Spectrum envelope analysis for interleaved sampled gratings with phase-shift

An analytical method is proposed for calculating reflection-spectrum envelope of interleaved sampled gratings with phase-shifts. Effects of parameters on reflection-spectrum envelope of the grating are discussed, such as two grating segment lengths, phase-shift and interleaved length. The unique optimal interleaved length can be obtained to provide the broadest flat-top reflection-spectrum envelope without ripples. Accuracy of the analytical expression is verified due to the calculated results in good agreement with the reflection spectra obtained by the piecewise uniform transform matrix method.