# 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 Notably, an accurate formulation of the latter for inhomogeneous media has only been given recently [unpublished].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.