TY  - JOUR
AU  - Sanz, Angel
AU  - Davidovic, Milena
AU  - Bozic, Mirjana
PY  - 2020
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2212
AB  - Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation,
which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al.
(J. Opt. Soc. Am. A 1986, 3, 536–540) found a paraxial solution to Maxwell’s equation in vacuum,
which includes polarization in a natural way, though still preserving the spatial Gaussianity
of the beams. In this regard, it seems that these solutions, known as Gauss-Maxwell beams,
are particularly appropriate and a natural tool in optical problems dealing with Gaussian beams acted
or manipulated by polarizers. In this work, inspired in the Bohmian picture of quantum mechanics,
a hydrodynamic-type extension of such a formulation is provided and discussed, complementing
the notion of electromagnetic field with that of (electromagnetic) flow or streamline. In this regard,
the method proposed has the advantage that the rays obtained from it render a bona fide description of the spatial distribution of electromagnetic energy, since they are in compliance with the local
space changes undergone by the time-averaged Poynting vector. This feature confers the approach a potential interest in the analysis and description of single-photon experiments, because of the direct connection between these rays and the average flow exhibited by swarms of identical photons (regardless of the particular motion, if any, that these entities might have), at least in the case of Gaussian input beams. In order to illustrate the approach, here it is applied to two common scenarios, namely the diffraction undergone by a single Gauss-Maxwell beam and the interference produced by a coherent superposition of two of such beams.
PB  - MDPI
T2  - APPLIED SCIENCES-BASEL
T1  - Bohmian-Based Approach to Gauss-Maxwell Beams
IS  - 5
VL  - 10
DO  - 10.3390/app10051808
ER  - 

@article{
author = "Sanz, Angel and Davidovic, Milena and Bozic, Mirjana",
year = "2020",
abstract = "Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation,
which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al.
(J. Opt. Soc. Am. A 1986, 3, 536–540) found a paraxial solution to Maxwell’s equation in vacuum,
which includes polarization in a natural way, though still preserving the spatial Gaussianity
of the beams. In this regard, it seems that these solutions, known as Gauss-Maxwell beams,
are particularly appropriate and a natural tool in optical problems dealing with Gaussian beams acted
or manipulated by polarizers. In this work, inspired in the Bohmian picture of quantum mechanics,
a hydrodynamic-type extension of such a formulation is provided and discussed, complementing
the notion of electromagnetic field with that of (electromagnetic) flow or streamline. In this regard,
the method proposed has the advantage that the rays obtained from it render a bona fide description of the spatial distribution of electromagnetic energy, since they are in compliance with the local
space changes undergone by the time-averaged Poynting vector. This feature confers the approach a potential interest in the analysis and description of single-photon experiments, because of the direct connection between these rays and the average flow exhibited by swarms of identical photons (regardless of the particular motion, if any, that these entities might have), at least in the case of Gaussian input beams. In order to illustrate the approach, here it is applied to two common scenarios, namely the diffraction undergone by a single Gauss-Maxwell beam and the interference produced by a coherent superposition of two of such beams.",
publisher = "MDPI",
journal = "APPLIED SCIENCES-BASEL",
title = "Bohmian-Based Approach to Gauss-Maxwell Beams",
number = "5",
volume = "10",
doi = "10.3390/app10051808"
}

Sanz, A., Davidovic, M.,& Bozic, M.. (2020). Bohmian-Based Approach to Gauss-Maxwell Beams. in APPLIED SCIENCES-BASEL
MDPI., 10(5).
https://doi.org/10.3390/app10051808

Sanz A, Davidovic M, Bozic M. Bohmian-Based Approach to Gauss-Maxwell Beams. in APPLIED SCIENCES-BASEL. 2020;10(5).
doi:10.3390/app10051808 .

Sanz, Angel, Davidovic, Milena, Bozic, Mirjana, "Bohmian-Based Approach to Gauss-Maxwell Beams" in APPLIED SCIENCES-BASEL, 10, no. 5 (2020),
https://doi.org/10.3390/app10051808 . .

