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IcedCoffee

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- How much energy is needed to emit EM wave when there are arrays of same emitters that interferes constructively?

I'm trying to wrap my head around the energy increment under constructive interference. In short, why does energy increase quadratically when each source emit EM wave that interferes constructively?

Suppose we have an array of identical and equidistant sources, each of which span the entire x-y plane and emits plane EM wave of the same frequency and amplitude. They emit EM wave in both positive and negative z directions, and the phase of each source is such that the EM waves interfere constructively in +z direction.

I get that the net field amplitude increases linearly as the wave propagates, and hence the energy increases quadratically. However, wouldn't each source emit the same amount of energy? Suppose the first source emits energy E in +z direction. For energy to increase quadratically, the second source must emit energy 3E, the third source must emit energy 5E, the fourth source must emit energy 7E, and so on.

The only difference seems to be that for each of the "identical" sources, there is pre-existing EM field of different amplitude. Does this make the difference? In other words, does the amount of energy required to generate EM field of a certain magnitude increases (linearly?) with the magnitude of pre-existing EM field?

Suppose we have an array of identical and equidistant sources, each of which span the entire x-y plane and emits plane EM wave of the same frequency and amplitude. They emit EM wave in both positive and negative z directions, and the phase of each source is such that the EM waves interfere constructively in +z direction.

I get that the net field amplitude increases linearly as the wave propagates, and hence the energy increases quadratically. However, wouldn't each source emit the same amount of energy? Suppose the first source emits energy E in +z direction. For energy to increase quadratically, the second source must emit energy 3E, the third source must emit energy 5E, the fourth source must emit energy 7E, and so on.

The only difference seems to be that for each of the "identical" sources, there is pre-existing EM field of different amplitude. Does this make the difference? In other words, does the amount of energy required to generate EM field of a certain magnitude increases (linearly?) with the magnitude of pre-existing EM field?