2019 IEEE 8th International Conference on Advanced Optoelectronics and Lasers (CAOL) 2019
DOI: 10.1109/caol46282.2019.9019582
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Differential operator formalism for axial optical vortex beam and the double-phase-ramp converter

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Cited by 3 publications
(3 citation statements)
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“…Let us now discuss a method to easily find the analytical solutions of the GPE (1) for multisingular initial conditions, Equation (4), in the linear case, g = 0. This method was introduced in the context of the paraxial wave equation in optics [40,41] (see also [82] for an application to a different system). In the following sections we will compare the solutions analytically obtained for the linear case, with some interesting examples calculated numerically for the full non-linear equation.…”
Section: Model and Systemmentioning
confidence: 99%
“…Let us now discuss a method to easily find the analytical solutions of the GPE (1) for multisingular initial conditions, Equation (4), in the linear case, g = 0. This method was introduced in the context of the paraxial wave equation in optics [40,41] (see also [82] for an application to a different system). In the following sections we will compare the solutions analytically obtained for the linear case, with some interesting examples calculated numerically for the full non-linear equation.…”
Section: Model and Systemmentioning
confidence: 99%
“…( 4), in the linear case, g = 0. This method was introduced in the context of the paraxial wave equation in optics [55,56] (see also [60] for an application to a different system). In the following sections we will compare the solutions analytically obtained for the linear case, with some interesting examples calculated numerically for the full non-linear equation.…”
Section: Model and Systemmentioning
confidence: 99%
“…The problems of the dark ray structure control studied in [7,40] admit an exhaustive analytical investigation based on the general theoretical approach in a view of differential operator formalism applicable to a wide range of diffraction situations. Its first application for singular skeleton description for the problem of passing Lagguerre-Gaussian beam through DPR-converter is presented in [41]. We hope that employment of differential operator formalism will greatly facilitate further development of the presented ideas in different diffractive tasks.…”
Section: Introductionmentioning
confidence: 99%