Analytical expressions for z-scan with arbitrary phase change in thin nonlocal nonlinear media

Abstract

Analytical expressions for the normalized transmittance of a thin material with simultaneous nonlocal nonlinear change in refraction and absorption are reported. Gaussian decomposition method was used to obtain the formulas that are adequate for any magnitude of the nonlinear changes. Particular cases of no locality are compared with the local case. Experimental results are reproduced (fitted) with the founded expressions.

Study of Structure–Third-Order Susceptibility Relation of Indandione Derivatives

“…Different methods have been applied for approximation of sample transmission function such as fast Fourier-transform, Huygens−Fresnel principle, and others. 19 In this work we employed analytical expressions for normal transmittance acquired with Gaussian decomposition method, 16 which is simple and particularly useful for describing weak nonlinearities in thin media.…”

“…Information on the magnitude of two-photon absorption and Kerr effect is acquired by analyzing the normalized transmission of the sample as a function of its position. Different methods have been applied for approximation of sample transmission function such as fast Fourier-transform, Huygens–Fresnel principle, and others . In this work we employed analytical expressions for normal transmittance acquired with Gaussian decomposition method, which is simple and particularly useful for describing weak nonlinearities in thin media.…”

Optothermal nonlinearity of silica aerogel

“…We found an increase in the n 2 value with respect to the not-dyed SA sample: n 2 = (−3.4 ± 0.2) × 10 −10 m 2 /W and (−1.4 ± 0.1) × 10 −10 m 2 /W respectively. The curve asymmetry is due to the presence of nonlinear absorption 24 (Fig.5A), while the nonlocality enhances the peak with respect to the valley 21 . Figure 5B reports the measurement of the nonlinear absorption β which is found to be (4.0 ± 0.2) × 10 −4 m/W, (6.8 ± 0.3) × 10 −5 m/W and (4.5 ± 0.2) × 10 −5 m/W at P = 0.2mW, 10mW and 19 mW.…”

“…3B from the expected lorentzian behavior is due to the presence of nonlocality. [21][22][23][24] Indeed, in a purely refractive medium nonlocality tends to deepen the valley and suppress the peak. 25 Furthermore, nonlocality acts on the transmission function broadening its tails (see Fig.3B).…”

Z-scan for thin media with more than one nonlocal nonlinear response

“…The model calculates the electric field profile at the exit of the nonlinear media and then numerically calculate its Fast Fourier Transform [20], to obtain the far field intensity distribution. In order to complete this model in [21] was discussed the influence of the nonlocality in materials with simultaneous nonlinear refraction and absorption; finally analytical expressions were presented for the normalized intensity of z-scan curves for arbitrary phase changes. In [22] it was demonstrated that the nonlocality affects the transverse spatial extension of the far field intensity distributions.…”