From: pcdhSpamMeSenseless@electrooptical.net   
      
   On 7/24/2015 6:18 PM, RichD wrote:   
   > On July 16, 2015 Phil Hobbs wrote:   
   >>> Recently, I attended a seminar of Hamilton's cone, or   
   >>> whatever it's called, inside crystals.   
   >>> Apparently, research continues on this phenomenon,   
   >>> there's still new stuff to uncover.   
   >>>   
   >>> At one point, the speaker said, "the direction of energy flow   
   >>> is different than the wave direction."   
   >>> ??   
   >>> If I recall correctly, the wave direction is given   
   >>> by the Poynting vector (the most mnemonic label in   
   >>> science):  E x H.  Am I now to believe the power   
   >>> doesn't flow the same way?   
   >>   
   >> You have to be careful about your terms.  Phase propagates as usual,   
   >> exp(i k x - omega t) for a plane wave.  However, in an anisotropic   
   >> crystal, the main part of the optical power doesn't necessarily   
   >> propagate along k.   
   >   
   > No doubt you're right, but I don't get it.  It's partly   
   > a matter of semantics - I don't grok the difference   
   > between 'phase propagation', 'wave propagation', and   
   > 'energy propagation'   
   >   
   > My memory of the physics, is that at a particular point   
   > and moment,  the field is represented by a 6-vector   
   > (3 x E, 3 x H), and the energy is given by E x H.   
   > That vector then 'travels', loosely speaking, to the   
   > neighboring point; hence velocity.  I don't understand   
   > how that could differ from energy flow (or optical power flow).   
   >   
   > --   
   > Rich   
   >   
      
   In an anisotropic medium, there are still plane wave solutions [i.e.   
   something times exp(i k dot x - omega t) ].  However, due to the   
   anisotropic electric and magnetic susceptibility, E and/or H aren't   
   orthogonal to _k_.  That means that E cross H doesn't lie along _k_, so   
   the Poynting vector (energy propagation) is in a different direction   
   from _k_ (phase propagation).   
      
   Cheers   
      
   Phil Hobbs   
      
   --   
   Dr Philip C D Hobbs   
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