Optical Phase Conjugation

April 15, 2007 · 4 Comments

I just posted about superconducting effects in nanoscale systems, and in particular, the phenomenon of Andreev reflection, and I forgot to mention something cool I came across a while back that I recently re-read: this paper by Carlo Beenakker (although it’s listed on arxiv, the pdf doesn’t seem to be of the actual paper; I read it in chapter 4 of this excellent book on mesoscopic physics, although some googling brings up a full pdf version here, which may or may not last.) Beenakker uses “the analogy between Andreev reflection and optical phase-conjugation to answer the question: why does a metal-superconductor junction have a resistance?” Apart from being a very clear and interesting way of looking at this process, the paper’s particularly relevant to me since we recently covered optical phase conjugation (by ‘degenerate’ four-wave mixing) in my modern optics class.

Simplistically, phase conjugation is a nonlinear process by which an electromagnetic wave $E_{0} cos(kx - \omega t)$ is reflected as $E_{0} cos(-kx - \omega t)$ (or alternatively $E_{0} cos(kx + \omega t)$ , which is why it is often referred to as being a time-reversal process). This is analogous to Andreev reflection for a number of reasons (the ‘pump’ photons in the four-wave mixing process are like Cooper pairs, the pump frequency is like the Fermi energy, and the excitation energy corresponds to the frequency difference between the pump beams and the incident ‘probe’ beam). If the analogy did fully hold, one would expect the normal metal to be disorder/resistance-free, just as a disordered medium appears transparent when back by a phase-conjugated medium - the phase-conjugated light gets rid of aberrations due to inhomogeneities. The point is that the analogy fails because of the extra phase shifts involved in Andreev reflection processes, which explains in a sense why normal metal-superconductor junctions aren’t fully transparent. I’m not sure if there’s any more explanatory power that can be extracted from this analogy, but it’s definitely a cool way of tying together these two processes.

References:
- Where I first learned about optical phase conjugation: section 7.2 of R. W. Boyd, Nonlinear Optics 2nd ed. (Elsevier, 2003).
- The original four-wave mixing phase conjugation paper: A. Yariv and D. M. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing“, Optics Letters 1 16 (1977).

Categories: Condensed Matter Physics · Interdisciplinary · Nanoscale Science · Papers · Photonics · Physics · Superconductivity

4 responses so far ↓

Optical Phase Conjugation « Perfectly Reasonable Deviations // April 17, 2007 at 12:37 pm

[...] Phase Conjugation Sujit Datta recently wrote a very cool post on optical phase conjugation. A couple of years ago, I wrote my [...]
David M. Pepper // April 23, 2007 at 11:20 am

I came across your blog when I Googled myself and it reminded me of some thoughts I had about phase conjugation of matter waves when I wrote the Scientific American artilce on the same in January 1986. Toward the end of the article, I pondered about what other fields can be wavefront-reversed other than light. I cited other E-M fields, such as microwaves, as well as phonons, etc. I then speculated about Boson-like “matter waves” such as elementary particles, and, perhaps, superconductivity and superfluidity. Without being aware of Andreev Scattering, I postulated that, perhaps, Cooper Pairs may be a suitable candidate (by the way, I made an error that Cooper Pairs were e-/e+ quasi-particles…of course, they are paired-electron or paired-hole quasi-particles!). I then received a letter from a reader correcting me about my error, as well as pointing out the existence of Andreev Scattering, that dated back prior to optical phase conjugation (I was humbled…). In my seminars on the field, I have since discussed (very briefly, since I am a laser-type and not a solid-state type) the notion of Andreev Scattering. From a very hand-waving perspective, it is interesting to note that Andreev Scattering has some interesting phase-conjugate properties: if one looks at ALL the effective quantum numbers, one can look at ideal phase conjugation as reversing all fundamental properties of the particle — namely, photon spin (or, Helicity), and photon momentum (k-vector). Andreev Scattering goes one step further: it also reverses the effective charge, since an incident electron wave will be “phase conjugated” by Andreev Scattering to produce a hole that propagates in the reverse direction (changing the sign of the k-vector, as is the case with photons). And, to conserve energy, momentum and effective charge, a Cooper pair is generated in the forward direction! (In an ideal optical PCM, a PAIR of photons are generated in the forward direction…). One can also ask interesting questions (exercise to the reader!) regarding comparing radiation pressure at a perfect mirror surface vs an indeal phase-conjugate mirror, PCM. Also, one can ask about the properties of a “phase-conjugate resonator” consisting of opposing Andreev-scattering surfaces — and compare this to an optical resonator, consisting of an optical cavity bound my one or two PCMs.

Best of luck in your studies!

With regards,
David M. Pepper.
Jason Ning // June 23, 2007 at 11:19 pm

Very nice blog!
Dr. William J. Stachnik // May 14, 2008 at 3:35 pm

Just passing through … I supported David’s work 10+ years ago. The ability to turn light back upon itself is a process rich with valuable applications. I wanted to determine what his current interests were in OPC.

metadatta.