We address here the case of fluctuations of the incident power due to either fluctuations of the laser itself, fluctuations of the locking system, or even fluctuations equivalent to shot noise. The incident power flux is assumed to be of Fourier frequency . The Fourier transform of the Heat equation (assuming a time dependence of all quantities in ) is
We also adopt the new dimensionless parameters and . With this notation, and by setting the (unchanged since the beginning) boundary conditions, we can specialize the solution to be entirely analogous in form to the static solution.
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