Four-wave mixing

Energy level diagram for a non-degenerate four-wave mixing process. The top energy level could be a real atomic or molecular level (resonant four-wave mixing) or a virtual level, far detuned off-resonance. This diagram describes the four-wave mixing interaction between frequencies f₁, f₂, f₃ and f₄.

When three frequencies (f₁, f₂, and f₃) interact in a nonlinear medium, they give rise to a fourth frequency (f₄) which is formed by the scattering of the incident photons, producing the fourth photon.

Given inputs f₁, f₂, and f₃, the nonlinear system will produce

${\displaystyle \pm f_{1}\pm f_{2}\pm f_{3}}$

From calculations with the three input signals, it is found that 12 interfering frequencies are produced, three of which lie on one of the original incoming frequencies. Note that these three frequencies which lie at the original incoming frequencies are typically attributed to self-phase modulation and cross-phase modulation, and are naturally phase-matched unlike FWM.

FWM is a fiber-optic characteristic that affects wavelength-division multiplexing (WDM) systems, where multiple optical wavelengths are spaced at equal intervals or channel spacing. The effects of FWM are pronounced with decreased channel spacing of wavelengths (such as in dense WDM systems) and at high signal power levels. High chromatic dispersion decreases FWM effects, as the signals lose coherence, or in other words, the phase mismatch between the signals increases. The interference FWM caused in WDM systems is known as interchannel crosstalk. FWM can be mitigated by using uneven channel spacing or fiber that increases dispersion. For the special case where the three frequencies are close to degenerate, then optical separation of the difference frequency can be technically challenging.

${\displaystyle f_{ijk}=f_{i}+f_{j}-f_{k},\mathrm {where} \,i,j\neq k}$

FWM finds applications in optical phase conjugation, parametric amplification, supercontinuum generation, Vacuum Ultraviolet light generation and in microresonator based frequency comb generation. Parametric amplifiers and oscillators based on four-wave mixing use the third order nonlinearity, as opposed to most typical parametric oscillators which use the second-order nonlinearity. Apart from these classical applications, four-wave mixing has shown promise in the quantum optical regime for generating single photons,[5] correlated photon pairs,[6][7] squeezed light[8][9] and entangled photons.[10]

• Optical phase conjugation, phase conjugate mirror
• Supercontinuum generation
• Kerr frequency comb
• Optical Kerr effect
• Lugiato–Lefever equation

• Encyclopedia of Laser Physics and Technology