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I posted previously about this topic a couple of years ago, and it really came across like a ton of bricks, but now that I have established some credibility, perhaps it will be read with some interest.

In the course of my career, (in the years 1986-1990), on two occasions I discussed with two very intelligent physics PhD.'s a problem that surfaces in regards to interference patterns. The first PhD. knew very little Optics and (around the year 1986) was asking me, "how can you possibly get an interference pattern? Are you telling me if I have one solution to Maxwell's equations, and a second solution, that the sum is not a solution?" I didn't have a good answer for him at the time. I told him there seems to be something non-linear going on, but I couldn't put my finger on it.

A couple years later, around 1990, I was working on the problem of reflections in sections of r-f cables with slightly different characteristic impedances with another older physics PhD., and the problem involved the Schellnukopf equations (Edit: A google shows these are the "Schoelkopf" equations after R.J. Schoelkopf). We were basically solving for what is the Fabry-Perot effect in Optics at normal incidence. After observing some of the effects we were seeing, the results seemed to be non-linear. The existence of a second beam seemed to affect what the first one did. I asked the older PhD. , "Are you sure these equations are linear". His reply was a very quick, "Of course they are linear". I really couldn't argue it further with him at this point.

About 20 years later, in 2008, it finally dawned on me the solution to this dilemma: In analyzing both of these systems, there is an energy equation=energy is conserved= and that equation is second order in the E-field parameter. The result is that there is a non-linear process in the E-field parameter going on in these systems that does make interference patterns not only possible, but quite commonplace. The systems are linear in the E-fields, but they are not linear in how the energy redistributes itself. The energy distribution does not need to obey linear principles, because the energy equations are second order in the E-field parameter.

Anyway, hopefully at least a couple of you find this good reading.

In the course of my career, (in the years 1986-1990), on two occasions I discussed with two very intelligent physics PhD.'s a problem that surfaces in regards to interference patterns. The first PhD. knew very little Optics and (around the year 1986) was asking me, "how can you possibly get an interference pattern? Are you telling me if I have one solution to Maxwell's equations, and a second solution, that the sum is not a solution?" I didn't have a good answer for him at the time. I told him there seems to be something non-linear going on, but I couldn't put my finger on it.

A couple years later, around 1990, I was working on the problem of reflections in sections of r-f cables with slightly different characteristic impedances with another older physics PhD., and the problem involved the Schellnukopf equations (Edit: A google shows these are the "Schoelkopf" equations after R.J. Schoelkopf). We were basically solving for what is the Fabry-Perot effect in Optics at normal incidence. After observing some of the effects we were seeing, the results seemed to be non-linear. The existence of a second beam seemed to affect what the first one did. I asked the older PhD. , "Are you sure these equations are linear". His reply was a very quick, "Of course they are linear". I really couldn't argue it further with him at this point.

About 20 years later, in 2008, it finally dawned on me the solution to this dilemma: In analyzing both of these systems, there is an energy equation=energy is conserved= and that equation is second order in the E-field parameter. The result is that there is a non-linear process in the E-field parameter going on in these systems that does make interference patterns not only possible, but quite commonplace. The systems are linear in the E-fields, but they are not linear in how the energy redistributes itself. The energy distribution does not need to obey linear principles, because the energy equations are second order in the E-field parameter.

Anyway, hopefully at least a couple of you find this good reading.

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