Abstract
Two fundamental principles of the mode-matching method-mode orthogonality and tangential field continuity conditions have been revisited in depth. With a finite number of modes employed in the conventional method, the tangential field continuity condition at the waveguide-discontinuity interface fails leading to a field mismatch error. We propose an alternate, superior mode-matching method implemented by reconstruction of the auxiliary coefficient matrix, rather than by applying the abovementioned continuity and orthogonality. Detailed transfer-matrix equations have been derived for the finite-mode-number case. We showed that the improved mode-matching method yields a smaller field mismatch error under equal computational effort. Examples of bent and faceted waveguide structure have been investigated and the numerical simulation results demonstrated that the newly proposed method has the merits of simple implementation, high accuracy, and high computational efficiency for application in high-index-contrast photonic integrated circuits.
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