TY  - JOUR
AU  - Davidović, Milena
AU  - Tatjana, Marković-Topalović
AU  - Sliško, Josip
AU  - Bozic, Mirjana
PY  - 2020
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2213
AB  - In the  same chapter of  his  book Opera geometrica, Torricelli published1 two discoveries:  1) initial velocity of a jet from a container increases with the square root of the depth of the hole¸ 2) he draw the pattern of  jets from three openings at the wall of a container filled with water to constant level H and determined the height of the hole  with maximal range. In studying the pattern Torricelli used the mentioned law of initial velocities and Galileo’s law of free fall and projectile motion. The first Torricelli’s discovery is now well known in physics education under the name Torricelli’s law. But the pattern of jets from a container entered into physics literature along two ways, which we propose to name: “da Vinci’s way” and “Torricelli’s way”.  Along “da Vinci’s way” educators and textbook authors (Ref. 2 and textbooks and articles cited by Biser3 and Atkin4) present incorrect drawings of jets in order to incorrectly “demonstrate”the correct Torricelli’s law. Along “Torricelli’s way” educators point out3-11 that the shape and range of a jet depend on the initial velocity as well as on the time of flight of a jet.  Using algebra and calculus (instead of geometry, proportions and narrative used by Torricelli and Galileo) the shape of trajectories, their envelope, range and meeting of two jets at an arbitrary datum level, are determined by quadratic function and quadratic equation.   Their detailed mathematical analysis is presented in this paper. 
In describing how the use of water and air through time has developed our scientific understanding, and how to bring fluid mechanics to the general public, E. Guyon and M. Guyon12 observed: “Water fountains and jets are still being built and are favorite public attractions but, alas, are seldom connected to their scientific meaning, unlike the Torricelli fountain shown in Fig. 1.”
PB  - American Association of Physics Teachers
T2  - The Physics Teacher
T1  - Visualizing properties of a quadratic function using Torricelli’S fountain
IS  - April
VL  - 58
DO  - 10.1119/1.5145475
ER  - 

@article{
author = "Davidović, Milena and Tatjana, Marković-Topalović and Sliško, Josip and Bozic, Mirjana",
year = "2020",
abstract = "In the  same chapter of  his  book Opera geometrica, Torricelli published1 two discoveries:  1) initial velocity of a jet from a container increases with the square root of the depth of the hole¸ 2) he draw the pattern of  jets from three openings at the wall of a container filled with water to constant level H and determined the height of the hole  with maximal range. In studying the pattern Torricelli used the mentioned law of initial velocities and Galileo’s law of free fall and projectile motion. The first Torricelli’s discovery is now well known in physics education under the name Torricelli’s law. But the pattern of jets from a container entered into physics literature along two ways, which we propose to name: “da Vinci’s way” and “Torricelli’s way”.  Along “da Vinci’s way” educators and textbook authors (Ref. 2 and textbooks and articles cited by Biser3 and Atkin4) present incorrect drawings of jets in order to incorrectly “demonstrate”the correct Torricelli’s law. Along “Torricelli’s way” educators point out3-11 that the shape and range of a jet depend on the initial velocity as well as on the time of flight of a jet.  Using algebra and calculus (instead of geometry, proportions and narrative used by Torricelli and Galileo) the shape of trajectories, their envelope, range and meeting of two jets at an arbitrary datum level, are determined by quadratic function and quadratic equation.   Their detailed mathematical analysis is presented in this paper. 
In describing how the use of water and air through time has developed our scientific understanding, and how to bring fluid mechanics to the general public, E. Guyon and M. Guyon12 observed: “Water fountains and jets are still being built and are favorite public attractions but, alas, are seldom connected to their scientific meaning, unlike the Torricelli fountain shown in Fig. 1.”",
publisher = "American Association of Physics Teachers",
journal = "The Physics Teacher",
title = "Visualizing properties of a quadratic function using Torricelli’S fountain",
number = "April",
volume = "58",
doi = "10.1119/1.5145475"
}

Davidović, M., Tatjana, M., Sliško, J.,& Bozic, M.. (2020). Visualizing properties of a quadratic function using Torricelli’S fountain. in The Physics Teacher
American Association of Physics Teachers., 58(April).
https://doi.org/10.1119/1.5145475

Davidović M, Tatjana M, Sliško J, Bozic M. Visualizing properties of a quadratic function using Torricelli’S fountain. in The Physics Teacher. 2020;58(April).
doi:10.1119/1.5145475 .

Davidović, Milena, Tatjana, Marković-Topalović, Sliško, Josip, Bozic, Mirjana, "Visualizing properties of a quadratic function using Torricelli’S fountain" in The Physics Teacher, 58, no. April (2020),
https://doi.org/10.1119/1.5145475 . .