MyntOptics Engineering Tools
Tools / Integrated photonics

Slab Waveguide Mode Solver

Exact analytic solution of the three-layer asymmetric slab: guided TE and TM modes from the transcendental dispersion equation — effective indices, cutoff thicknesses, the single-mode window, confinement factors and field profiles. The 1-D physics that every strip and rib waveguide is built on.

Platform

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nm
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nm

Summary

Guided modes

What this means

Mode field profile

Effective index vs core thickness

Method: guided modes satisfy the slab dispersion relation κd − φ₂ − φ₃ = mπ, with transverse wavenumber κ = k₀√(n₁²−neff²), decay constants γᵢ = k₀√(neff²−nᵢ²), and interface phases φᵢ = atan(ρᵢ·γᵢ/κ) where ρ = 1 for TE and ρ = (n₁/nᵢ)² for TM. Roots are bracketed per mode order and refined by bisection to machine precision. Confinement Γ is the analytic fraction of |E|² (TE) inside the core. The 2-D physics of strip/rib guides adds lateral confinement — treat these numbers as the exact 1-D backbone and a strong first estimate.
Why does the single-mode window matter so much?
Phase devices — interferometers, rings, WDM filters — assume one mode with one effective index. A second guided mode carries its own phase velocity: power that couples into it at any imperfection re-interferes downstream as ripple, crosstalk and unexplainable fringes. Staying single-mode (or managing higher modes deliberately) is design rule #1 of integrated photonics.