Hi All - I am trying to immerse myself in NLO and purchased Robert W. Boyd's Third Edition on Nonlinear Optics. I'm already struggling just 3 pages into the book.(adsbygoogle = window.adsbygoogle || []).push({});

We are looking at the polarization of a material in a NLO chromophore, so:

P(t)=[tex]\epsilon[/tex] [X(1)E(t)+X(2)E^{2}(t)+X(3)E^{3}(t)......]

where P is the polarization at time t, X is the NLO susceptibility for the corresponding ordered response, and E(t) is the strength of the applied electric field.

The text goes on to say "One might expect that the lowest-order correction term X(2)E^{2}(t) to be comparable to the linear response, X(1)E(t), when the amplitude of the applied field, E(t), is equal to the characteristic atomic electric field E(atomic)=e/4[tex]\pi[/tex][tex]\epsilon[/tex]_{0}a_{0}^{2}"

Then they derive a whole bunch of stuff, which I follow, but my question is why do we expect the second-order polarization to equal the first-order polarization when the applied field equals E(atomic)?

Why is that

if E(applied)=E(atomic) then

X(1)E(t)=X(2)E^{2}(t)

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# Nonlinear Optics

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