Magneto-Fluid Dynamics Seminar
Does a photon have a linear polarizability and why does it matter?
Speaker: Ilya Dodin, PPPL and Princeton University
Location: Warren Weaver Hall 905
Date: Tuesday, October 10, 2017, 11 a.m.
Synopsis:
A photon (phonon, plasmon, etc) has a linear polarizability. To see this and to understand why this matters, it helps to set aside Maxwell's equations and quantum mechanics per se and start with the following basic physics. Suppose a rapidly oscillating wave field in a weakly inhomogeneous linear medium. Assuming the dispersion operator for the wave field is known, a reduced operator can be defined that governs just the wave envelope. Using the Weyl calculus, an asymptotic approximation of the reduced operator can then be constructed to any power n in the geometrical-optics (GO) parameter. The corresponding truncations yield GO (n = 0), extended GO (n = 1), and quasioptics (n = 2). Notably, an accurate formulation of the latter for inhomogeneous media has only been given recently [unpublished]. But there is even more to this approach. For waves propagating in modulated media (i.e., interacting with other waves), a reduced operator can be derived similarly for Floquet envelopes. The modulation-dependent term in this operator serves as the ponderomotive Hamiltonian of a wave, and its derivative with respect to the (loosely speaking) modulation intensity serves as the wave polarizability [Phys. Rev. A 95, 032114 (2017)]. When applied to charged particles treated as quantum waves, this gives the conventional particle polarizability. Conversely, when applied to classical waves, this defines an effective linear polarizability of a photon (phonon, plasmon, etc). Using this concept, one can interpret modulational dynamics (MD) of nonlinear electromagnetic waves as linear dispersive dynamics of a polarizable photon gas. This significantly simplifies calculations of MD and makes them less error-prone than the standard Maxwell--Vlasov approach [J. Plasma Phys. 83, 905830201 (2017)]. Even more generally, quasilinear MD of all wave ensembles are governed by Wigner--Moyal-type equations that are identical up to a (generally non-Hermitian) Hamiltonian. Then, for example, the modulational instability in the nonlinear Schrodinger equation, the zonostrophic instability of drift-wave turbulence, and the standard two-stream collisionless-plasma instability formally appear as essentially the same effect. In a broader context, elaborating on this approach seems promising for studying inhomogeneous wave turbulence.