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Laser Beam Propagation in Nonlinear Optical Media by Shekhar Guha

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3.2.2      Reduction of deff to expressions in the literature

According to Ref. [2] (page 27), ‘the correct expressions for the deffssf and deffsff.. were first obtained by Lavrovskaya et al.’ [3]). Since the explicit expressions (without walk-off) for the ssf and sff cases are given in Ref. [2], we first check the expressions above to see if we obtain the same results.

For crystals belonging to point group mm2, there are 5 non-zero d coefficients: d15, d24, d31, d32 and d33. For a Type I (ssf) interaction, deff(ω1) is obtained from Table 3.3 as:

deff(ω3)=efi(ω3)dilulss =d15efX(ω3){esZ(ω1)esX(ω2)+esX(ω1)esZ(ω2)} +d24efZ(ω3){esY(ω1)esZ(ω2)+esZ(ω1)esY(ω2)} +d31efZ(ω3)esX(ω1)esX(ω2) +d32efZ(ω3)esY(ω1)esY(ω2) +d33efZ(

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