Abstract
An accurate coupled-mode analysis of a grating-assisted directional coupler is presented using the singular perturbation technique. The optical fields in the coupler are represented by a linear combination of para-axial wave fields for each isolated waveguide. The para-axial wave fields are expanded using the multiple space-scales and solved so that they satisfy the para-axial wave equation for the coupled structure in the respective order of perturbation. This leads to the nonorthogonal coupled-mode equations which are accurate in the second order of perturbation. The proposed coupled-mode theory is applied to the analysis of two nonidentical coupled waveguides attached with a sinusoidal grating layer. The calculated wavelength response in the power transfer shows a close agreement with that obtained by a direct numerical analysis using the Fourier series expansion method.
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