From: r_delaney2001@yahoo.com   
      
   On July 24, Phil Hobbs wrote:   
   >>>> Recently, I attended a seminar of Hamilton's cone, or   
   >>>> whatever it's called, inside crystals.   
   >>>> 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:  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).   
   >   
   > 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).   
      
   OK, I think I get the idea: the wave propagates as   
   usual, but Poynting points in a different direction.   
      
   As I suspected, it's a matter of semantics -   
   'energy flow' doesn't imply flow, as a river, but   
   indicates the direction of E x H.   
      
   Thanks. Can you recommend a text which explores this further?   
      
   --   
   Rich   
      
   --- SoupGate-Win32 v1.05   
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