Microwave Optics Adam Parry Mark Curtis Sam Meek

Microwave Optics Adam Parry Mark Curtis Sam Meek Santosh Shah Acknowledgements: Fred, Geoff, Lise and Phil Junior Lab 2002

History of Microwave Optics • WW 2 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

Reflection S • Angle of incidence equals angle of reflection q. I q. R M

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. 12 cm • Traversed 10 antinodes • Final probe pos: 32. 02 cm • = 2*(46. 12 -32. 02)/10 • = 2. 82 cm – Method B: • Initial T pos: 20 cm • Initial R pos: 68. 15 cm • Traversed 10 minima • Final R pos: 53. 7 cm • = 2. 89 cm

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

Single Slit Diffraction – 13 cm

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 M

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: Trial 1 Trial 2 • D 1= 50 cm • H 1=7. 5 cm • H 2= 13. 6 cm • D 1= 45 cm • H 1=6. 5 cm • H 2= 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: • In Pasco experiment, alpha(incident angle) was 0.

Fabry-Perot Interferometer • d 1 = distance between reflectors for max reading – d 1 = 31 cm • d 2 = distance between reflectors after 10 minima traversed – d 2 = 45. 5 cm • lambda = 2*(d 2 – d 1)/10 = 2. 9 cm • Repeated the process – d 1 = 39 cm – d 2 = 25 cm – lambda = 2. 8 cm

Michelson Interferometer • Studies interference between two split beams that are brought back together.

Michelson Interferometer Constructive Interference occurs when:

Michelson Interferometer – X 1 = A pos for max reading = 46. 5 cm – X 2 = A pos after moving away from PR 10 minima = 32. 5 cm – Same equation for lambda is used – Lambda = 2. 8 cm 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) 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) Transverse Magnetic Case at oblique incidence

Brewster’s Angle • Plotting reflection and transmission(for reasonable n 1 and n 2)

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.

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

Bragg Diffraction (Pasco)

Bragg Diffraction(Unilab) • Maxima Obtained Maxima Predicted Wax lenses were used to collimate the beam

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

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/I 30/node 5. html