ece-1466 modern optics course notes part 4

April 02002 Chuck DiMarzio, Northeastern University 10100-4-1

ECE-1466Modern OpticsCourse Notes

Part 4

Prof. Charles A. DiMarzio

Northeastern University

Spring 2002

April 02002 Chuck DiMarzio, Northeastern University 10100-4-2

Polarized Light

• Starting Point– Maxwell’s Equations

– Homogeneous Medium

– Isotropic Medium

• Solution– Plane Waves

– Transverse Fields

• Eigenstates

• General Solution

x

y

x

yor

x

y zE

April 02002 Chuck DiMarzio, Northeastern University 10100-4-3

Some Mechanisms of Interaction

• Dielectric Interface– Oblique Incidence

– Scattering

• Material Properties– Linear Birefringence

– Circular Birefringence, AKA Optical Activity

April 02002 Chuck DiMarzio, Northeastern University 10100-4-4

Linear Polarization

E

x

y

April 02002 Chuck DiMarzio, Northeastern University 10100-4-5

Circular Polarization

tE

x

-y

April 02002 Chuck DiMarzio, Northeastern University 10100-4-6

Unpolarized LightEx

Ey

April 02002 Chuck DiMarzio, Northeastern University 10100-4-7

Polarizing Components

April 02002 Chuck DiMarzio, Northeastern University 10100-4-8

Fresnel ReflectionBoundary Conditions

Dnormal=

Dtangential=0Etangential

0Enormal

Dnormal

Dtangential

0Enormal

0Etangential

April 02002 Chuck DiMarzio, Northeastern University 10100-4-9

Polarization Labels

• Plane of Incidence– Normal & Incident

Ray

• P-Polarization (TM)– E Parallel to Plane of

Incidence

• S-Polarization (TE)– E Senkrecht =

Perpendicular to Plane of Incidence

Er

Ei

Et

Hi

Hr

Ht

Er

Ei

Et

Hi

Hr Ht

April 02002 Chuck DiMarzio, Northeastern University 10100-4-10

S-Polarization (1)

April 02002 Chuck DiMarzio, Northeastern University 10100-4-11

S-Polarization (2)

April 02002 Chuck DiMarzio, Northeastern University 10100-4-12

Fresnel Coefficient SummaryExample

0 20 40 60 80-1

-0.5

0

0.5

1Fresnel Reflection: Air to Glass, n=1.5

q, Angle, Degrees

s

p

s

p

April 02002 Chuck DiMarzio, Northeastern University 10100-4-13

Special Angles

1 2 3 410

20

30

40

50

60

70

80

90

n, Index of refraction

An

gle,

Deg

rees

Critical Angle (medium to air)

Brewster’s Angle(air to medium)

Brewster’sAngle (medium to air)

April 02002 Chuck DiMarzio, Northeastern University 10100-4-14

Power Coefficients

0 20 40 60 80-20

-15

-10

-5

0Fresnel Reflection: Air to Water, n=1.33

q, Angle, Degrees

R, T

, dB

RS

RP

TS

TP

April 02002 Chuck DiMarzio, Northeastern University 10100-4-15

Fresnel Reflection Examples (1)Air to ZnSe (IR)Air to Glass

0 20 40 60 800

0.2

0.4

0.6

0.8

1Fresnel Reflection: Air to Glass, n=1.5

q, Angle, Degrees

R, T

0 20 40 60 800

0.2

0.4

0.6

0.8

1Fresnel Reflection: Air to ZnSE in IR, n=2.4

q, Angle, Degrees

R, T

RS RP

TS

TP

RS

RP

TS

TP

April 02002 Chuck DiMarzio, Northeastern University 10100-4-16

Fresnel Reflection Examples (2)Glass to Air Amplitude Glass to Air Phase

0 20 40 60 800

0.2

0.4

0.6

0.8

1Fresnel Reflection: Glass, n=1.5, to Air

q, Angle, Degrees

R, T

RSRP

TSTP

0 20 40 60 80 100-200

-150

-100

-50

0

50

100

150

200Fresnel Reflection: Glass, n=1.5, to Air

q, Angle, Degrees

Ph

ase,

Deg

rees RP

RS

TSTP

RP

April 02002 Chuck DiMarzio, Northeastern University 10100-4-17

Device ApplicationsDevice

Inputin Eigenvectorsof Device

Output

EndViews

April 02002 Chuck DiMarzio, Northeastern University 10100-4-18

Wire Grid Polarizers

April 02002 Chuck DiMarzio, Northeastern University 10100-4-19

Polaroid H Sheets

April 02002 Chuck DiMarzio, Northeastern University 10100-4-20

Waveplates (1)

April 02002 Chuck DiMarzio, Northeastern University 10100-4-21

Waveplates (2)

April 02002 Chuck DiMarzio, Northeastern University 10100-4-22

E/O Modulator

eiV/V

e-iV/V

April 02002 Chuck DiMarzio, Northeastern University 10100-4-23

Optical ActivityDevice

April 02002 Chuck DiMarzio, Northeastern University 10100-4-24

Fresnel Rhomb

0 20 40 60 80 100-200

-150

-100

-50

0

50

100

150

200Fresnel Reflection: Glass, n=1.5, to Air

q, Angle, Degrees

Ph

ase,

Deg

rees

RSRP

45 Deg

• Functions as QWP– True Phase Shift rather

than Time Delay

– Broadband: Limited only by material Dispersion