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  - Davidović, Milos D.
AU  - Sanz, Angel S.
AU  - Božić, Mirjana
AU  - Vasiljević, Darko
PY  - 2018
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/983
AB  - In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where the diffraction of laser light appears in the region of geometric shadow, while intensity oscillations are observed in the non-obstructed area. On both sides of the edge, there are also very long light traces along the normal to the edge of the obstacle. The theoretical explanation of this phenomenon is based on the Fresnel-Kirchhoff diffraction theory applied to the Gaussian beam propagation behind the obstacle. In this paper, we supplement this explanation by considering electromagnetic flow lines, which provide a more complete interpretation of the phenomenon in terms of electric and magnetic fields and flux lines; at the same time, that can be related to average photon paths.
PB  - Springer New York LLC
T2  - Journal of Russian Laser Research
T1  - Trajectory-based interpretation of laser light diffraction by a sharp edge
EP  - 447
IS  - 5
SP  - 438
VL  - 39
DO  - 10.1007/s10946-018-9738-9
ER  - 

@article{
author = "Davidović, Milena and Davidović, Milos D. and Sanz, Angel S. and Božić, Mirjana and Vasiljević, Darko",
year = "2018",
abstract = "In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where the diffraction of laser light appears in the region of geometric shadow, while intensity oscillations are observed in the non-obstructed area. On both sides of the edge, there are also very long light traces along the normal to the edge of the obstacle. The theoretical explanation of this phenomenon is based on the Fresnel-Kirchhoff diffraction theory applied to the Gaussian beam propagation behind the obstacle. In this paper, we supplement this explanation by considering electromagnetic flow lines, which provide a more complete interpretation of the phenomenon in terms of electric and magnetic fields and flux lines; at the same time, that can be related to average photon paths.",
publisher = "Springer New York LLC",
journal = "Journal of Russian Laser Research",
title = "Trajectory-based interpretation of laser light diffraction by a sharp edge",
pages = "447-438",
number = "5",
volume = "39",
doi = "10.1007/s10946-018-9738-9"
}

Davidović, M., Davidović, M. D., Sanz, A. S., Božić, M.,& Vasiljević, D.. (2018). Trajectory-based interpretation of laser light diffraction by a sharp edge. in Journal of Russian Laser Research
Springer New York LLC., 39(5), 438-447.
https://doi.org/10.1007/s10946-018-9738-9

Davidović M, Davidović MD, Sanz AS, Božić M, Vasiljević D. Trajectory-based interpretation of laser light diffraction by a sharp edge. in Journal of Russian Laser Research. 2018;39(5):438-447.
doi:10.1007/s10946-018-9738-9 .

Davidović, Milena, Davidović, Milos D., Sanz, Angel S., Božić, Mirjana, Vasiljević, Darko, "Trajectory-based interpretation of laser light diffraction by a sharp edge" in Journal of Russian Laser Research, 39, no. 5 (2018):438-447,
https://doi.org/10.1007/s10946-018-9738-9 . .

TY  - JOUR
AU  - Davidović, Milena
AU  - Davidović, Miloš D.
AU  - Sanz, Angel S
AU  - Božić, Mirjana
AU  - Vasiljević, Darko
PY  - 2018
UR  - https://link.springer.com/article/10.1007/s10946-018-9738-9
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1753
AB  - In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where the diffraction of laser light appears in the region of geometric shadow, while intensity oscillations are observed in the non-obstructed area. On both sides of the edge, there are also very long light traces along the normal to the edge of the obstacle. The theoretical explanation of this phenomenon is based on the Fresnel–Kirchhoff diffraction theory applied to the Gaussian beam propagation behind the obstacle. In this paper, we supplement this explanation by considering electromagnetic flow lines, which provide a more complete interpretation of the phenomenon in terms of electric and magnetic fields and flux lines; at the same time, that can be related to average photon paths.
PB  - Springer
T2  - Journal of Russian Laser Research
T1  - Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge
VL  - 39
DO  - 10.1007/s10946-018-9738-9
ER  - 

