Numerical estimate of nonlinear optical quantities. A laser beam of frequency ω carrying 1 W of power is focused to a spot size of 30-μm diameter in a crystal having a refractive index of n = 2 and a second-order susceptibility of χ(2) = 4 × 10-11 m/V. Calculate numerically the amplitude P(2ω) of the component of the nonlinear polarization oscillating at frequency 2ω. Estimate numerically the amplitude of the dipole moment per atom μ(2ω) oscillating at frequency 2ω. Compare this value with the atomic unit of dipole moment (ea0, where a0 is the Bohr radius) and with the linear response of the atom, that is, with the component μ(ω) of the dipole moment oscillating at frequency ω. We shall see in the next chapter that, under the conditions stated above, nearly all of the incident power can be converted to the second harmonic for a 1-cm-long crystal.