# 2003SP_MicrowaveOptics - The University of Oklahoma ...

Urban and Civil

Nov 15, 2013 (4 years and 7 months ago)

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Microwave Optics

Mark Curtis

Sam Meek

Santosh Shah

Acknowledgements:

Fred, Geoff, Lise and Phil

Junior Lab 2002

History of Microwave Optics

WW2 in England Sir John Randall and Dr.
H. A. Boot developed magnetron

Produced microwaves

Percy Spencer tested the magnetron at
Raytheon

Noticed that it melted his candy bar

Also tested with popcorn

Designed metal box to contain

microwaves

First home model
-

\$1295

Magnetron

Oldest, still used in microwave ovens

Accelerates charges in a magnetic field

Klystron

Smaller and lighter than Magnetron

Creates oscillations by bunching
electrons

How to Make Microwaves

Gunn Diode

Solid State Microwave Emitter

Drives a cavity using negative resistance

Equipment Used

transmitter

Intensity vs. Distance

Shows that the intensity is related to the inverse square of the

distance between the transmitter and the receiver

Distance v. Intensity
R
2
= 0.9887
0
2
4
6
8
10
12
14
16
18
20
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1/sqrt(Intensity)
Distance (9 inch tiles)
Reflection

Angle of incidence
equals angle of
reflection

q
I

q
R

Angle of Incidence v. Angle of Reflection
0
50
100
150
200
250
300
350
280
290
300
310
320
330
340
Angle of Incidence (degrees)
Angle of Reflection (degrees)
Measuring Wavelengths of Standing Waves

Two methods were used

A) Transmitter and probe

Our data

Method A:

Initial probe pos: 46.12cm

Traversed 10 antinodes

Final probe pos: 32.02cm

= 2*(46.12
-
32.02)/10

= 2.82cm

Method B:

Initial T pos: 20cm

Initial R pos: 68.15cm

Traversed 10 minima

Final R pos: 53.7cm

= 2.89cm

Refraction Through a Prism

Used wax lens to collimate beam

No prism

max = 179
o

Empty prism

max = 177
o

Empty prism absorbs only small
amount

Prism w/ pellets

max = 173
o

Measured angles of prism w/
protractor

q
1

= 22 +/
-

1
o

q
2

= 28 +/
-

2
o

Used these to determine n for
pellets

n = 1.25 +/
-

0.1

Polarization

Polarization
-0.1
0
0.1
0.2
0.3
0.4
0.5
0
100
200
300
400
Intensity (mA) at 30x
Series1

Microwaves used are vertically polarized

Intensity depends on angle of receiver

Vertical and horizontal slats block parallel
components of electric field

Single Slit Interference

Used 7 cm and 13 cm slit widths

This equation assumes that we are near the
Fraunhofer (far
-
field) limit

q
n
d

sin
Single Slit Diffraction

7cm

Single Slit Diffraction - 7 cm
0
2
4
6
8
10
12
14
16
18
0
10
20
30
40
50
60
70
80
90
Angle (degrees)
Intensity
o
o
66
.
55
4
.
24
2
1

q
q
Not in the
Fraunhofer limit,
so actual minima
are a few degrees
off from expected
minima

Single Slit Diffraction

13cm

o
o
4
.
26
8
.
12
2
1

q
q
Single Slit Diffraction - 13 cm
0
1
2
3
4
5
6
0
10
20
30
40
50
60
70
80
90
Angle (degrees)
Intensity
Double Slit Diffraction

Diffraction pattern due to the interference of waves from

a double slit

Intensity decreases with distance y

Minima occur at d sinθ = mλ

Maxima occur at d sinθ = (m + .5) λ

Double Slit Diffraction

Double Slit Interference (d=.09m)
0
1
2
3
4
5
0
20
40
60
80
100
Angle of Reciever (deg.)
Intensity (V)
Mirror

Extension

S

Interferometer

One
portion of wave travels in
one path, the other in a
different path

Reflector reflects part of
the wave, the other part is
transmitted straight
through
.

