Cross-phase modulation is the change in the optical phase of a light beam caused by the interaction with another beam in a nonlinear medium, specifically a Kerr medium. This can be described as a change in the refractive index:
where n2 is the nonlinear index. Here, the intensity I(1) of beam 1 causes a refractive index change for beam 2.
Compared with the corresponding equation for self-phase modulation, there is an additional factor of 2. This factor 2 is valid for beams with the same polarization; for cross-polarized beams in isotropic media (e.g. glasses), it must be replaced with 2/3.
A more fundamental description of cross-phase modulation effects refers to the nonlinear polarization caused in the medium, based on the χ(3) nonlinearity. For example, the above-mentioned factor 2 can be understood on that basis.
Effects of Cross-phase Modulation
Cross-phase modulation can be relevant under different circumstances:
- It leads to an interaction of laser pulses in a medium, which allows e.g. the measurement of the optical intensity of one pulse by monitoring a phase change of the other one (without absorbing any photons of the first beam). This is basis of a scheme for quantum nondemolition (QND) measurements.
- The effect can also be used for synchronizing two mode-locked lasers using the same gain medium, in which the pulses overlap and experience cross-phase modulation.
- In optical fiber communications, cross-phase modulation in fibers can lead to problems with channel cross-talk.
- Cross-phase modulation is also sometimes mentioned as a mechanism for channel translation (wavelength conversion), but in this context the term typically refers to a kind of cross-phase modulation which is not based on the Kerr effect, but rather on changes in the refractive index via the carrier density in a semiconductor optical amplifier.
|||M. N. Islam et al., “Cross-phase modulation in optical fibers”, Opt. Lett. 12 (8), 625 (1987), doi:10.1364/OL.12.000625|
|||M. Shtaif, “Analytical description of cross-phase modulation in dispersive optical fibers”, Opt. Lett. 23 (15), 1191 (1998), doi:10.1364/OL.23.001191|
|||A. Fellegara and S. Wabnitz, “Electrostrictive cross-phase modulation of periodic pulse trains in optical fibers”, Opt. Lett. 23 (17), 1357 (1998), doi:10.1364/OL.23.001357|
|||M. Margalit et al., “Cross phase modulation squeezing in optical fibers”, Opt. Express 2 (3), 72 (1998), doi:10.1364/OE.2.000072|
|||N. Matsuda et al., “Observation of optical-fibre Kerr nonlinearity at the single-photon levels”, Nature Photon. 3, 95 (2009), doi:10.1038/nphoton.2008.292|
|||G. P. Agrawal, Nonlinear Fiber Optics, 4th edn., Academic Press, New York (2007)|
|||R. Paschotta, tutorial on "Passive Fiber Optics", Part 11: Nonlinearities of Fibers|