Newport Optics Junior Lab 2 Brady Longenbaugh Jamie Hegarty Will Keller Matt Meizlish Melanie Carter

Outline Review –Laser theory –Beam expansion –Interferometry Fourier Analysis –1D –Coherence length –2D Coherence –Time and length –Experiment –Results Diffraction –Theory –Experiment –Results w/ comparison Babinet’s Principle Conclusion

Review – Laser Theory Monochromatic? …not really frequency Reltive intensity Output of our laser has three harmonic modes – frequencies separated by quantity, where L is the length of the laser cavity Consecutive modes have perpendicular polarization polarization

__ Review – Beam Expansion Galilean beam expansion fefe fofo Keplerian beam expansion fefe fofo f e = eyepiece focal length f o = objective focal length Magnification = fofo fefe

Light from laser bounces off mirror then goes through a beam expander Beam bounces off another angled mirror then goes through half-silvered mirror Half-silvered mirror splits beam. Bounces off mirrors one and two Beams bounce off/pass through half-silvered mirror, hit target Different distances between mirrors and silvered mirror => interference Review - Interferometry

Fourier Transform(1D) We take our wavetrain and do a Fourier Transform on it and then get the power spectrum: We can use the power spectrum to give us the width of frequency distribution which leads to the line width which in turn gives us the coherence length

Fourier to Coherence Length Get a frequency distribution from the power spectrum We get the “line width” from the width of frequency distribution The coherence length is simply:

Fourier Transform in 2D Fourier Transform from aperture to new image plane

Fourier in 2D The basic equation for Fraunhofer Diffraction is given as: With the Aperture Equation given as: A few variable substitutions: Gives you the transformable form: With inverse:

Coherence – Time and Length Laser frequencies shift in and out of phase Coherence length, L, is distance between consecutive points of phase similarity Also, L is related to frequency difference Coherence time is that associated with this length lclc l c = T =

Coherence – Experiment Set up experiment as shown, with mirror 2 on sliding base Adjust one mirror until five interference fringes are visible on the card Start mirror 2 same dist. from half-silvered mirror as mirror 1 Move in 1 cm increments Move mirror around to find high/low contrast mirror 2 mirror 1

Coherence – Method I max - I min I max + I min ________ Contrast =

Coherence – Results Low Contrast vs. High Contrast Contrast: 9.62%Contrast: 57.04%

Diffraction – Results 1 row of dots 0.06mm spacing 0.08mm spacing 0.12mm spacing (cracked filter)

Diffraction – Results Multiple rows of dots –All 0.12mm x 0.08mm 1 row 2 rows 3 rows 4 rows

Diffraction – Results Random vs. Rectangular array (dots)

Diffraction – Results Angular arrays (60°)

Diffraction – Results Random array of Asterisks 0.05mm high 0.1mm high

Diffraction – Results Random array of “S” shapes 0.05mm high0.1mm high

Diffraction – Results Arrays of “A” shapes one row random rectangular array hexagonal array

Diffraction – Results Face vs. Side-centered lattice (dots) face-centeredside-centered

Diffraction – Results Random array – One vs. Two layers one layertwo layers

Diffraction – Results Hexagonal array – One vs. Two layers one layertwo layers

Diffraction – Results Rectangular array – One vs. Two layers one layertwo layers

Diffraction – Results Miscellaneous two layers rectangular 5° offset wire mesh random.: array

1. A screen with obstacles will produce the same diffraction pattern as a screen with holes of the same shape and size 2. If the two are overlapped, the resultant intensity is zero. Babinet’s Principle

Conclusion Review –Laser theory –Beam expansion –Interferometry Fourier Analysis –1D –Coherence length –2D Coherence –Time and length –Experiment –Results Diffraction –Theory –Experiment –Results w/ comparison Babinet’s Principle Conclusion

References Hecht, Optics 3 rd & 4 th ed. Newport, Projects in Optics Workbook Jenkins and White, Fundamentals of Optics Adobe Photoshop 6.0 Fowles, Intro to Modern Optics