Published in Applied Physics B, the study utilized a modified z-scan technique to investigate the material’s response to femtosecond laser pulses with peak intensities reaching up to 10 terawatts per square centimeter. The primary finding indicates that the effective quintic nonlinear refractive index is significantly smaller in magnitude than values previously reported in the literature, challenging existing models of high-intensity light propagation in this canonical dielectric.

The investigation focused on the higher-order nonlinear optical response of fused silica, specifically the quintic term that becomes relevant at extreme intensities. In standard laser physics, the interaction between light and matter is often described by the cubic Kerr effect, where the refractive index changes linearly with intensity. However, at the ultra-high intensities achievable with femtosecond pulses, higher-order terms, such as the quintic nonlinearity, can become comparable to the cubic response. Accurately quantifying these higher-order effects is critical for modeling pulse propagation, self-compression, and filamentation dynamics in optical materials.

The study employed a modified z-scan method that explicitly accounts for both cubic and quintic contributions to the nonlinear phase shift. The classical z-scan technique measures the transmittance of a beam through an aperture as a nonlinear sample is scanned through the focal waist of a laser. By using an imaging configuration where the detection plane coincides with the linear beam waist, the researchers enhanced the sensitivity of the measurement by up to a factor of three compared to the standard far-field implementation. This modification allows for the detection of weak nonlinear signals, including the subtle contributions from the quintic term.

Experiments were conducted at two wavelengths: the fundamental frequency of 1033 nm and its second harmonic at 517 nm. The laser source delivered 2 millijoule pulses with a duration of approximately 196 femtoseconds. The samples consisted of thin fused silica plates, with a thickness of 0.17 millimeters, which were translated along the beam axis. The setup was designed to minimize parasitic nonlinear effects from other optical components by using reflective optics wherever possible, ensuring that the measured signal primarily originated from the sample itself.

The results showed that a statistically significant deviation from the purely cubic Kerr response was observed only at the highest intensities. At lower intensities, the experimental data were adequately described by the cubic nonlinearity alone. As the intensity increased, systematic deviations emerged, which were interpreted within a perturbative cubic-quintic model. The analysis yielded an effective quintic nonlinear refractive index of negative 5.5 times 10 to the power of minus 6 square centimeters per terawatt squared at 1033 nm, with a confidence interval of plus or minus 1.2 times 10 to the power of minus 6.

At the second harmonic wavelength of 517 nm, the measured effective quintic index was negative 12 times 10 to the power of minus 6 square centimeters per terawatt squared, with a larger uncertainty of plus or minus 4 times 10 to the power of minus 6. These values correspond to fifth-order nonlinear susceptibilities of negative 9.5 times 10 to the power of minus 43 meters to the fourth power per volt to the fourth power at 1033 nm, and negative 21 times 10 to the power of minus 43 meters to the fourth power per volt to the fourth power at 517 nm. The study notes that these values are approximately one to two orders of magnitude lower than those reported in previous experimental works.

A key limitation of the study is the potential contribution of plasma-induced refractive effects to the observed higher-order response. At the intensities used, which were near half the material damage threshold, multiphoton absorption could generate free electrons. Although nonlinear absorption was not directly detected in the transmitted energy measurements, the generation of a plasma cannot be completely excluded. A simple estimate using the Drude model suggests that the refractive index change due to plasma could be comparable to the nonlinear index change attributed to the fitted quintic term.

Consequently, the authors emphasize that the reported values should be regarded as upper bounds for the magnitude of the negative quintic nonlinear refractive index of fused silica, rather than as direct measurements of the intrinsic material parameter. The experiment does not allow for an unambiguous distinction between a genuine fifth-order susceptibility contribution and other mechanisms producing an intensity-dependent refractive correction.

Previous models that assumed larger quintic nonlinearities predicted that the total nonlinear phase shift would vanish at intensities around 1 terawatt per square centimeter. However, the current results indicate that such a strong quintic contribution is not present in fused silica under the tested conditions.

The modified z-scan method provided the necessary sensitivity to detect the small deviations from cubic behavior. By using the known value of the cubic refractive index to infer the effective peak intensity, the team was able to constrain the physically reasonable values of the quintic coefficient more effectively.

The findings underscore the need for careful interpretation of nonlinear optical measurements, particularly when operating near the damage thresholds of optical materials.

Subject of Research: Fused silica quintic nonlinear refractive index measurement with modified z-scan technique

Article Title: Fused silica quintic nonlinear refractive index measurement with modified z-scan technique

Article References: Poezzhalov, D., Poteomkin, A., Arsentev, S., Gacheva, E., Mironov, S., & Khazanov, E. (2026). Fused silica quintic nonlinear refractive index measurement with modified z-scan technique. Applied Physics B, 132(7), Article 87. https://doi.org/10.1007/s00340-026-08697-y

Image Credits: AI Generated

DOI: 10.1007/s00340-026-08697-y

Keywords: Fused, silica, quintic, nonlinear, refractive, index, measurement, modified, z-scan, technique, scientific research