Microwave OpticsAdam 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. DistanceShows that the intensity is related to the inverse square of the distance between the transmitter and the receiver

Distance v. Intensity

R2 = 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)

Dis

tan

ce (

9 in

ch

tiles)

Reflection

• Angle of incidence equals angle of reflection

MS

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)

Ang

le o

f Ref

lect

ion

(deg

rees

)

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 1 = 22 +/- 1o

2 = 28 +/- 2o

– Used these to determine n for pellets

• n = 1.25 +/- 0.1

Polarization

• Orientation of E field

• Polarizer blocks components perpendicular to its alignment

• Polarizer reduces intensity of light

PolarizationPolarization

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 100 200 300 400

Angle of receiver (deg.)

Inte

nsit

y (

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 InterferenceUsed 7 cm and 13 cm slit widths

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

nd sin

Single Slit Diffraction – 7cmSingle 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)

Inte

nsi

ty

o

o

66.55

4.24

2

1

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

Single Slit Diffraction - 13 cm

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80 90

Angle (degrees)

Inte

nsity

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)

012345

0 20 40 60 80 100

Angle of Reciever (deg.)

Inte

nsi

ty (V

)

MirrorExtension

S

M

• 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

• D1= 50 cm

• H1=7.5 cm

• H2= 13.6 cm

= 2.52 cm

2 21 1 2

nd h d

Condition for Maximum:

• D1= 45 cm

• H1=6.5 cm

• H2= 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.

md cos2

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:

nLL fm 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

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

TM Case

• Plotting reflection and transmission(for reasonable n1 and n2)

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)

Inte

nsi

ty

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. thetaWe 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).

nd sin2

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.)

Inte

ns

ity

(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)

Mete

r R

ead

ing

(m

V)

0.45

0.20

2

1

3.46

2.21

2

1

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)

Inte

nsi

ty

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