@article{
author = "Davidović, Milena and Davidović, Miloš D. and Sanz, Angel S and Božić, Mirjana and Vasiljević, Darko",
year = "2018",
abstract = "In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where the diffraction of laser light appears in the region of geometric shadow, while intensity oscillations are observed in the non-obstructed area. On both sides of the edge, there are also very long light traces along the normal to the edge of the obstacle. The theoretical explanation of this phenomenon is based on the Fresnel–Kirchhoff diffraction theory applied to the Gaussian beam propagation behind the obstacle. In this paper, we supplement this explanation by considering electromagnetic flow lines, which provide a more complete interpretation of the phenomenon in terms of electric and magnetic fields and flux lines; at the same time, that can be related to average photon paths.",
publisher = "Springer",
journal = "Journal of Russian Laser Research",
title = "Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge",
volume = "39",
doi = "10.1007/s10946-018-9738-9"
}

Davidović, M., Davidović, M. D., Sanz, A. S., Božić, M.,& Vasiljević, D.. (2018). Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge. in Journal of Russian Laser Research
Springer., 39.
https://doi.org/10.1007/s10946-018-9738-9

Davidović M, Davidović MD, Sanz AS, Božić M, Vasiljević D. Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge. in Journal of Russian Laser Research. 2018;39.
doi:10.1007/s10946-018-9738-9 .

Davidović, Milena, Davidović, Miloš D., Sanz, Angel S, Božić, Mirjana, Vasiljević, Darko, "Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge" in Journal of Russian Laser Research, 39 (2018),
https://doi.org/10.1007/s10946-018-9738-9 . .

TY  - JOUR
AU  - Sanz, Angel S.
AU  - Davidović, Milena
AU  - Božić, Mirjana
PY  - 2015
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/703
AB  - Atomic three-grating Mach Zehnder interferometry constitutes an important tool to probe fundamental aspects the quantum theory. There is, however, a remarkable gap in the literature betweenthe oversimplified models and robust numerical simulations considered to describe the corresponding experiments. Consequently, the former usually lead to paradoxical scenarios, such as the wave-particle dual behavior of atoms, while the latter make difficult the data analysis in simple terms. Here these issues are tackled by means of a simple grating working model consisting of evenly-spaced Gaussian slits. As is shown, this model suffices to explore and explain such experiments both analytically and numerically, giving a good account of the full atomic journey inside the interferometer, and hence contributing to make less mystic the physics involved. More specifically, it provides a clear and unambiguous picture of the wavefront splitting that takes place inside the interferometer, illustrating how the momentum along each emerging diffraction order is well defined even though the wave function itself still displays a rather complex shape. To this end, the local transverse momentum is also introduced in this context as a reliable analytical tool. The splitting, apart from being a key issue to understand atomic Mach-Zehnder interferometry, also demonstrates at a fundamental level how wave and particle aspects are always present in the experiment, without incurring in any contradiction or interpretive paradox. On the other hand, at a practical level, the generality and versatility of the model and methodology presented, makes them suitable to attack analogous problems in a simple manner after a convenient tuning.
PB  - Academic Press Inc.
T2  - Annals of Physics
T1  - Full quantum mechanical analysis of atomic three-grating Mach-Zehnder interferometry
EP  - 221
SP  - 205
VL  - 353
DO  - 10.1016/j.aop.2014.11.012
ER  - 

