I'm curious about the configuration of the reflected circularly polarised light for a half-wave plate on a mirror.
A half wave plate will flip the handedness of CP light (left -> right, or right -> left). Similarly, upon reflection from a mirror, CP handedness will also flip. So, if we imagine R incidence, if a half wave plate is atop a mirror, will the CP light be flipped at the bottom of the HWP (becomes L), then flipped by mirror (becomes R again), then passes back through the HWP to be flipped again (so finally leaves as L). So R -> L or L-> R for a HWP/mirror configuration?
Theoretically, half wave plate provide a pi phase delay along the optical axis. in the optical system composed of HWP and mirror, the phase delay caused by HWP will be 2pi in the whole process, thus HWP can be treated as inexistence.So R -> L or L-> R for HWP/mirror configuration in accord with only mirror configuration.
However, half wave plate with 100% transmission effciency and pi phase delay is unpractical. if half wave plate also reflect the incident wave, the result will be different.
I hope my answer can help you.
Indeed putting a half wave plate in front of a mirror will lead to a phase shift of 2Pi which mainly reproduces the original beam.
The residual reflections on the anti-reflex coated surfaces of the wave-plate can be ignored if they show a different pointing than the main beam. This can be realized by tilting the plate in respect to the mirror.
The compensation of the two passes in the plate is only observable if the plate is precisely a half wave plate. This is only true for the layout wavelength. Using multi order plates the setup (in combination with a polarizer) can be used to coarsely set the laser intra cavity wave length.
Hi Mitchell --
That's a fun yet instructive optics problem, especially if you were to tack on minor tweaks to make other interesting scenarios -- some examples could include using a quarter-wave plate. launching elliptical polarization (like Ex=Ey&&phi!=pi/2 or Ex!=Ey&&phi=pi/2), tuning the axes of the wave plate to be at different angles than the semi-major and minor axes of the polarization ellipse (for elliptically-polarized light). or using a non-normal incidence angle where the phase shift is no longer the same for both polarization components.
There isn't much to add to what has already been said in confirming your line of thinking, so I'll just add one extra bit that only matters for situations involving very short pulses: when using waveplates with pulses containing only a few laser cycles, it's important to remember that a full-wave retardation (like in your scenario above) still constitutes a one-cycle delay (or multi-cycle integer delay, if using a multi-order half-wave plate) between the o-wave and the e-wave. If the pulse is, for example, only two cycles long, then the emerging o- and e-waves are no longer well-overlapped in time after being delayed by one cycle, so the effect is no longer null (as in the case with long-pulse/cw light, where a delay of a full 2pi is essentially negligible) and the polarization is time-varying.
Thanks for the good idea, ~Eric
Actually, I have discussed a similar but more complex system. I apply an HR and a PR coating to the quarter wave plate and use the Gires-Tournois interferometer as power scalable intra-cavity frequency-selective element.
https://www.spiedigitallibrary.org/proceedings/Download?urlId=10.1117%2F12.2289516
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