Nonlinear Optics

Abstract

The polarization of a dielectric medium depends nonlinearly on the amplitude of the electromagnetic field. Nonlinear dielectric media are suitable for frequency conversion of radiation. Nonlinear media can be crystals, glasses, liquids or vapors. We discuss: frequency multiplication; difference frequency generation; parametric oscillation; four wave mixing; stimulated Raman scattering. In connection with four-wave mixing, we show how the frequencies of a frequency comb can be determined.

Problems

35.1

Two monochromatic optical waves (wavelengths near 600 nm) are focused on a photodetector. The photodetector generates a microwave signal at beat frequencies. The smallest beat frequency is 200 MHz. Calculate the wavelength difference of the two optical waves.

35.2

Nonlinear polarization.

• (a) Show that a strong electric field applied to a hydrogen atom gives rise to nonlinear polarization of any order. [Hint: make use of the Taylor expansion of $(1+x)^{-2}$].

• (b) Estimate the values of $\chi ^{(2)}$, $\chi ^{(3)}$ and $\chi ^{(4)}$; $\chi ^{(1)}$ is of the order of unity. [Hint: the lowest-order correction term $P^{(2)}$ would be comparable to $P^{(1)}$ if the amplitude A of the field is of the order of the strength of field acting on an electron in an H atom.]

35.3

Show that (35.21) follows from (35.20). Estimate the value of $n_2$. [Hint: use the estimate of $\chi ^{(3)}$ in the preceding problem.]