@article{
author = "Sanz, Angel S. and Davidović, Milena and Božić, Mirjana",
year = "2015",
abstract = "Atomic three-grating Mach Zehnder interferometry constitutes an important tool to probe fundamental aspects the quantum theory. There is, however, a remarkable gap in the literature betweenthe oversimplified models and robust numerical simulations considered to describe the corresponding experiments. Consequently, the former usually lead to paradoxical scenarios, such as the wave-particle dual behavior of atoms, while the latter make difficult the data analysis in simple terms. Here these issues are tackled by means of a simple grating working model consisting of evenly-spaced Gaussian slits. As is shown, this model suffices to explore and explain such experiments both analytically and numerically, giving a good account of the full atomic journey inside the interferometer, and hence contributing to make less mystic the physics involved. More specifically, it provides a clear and unambiguous picture of the wavefront splitting that takes place inside the interferometer, illustrating how the momentum along each emerging diffraction order is well defined even though the wave function itself still displays a rather complex shape. To this end, the local transverse momentum is also introduced in this context as a reliable analytical tool. The splitting, apart from being a key issue to understand atomic Mach-Zehnder interferometry, also demonstrates at a fundamental level how wave and particle aspects are always present in the experiment, without incurring in any contradiction or interpretive paradox. On the other hand, at a practical level, the generality and versatility of the model and methodology presented, makes them suitable to attack analogous problems in a simple manner after a convenient tuning.",
publisher = "Academic Press Inc.",
journal = "Annals of Physics",
title = "Full quantum mechanical analysis of atomic three-grating Mach-Zehnder interferometry",
pages = "221-205",
volume = "353",
doi = "10.1016/j.aop.2014.11.012"
}

Sanz, A. S., Davidović, M.,& Božić, M.. (2015). Full quantum mechanical analysis of atomic three-grating Mach-Zehnder interferometry. in Annals of Physics
Academic Press Inc.., 353, 205-221.
https://doi.org/10.1016/j.aop.2014.11.012

Sanz AS, Davidović M, Božić M. Full quantum mechanical analysis of atomic three-grating Mach-Zehnder interferometry. in Annals of Physics. 2015;353:205-221.
doi:10.1016/j.aop.2014.11.012 .

Sanz, Angel S., Davidović, Milena, Božić, Mirjana, "Full quantum mechanical analysis of atomic three-grating Mach-Zehnder interferometry" in Annals of Physics, 353 (2015):205-221,
https://doi.org/10.1016/j.aop.2014.11.012 . .

TY  - JOUR
AU  - Davidović, Milena
AU  - Sanz, Angel S.
AU  - Božić, Mirjana
PY  - 2015
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/718
AB  - Bohmian mechanics, a hydrodynamic formulation of quantum mechanics, relies on the concept of trajectory, which evolves in time in compliance with dynamical information conveyed by the wave function. Here, this appealing idea is considered to analyze both classical and quantum interference, thus providing an alternative and more intuitive framework to understand the time evolution of waves either in terms of the flow of energy (for instance, for mechanical waves, sound waves, and electromagnetic waves) or analogously the flow of probability (quantum waves). Furthermore, this procedure also supplies a more robust explanation of interference phenomena, which currently is only based on the superposition principle. That is, while this principle only describes how different waves combine and what effects these combinations may lead to, flow lines provide a more precise explanation on how the energy or probability propagates in space before, during, and after the combination of such waves, without dealing with them separately (i.e., the combination or superposition is taken as a whole). In this sense, concepts such as constructive and destructive interference, typically associated with the superposition principle, physically correspond to more or less dense swarms of (energy or probability) flow lines. A direct consequence of this description is that, when considering the distribution of electromagnetic energy flow lines behind two slits, each one covered by a differently oriented polarizer, it is naturally found that external observers' information on the slit crossed by single photons (understood as energy parcels) is totally irrelevant for the existence of interference fringes, in striking contrast to what is commonly stated and taught.
PB  - Springer New York LLC
T2  - Journal of Russian Laser Research
T1  - Description of classical and quantum interference in view of the concept of flow line
EP  - 342
IS  - 4
SP  - 329
VL  - 36
DO  - 10.1007/s10946-015-9507-y
ER  - 

