1. PHYS 408 Applied Optics (Lecture 20) JAN-APRIL 2016 EDITION JEFF YOUNG AMPEL RM 113

2. Quiz #10 1.If you reversed the direction of all the plane waves diffracting away from a slit, the intensity distribution of the resulting in-coming field in the plane of the slit would be a perfect top-hat function: T/F 2.The intensity distribution on a screen far away from an aperture illuminated by a monochromatic source is everywhere the square of the Fourier Transform of the aperture, regardless of the angle on the screen with respect to the optic axis (i.e. the Fourier Transform property holds regardless of whether the paraxial approximation is satisfied): T/F 3.Evanescent electric fields cannot be generated near an aperture because they can’t propagate: T/F 4.All of this diffraction stuff somehow explains why we can’t see individual atoms with our eyes: T/F

3. Quick review of key points from last lecture The key to diffraction is realizing that if you do a 2D Fourier Transform of the field distribution in some x-y plane, and assume that you can relate that to a forward, z-propagating overall field, then each of the 2D Fourier components, maps uniquely onto a 3D planewave propagating normal to the plane. The wavevector in the propagation direction of each of these 3D planewaves is given by, and the relative amplitudes of each of these 3D planewaves is given directly by the 2D Fourier amplitude of the corresponding in-plane component of the field in the aperture. In the paraxial limit (meaning that the sin or tan of the angle on some screen far from the aperture where the intensity of the diffracted field is significant, can be approximated as just the angle), each of these 3D plane waves, propagating at an angle

4. Today: Explaining the “magic” behind Gaussian beams

5. Gaussian beams and Fourier Optics What is the 2D Fourier Transform of our (0,0) Gaussian beam at the beam waist? Write the expression for the diffracted field for z>0 based on a 3D planewave decomposition at the beam waist. Using the paraxial approximation show that this diffracted field is exactly our generalized Gaussian beam!