1. 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

2. 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 5 th, 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.

3. 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 5 th, 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.

4. An arbitrary function f(t) as a sum of harmonic functions A spatial function f(x,y) as a sum of harmonic spatial functions.

5. Principle of Fourier Optics: Arbitrary wave in free space can be analyzed as a superposition of plane waves

7. 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.

8. Effect of thin optic element on plane wave

9. 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.

10. Scanning

11. Fresnel Lens Spatially varying phase structure Developed by Fresnel for lighthouses.

12. Fresnel ZONE plate

13. 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).

14. Transfer Function

15. 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.

16. Functions and their Fourier transforms

17. Far Field of Fraunhofer appoximation d

18. 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 and combination.