Re: conservation in reversed doppler effects in photonic crystals?

James,

The article you refer can be referenced for others interested in the 
subject as PRL, 91, 133901 (2003). The article deals with an analytical 
approach and computational simulation of a temporary compression and 
relaxation in non-linear (photonic) materials.  One effect of this 
compression and relaxation is a change in the dielectric constant of the 
material(and thus its index of refraction).  The investigators have 
utilized a shockwave compression to establish a sharp, rapidly moving 
boundary between the compressed material and the relaxated material.  The 
net effect is to lower the optical bandgap of the compressed material to 
lower energy.

It is well established that at the bandgap edge, the reflectivity of a 
material increases sharply (this is really the heart of the matter and 
involves surface and bulk exciton energetics which I will not deal with 
here).  So, by shifting the bandgap edge to lower energy photons with 
energies within that compressed bandgap can be tranmsitted through the 
relaxed portion of the material until they meet the sharp, rapidly 
moving boundary edge with the compressed material.  At that point, they 
undergo bandgap reflection. But at what frequency?  

The investigators access that since the band gap acts at a lower energy 
than the relaxed material, it will reflect photons associated with this 
lower energy.  They term this a "reverse Doppler effect", in which they 
attribute an object-type character to their shock front.  Whether a shock 
front is an "object" could be debated, but their arguments for the 
physical phenomena seem sound.

As for your argument that this process is non-symmetric and mean a loss 
of energy conservation, I find little support.  That is, if you are 
implying that an oppositely moving shockwave will also "downshift" (sic) 
the photon energy.  I don't think you appreciate that not only is the 
bandgap narrowing on compression, its position with respect to the vacuum 
level is also changing.  I would suspect without thorough investigation 
that the oppositely moving shockwave will reflect photons with higher 
energy than are incident, and that the process is symmetric.

Yours,

---* Dr. Ken Beck