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This post is related to a posting I did a couple of days ago, but I will go into more detail on this one, and it should be more easy to see the concept that is presented. A number of years ago, I was explaining interference concepts to a physics Ph.D. who had very little background in optics. In discussing the two-slit experiment, he was rather puzzled how a non-linearity had surfaced in that the sum of the individual intensity patterns was not the resultant intensity pattern that emerged. His argument, which really contained a good deal of validity, was that the wave equations we were using were Maxwell's and were completely linear, and the superposition of solutions should thereby be a solution. Thereby, how could any non-linear features ever emerge in a system, (such as intensity patterns that didn't superimpose), from a system that was defined by completely linear equations. My instincts at the time were that there must be some hidden non-linearity somewhere, but I was unable to pinpoint it. It was only quite a number of years later, upon solving a Fabry-Perot type interference problem, that the "hidden non-linearity" became apparent. The energy equation, which is basically intensity I=n*E^2, is also used in the computations along with the wave equation (that comes from Maxwell's equations), and thereby we have a governing equation in our system that is non-linear in the E-field. The equations that determine the E-fields (Maxwell's) are all linear in the E-fields and so the E-fields will always obey linear principles, but the energy equations are not of a linear form, so that we can expect to see cases where linear principles are not obeyed in regards to the energy. e.g. MTF (modulation transfer function) computations work in the incoherent cases, but do not work for coherent sources. Another example where we see linear behavior in the E-fields but not in the energy is when two plane waves are incident on a single interface from opposite directions. (such as in an optical interferometer). In this case, the fresnel coefficients (E-field coefficients for transmission and reflection) remain good numbers when both sources are present, but the energy reflection (e.g. R=rho^2) and transmission coefficients are no longer valid in this coherent case with the two incident plane waves interfering. There is no requirement that the system needs to be linear in the energy response, and in the case with two mutually coherent sources present, (one from each direction), the energy coefficients "R" and "T" can not be used to determine the outcome. Instead the individual E fields from each source need to be split using the fresnel coefficients, and the resulting E fields added (emerging from the junction in each direction), before computing the energy of each. The result turns out to depend on the relative phases of the incident plane waves, and energy is 100% conserved. It is actually possible in the case of a 50-50 energy split from the junction for each individual beam to have 100% of the energy emerge to the right with two sources present. By proper adjustment of the phase, 100% of the energy can alternatively be made to emerge to the left. i.e. the two sources are completely recombined by the beamsplitter. (Note for R=1/2 (50-50 split), the fresnel rho=+/-1/(sqrt(2))