A Quantitative Study of the Effect of Cladding Thickness on Modal Confinement Loss in Photonic Waveguides

There has been increasing interest in making the photonic devices more and more compact in the integrated photonics industry, and one of the important questions for manufacturers and design engineers is how to quantify the effect of the finite cladding thickness on the modal confinement loss of photonic waveguides. This requires at least six to seven digits accuracy for the computation of propagation constant $\beta$ since the modal confinement loss is proportional to the imaginary part of $\beta$ that is six to seven orders of magnitude smaller than its real part by the industrial standard. In this paper, we present an accurate and efficient method to compute the propagation constant of electromagnetic modes of photonic waveguides with arbitrary number of (nonsmooth) inclusions in a layered media. The method combines a well-conditioned boundary integral equation formulation for photonic waveguides which requires the discretization of the material interface only, and efficient Sommerfeld integral representations to treat the effect of the layered medium. Our scheme is capable of calculating the propagation loss of the electromagnetic modes with high fidelity, even for waveguides with corners imbedded in a cladding material of finite thickness. The numerical results, with more than $10$-digit accuracy, show quantitatively that the modal confinement loss of the rectangular waveguide increases exponentially fast as the cladding thickness decreases.