Exactly solvable profiles of quasi-rectangular Bragg filter with dispersion compensation

The four-parametric family of exactly solvable profiles of the Bragg reflector is found. Compared to the known solution we take into account slow frequency modulation of the refractive index. The shape of the reflection spectrum is shown to be trapezoidal. The group delay characteristic is demonstrated to be nearly linear within the band of high reflectance. The qualitative analysis reveals the domains of parameters where the solution corresponds to the quasi-rectangular filter with simultaneous dispersion compensation. Simple formulae for main filter characteristics and estimations for experimental parameters of a fibre Bragg grating are discussed.