Reflection peak wavelengths for sampled fiber Bragg gratings without chirp

Analytic expression for the reflection peak wavelengths (RPWs) of sampled fiber Bragg grating (SFBG) without chirp is derived and confirmed. Firstly, the refractive-index modulation depth, corresponding to center wavelength, of seeding grating and Fourier series of sampled fiber Bragg grating's refractive-index modulation are obtained. Then the refractive-index modulation depth and local grating periods of sampled fiber Bragg grating are derived. Aided with them, the expression for reflection peak wavelengths of sampled fiber Bragg grating is achieved. Since the duty cycle and the sampling period are involved, the expression guarantees the accuracy of calculated reflection peak wavelengths. In the simulations, with different duty cycle or sampling period, there are agreements between the calculated reflection peak wavelengths (or channel spacing) and numerical reflection spectra. Moreover, this expression is not only available for uniform sampled fiber Bragg grating, but also for AC-apodized and AC-DC-apodized sampled fiber Bragg grating.