2003SP_MicrowaveOptics - The University of Oklahoma ...

daughterduckUrban and Civil

Nov 15, 2013 (3 years and 10 months ago)

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Microwave Optics

Adam Parry

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


Used in radar detection


Percy Spencer tested the magnetron at
Raytheon


Noticed that it melted his candy bar


Also tested with popcorn


Designed metal box to contain


microwaves


Radar Range


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

receiver

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


B) Transmitter and receiver


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
Angle of receiver (deg.)
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


Receiver


Path 2: Reflects off C to B


through C


Receiver


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)
Meter Reading (mV)


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