Efficient approximation to calculate time delay and dispersion in linearly chirped periodical microphotonic structures

The Bloch mode propagation through the chirped periodical structure is defined by its local dispersion relation. In a slowly varying structure its time delay is the integral of the local inverse group velocity along the propagation direction. The integration can be strongly simplified for linearly chirped structures if the assumption is made that the local dispersion relation is just a scaled and shifted version of the dispersion relation at the input. This assumption leads to exact solutions for the structures with locally uniaxial deformation and provides a good approximation for arbitrary structures with small chirps. The approach is demonstrated for high index contrast chirped Bragg mirrors and complicated photonic crystal waveguide structures, including coupled waveguides and a slow group velocity waveguide.