The papers are correctly posted in Lubos answer and, if this is all you need, than you can skip this answer
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If two coherent light beams are counter propagating in perfect phase opposition the Poynting vectors are of equal magnitude and directly opposed. The total field is null everywhere those conditions apply and energy is null. This comply with Maxwell equations and the Superposition Principle. The issue that Energy+Energy=0 derives from Superposition Principle.
I think that the Nonradiation_condition uses the same superposition principle to cancel the energy in a region outside a finite one. Paul Ehrenfest, Goedeck, Haus, and Douglas Pinnow.
And goes like this (from the same WP-link):
"a distribution of accelerated charges will radiate if and only if it has Fourier components synchronous with waves traveling at the speed of light."
I suspect that the charge do not have a sensor to see if the conditions of radiation are met or not met. The charge always radiate electrostatic field and due to the relativity of motion the radiated pattern can be constructive or not. When it is desctructive (as in the sense of the nonradiation condition) we measure and obtain 0 energy outside the region but the particles always radiate energy at the same rate.
The motion of the particle induce the waves in the radiated electrostatic field.
And when it cancels: energy is not there. 'Cancel', 'Vanish', 'Destroyed'.
This Nonradiation condition, and also the anti-laser experiment work the same way in the vacuum where there are no absorbers, no heat, no particles, ...
I'm clearly stating that the only radiation of any charge is originated only on its continuos electrostatic field.
There is a magical thinking when we say that the particle radiates if it is in motion or other particles in the vicinity are in motion. To be physical It can not be like this, simply.
Explore visually this Radiation2D.exe and its formulation "NEW MATHEMATICAL METHOD FOR RADIATION FIELD OF MOVING CHARGE" by T. Shintake.
To see how we like to complicate the radiation issue see :
"The simplest, and the full derivation of Magnetism as a Relativistic side efect of ElectroStatics" by Hans de Vries;
(I've explored this issue PSE-here, but here I've added the nonradiation condition argument)
EDIT add: time-reversal and information loss
The experiment is not time-simetric because after the cancelation any information that could be equally encoded in both of the beams are definitelly lost.
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