The conversion of photon frequency is an important function in quantum communication and quantum computation. Yet it is nontrivial because the frequency of a photon is related to the energy, thus to change the frequency of a photon, additional energy input is required. One way to achieve this is by non-linear optical effect where the relationship between polarization P and electric field ε can be expressed as the following equation:
χ is the electric susceptibility. For higher order, χ are very small numbers, so when the intensity is small, the nonlinear terms can be neglected. But when the intensity is very high, we have to consider these terms. Some of the common second order nonlinear optics phenomenum can be illustrated by the following diagram:
Figure 1. Diagram for second order nonlinear optics processes. (a) Sum frequency mixing. (b) Frequency doubling. (c) Down conversion.
In these second-order nonlinear process, two photons annihilate into one single photon or in the case of the down conversion, one photon split into two photons. The process obeys energy conservation law. A very long optical path is required to achieve the desirable frequency conversion since the nonlinear process is very weak. Moreover, strict phase matching conditions should be met so that the waves generated can undergo constructive interference, hence be able to be extracted.