We present for the first time a comparison under similar circumstances between Laguerre-Gauss beams (LGBs) and Bessel beams (BB), and show that the former can be a better option for many applications in which BBs are currently used. By solving the Laguerre-Gauss differential equation in the asymptotic limit of a large radial index, we find the parameters to perform a peer comparison, showing that LGBs can propagate quasi-nondiffracting beams within the same region of space where the corresponding BBs do. We also demonstrate that LGBs, which have the property of self-healing, are more robust in the sense that they can propagate further than BBs under similar initial conditions.
Considering that the nonlinear photoinduced phase shift to a Gaussian beam in a thin sample of nonlocal nonlinear media can be modeled as a Gaussian function to some real power the far-field can be calculated using the Fraunhofer integral. In this paper we calculate numerically this integral to obtain the on-axis intensity in a Z -scan experiment or the intensity pattern in a self-phase modulation experiment. Experimental results of samples under cw illumination are fitted using the model with a good correspondence between experimental and numerical results. The model presented is adequate to describe samples with any magnitude of the maximum nonlinear photoinduced phase shift of purely refractive local or nonlocal nonlinear thin media.
In this work we present a simple model that can be used to calculate the far field intensity distributions when a Gaussian beam cross a thin sample of nonlinear media but the response can be nonlocal.
This paper explains and illustrates the application of the evolution operator method to solve problems in quantum mechanics. Currently, this method has been proposed as a useful way to overcome some misconceptions in quantum mechanics. To illustrate the method, we apply it to analyze and study the case of a quantum system inside an infinite square well potential (ISWP), and compare this result with that obtained using the traditional method. Also, we analyze the collapse and revival phenomenon in the ISWP. In this case, we argue that the usual approach to studying this effect requires one to extend the function’s domain to infinity; however, there has not been any assurance that this extension preserves the self-adjointness of the Hamiltonian operator. The self-adjointness of the Hamiltonian operator is a vital requirement to guarantee the uniqueness of the Schrödinger equation’s solution.
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.
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