with

γ2(r1,t1)=b1(r1,t1)b2(r1,t1)

(4.120)

and

a1(r1,t1)=δδ1K1er12et12+δK1p1eϱ2r12eτ2t12+σ24a2(r1,t1)=δ2δ1p1K12er12(1+ϱ2)eτ2t12a3(r1,t1)=a1(r1,t1)24a2(r1,t1).

(4.121)

4.3.5      SFG power and energy conversion efficiency for collimated Gaussian beams with phase mismatch (σ ≠ 0) and no pump depletion

Diffraction - No Beam Walk-off - No Absorption - No Pump Depletion - No Phase Mismatch - Yes

In the nondepleted pump case, the irradiance at the sum frequency given in Eqn. 4.82 can be integrated over the beam area and time to provide the power and energy outputs. Assuming that the incident beams are both circular Gaussian in cross-section and are constant in time, we obtain from Eqns. 4.82 and 4.102

P3()=2πr0120I3()r1dr1

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