Fabry-Perot resonator

Screen

L

nk

c

oro

oro

resL

n

0 Bv D

tx

D

jH

tx

B

E

Maxwell’s equations

general properties of linear waves

0tc

1

z 2

2

22

2

ctzGctzFt,z

wavesnonlinear,ccif ,chaos,solitons,shocks

magneticandelectric kineticandpotential

12010

361

104

H

EZ

9

7

c

¥

io

roref E

ER

Reflection coefficient

Transmission coefficientX

E

H

E

H

E

H

0

io

totrans E

ET

1c2c

1c2c

ZZ

ZZ

1c2c

2c

ZZ

Z2

What if?

a

Two perfectly conducting parallel sheets.Two plane waves.

a

Parallel plates

]/[

2axmztj

y ej

AE

ztjaxjmaxjmy eee

j

AE //

2

ztjy e

a

xmAE

sin

= 0 implies no propagation in the z direction; must be real for propagation x

za

Two plane waves.

]/[ axmztje

xk

npropagatio wavereal β 2

c1c

phasev

groupv

1

2

c1c

2

c1c

2

c1

c

a

cm where c

waveguide Ey is independent of y coordinate

a

cc

2f cc a2

c

GHz5.1fc

GHz5fc cm10a

cm3a

MHz100radio FM MHz1radio AM a

cc

2

f cc a2

c

MHz50fc

m 3a

0t

E

c

1

z

E2

y2

22

y2

Derive a dispersion relation for plane waves in a vacuum.

)zt(jyoy eEE

0)j()j( 22

1

lossless media

m25.0

s

m102c 8

wave

25.0

102 8

?ε

?f

r

wavec

f MHz 8002

wave

vacuumr c

cε

2

8

8

102

103

4

9

Plane EM wave

Compute

lossy material

H

EZc

j

j

3610

102j108.5

104102jZ

967

76

c

36

10102j108.5104102j

96776

jj j

copper @ f = 1 MHzCopper is a

good conductor.Phase shift of

r = 36; µr = 4;= 1

H

EZc

j

j

361036

10j1

104410jZ

99

79

c 1j1

1600j 2

8j

e106

zuE xt10cose100 9x

yuH

8xt10cose

106

100 9x

x

y

z H

E

wet soil = 10-2; r = 15; r = 1

f comments

60 Hz 2 x 105 good conductor 1 MHz 12 quasi conductor 100 MHz 0.12 quasi-dielectric 10 GHz 1.2 x 10-3 good dielectric

dsBm

Square loop - area = 4m2 - 2 resistors

V2.1dt

dV m

gen

2 4xB = -0.3t T

A2.06

2.1

42

VI gen

4t3.0

dlBumotionV

Sliding bar - nonuniform B

R xB = Bo x T

utx

x

d

tdBuV o2

motion

xduBo

wireconduction EAI Displacement current = ?

dt

dEAI capacitorntdisplaceme

R

wire

conduction

A

IE

dt

AI

d

AI wire

conduction

capacitorntdisplaceme

2earthsunearth.atsun.from r4SP

Power from sun

Watts108.2

105.14101P26

2113sun.from

2earthearth.ateats.earth rSP

Watts103.1

104.6101P17

263eats.earth

Help!

= 10 -3 / cm2

Help!

I willproctor

the exam.