1. PHYS 408 Applied Optics (Lecture 13)
Jan-April 2016 Edition
Jeff Young
AMPEL Rm 113

2. Midterm Survey
12 responses before midterm, 10 post midterm, no major differences:
- The good: generally happy with lecture format, with activities, emphasis on concepts, and practical examples
- The not so good: most concern over homework being hard and long and perceived as not useful; pre-reading doesn’t necessarily help with concepts; some requests for more clearly articulated questions, and more details in posted lecture slides; use data cam instead of board; cover stuff in lecture directly related to solving homework problems
- Self analysis: largely that should spend more time doing pre-reading and getting to class, and starting homework earlier
- Peer analysis: wake up and participate more
- Workload: hr/wk
- TA assistance (lecture and labs); generally positive

3. Discuss My analysis of results Possible changes:
A) Can use data cam if you prefer (test drive and vote?)
B) Make sure we reiterate explain clearly what the question is asking for in lectures
C) Pre-reading: encourage you to just Google or Wikipedia the general topic that is going to be covered?
D) Be more clear in homework question expectations.
Prefer not to change:
E) more math and homework related content in lectures (that is what the help sessions are for, and hardly anyone is showing up)
F) I have been adding more notes to the lecture slides…can add more, but also want to encourage note- taking and attendance….?
G) Note sure about homework: a large part of what you will be expected to do in a job involves analysis and numerical solution of problems….quantity is less than in previous years…

4. Quick review of key points from last lecture
Gaussian beams have various mathematical representations, but fundamentally are characterized by only two independent parameters.
Can choose the independent parameters from (R(z), w(z), z0, w0, l, etc.), but once you know those two independent parameters, you can define the Gaussian function everywhere in space.
The radius of curvature of the Gaussian wavefronts is infinite at z=0 and z=+ infinity and – infinity, and is a minimum (most curved) at z= z0, where z0 is the Rayleigh length.
They are only useful in practice for paraxial beams that do not diverge “too much”

5. The q parameterization

6. The real and imaginary parts of 1/q
What are R and w at z=z_0?
If you knew R and W at some z value, do you know everything about the beam, everywhere else?
Must be yes since only two parameters…algorithm for finding lambda and z_0? (only unknown in q(z), since know z R and w, is lambda…solve for lambda, use imaginary part of q to get z_0

7. Follow q through a paraxial optical system

8. The ABCD Matrix: Ray Optics
Fundamentally based on Fermat’s Principle, which is?

9. Fermat’s Principle
Sketch refraction example…Fermat’s principle used to “derive” reflection and refraction angles, of “rays”, then more complicated geometrical surfaces are dealt with using the rays.

10. Examples
Sketch how Fermat’s principle would be used to get the refraction angle

11. Examples
Tell them to work out the single interface themselves at home, but give it, and the free space propagation Matrix, derive the thin lens result in class.

12. Examples

13. 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

14. 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?