Four-wave Mixing | previous | next | feedback |
Definition: an interaction of light waves based on a χ(3) nonlinearity
Four-wave mixing is a nonlinear effect arising from a third-order optical nonlinearity, as is described with a χ(3) coefficient. It can occur if at least two different frequency components propagate together in a nonlinear medium such as an optical fiber. Assuming just two input frequency components ν1 and ν2 (with ν2 > ν1), a refractive index modulation at the difference frequency occurs, which again creates sidebands for each of the input waves (Figure 1). In effect, two new frequency components are generated: ν3 = ν1 - (ν2 - ν1) = 2 ν1 - ν2 and ν4 = ν2 + (ν2 - ν1) = 2 ν2 - ν1.
Figure 1: Generation of new frequency components via four-wave mixing.
As four-wave mixing is a phase-sensitive process (i.e., the interaction depends on the relative phases of all beams), its effect can efficiently accumulate over longer distances e.g. in a fiber only if a phase-matching condition is satisfied. This is the approximately the case if the frequencies involved are close to each other, or if the chromatic dispersion profile has a suitable shape. In other cases, where there is a strong phase mismatch, four-wave mixing is effectively suppressed. In bulk media, phase matching may also be achieved by using appropriate angles between the beams.
Four-wave mixing in fibers is strongly related to self-phase modulation and cross-phase modulation: all these effects originate from the same (Kerr) nonlinearity and differ only in terms of degeneracy of the waves involved.
Four-wave mixing is relevant in a variety of different situations. Some examples are:
- It can be involved in strong spectral broadening in fiber amplifiers e.g. for nanosecond pulses. For some applications, this effect is made very strong and then called supercontinuum generation. Various nonlinear effects are involved here, and four-wave mixing is particularly important in situations with long pump pulses.
- Four-wave mixing can have important deleterious effects in optical fiber communications, particularly in the context of wavelength division multiplexing, where it can cause cross-talk between different wavelength channels, and/or an imbalance of channel powers. One way to suppress this is avoiding an equidistant channel spacing.
- Four-wave mixing is applied for spectroscopy, most commonly in the form of coherent anti-Stokes Raman spectroscopy (CARS), where two input waves generate a detected signal with slightly higher optical frequency. With a variable time delay between the input beams, it is also possible to measure excited state lifetimes and dephasing rates.
- Four-wave mixing can also be applied for phase conjugation, holographic imaging, and optical image processing.
Bibliography
| [1] | C. W. Thiel, Four-wave mixing and its applications, http://www.physics.montana.edu/students/thiel/docs/FWMixing.pdf |
See also: nonlinearities, Kerr effect, phase matching, dispersion, supercontinuum generation, wavelength division multiplexing
