Adam Parry Mark Curtis Sam Meek Santosh Shah 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

Reflection M S qI qR Angle of incidence equals angle of reflection

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 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

Single Slit Diffraction – 13cm

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 D1= 50 cm H1=7.5 cm H2= 13.6 cm = 2.52 cm D1= 45 cm Condition for Maximum: Trial 1 Trial 2 D1= 50 cm H1=7.5 cm H2= 13.6 cm = 2.52 cm 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:

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

Transverse Electric Case at 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

Transverse Magnetic Case at TM Case Electric Field Parallel to Boundary Using Maxwell’s Equations (1 = 2 =1) P polarization 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.

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 Air in between Study of transmittance with prism separation Presence of second prism “disturbs” total internal reflection. Transmitter 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 –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