Abstract
The symmetric dielectric slab waveguide serves as an important canonical structure for the high-speed high-bandwidth optical and opto-electronic silicon-on-insulator interconnects. A stochastic model of propagation loss, due to electromagnetic wave scattering with surface-roughness of the nano-scale waveguide excited at frequencies in the 100s of THz, provides useful insights for analysis and design optimization of optical interconnects. In this work, we propose an analytic solution for the stochastic scattering integral based on contour integration of the exponential autocorrelation function in the complex s-plane that improves performance at larger autocorrelation length values, compared to previous works. An expression is proposed for computing the upper-bound value of scattering loss. Results show that the proposed 2D formulation offers reasonable correlation against data from experimental measurements of loss by previous investigators, while several discrepancies are noted compared to previous 2D models. An expression is proposed for the transverse magnetic (TM) modal field amplitude, and several discrepancies in the transverse electric (TE) modal amplitudes are noted compared to previous works. A method is proposed for computation of the effective index (and propagation constant) for arbitrary cladding that improves convergence of the Newton search method, and it is compared to two other methods. Background discussions include the stochastic theory and assumptions that lead to the stationary and ergodic treatment of the surface-roughness, extension of the ensemble-average and time-average to the spatial domain, and effective thickness due to the Goos-Hänchen shift.
Highlights
T E high-speed high-bandwidth information revolution depends, in part, on advanced interconnect technologies, including opto-electronic and optical interconnects comprised of silicon-on-insulator (SOI) nano-scale dielectric waveguides which carry information bits as THz electromagnetic waves propagating through complex on-chip structures that exhibit random imperfections, such as surfaceroughness [1]–[6]
A 2D analytic model derived in the novel work of [24], [25] is discussed in section II for the stochastic characterization of scattering loss in the symmetric dielectric slab waveguide exhibiting surfaceroughness according to the exponential autocorrelation function (ACF)
Background discussion is provided in section A on the stochastic theory and assumptions that enable stationary and ergodic treatment of the symmetric dielectric slab waveguide with surface-roughness exhibiting an exponential autocorrelation function, where the ensemble average and the spatial average operators are defined
Summary
T E high-speed high-bandwidth information revolution depends, in part, on advanced interconnect technologies, including opto-electronic and optical interconnects comprised of silicon-on-insulator (SOI) nano-scale dielectric waveguides which carry information (data) bits as THz electromagnetic waves propagating through complex on-chip structures that exhibit random imperfections, such as surfaceroughness [1]–[6]. A 2D analytic model derived in the novel work of [24], [25] is discussed in section II for the stochastic characterization of scattering loss in the symmetric dielectric slab waveguide exhibiting surfaceroughness according to the exponential autocorrelation function (ACF). Work is currently underway to develop efficient stochastic FDTD models in 2D and 3D, to be used in further characterization of scattering loss due to surface-roughness in nanoscale opto-electronic and optical interconnects comprised of dielectric waveguides with arbitrary geometry and material operated at frequencies in 100s of THz
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