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Scalar theory of low-contrast Bragg waveguides

An analytic approach is proposed to synthesise the optimal structure of the quasi-periodic cladding of a waveguide and an efficient numerical method is developed for determining the complex eigenvalues corresponding to low-loss Bragg modes. It is shown that, under the assumption that variations in the refractive index are small, the complete system of Maxwell's equations is reduced to a scalar wave equation, which can be solved by the method of finite differences.