Chapter 11, Problem 11.5P

Consider two x-polarized waves that counter-propagate along the z axis. The wave traveling in the forward z direction is of frequency ω₁; the backward z propagating wave is at frequency ω _1, where ω < ω₁. Both frequencies are very slightly detuned on either side of their mean frequency, ω _0: such that ω₀ - ω₁ = ω₁ – ω₀ <<₁. Using the complex field forms, construct the expression for the total electric field, and from this, find the power density distribution (proportional to EE* ). Your answer should be in the form of a '’standing wave" that in fact moves slowly along the z axis. Find an expression for the velocity of the wave pattern in terms of given or known parameters. Does the pattern move in the forward or backward z direction?