Energy conservation in collective coherent emission by dipole oscillators

Coherent emission from two or more classical damped oscillators leads to an apparent violation of conservation of energy if the oscillators are assumed to emit independently. To resolve this apparent paradox, it is necessary to include effects related to cooperative decay, wherein each oscillator modifies the damping rate of the other oscillators. We show how these effects are included for two radiating oscillators and for a line of N oscillators. The relation between cooperative decay, optical coherent transients, and superradiance is discussed.