How will a Lithium Niobate crystal respond to two light waves with different phases passing through it simultaneously?
You might be asking about "optical rectification" which is a nonlinear effect. The second wave isn't necessary. A single beam can produce a static electric field by this effect just fine. It happens because charges are more easily displaced in one direction than another so they spend more time being displaced in one direction than the other, thus a DC electric field arises.
I was asking about two waves passing through the crystal in opposite direction and whether they can produce an electric field or not ?
Well the light itself has an electric field. The waves travelling in opposite directions will produce a standing wave, which may be what you are thinking. The standing wave, however, does not produce a static field or even a DC component to the field. A standing wave can produce large amplitudes, but the field oscillates +/- within this envelope.
Given that a single wave can produce a DC field via the second order nonlinear
effect of "optical rectification," it seems logical that two counter-propagating
waves would each generate their own DC field. These DC fields would oppose each
other, such that the optical rectification effect would be smaller, compared to the
case of a single wave passing through the LiNbO3. The fact that the two waves are
out of phase would reduce the possibility of third order nonlinear effects arising,
e.g., difference frequency generation.
Hi Arpit, My nonlinear optics is a bit rusty but Raymond's answers captures the essential points. Also see M. Bass et. al Phys Rev. LettsOct1962 http://dx.doi.org/10.1103/PhysRevLett.9.446 "For a qualitative understanding of this effect consider a crystal whose symmetry is sufficiently low to provide a preferred internal direction, so that the polarization induced by an applied electric field need not reverse exactly when the field is reversed. If the applied electric field varies sinusoidally in time, then a net time average polarization will be developed, in analogy with the dc currents in ordinary electronic rectifier". The nonlinear process is CHi2, generating sum (2f) and difference (dc) components. The wave-vectors (generalised as k1+k2 = k3 ) and photon energies (generalised as E1+E2=E3) are conserved and it is a vector process, which is why the polarization and phase-matching is important (e.g.Ref: SPIE Vol. 1561 Inorganic Crystals for Optics, Electro-Optics, and Frequency Con version(1991) / 119). Normally for frequency doubling the phase matching is achieved because the nonlinear coefficient is a tensor and the cristal has different refractive indices depending on its orientation. The nonlinear coefficient generates the harmonic component with a different polarization compared with the pump light. Phase-matching occurs because the refractive indices at the two wavelengths are the same (biaxial crystal).
Returning to your question, counter-propagating the beams gives k1+k2=0, so there is no second harmonic from the cross product but each beam will individually generate a second harmonic component (k1+k1 and k2+k2) which may be phase-matched. If I understand Raymond's and M. Bass' paper explanation of the physical behaviour correctly, the expected value of the displacement of the atoms within the crystal is not zero so the dc component would depend on the crystal axis not the direction of the light. I hope that this helps.
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