Problem: Linear Array of Emitters, Superlattice

  Consider a linear array of N identical radiation sources, placed at positions . Each source emits radiation at frequency , wavenumber k, amplitude A and the sources are coherent with zero phase difference. We detect the radiation with intensity (defined as the time-averaged amplitude square) with a detector positioned along the line of the array, far away from the sources.

Introduce a static modulation to the position of the sources, described by , where with and . In qualitative terms, what will we see in I(k) as approaches zero? Discuss the peaks between and in greater detail: Calculate the first correction to the magnitude of the main peaks, and the magnitude of the strongest side peaks. (Note: Assume . The calculation of intensity becomes simplified if you concentrate on terms of order .)