A modified method of lines (MoL) technique is presented for calculating the reflection characteristics of apodised fibre gratings. To demonstrate the technique, reflection spectra of fibre gratings with triangular and diamond apodisation profiles have been calculated showing significant side-lobe suppression. MoL can accurately calculate not only average power but also field and phase distribution across reflected waves. It has been shown that the phase of the reflected light is maximally affected at the edge of the grating stop-band
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