{ FILLEDGUIDE.PDE
This problem models an inhomogeneously filled waveguide.
See discussion in Help section "Electromagnetic Applications | Waveguides".
}
title "Filled Waveguide"
select
modes = 8 { This is the number of Eigenvalues desired. }
ngrid=30 regrid=off
variables
hx,hy
definitions
cm = 0.01 ! conversion from cm to meters
b = 1*cm ! box height
L = 2*b ! box width
epsr
epsr1=1
epsr2=1.5
ejump = 1/epsr2-1/epsr1 ! the boundary jump parameter
eps0 = 8.85e-12
mu0 = 4e-7*pi
c = 1/sqrt(mu0*eps0) ! light speed
k0b = 4
k0 = k0b/b
k02 = k0^2 ! k0^2=omega^2*mu0*eps0
curlh = dx(Hy)-dy(Hx) ! terms used in equations and BC’s
divh = dx(Hx)+dy(Hy)
equations
Hx: dx(divh)/epsr - dy(curlh/epsr) + k02*Hx - lambda*Hx/epsr = 0
Hy: dx(curlh/epsr) + dy(divh)/epsr + k02*Hy - lambda*Hy/epsr = 0
boundaries
region 1 epsr=epsr1
start(0,0)
natural(Hx) = 0 value(Hy)=0
line to (L,0)
value(Hx) = 0 value(Hy)=0 natural(Hy)=0
line to (L,b)
natural(Hx) = 0 value(Hy)=0
line to (0,b)
value(Hx) = 0 natural(Hy)=0
line to close
region 2 epsr=epsr2
start(b,b)
line to (0,b) to (0,0) to (b,0)
natural(Hx) = normal(-ejump*divh,ejump*curlh)
natural(Hy) = normal(-ejump*curlh,-ejump*divh)
line to close
monitors
contour(Hx) range=(-2,2)
contour(Hy) range=(-2,2)
plots
contour(Hx) range=(-2,2) report(k0b) report(sqrt(abs(lambda))/k0)
surface(Hx) range=(-2,2) report(k0b) report(sqrt(abs(lambda))/k0)
contour(Hy) range=(-2,2) report(k0b) report(sqrt(abs(lambda))/k0)
surface(Hy) range=(-2,2) report(k0b) report(sqrt(abs(lambda))/k0)
summary export
report(k0b)
report lambda
report(sqrt(abs(lambda))/k0)
end