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.
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.
Abstract:The Stern-Gerlach experiment (SGE) is one of the foundational experiments in quantum physics. It has been used in both the teaching and the development of quantum mechanics. However, for various reasons, some of its quantum features and implications are not fully addressed or comprehended in the current literature. Hence, the main aim of this paper is to demonstrate that the SGE possesses a quantum nonlocal character that has not previously been visualized or presented before. Accordingly, to show the nonlocality into the SGE, we calculate the quantum correlations C(z, θ) by redefining the Banaszek-Wódkiewicz correlation in terms of the Wigner operator, that is C(z, θ) = Ψ|Ŵ(z, p z )σ(θ)|Ψ , whereŴ(z, p z ) is the Wigner operator,σ(θ) is the Pauli spin operator in an arbitrary direction θ and |Ψ is the quantum state given by an entangled state of the external degree of freedom and the eigenstates of the spin. We show that this correlation function for the SGE violates the Clauser-Horne-Shimony-Holt Bell inequality. Thus, this feature of the SGE might be interesting for both the teaching of quantum mechanics and to investigate the phenomenon of quantum nonlocality.
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.
In this work we present numerical results of the far field intensity distributions obtained for a Gaussian beam after crossing a thin nonlinear nonlocal material that exhibit nonlinear refraction and absorption. The distributions are obtained for different positions along the Z axis and different signs of the nonlinear absorption. The results demonstrate that the far field intensity patterns obtained for strong nonlocal media are more affected by the presence of the nonlinear absorption than weak nonlocal media.
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