1. PHYS 408 Applied Optics (Lecture 14)
Jan-April 2017 Edition
Jeff Young
AMPEL Rm 113

2. Quick review of key points from last lecture
ABCD matrices are reasonably easy to derive for individual optical elements (and propagation) based on a combination of Fermat’s principle and ray optics.
They can be used, for instance, to derive the focal length of a thin lens in terms of the refractive index of the glass and the radii of curvature of the surfaces.
One can transform either q(z) or 1/q(z) using the ABCD matrix elements (NOT DIRECT MATRIX MULTIPLICATION) in slightly different ways. Both can provide useful insight and/or efficient ways of understanding the effect of the optical element on a Gaussian beam.

3. Gaussian Example #1 (free space propagation)
Emphasize that this is a “single Gaussian” defined everywhere in space by two parameters, this just “propagates” the q or 1/q parameters

4. Gaussian Example #2 (effect of a thin lens)
Given a lens of known focal length f, what is of interest to calculate/know?
See handwritten notes: emphasize that now dealing with the transformation between two distinct Gaussian beams (through the lens). Extend both with red pen

5. And the answer is ….. z2 Interpret?
Focus off, radius of curvature at nominal focus, minimum spot size z2
Interpret?

6. Resonators/Cavities: Generalize
What is a resonator? Examples? From earlier in the course?
Fabry-Perot (plane mirrors)
Preface this change of topics with the fact we now have a bunch of tools that can be used to analyze resonators/cavities in more generality.