EMLAB

1

Plane wave reflection and transmission

EMLAB

2Reflection of uniform plane waves at normal incidence

EMLAB

3Boundary conditions

tritri HHHEEE , (at the interface, z =0)

EMLAB

4Reflection from perfect electric conductor

0,0 tritri HHHEEE (at the interface, z =0)

112

12

)0( 2

010 sin2)( 11ii

zjzjri EzjEee EEE

EMLAB

5Example

EMLAB

6

}Re{2

1})(Re{

2

1 *2*ininininr HEHES

EMLAB

7Wave reflection from multiple interfaces

ljZZ

ljZZZZ

L

Lin

tan

tan

0

00

1

1

in

in

lj

ljin

232

2232 tan

tan

EMLAB

8Example : radome

31

),3,2,1(2 mml

3232

2232 tan

tan

lj

ljin

0 2 4 6 8 10 12 14 16 180

0.2

0.4

0.6

0.8

1

Reflection

Transmission

EMLAB

9Example : anti-reflection coating

Calculate the refractive index and minimum thickness for the glass coating to provide total transmission from air to the glass at a free space wavelength of 570nm. refractive index of the glass is n3=1.45.

313312

nm][1194

)12( 2

ml

2.12

022

rn

(n: refractive index)

EMLAB

10Plane wave refraction at oblique incidence angles

EMLAB

11Plane of incidence

EMLAB

12

s-polarization (perpendicular) p-polarization (parallel)

If an EM wave approaches a surface obliquely, it is easier to decompose the field into two components, s-polarization and p-polarization.

EMLAB

13p-polarization (E-field parallel to the plane of incidence)

)cos,sinsin,cos(sin kk

11111 2),sin,0,(cos kk

,2

),sin,0,cos( 11111 kk

22222 2),sin,0,(cos kk

1111101 ,),cos,0,sin( EE

1111101 ,),cos,0,sin( EE

2222202 ,),cos,0,sin( EE

EMLAB

14E-field tangential component continuity

10110110 coscos TEREE

EMLAB

15

• phase matching condition (Snell’s law)

EMLAB

16H-field tangential component continuity

2

20

1

10

1

10

TEREE

)sin,0,(cos 1111 kk

101

10110 ˆ

ˆEy

EkH

)cos,0,sin( 11101 EE

EMLAB

17

2

10

1

10

1

10

TEREE

210110110 coscoscos TEREE TR1

2

cos

cos1

TR2

11

1122

12

2

1

1

22

1

1

2

coscos

cos2

coscos

2

cos

cos2

TT

1122

1122

2

1

1

2

2

1

1

2

2

1

1

2

coscos

coscos

coscoscoscos

2cos

cos

TR

EMLAB

18Reflection coefficient for parallel polarization

EMLAB

19Reflection coefficient for perpendicular polarization (s)

EMLAB

20Example

EMLAB

21

EMLAB

22

EMLAB

23Total reflection

EMLAB

24Optical fiber

EMLAB

25

TV antenna

TV signal transmitting antenna

TV signals are transmitted as EM wave with horizontal polarization.

Wave propagation

EMLAB

26Polarization of EM waves

Source current

Source current

EMLAB

27Reflection from ionosphere

EMLAB

28Reflection from ground and troposphere

EM waves undergo reflections and diffractions while propagat-ing toward receivers.

EMLAB

292-Ray Ground Reflection

• For d>> hr, ht,

– low angle of incidence allows the earth to act as a reflector– the reflected signal is 180 out of phase– Pr 1/d4

RT

ht hr

Phase shift!

d

EMLAB

30

Rcj

SRT

RcjR

cj

S

Rcj

RT eRGGR

e

R

eR

R

eGGH

1

44)(

121

21

4

222

2

2

2

2

1

4

2cos1

4

R

hhGGP

R

hkh

RGGP

R

hkhR

RGGPP

RTRTT

RTRTT

RTRTTR

EMLAB

31

4

1

R

2

1

R