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The basic Sheik-Bahae formalism has been extended to include the possibility of nonlocal response of samples in Z-scan experiments. This is made possible by introducing a nonlocal parameter in the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample. This phase shift has been optimized to be appropriate for describing the Z-scan results of samples with thicknesses much smaller than the Rayleigh length of the Gaussian beams (thin samples). Using this kind of phase shift, the basic formulas for the on-axis Gaussian beam transmittance in the far-field and peak-to-valley separation distance and transmittance difference have been provided. A simple method has been devised for obtaining the nonlinear index of refraction as well as the nonlocal parameter from the Z-scan curves. This method can be of great assistance in determining the more precise values of the nonlinear index of refraction when the sample response is nonlocal. The main criterion for the applicability of our model has been established in terms of the measurable Z-scan data.

The presence of background gases is typical in most pulsed laser deposition (PLD) applications and there is a need for methods which do not suffer from the oversimplified assumption of collisionless transfer of the target atoms onto the substrate in analytical descriptions. In this work, we give a microscopic description of a thermalization process by following the history of each ablated particle by Monte Carlo calculations. TRIM code (SRIM2010), which is capable of quantum mechanical treatment of ion–atom collisions, has been used in our simulations. Various kinetic parameters of ablated Al ions during target-to-substrate transfer have been calculated to demonstrate the efficient role of background gas atoms in thermalization of ions. Moreover, the growing parameters of interest in PLD have been calculated to achieve the optimal deposition conditions in the presence of a background gas. A base pressure of 1 × 10−1 Torr and 2–3 cm of target-to-substrate distance have been found to be the optimal conditions in PLD of Al in Ar gas environment. Our model can be used to obtain the first estimates of nonreactive PLD parameters, such as the background gas pressure and the target-to-substrate distance for the growth of even more complex materials in the presence of different background gases.

Knowing the Gaussian beam parameters, such as its radius of curvature and spot size during propagation in nonlinear Kerr media, is of paramount importance in describing the observable far-field diffraction ring patterns as well as in design and stability analysis of Kerr-lens mode-locked resonators. Specifically, the sign of the beam radius of curvature after exiting these media has been proposed to be of assistance in recognizing their optical nonlinearity sign through determining the type of diffraction ring pattern in the far field. In order to be able to trace the evolution of the beam parameters in the Gaussian beam formalism, we have used the common aberration-free theory. We have shown that the nonlinear propagation problem of a fundamental Gaussian beam in a Kerr medium with an intensity-dependent index of refraction can be handled by assuming a ducting index profile along the propagation direction. Knowing the familiar ABCD matrix of a duct, the evolution of the mentioned beam parameters can be traced during propagation using the ABCD law in Gaussian beam theory. We have validated our ducting model by comparing its results with the outcomes of one widely used and accepted model which has been known to yield consistent results when electronic optical nonlinearity prevails. We have shown that when thermal optical nonlinearity is dominant, as in diffraction ring observation experiments, our ducting model yields sensible results and should be used. Our model predicts that when the sign of the thermal nonlinearity and the beam radius of curvature on the entrance plane of the medium are positive, the sign of the beam radius of curvature on the exit plane may have either sign, depending on the medium thickness used in the experiment. Hence, two types of diffraction ring pattern may be obtained using the same medium with two different thicknesses and this may cast doubt on the validity of the methods proposing the detection of the optical nonlinearity signs by observing these patterns. We have proposed a simple procedure for experimentally obtaining the two different types of diffraction pattern from the same medium.