Third-Order Nonlinearity Measurement Techniques

*Allen Moses Samuel Elizabeth*

#### **Abstract**

To measure the degenerate (single-frequency) optical nonlinearities, third-order nonlinearity measurement and their related techniques were employed. When a laser beam is induced on a nonlinear (NL) medium, a phase change is easily identified using third-order nonlinearity measurement techniques (Z-scan). When the sample material is scanned on Z-axis, the phase change is denoted by sign and magnitude, the refractive index which is directly related to the change in the index of refraction. The nonlinear absorption from the absorption coefficient is independent of the index of refraction which is a required parameter for calculating nonlinear refraction. Further, the change in transmission caused by nonlinear absorption of the subjected material is related to the change in absorption coefficient which is easily determined by the Z-scan technique. From Z-scan responses, real and imaginary parts of third-order nonlinear susceptibility (χ<sup>3</sup> ) can be determined. The Z-scan technique is an interesting process that leads to optical power limiting and nonlinear optical propagation.

**Keywords:** nonlinear optics, nonlinear absorption, nonlinear refractive index, nonlinear absorption coefficient, and nonlinear susceptibility

#### **1. Introduction**

To examine the irritation dynamics and time-resolved technique under sonorant agitation, Z-scan is an effective tool. The intensity-dependent nonlinear (NL) absorption coefficient (Δα) and magnitude of the nonlinear index (n2) (Kerr nonlinearity) are vital key factors for photo-induced dissociation in reduced crystals, optical material, and photonic applications [1, 2]. Nonlinear absorption (NLA) and nonlinear refraction (NLR) in solid and liquid can be effectively measured using the Z-scan technique [3]. This method is relatively simple due to its single-beam technique measuring both the sign and magnitude of NLR and NLA, and its spatial beam distortions principle is purely dependent on the sign of the nonlinearity [2]. Methods like beam distortion [4], elliptical polarization [5], multi-wave mixing [6], nonlinear interferometry [7], the indexing change (Δn), and absorption change (Δα) can be done directly without curve fitting. Z-scan method is the most sensitive mechanism that directly determines the refractive index change. The electronic structure of materials is shed by the frequency dispersion study from the nonlinear susceptibility (χ) due to the internal atomic and molecular resonances. The advantage reveals that

Z-scan studies become a fundamental screening for third-order nonlinearity [3, 8]. The sample is placed on the Z-axis along with the positive and negative directions, and the input laser beam was converted into polarized Gaussian beam along the waist of the motorized translation stage [9] as shown in **Figure 1**.
