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### Microwave Optics

Acknowledgements:

Fred, Geoff, Lise and Phil

Junior Lab 2002

Adam Parry

Mark Curtis

Sam Meek

Santosh Shah

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

Intensity vs. Distance

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

distance between the transmitter and the receiver

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

- Method A:

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

- 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

Single Slit Diffraction – 7cm

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

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

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:

- D1= 50 cm
- H1=7.5 cm
- H2= 13.6 cm
= 2.52 cm

Trial 1

Trial 2

- D1= 45 cm
- H1=6.5 cm
- H2= 12.3 cm
= 2.36 cm

Fabry-Perot Interferometer

- Incident light on a pair of partial reflectors
- Electromagnetic waves in phase if:
- 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:

S

M

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

Brewster’s Angle

- Angle at which wave incident upon dielectric medium is completely transmitted
- Two Cases
- Transverse Electric
- Transverse Magnetic

Equipment

Setup

TE Case

S polarization

- Electric Field transverse to boundary
- Using Maxwell’s Equations (1 = 2 =1)

Transverse Electric Case at

oblique incidence

NO BREWSTER’S ANGLE

TM Case

P polarization

- Electric Field Parallel to Boundary
- Using Maxwell’s Equations (1 = 2 =1)

Transverse Magnetic Case at

oblique incidence

Brewster’s Angle

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

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 (our results)Bragg Diffraction maximum

- 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

Bragg Diffraction (Pasco) maximum

Bragg Diffraction(Unilab) maximum

Maxima

Predicted

- Maxima Obtained

Wax lenses were used to collimate the beam

Frustrated Total Internal Reflection maximum

- Two prisms filled with oil
- Air in between
- Study of transmittance with prism separation
- Presence of second prism “disturbs” total internal reflection.

Transmitter

Detector

Optical Activity Analogue maximum

- 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 maximum

- www.joecartoon.com
- www.mathworld.wolfram.com
- www.hyperphysics.phy-astr.gsu.edu/hbase
- www.pha.jhu.edu/~broholm/I30/node5.html

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