On Friday, January 29, 2016 at 10:33:23 AM UTC-5, Phil Hobbs wrote:   
   > On 01/28/2016 08:11 PM, ggherold@gmail.com wrote:   
   > > So we have been using these 0.3 ND (1/2 power) inconel   
   > > filters as beam splitters and 90 degree phase shifters   
   > > in a michelson interferometer... we also pick off the   
   > > reflected beam to get the other phase (sine and cosine).   
   > > Sometime several years ago someone-sigma changed the coating   
   > > to chromium, but didn't tell us.  We can still get inconel   
   > > ND from elsewhere.  So that OK   
   > >   
   > > There is some uncertainty about where the   
   > > phase shift is, at the inconel/ air(glass) interface,   
   > > or is it the absorption in the inconel itself.   
   > > The fact that a 90 degree shift happens at 0.3ND   
   > > seems to point directly at absorption to me....   
   > > Is there something I might be missing?   
   > > 0.3 chormium has less absorption...   
   > > hah! use some numbers to test theory,   
   > > what a concept.   
   > >   
   > > George H.   
   > >   
   >   
   > We talked about this a year ago.  I still think it's cool--lossless   
   > beamsplitters are linear systems, but metal ones aren't, because the   
   > total loss depends on the sum of the E fields in the two arms.  (Of   
   > course this works best in the S polarization, where the two arms have   
   > the same direction of E.)   
   >   
   > If you write the Fresnel formulae in terms of *k* instead of the   
   > incident and refracted angles, lossy media and TIR are a lot easier to   
   > account for.  (The matching of transverse *k* at the boundary is the   
   > physics behind the formulae, of course.)  That's on P. 187 of my second   
   > edition or P. 167 of the first.   
   >   
   > I haven't gone through the math for this particular case though.   
   >   
   > Cheers   
   >   
   > Phil Hobbs   
   >   
   Thanks Phil, I'd forgotten we talked about it already.   
   I was hoping for some quick and dirty result from the Kramers-Kronig   
   relations.  I guess to really understand it I've got to work through   
   all the boundary conditions.  (I haven't cracked open Jackson in a while)   
   For inconel maybe I can use the complex index of refraction for nickel?   
      
   George H.   
   >   
   >   
   > --   
   > Dr Philip C D Hobbs   
   > Principal Consultant   
   > ElectroOptical Innovations LLC   
   > Optics, Electro-optics, Photonics, Analog Electronics   
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