PHYS 408 Applied Optics (Lecture 18) Jan-April 2016 Edition Jeff Young AMPEL Rm 113

Quiz #9 The Finesse of a resonator has units of frequency: T/F The ratio of the internal field intensity to the incident field intensity when a resonator cavity mode is excited on resonance is proportional to the square of the Finesse: T/F The full width at half maximum of a resonator transmission peak is directly proportional to the inverse cavity lifetime: i.e. DnFWHM=constant * 1/tp: T/F The proportionality constant in 3. is 2p: T/F

Quick review of key points from last lecture The Fabry-Perot cavity transmission function is useful for identifying important parameters that characterize real-life cavities. The two main parameters are the cavity Finesse, and the Free Spectral Range. These are sufficient for a symmetric cavity, but if not symmetric, the maximum on-resonance transmission is also needed. All of these parameters are related to the two mirror reflectivities and the length of the cavity. Going to a Gaussian, curved-mirror cavity, the absolute value of the transmission would only match the Fabry-Perot transmission if the excitation beam transverse profile was mode-matched to the Gaussian of interest, but the mode lifetimes and free spectral range are the same. There is also an offset of the absolute cavity resonance frequencies due to the (generalized) Gouy phase.

Physical interpretation(s) of Finesse What are the two most intuitive/important physical interpretations of the Finesse of a quasi-mode? Cavity lifetime Internal intensity enhancement

Key relations for high-finesse cavities Sketch the incident and internal field profiles on resonance, and half way between resonances

Extrinsic sources of loss Finite mirror size No longer a Gaussian, how will it propagate? Know how Gaussians propagate, know how plane and spherical waves propagate, what about a more general field structure?

Fourier Optics: empirical approach Dx d Propagation through a slit a very similar problem…

What does this suggest? Why does this sort of make sense, based on what we know about plane waves? Hint: what is a good guess for what the electric field distribution is in the plane of the slit? Want a functional form, E(x). Pause, let them work on it

? Analyze kx x Eslit -Dx/2 Dx/2 Dx/2 -Dx/2 ? Let them work on it, emphasize what the argument is

? So have: x kx d Eslit Dx Dx/2 -Dx/2 x Dx/2 -Dx/2 x kx ? What seems to be happening here? How can these be related? Spend awhile on this…see if they can get to relating to 3D plane waves and association of kx/omega with a direction. Don’t forget pi in definition of sinc! Relate this to expansion in terms of plane waves