Finite-Difference Analysis of Waveguides

THE UNIVERSITY OF TEXAS AT EL PASO

Pioneering 21st Century Electromagnetics and Photonics

The finite-difference method (FDM) provides a simple way analyze all forms of waveguides. It is simple to formulate and easy to implement. The basis code uses a uniform grid so it is not has efficient as finite element methods that use more efficient unstructured grids.

SLAB VS. CHANNEL WAVEGUIDES CHANNEL WAVEGUIDES FOR INTEGRATED

CHANNEL WAVEGUIDES FOR RADIO FREQUENCIES

CHANNEL WAVEGUIDES FOR PRINTED CIRCUITS

RIGOROUS HYBRID MODE ANALYSIS

2 2

2

x x

y y

a aΩ

a a

Ω PQ

2 2

Ax x

A Ω

1 1

1 1

e h e h

x zz y x zz x yy

e h e h

y zz y xx y zz x

D ε D D ε D μP

D ε D μ D ε D

1 1

1 1

h e h e

x zz y x zz x yy

h e h E

y zz y xx y zz x

D μ D D μ D εQ

D μ D ε D μ D

Standard eigen-value equation

Rib waveguide analysis

QUASI-TE/TM MODE ANALYSIS

2 2

2 2

Mode:

Mode:

x xx x x

y yy y y

E

E

Ω a a

Ω a a

2 1 1 1 1

2 1 1 1 1

E H H E E H H E

xx x zz y x zz y x zz x yy y zz y xx

E H H E E H H E

yy y zz x y zz x y zz y xx x zz x yy

Ω D ε D D μ D D ε D μ D μ D ε

Ω D ε D D μ D D ε D μ D μ D ε

Observing how strongly linearly polarized the hybrid modes are, we can approximate the smaller components to be zero. This simplifies the analysis and makes it more efficient.

We see that the modes tends to be strongly linearly polarized.