This article introduces the nonlinear refractive index and the nonlinear refractive index characteristics of common materials.

A parameter used to quantitatively describe the magnitude of the Kerr nonlinearity of a medium

When high-intensity light propagates through a medium, nonlinear effects result. The simplest of these is a proportional change (usually an increase) of the Kerr effect to the light intensity I

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where n2 is the nonlinear refractive index coefficient. Its common unit is m2/W or cm2/W. Typically, the nonlinear index of refraction is measured using linearly polarized light. For non-birefringent crystals, the nonlinear index of refraction under circular polarization is typically 1/3 smaller.

When the light intensities are very high, the above equation for the nonlinear index of refraction may require a higher order correction. For example, a bin proportional to the square of the index of refraction is required, and its coefficient is negative, so that the Kerr effect saturates.

In addition to the Kerr effect (pure electronic nonlinearity), the electrical energy also significantly affects the value of the nonlinearity index [4,5]. In this case, the electric field of the beam produces a density change (acoustic wave), which affects the refractive index through the photoelastic effect. But this mechanism involves a significant time delay and is therefore only suitable for relatively slowly changing power modulations, not for ultrashort pulses. The contribution of this low-speed (MHz) electrostriction in fiber is 10-20% of the usual Kerr effect.

For transparent crystals and glasses, n2 is typically 10-16 cm2/W to 10-14 cm2/W. For example, silica fiber has a low nonlinear refractive index at a wavelength of about 1.5um, which is 2.7•10-16 cm2/W, while the nonlinear refractive index of some vulcanized glass is several hundred times or even higher. Semiconductor materials also have a high nonlinear index of refraction. Studies have shown that the nonlinear refractive index coefficient is proportional to the inverse of the fourth power of the bandgap energy, and also depends on the wavelength of the test light [2]. The nonlinear refractive index coefficient can also be negative (self-defocusing nonlinear effects), especially when the photon energy is higher than 70% of the energy of the bandgap.

Materials with high nonlinear refractive index coefficients generally have small bandgap energies, and therefore also tend to exhibit strong two-photon absorption (TPA). For some applications, such as channel switching in telecommunication systems, this is disadvantageous.

The nonlinear index of refraction coefficient of a sample is usually measured using a z-scan technique, which is based on the self-focusing effect of a Kerr lens.

The nonlinearity of the fiber can be quantified by measuring the spectral broadening resulting from the phase modulation. However, it is important to note that in non-PM fibers the polarization state of the light will change, which may affect the measurement results. In addition, this measurement is an average of the material properties of the fiber core and cladding.