Lloyd’s Mirror

Lloyd’s Mirror

D
1
= 50 cm

H
1
=7.5 cm

H
2
= 13.6 cm

= 2.52 cm

2 2
1 1
2
n
d h d

  
Condition for Maximum:

D
1
= 45 cm

H
1
=6.5 cm

H
2
= 12.3 cm

= 2.36 cm

Trial 1

Trial 2

Fabry
-
Perot Interferometer

Incident light on a pair of partial reflectors

Electromagnetic waves in phase if:

In Pasco experiment, alpha(incident angle) was 0.

m
d

cos
2
Fabry
-
Perot Interferometer

d1 = distance between reflectors for max reading

d1 = 31cm

d2 = distance between reflectors after 10 minima traversed

d2 = 45.5cm

lambda = 2*(d2

d1)/10 = 2.9cm

Repeated the process

d1 = 39cm

d2 = 25cm

lambda = 2.8cm

Studies interference between two split beams that are brought

back together.

Michelson Interferometer

Michelson Interferometer

Constructive Interference occurs when:

n
L
L
f
m

2
Michelson Interferometer

Split a single wave into two parts

Brought back together to create
interference pattern

A,B

reflectors

C

partial reflector

Path 1: through C

reflects off A
back to C

Path 2: Reflects off C to B

through C

Same basic idea as Fabry
-
Perot

X1 = A pos for max reading = 46.5cm

X2 = A pos after moving away from
PR 10 minima = 32.5cm

Same equation for lambda is used

Lambda = 2.8cm

S

M

reflectors

Brewster’s Angle

Angle at which wave incident upon dielectric
medium is completely transmitted

Two Cases

Transverse Electric

Transverse Magnetic

Equipment

Setup

TE Case

Electric Field
transverse to boundary

Using Maxwell’s
Equations (

1
=

2

=1)

Transverse Electric Case at

oblique incidence

sin( )
sin( )
2sin cos
sin( )
r
i
t
i
E
E
E
E
q q
q q
q q
q q

 

NO BREWSTER’S ANGLE

S polarization

Electric Field Parallel to
Boundary

Using Maxwell’s
Equations (

1
=

2

=1)

Transverse Magnetic Case at

oblique incidence

P polarization

tan( )
tan( )
2sin cos
sin( ) cos( )
r
t
t
t
E
E
E
E
q q
q q
q q
q q q q

 
 
TM Case

Plotting reflection and transmission(for reasonable n
1

and
n
2
)

Brewster’s Angle

Brewster’s Angle (our results)

Brewster's Angle
0
1
2
3
4
5
6
0
10
20
30
40
50
60
70
80
Angle (degrees)
Intensity
Horizontal
Vertical
Setting the T and R for vertical polarization, we found the maximum

reflection for several angles of incident.

We then did the same for the horizontal polarization and plotted

I vs. theta

We were unable to detect Brewster’s Angle in our experiment.

Bragg Diffraction

Study of Interference patterns
of microwave transmissions in
a crystal

Two Experiments

Pasco ( d = 0.4 cm, λ = 2.85 cm)

Unilab (d = 4 cm, λ = 2.85 cm).

q
n
d

sin
2
Condition for constructive interference

Bragg Diffraction (Pasco)

Bragg Diffraction [100] Symmetry
0
0.5
1
1.5
2
2.5
3
3.5
0
10
20
30
40
Grazing Angle (deg.)
Intensity (V)
Bragg Diffraction(Unilab)

Maxima
Obtained

Unilab Bragg Diffraction
0
10
20
30
40
50
60
70
0
10
20
30
40
50
60
Angle(Degrees)

0
.
45
0
.
20
2
1

q
q

3
.
46
2
.
21
2
1

q
q
Maxima

Predicted

Wax lenses were used to collimate the beam

Frustrated Total Internal Reflection

Two prisms filled with
oil

Air in between

Study of transmittance
with prism separation

Presence of second prism
“disturbs” total internal
reflection.

Transmitter

Detector

Frustrated Total Internal Reflection

Frustrated Total Internal Reflection
0
5
10
15
20
25
30
0
0.5
1
1.5
2
2.5
3
Prism Separation (cm)
Intensity
Optical Activity Analogue

E
-
field induces current in
springs

Current is rotated by the
curve of the springs

E
-
field reemitted at a
different polarization

Red block (right
-
handed
springs) rotates
polarization

25
o

Black block (left
-
handed
springs) rotates
polarization 25
o

References

www.joecartoon.com

www.mathworld.wolfram.com

www.hyperphysics.phy
-
astr.gsu.edu/hbase

www.pha.jhu.edu/~broholm/I30/node5.html