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

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

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.

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.

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?

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

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

Free spectral range and allowed mode frequencies

Modified Gaussian Modes (Hermite- Gaussian)

Hermite-Gaussian beams (con’t)

Finally

Intensity distributions

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

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)