Benm
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The similarity between electron orbits and TEM mode patterns is no coincidence at all.
Both find their roots in the wavefunction. For atoms this is a 3 dimensional function, for lasers it is a 2 dimensional function since we usually accept the longitudinal component als 'multimode' by default.
Without making things more complicated then they are, both are the result of exactly the same thing: distributing energy density in resonance over a finite area (or volume).
These patterns are very universal, and even work with one dimensional systems: for example, you can pluck a guitair string at its ground frequency, or any harmonic, but nothing in between. This is so because it has a defined length, and both ends must be at a vibrational minumum. You can fit 1, 2, 3 or more maxima between those, resulting in exactly the same pictures as the hydrogen orbitals, but obiously only a line trough them since we are working with 1 dimension only.
Btw: if you compare the hydrogen orbitals to laser pictures, you should notice that the enumeration is a bit different. What is labeled as 2,1,0 and 2,1,1 is named TEM 01 and 10 with lasers, but this is a matter of nomenclature, not of fundamental difference.
Both find their roots in the wavefunction. For atoms this is a 3 dimensional function, for lasers it is a 2 dimensional function since we usually accept the longitudinal component als 'multimode' by default.
Without making things more complicated then they are, both are the result of exactly the same thing: distributing energy density in resonance over a finite area (or volume).
These patterns are very universal, and even work with one dimensional systems: for example, you can pluck a guitair string at its ground frequency, or any harmonic, but nothing in between. This is so because it has a defined length, and both ends must be at a vibrational minumum. You can fit 1, 2, 3 or more maxima between those, resulting in exactly the same pictures as the hydrogen orbitals, but obiously only a line trough them since we are working with 1 dimension only.
Btw: if you compare the hydrogen orbitals to laser pictures, you should notice that the enumeration is a bit different. What is labeled as 2,1,0 and 2,1,1 is named TEM 01 and 10 with lasers, but this is a matter of nomenclature, not of fundamental difference.
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I'm sure it's simple, but we got to find it. It's what Michio Kaku is trying to find. I believe Einstein also was on the search for it. Michio Kaku will mention him a lot. If string theory continues to be more understood and becomes more obviously valid, then we may start find these things out.