1. PHYS 408 Applied Optics (Lecture 14)
Jan-April 2016 Edition
Jeff Young
AMPEL Rm 113

2. Quiz #7
The ABCD matrix is the same as the M matrix used to analyze thin films: T/F
The Gaussian q parameter is a function of z: T/F
The ABCD matrix associated with propagation in a uniform medium over a distance d changes the z0 value of a Gaussian input beam: T/F
I did my homework and derived the ABCD matrix for a curved interface between two dielectrics: T/F

3. 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 matrices 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.

4. 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

5. Gaussian Example #2 (effect of a thin lens)
From the sketch, what are q1 and 1/ q1 at entrance to lens?
What is the relevant ABCD matrix to propagate just through the lens?
See handwritten notes: emphasize that now dealing with the transformation between two distinct Gaussian beams (through the lens). Extend both with red pen
What are q2 and 1/ q2 just after the lens?

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

7. Resonators/Cavities
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.