Accurate analytical expression for reflection-peak wavelengths of sampled Bragg grating

An analytical expression for calculating the reflection-peak wavelengths of sampled Bragg grating (SBG) is achieved for the first time. The index modulation distribution of SBG is expanded into Fourier series; then the equivalent index modulation and local Bragg period are obtained to derive the expression. Consequently, the introduction of duty cycle and sampling period ensures the accuracy of expression. The phase-matching condition is well explained by the constant phase shift technique. Under this condition, the calculated results based on expression are in good agreement with the numerical reflection spectra obtained by the piecewise uniform method