Glossary entry

Kerr effect

An intensity-dependent change in refractive index in an optical medium. The third-order nonlinear optical effect underlying self-phase modulation, four-wave mixing, and ultrafast optical switching.

The optical Kerr effect is the change in refractive index of a medium under high optical intensity:

n(I) \;=\; n_0 + n_2 \, I,

where $n_2$ is the nonlinear-index coefficient (also called the Kerr coefficient) with units of m²/W. The effect arises from the third-order nonlinear susceptibility $\chi^{(3)}$ :

n_2 \;=\; \frac{3 \chi^{(3)}}{4 \varepsilon_0 c n_0^2}.

The Kerr effect is instantaneous on optical timescales (response time set by electronic polarizability, typically $<$ 10 fs) and isotropic in centrosymmetric media (where second-order $\chi^{(2)}$ vanishes).

Typical Kerr coefficients at 1550 nm:

Material	$n_2$ (m²/W)
Fused silica	$2.6 \times 10^{-20}$
Silicon	$4.5 \times 10^{-18}$ (~170× silica)
Silicon nitride (Si $_3$ N $_4$ )	$2.4 \times 10^{-19}$ (~10× silica)
Chalcogenide glass (As $_2$ S $_3$ )	$3 \times 10^{-18}$
Lithium niobate	$1 \times 10^{-19}$
Diamond	$1.3 \times 10^{-19}$

Applications of the Kerr effect:

Use case	Mechanism
Self-phase modulation	Single pulse modulating its own phase
Cross-phase modulation (XPM)	One pulse modulating the phase of another co-propagating pulse
Four-wave mixing (FWM)	Three input wavelengths generating a fourth via $\chi^{(3)}$
Modulation instability	Spontaneous spectral broadening in anomalous-dispersion fiber
Soliton propagation	Balance of SPM-induced spectral broadening with anomalous dispersion
Frequency comb generation	Kerr nonlinearity in high-Q microresonators producing octave-spanning combs
All-optical switching	Kerr-induced phase shift gating signal flow
Self-focusing / filamentation	Intensity-dependent index lensing the beam

The Kerr effect is the basis for optical frequency combs in microresonators (Kerr combs) — high-finesse microresonators on platforms like silicon nitride, lithium niobate, or aluminum nitride pumped by a narrow-linewidth CW laser convert input power into a comb of equally-spaced spectral lines via cascade four-wave mixing. These are used in optical clocks, ranging, and on-chip spectroscopy.

The Kerr effect distinguishes from the linear electro-optic (Pockels) effect in two key ways: Kerr is intensity-dependent (depends on $|E|^2$ ), while Pockels is field-linear (depends on $E$ ). Both produce refractive-index modulation, but with very different drive characteristics and applications.