Doctor Modes™ can analyze the following waveguide cross-sections:

                                                    ▪ Slab              ▪ Rib             ▪ Circle             ▪ Trapeze     

                                                    ▪ Channel       ▪ Strip           ▪ Ellipse            ▪ Traingle 

The analysis can be made to either a single waveguide or parallel waveguides (directional coupler) structure. Effects such as material dispersion, temperature and doping variations can be considered for Silicon (SOI), Lithium Niobate (LiNbO3), Silicon-Dioxide (optical fiber) and custom made platform (via Material Manager). Consequently, the refractive index of the material, n, is not necessarily constant but rather may be dependent n(λ,T,ΔNdoping).

The software finds and sorts the supported waveguide modes by employing analytical methods, and displays significant details about them. Among the methods are: Planar Slab (Maxwell), Shadow Region (Marcatili), Effective Index Method, Circle (Maxwell) and an Exact solution applied by the Galerkin method.

For the supported modes, the field components, power and polarization distribution in space can be plotted in 1D, 2D and 3D. The results derived by the various methods can be compared in a single table.

The Exact solution is a 3D full-vector solution which is based on the Galerkin procedure (global expansion). The basis had been carefully chosen and optimized such that the solution is reduced to a basic eigenvalue problem (matrix handling) and the elements of the matrix are obtained analytically without any numerical calculations. There are currently three basis:

• Sine basis
• Slab modes basis: Guided + Radiated slab modes solution for single/parallel guides (Fourier basis)
• Hermite-Gauss basis

For the Fourier basis (preferred), an impressive 4-7 digits of convergence for the mode effective index in Silicon Photonics platform is achieved for 20 terms in either single or parallel guides. The method was compared with other solutions over popular structures, and obtained accurate results with minimal running time (No domain-decomposition or meshing is invoked), see case study. 

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The built-in Analysis Tool can be used to examine how a certain property of the waveguide changes when other parameters varies. For example, one may wish to examine the number of modes exist in a rib waveguide while changing its slab height at 10nm steps. The Linkage Tool can be used through the Analysis Tool to link a change in one parameter to a change of another. For example, increasing the height of the slab within the gap region in a parallel guides waveguide (DC) when decreasing the width of the gap, i.e., linking HGap to WGap.

For the trapeze cross-section, several profiles are available: Straight, Erfc (Error Function), Quadratic, Exponent and Gaussian. 

Below, some of the cross-sections which can be analyzed by Doctor Modes™: