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filledguide

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{ 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

 

 


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