Influence of the photoinduced focal length of a thin nonlinear material in the Z-scan technique

Abstract

In this paper the response purely refractive of a thin nonlinear material, in the z-scan technique experiment, is modeled as a lens with a focal length that is a function of some integer power of the incident beam radius. We demonstrate that different functional dependences of the photoinduced lens of a thin nonlinear material give typical z-scan curves with special features. The analysis is based on the propagation of Gaussian beams in the approximation of thin lens and small distortion for the nonlinear sample. We obtain that the position of the peak and valley, the transmittance near the focus and the transmittance far from the Rayleigh range depend on the functional dependence of the focal length. Special values of the power reproduce the results obtained for some materials under cw excitation.

Ultrafast nonlinear optical properties of TiO2nanoclusters at 850 nm

“…The time dependence for the nonlinear refractive index is multicausal. There is evidence that a z-scan [9] does not distinguish the phenomena that generate the nonlinearity -the typical distance between peak and valley in the transmission proportional to the Raleigh length is reasonable for a fast nonlinearity. Other phenomena, such as thermal lensing, has different dependencesuch behavior makes it reasonable to assume that the particular z-scan signature could be affected by the nonlinear effects of low and high order as well as the particular phenomena that cause the effect.…”

Boosting optical nonlinearity in epsilon-near-zero trilayer coatings

“…The focal length of the thermal lens caused by the thermal lens effect can be described as a function of the sample position in which the laser and sample parameters E p , f L , ω ( z ), and L are fixed experimentally. E. R. Lara et al modeled the sample with varying refractive index as an equivalent lens and demonstrated that normalized transmittance curves are focal length dependent by using the transmission matrix method; 20 for f > z 0 , the normalized transmittance of closed-aperture Z-scan can be written as…”

“…This radial temperature gradient leads to a thermal lens effect. The focal length of the equivalent lens f (z) can be described as 19 20 for f 4 z 0 , the normalized transmittance of closed-aperture Z-scan can be written as…”

Two nonlinear optical processes in Z-scan curves of a bleached photographic film

“…This model is based on the idea that when a thin nonlinear medium is illuminated by a Gaussian beam, the effect over the beam can be described as that of a lens with a focal length F given by [14]:…”

“…We include this idea in two models to describe the experimental behavior observed in [10]. One of the models is based on the idea of that a lens is photoinduced in the samples with a focal length that depends on the incident beam radius to some power [14] but this power changes with the position of the sample. The second model is based on the nonlocality of the nonlinear response of the sample [15], that also can change with the position.…”