise method is presented for rigorously calculating the power penalty due to the combined implications of the amplitude and phase response ripples of a dispersion compensating fiber Bragg grating and the chirp of the transmitted optical signal. By using trigonometric series to represent the ripples, the calculated penalty can be positive or negative, as obtained in numerical simulations and measurements, depending on the signal chirp and ripple within the modulated signal bandwidth. An approximate upper bound on the power penalty is also presented as an extension of earlier results that always yield positive penalties. Calculated and measured results are compared for two 10-Gb/s return-to-zero (RZ) signals with distinct chirp properties.