Optical Kerr effect

• The term in the expansion of the of the nonlinear polarisation responsible for the optical (or AC) Kerr is of the form

P=e0[c(1) +c(3) (Ew)2] Ewcos(wt)

• Recall that c(1) =n2-1 and by comparison we have

[c(1) +c(3) (Ew)2]=n’2-1

where n’ is the refractive index modified by the presence of the optical field

• We can rewrite the refractive index as

n’=n+n2I(r,t)

and n2 is the nonlinear refractive index (units m2W-1)

• We have used the fact that I=(nce0/2)|E|2

• The spatial part I(r) gives rise to self-focussing

• The temporal part I(t) gives rise to self-phase modulation

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