@article{
author = "Davidović, Milena and Sanz, Angel S. and Božić, Mirjana",
year = "2015",
abstract = "Bohmian mechanics, a hydrodynamic formulation of quantum mechanics, relies on the concept of trajectory, which evolves in time in compliance with dynamical information conveyed by the wave function. Here, this appealing idea is considered to analyze both classical and quantum interference, thus providing an alternative and more intuitive framework to understand the time evolution of waves either in terms of the flow of energy (for instance, for mechanical waves, sound waves, and electromagnetic waves) or analogously the flow of probability (quantum waves). Furthermore, this procedure also supplies a more robust explanation of interference phenomena, which currently is only based on the superposition principle. That is, while this principle only describes how different waves combine and what effects these combinations may lead to, flow lines provide a more precise explanation on how the energy or probability propagates in space before, during, and after the combination of such waves, without dealing with them separately (i.e., the combination or superposition is taken as a whole). In this sense, concepts such as constructive and destructive interference, typically associated with the superposition principle, physically correspond to more or less dense swarms of (energy or probability) flow lines. A direct consequence of this description is that, when considering the distribution of electromagnetic energy flow lines behind two slits, each one covered by a differently oriented polarizer, it is naturally found that external observers' information on the slit crossed by single photons (understood as energy parcels) is totally irrelevant for the existence of interference fringes, in striking contrast to what is commonly stated and taught.",
publisher = "Springer New York LLC",
journal = "Journal of Russian Laser Research",
title = "Description of classical and quantum interference in view of the concept of flow line",
pages = "342-329",
number = "4",
volume = "36",
doi = "10.1007/s10946-015-9507-y"
}

Davidović, M., Sanz, A. S.,& Božić, M.. (2015). Description of classical and quantum interference in view of the concept of flow line. in Journal of Russian Laser Research
Springer New York LLC., 36(4), 329-342.
https://doi.org/10.1007/s10946-015-9507-y

Davidović M, Sanz AS, Božić M. Description of classical and quantum interference in view of the concept of flow line. in Journal of Russian Laser Research. 2015;36(4):329-342.
doi:10.1007/s10946-015-9507-y .

Davidović, Milena, Sanz, Angel S., Božić, Mirjana, "Description of classical and quantum interference in view of the concept of flow line" in Journal of Russian Laser Research, 36, no. 4 (2015):329-342,
https://doi.org/10.1007/s10946-015-9507-y . .

TY  - JOUR
AU  - Davidović, Milena
AU  - Sanz, Angel S.
AU  - Božić, Mirjana
AU  - Arsenović, Dušan
AU  - Dimić, Dragan
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/546
AB  - We present a trajectory-based interpretation of Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot. This approach is based on the equation of the trajectory associated with the quantum probability current density in the case of massive particles, and the Poynting vector for the electromagnetic field in the case of photons. Both the form and properties of the evaluated photon trajectories are in good agreement with the averaged trajectories of single photons observed recently in Young's experiment by Steinberg's group at the University of Toronto. In the case of the Arago-Fresnel laws for polarized light, the trajectory interpretation presented here differs from interpretations based on the concept of 'which-way' (or 'which-slit') information and quantum erasure. More specifically, the observer's information about the slit that the photons went through is not relevant to the existence of interference; what is relevant is the form of the electromagnetic energy density and its evolution, which will model consequently the distribution of trajectories and their topology. Finally, we also show that the distributions of end points of a large number of evaluated photon trajectories are in agreement with the distributions measured at the screen behind a circular disc, clearly giving rise to the Poisson-Arago spot.
T2  - Physica Scripta
T1  - Trajectory-based interpretation of Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot for photons and massive particles
DO  - 10.1088/0031-8949/2013/T153/014015
ER  - 

@article{
author = "Davidović, Milena and Sanz, Angel S. and Božić, Mirjana and Arsenović, Dušan and Dimić, Dragan",
year = "2013",
abstract = "We present a trajectory-based interpretation of Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot. This approach is based on the equation of the trajectory associated with the quantum probability current density in the case of massive particles, and the Poynting vector for the electromagnetic field in the case of photons. Both the form and properties of the evaluated photon trajectories are in good agreement with the averaged trajectories of single photons observed recently in Young's experiment by Steinberg's group at the University of Toronto. In the case of the Arago-Fresnel laws for polarized light, the trajectory interpretation presented here differs from interpretations based on the concept of 'which-way' (or 'which-slit') information and quantum erasure. More specifically, the observer's information about the slit that the photons went through is not relevant to the existence of interference; what is relevant is the form of the electromagnetic energy density and its evolution, which will model consequently the distribution of trajectories and their topology. Finally, we also show that the distributions of end points of a large number of evaluated photon trajectories are in agreement with the distributions measured at the screen behind a circular disc, clearly giving rise to the Poisson-Arago spot.",
journal = "Physica Scripta",
title = "Trajectory-based interpretation of Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot for photons and massive particles",
doi = "10.1088/0031-8949/2013/T153/014015"
}

