• Applications of Brewster’s and TIR effects• Slab waveguide and Brillouin’s waves • Transmission line (TL) concept• Parallel-plate waveguide (PPWG) with the TEM wave• Telegrapher equations for PPWG • General telegrapher equations

Elements of electromagnetic field theory and guided waves

Application of Brewster and TIR effectsNatural pol. (chaoticellipse) Linear

2. Slab optical waveguide

1. Lossless polarization of natural light

Optical waveguide

Simple mirror

Polariz. rotator

x

Linear

Brillouin waves in a slab WGy

TEevenyEeee

eE

eRReRReR

eReeEE

ReREE

yyjyj

djzj

tr

yjzjyjzjyjzj

yjzjyjzjyjzjtr

djyzx

yy

y

z

yzyzyz

yzyzyz

y

cos)(1

12

...)

(

,cos,sin,

0.

.

z

R+

R-

d/2

R+

R-

d/2

Ei

Ei

Etr

Etr

Odd TE modes

TEoddyEeee

eE

eRReRReR

eReeEE

yyjyj

djzj

tr

yjzjyjzjyjzj

yjzjyjzjyjzjtr

yy

y

z

yzyzyz

yzyzyz

sin)(1

12

...)

(

1.

.

z

R+

R-

d/2

R+

R-

d/2

Ei

Ei

Etr

Etr

xx

x

Both E0 and E1 comprise exp(-jzz)

Transmission Line concept (z≡)

e-jz =e-

z

x z

Confined TL

zx

zx

zx zx

x z

x z

e-jz =e-z

Open TL

Parallel-Plate Waveguide with a TEM wave

Medium with and

L and C p.u.l.y

w

dxz

Inductance p.u.l.

Capacitance p.u.l.

Telegrapher equations for PPW

- field inside

V, I - response of the plates to fields inside

Wave impedance Phase velocity

yy

General telegrapher equations

Similarly