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
How to Make Microwaves
• Magnetron
• Oldest, still used in microwave ovens
• Accelerates charges in a magnetic field
Klystron
•Smaller and lighter than Magnetron
•Creates oscillations by bunching
electrons
Gunn Diode
•Solid State Microwave Emitter
•Drives a cavity using negative resistance
Equipment Used
receiver
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
20
2
R = 0.9887
Distance (9 inch tiles)
18
16
14
12
10
8
6
4
2
0
0
0.2
0.4
0.6
0.8
1/sqrt(Intensity)
1
1.2
1.4
Reflection
qI qR
• Angle of incidence
equals angle of
reflection
Angle of Incidence v. Angle of Reflection
Angle of Reflection (degrees)
350
300
250
200
150
100
50
0
280
290
300
310
320
Angle of Incidence (degrees)
330
340
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 = 179o
Empty prism – max = 177o
Empty prism absorbs only small
amount
• Prism w/ pellets – max = 173o
• Measured angles of prism w/
protractor
 q1 = 22 +/- 1o
 q2 = 28 +/- 2o
– Used these to determine n for
pellets
• n = 1.25 +/- 0.1
Polarization
Polarization
Intensity (mA) at 30x
0.5
0.4
0.3
0.2
Series1
0.1
0
-0.1
0
100
200
300
400
Angle of receiver (deg.)
• 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
d sin q  n
This equation assumes that we are near the
Fraunhofer (far-field) limit
Single Slit Diffraction – 7cm
q1  24.4
Single Slit Diffraction - 7 cm
o
q 2  55.66
18
o
16
14
Not in the
Fraunhofer limit,
so actual minima
are a few degrees
off from expected
minima
Intensity
12
10
8
6
4
2
0
0
10
20
30
40
50
Angle (degrees)
60
70
80
90
Single Slit Diffraction – 13cm
q1  12.8
o
6
o
5
4
Intensity
q 2  26.4
Single Slit Diffraction - 13 cm
3
2
1
0
0
10
20
30
40
50
Angle (degrees)
60
70
80
90
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
Mirror
Extension
S
Intensity (V)
Double Slit Interference (d=.09m)
5
4
3
2
1
0
0
20
40
60
Angle of Reciever (deg.)
80
100
Lloyd’s Mirror
• 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
Condition for Maximum:
n
d  h  d1 
2
2
1
2
Trial 1
Trial 2
• D1= 50 cm
• H1=7.5 cm
• H2= 13.6 cm
• D1= 45 cm
• H1=6.5 cm
• H2= 12.3 cm
= 2.52 cm
= 2.36 cm
Fabry-Perot Interferometer
• Incident light on a pair of partial reflectors
• Electromagnetic waves in phase if:
2d cos  m
•In Pasco experiment, alpha(incident angle) was 0.
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
Michelson Interferometer
• Studies interference between two split beams that are brought
back together.
Michelson Interferometer
Constructive Interference occurs when:
2 Lm  L f  n
Michelson Interferometer
– 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
reflectors
S
M
• 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
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
S polarization
• Using Maxwell’s
Equations (1 = 2 =1)
Er  sin(q  q )

Ei
sin(q  q )
Et 2 sin q  cos q

Ei
sin(q  q )
Transverse Electric Case at
oblique incidence
NO BREWSTER’S ANGLE
TM Case
• Electric Field Parallel to
Boundary
P polarization
• Using Maxwell’s
Equations (1 = 2 =1)
Er tan(q  q )

Et tan(q  q )
Et
2sin q  cos q

Et sin(q  q ) cos(q  q )
Transverse Magnetic Case at
oblique incidence
Brewster’s Angle
• Plotting reflection and transmission(for reasonable n1 and
n2)
Brewster’s Angle (our results)
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.
Brewster's Angle
6
5
Intensity
4
Horizontal
3
Vertical
2
1
0
0
10
20
30
40
50
Angle (degrees)
60
70
80
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).
Condition for constructive interference
2d sin q  n
Bragg Diffraction (Pasco)
Bragg Diffraction [100] Symmetry
3.5
Intensity (V)
3
2.5
2
1.5
1
0.5
0
0
10
20
Grazing Angle (deg.)
30
40
Bragg Diffraction(Unilab)
• Maxima
Obtained
q1  20.0

q

21
.
2
Maxima 1
Predicted q  46.3
2

q 2  45.0
Wax lenses were used to collimate the beam
Unilab Bragg Diffraction
Meter Reading (mV)
70
60
50
40
30
20
10
0
0
10
20
30
Angle(Degrees)
40
50
60
Frustrated Total Internal Reflection
• Two prisms filled with
oil
Transmitter
• Air in between
• Study of transmittance
with prism separation
• Presence of second prism
“disturbs” total internal
reflection.
Detector
Frustrated Total Internal Reflection
Frustrated Total Internal Reflection
30
25
Intensity
20
15
10
5
0
0
0.5
1
1.5
Prism Separation (cm)
2
2.5
3
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 –25o
• Black block (left-handed
springs) rotates
polarization 25o
References
•
•
•
•
www.joecartoon.com
www.mathworld.wolfram.com
www.hyperphysics.phy-astr.gsu.edu/hbase
www.pha.jhu.edu/~broholm/I30/node5.html