1. PHYS 408 Applied Optics (Lecture 16) JAN-APRIL 2016 EDITION JEFF YOUNG AMPEL RM 113

2. Quiz #8 1.The cavity stability criterion is distinct from the criterion for determining actual resonator modes: T/F 2.The ABCD matrix element transformation of a Gaussian beam can be used to prove that a mirror with radius of curvature equal to that of a Gaussian mode at a certain location, will reflect that Gaussian exactly back on itself: T/F 3.A spherical wave has a well defined wave vector k: T/F 4.I would have done better on the midterm if I had reviewed and understood all of the preceding lecture material: T/F

3. Quick review of key points from last lecture The stability criterion for curved-mirror cavities is less stringent than the criterion for the cavity to actually support a resonant mode(s). Either ray optics or Gaussian beam optics, both involving the ABCD matrix elements, can be used to derive the cavity stability criterion. Simple ABCD q conversion can be used to easily show that a curved mirror with a radius of curvature matching a Gaussian mode’s curvature at some location, will reflect that Gaussian into a counter-propagating version of exactly the same Gaussian.

4. A unique Gaussian is “supported” or “conserved” by two mirrors of radii R 1 and R 2 separated by a distance d. It may or may not be stable.

5. Review up to here: Given R 1 and R 2, can solve for range of d’s where there can be a stable cavity using the stability criterion For a given d, figure out “the Gaussian” for which the radius of curvatures a distance d apart are equal to R 1 and R 2 (see homework #4) one approach is to use q=(Aq+B)/Cq+D) where ABCD correspond to a “round trip” ABCD matrix for the cavity. Solve for q at some z position (say one of the two mirror positions) in terms of the round trip ABCD matrix elements another approach is to use fact that know R(z 1m )=R 1 and R(z 2m )=-R 2, and these two values can be used to solve for q(z) Next?

6. Additional criterion for actual modes What is the additional criterion? What is  (z) for our Gaussian beam?

7. Mode criterion What is q and where does it come from? Do any of these terms depend on the curvature of the mirrors?

8. Free spectral range and allowed mode frequencies

9. Modified Gaussian Modes (Hermite- Gaussian)

10. Hermite-Gaussian beams (con’t)

11. Finally

12. Intensity distributions

13. Impact on Free Spectral Range and Allowed Mode Frequencies?  F  Recognize this if you have done the cavity lab?  F 

14. Real cavities What is the lifetime of all these modes we have solved for so far? Answer: Infinite…as per the definition of a mode (recall?) What has been left out of all in all of this generic mode stability and phase criteria so far, when comparing to real physical systems? Answer: a)reflectivity of at least one of the mirrors must be <1 to allow one to use the modes (intrinsic, unitary) b)Material imperfections (scattering losses, absorption etc.) (extrinsic, non-unitary)