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By invoking the slowing-varying amplitude approximation (see ref 3), the wave equation describing generation of the forward-going RFWM signal field can be written as: E4()/r= i/2ce0 e4*•P(3)()e-iδk4•r = i/2ce0 e4*•P̃(3)()e-ik•r where the factor eiks•r appearing in our definition of the third-order polarization (eq 10), e4*•P(3)()= e4*•P̃(3)()eiks • r, leads to a net spatial dependence of e-i(k4-ks) • r)= e-ik• r. For the small-signal limit obtained when incident beams propagate (with negligible modification) through an optically thin sample of length l, integration of the wave equation yields E4() ∞ e*4 •P̃(3)()e-ikl/2lsinc(kl/2), with the corresponding signal intensity given by I4() ∞ |E4()|2 ∞ |e4*•P̃(3)() |2l2sinc2(kl/2). Momentcum onservation or phase-matching criteria are reflected in the behavior of the sinc2(kl/2) function, which peaks sharply (for finite l) at k ) |k| ) 0 or k4 ) ks, where ks ) k1-k2-k3.
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