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Doctor Modes can analyze the following waveguide cross-sections:


▪ Slab      ▪ Channel      ▪ Rib      ▪ Strip      ▪ Circle      ▪ Ellipse     ▪ Trapeze     ▪ Traingle 


The analysis can be made to either a single waveguide or a double waveguide, i.e. directional coupler, structures. This intended for any material, however, for Silicon (SOI), Lithium Niobate (LiNbO3) and Silicon-Deoxide (optical fiber) effects such as material dispersion, temperature and doping variations can be accounted for. Consequently, the refractive index of the material (nis not constant but 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-vectorial solution which is based on the Galerkin procedure (global expansion). The basis had been carefully chosen and optimized such that the solution is carried by matrix handling without any numerical calculations (the solution is entirely analytic). An outstanding 7-digits (10⁻⁷) convergence for the mode effective index in cut-off condition can be achieved for only 25 terms.


The Analysis Tool can 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 channel waveguide while changing its width and height at steps of 10nm.


For the trapeze cross-section, several profiles are available: Straight, Erfc, Quadratic, Exponent and Gaussian. Below, some of the cross-sections that can be analyzed by Doctor Modes

The Analysis Tool can be used to examine how a property value is changed while other parameters varies. Once a run is completed, the map can be saved to memory and can be analyzed in specific ranges without the need to rerun the simulation again for the new range. The map can also be saved to a file and its data can be fitted by the Fitting Tool. Two analyses can be performed in parallel in the two different graphs

The Fitting Tool can try fitting known expressions to an active plot in the current graph. If more than one active plot exists, then plots can be merged before fitted. 1D/2D fittings are currently available (3D fitting will be available soon). The explicit expression obtained by the fit can be copied to clipboard (in latex format) or be tagged within the current graph. Basic algebraic function, such as derivatives and integrals, can be made by the Algebraic Tool on the expression obtained

The Algebraic Tool can perform basic algebraic functions, such as derivatives and integrals, on a fitted expression generated by the Fitting Tool. The resulting equation can be plotted in the current graph, tagged in, or be copied to clipboard (in latex format)

The Exact solution is based on the Bubnov-Galerkin procedure which apply a global expansion solution on Maxwell equations. The solution solves the 3D full-vector Maxwell equation

Employing the Galerkin method with our algorithm holds several significant advantages compared to other commercial mode solvers:

  • Solving one eigenvalue problem is much faster than dealing with a meshgrid as required by numerical solvers such as FDTD, FEM and BPM.

  • Spurious solutions are not generated 

  • There is no boundary limitation (finite computational domain, Ω). Our basis converges at x,y=±∞


These advantages yield a fast and reliable simulation without missing supported modes, even those near cutoff.


The disadvantages of the method:

  • The size of the matrix, which depends on the number of terms (N), grows by a factor of (2N)² 

  • 3-digits convergence for the fundamental mode is obtained for typical waveguides dimension (N=40)




    The Exact solution is based on the Bubnov-Galerkin procedure which apply a global expansion solution on Maxwell equations. The solution solves the 3D full-vector Maxwell equation





    In order to overcome these disadvantages, the Exact solution offers the Rigorous Analysis strategy. In this strategy, the basis is optimized according to the geometry of the waveguide. The simulation is comprised of several runs, where in each run, the results are analyzed and the basis is reoptimized. This strategy yields three major improvements:

    • Simulating with fewer terms while obtaining the required convergence digits

    • Higher convergence accuracy, >7 digits can be attained

    • Finding modes that are at the "edge" of cutoff (driving the software to its maximum performance)


    Note that although making several runs takes longer time, working with fewer terms usually shorten the overall time compared to the case of one run with high number of terms. Below, a screenshot of the Exact method settings dialog

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