Waveguide mode solver
This Mathematica notebook is a tutorial for a waveguide mode solver.
It bases on a 2D plane-wave expansion method which includes gain and
losses. A detailed description of the method and its application to
explain waveguide mode competition in InGaN laser diodes can be found in
U. T. Schwarz and B. Witzigmann,
Optical properties of edge-emitting lasers: measurement and simulation,
invited chapter in Nitride Semiconductor Devices, edited by J. Piprek,
Wiley-VCH (2007) ISBN-10: 3-527-40667-0.
The notebook contains two implementations of the waveguide mode solver.
The first version employs analytical integration while the second
version uses a numerical integration. While the first version allows a
textbook-like definiton of the problem and its solution, it is limited
to not too complex situation, because of the complexity of the
analytical integration of piecewise defined functions. The numerical
version is capable to treat reasonable large scale problems, while
still implemented with only very few lines of code. This notebook may
also be seen as a blueprint for an implementation in some other program
language (C++), but the numerical code in Mathematica is actually very
fast.
The original C++ version of the code was used for waveguide mode
simulations of InGaN quantum well and Gas/Al- GaAs quantum wire laser
diodes:
U. T. Schwarz, M. Pindl, E. Sturm, M.
Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, Influence of
ridge geometry on lateral mode stability of (In/Al)GaN laser diodes ,
phys. stat. sol. (a) 202, 261 (2005).
T. Herrle, S. Schmult, M. Pindl, U. T. Schwarz, W. Wegscheider,
T-shaped waveguides for quantum-wire intersubband lasers, Phys. Rev. B
72, 035316 (2005).
Different versions are provided for compatibility reasons:
2D-Waveguide-MM.nb (full versions with all comments)
2D-Waveguide-MM.pdf (pdf printout of full versions with all comments)
2D-Waveguide-MM-analytical.nb (comments removed)
2D-Waveguide-MM-analytical2.nb (comments removed, Mathematica 2.0 compatible)
2D-Waveguide-MM-numerical.nb (comments removed)
2D-Waveguide-MM-numerical2.nb (comments removed, Mathematica 2.0 compatible)
--> home