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Trivia Question
Where is the largest laser system in the world?
(a) Andrews Air Force Base
(b) USS Enterprise
(c) Area 51, located in ????
(d) Sandia National Lab, New Mexico
(e) Lawrence Livermore National Lab, California
Trivia Question
Where is the largest laser system in the world?
(e) Lawrence Livermore National Lab, California
National Ignition Facility (NIF) – is a quest for clean
fusion energy. Pellets of hydrogen of fused using intense
laser pulses.
July 5th, 2012: 192 laser beams delivered 1.85MJ and
500 trillion watts of power (short time period). 1000
times more power than used by US at any instant of
time.
Trivia Question
Where is the largest laser system in the world?
(e) Lawrence Livermore National Lab, California
National Ignition Facility (NIF) – is a quest for clean
fusion energy. Pellets of hydrogen of fused using intense
laser pulses.
July 5th, 2012: 192 laser beams delivered 1.85MJ and
500 trillion watts of power (short time period). 1000
times more power than used by US at any instant of
time.
An arbitrary function f(t) as a sum of
harmonic functions
A spatial function f(x,y) as a sum of harmonic
spatial functions.
Principle of Fourier Optics: Arbitrary
wave in free space can be analyzed as
a superposition of plane waves
Spatial Spectral Analysis
Spatial spectral component in the x direction deflects the beam upward (or
downward). NOTE: the ‘optical element’ is only changing the PHASE of the plane
wave similar to the analysis in chapter 2.
Effect of thin optic element on plane
wave
Optical interconnects
Imagine each ‘pixel’ on the left is covering an optical fiber. The phase gratings
can be used to ‘route’ the optical signals to another set of optical fibers by
deflecting the beams using the phase gratings.
Scanning
Fresnel Lens
Spatially varying
phase structure
Developed by Fresnel for
lighthouses.
Fresnel ZONE plate
Transfer Function of Free Space
• The wave is INPUT at z=0 with an input wave f(x,y)=U(x,y,0).
• The wave propagates through a distance d.
• The output wave at z=d is given by g(x,y)=U(x,y,d).
The Big Picture: we are developing the mathematical formalism to describe what
happens when you send waves through RESTRICTED openings (ie. diffraction).
Transfer Function
kz  k  kx  k y
2
2
2
2
Huygen’s Principle
Break up wavefront into an infinite number of point
sources (ie. spherical waves). New wavefront is SUM
of these infinite number of point sources. New
wavefront becomes tangent to spherical wavefronts.
Functions and their Fourier transforms
Far Field of Fraunhofer appoximation
d
Use a Lens to spatially Fourier
Transform an Input wave
Note: Incoming wave can be thought of as a sum of plane waves. Each plane wave
comes to focus at a different point in the focal plane. Each point in the focal plane
corresponds to a unique  x and  y combination.