Davidović, M., Sanz, A. S., Božić, M., Arsenović, D.,& Dimić, D.. (2013). Trajectory-based interpretation of Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot for photons and massive particles. in Physica Scripta.
https://doi.org/10.1088/0031-8949/2013/T153/014015

Davidović M, Sanz AS, Božić M, Arsenović D, Dimić D. Trajectory-based interpretation of Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot for photons and massive particles. in Physica Scripta. 2013;.
doi:10.1088/0031-8949/2013/T153/014015 .

Davidović, Milena, Sanz, Angel S., Božić, Mirjana, Arsenović, Dušan, Dimić, Dragan, "Trajectory-based interpretation of Young's experiment, the Arago-Fresnel laws and the Poisson-Arago spot for photons and massive particles" in Physica Scripta (2013),
https://doi.org/10.1088/0031-8949/2013/T153/014015 . .

TY  - JOUR
AU  - Davidović, Milena
AU  - Sanz, Angel S.
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/553
AB  - Young's two-slit experiment constitutes the paradigm of quantum complementarity. According to the complementarity principle, complementary aspects of quantum systems cannot be measured at the same time by the same experiment. This has been a long debate in quantum mechanics since its inception. But is this a true constraint? In 2011, an astounding realization of this experiment showed that perhaps this is not the case, and the boundaries to our understanding of the quantum world are still far away.
T2  - Europhysics News
T1  - How does light move?: Determining the flow of light without destroying interference
EP  - 36
IS  - 6
SP  - 33
VL  - 44
DO  - 10.1051/epn/2013604
ER  - 

@article{
author = "Davidović, Milena and Sanz, Angel S.",
year = "2013",
abstract = "Young's two-slit experiment constitutes the paradigm of quantum complementarity. According to the complementarity principle, complementary aspects of quantum systems cannot be measured at the same time by the same experiment. This has been a long debate in quantum mechanics since its inception. But is this a true constraint? In 2011, an astounding realization of this experiment showed that perhaps this is not the case, and the boundaries to our understanding of the quantum world are still far away.",
journal = "Europhysics News",
title = "How does light move?: Determining the flow of light without destroying interference",
pages = "36-33",
number = "6",
volume = "44",
doi = "10.1051/epn/2013604"
}

Davidović, M.,& Sanz, A. S.. (2013). How does light move?: Determining the flow of light without destroying interference. in Europhysics News, 44(6), 33-36.
https://doi.org/10.1051/epn/2013604

Davidović M, Sanz AS. How does light move?: Determining the flow of light without destroying interference. in Europhysics News. 2013;44(6):33-36.
doi:10.1051/epn/2013604 .

Davidović, Milena, Sanz, Angel S., "How does light move?: Determining the flow of light without destroying interference" in Europhysics News, 44, no. 6 (2013):33-36,
https://doi.org/10.1051/epn/2013604 . .

TY  - JOUR
AU  - Davidović, Milena
AU  - Sanz, Angel S.
AU  - Božić, Mirjana
AU  - Arsenović, Dušan
PY  - 2012
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/469
AB  - The coherence effects induced by external photons coupled to matter waves inside a Mach-Zehnder three-grating interferometer are analyzed. Alternatively to atom-photon entanglement scenarios, the model considered here only relies on the atomic wavefunction and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. Good quantitative agreement is found when comparing the results obtained from our model with the experimental data.
T2  - Journal of Physics A-Mathematical and Theoretical
T1  - Coherence loss and revivals in atomic interferometry: a quantum-recoil analysis
IS  - 16
VL  - 45
DO  - 10.1088/1751-8113/45/16/165303
ER  - 

@article{
author = "Davidović, Milena and Sanz, Angel S. and Božić, Mirjana and Arsenović, Dušan",
year = "2012",
abstract = "The coherence effects induced by external photons coupled to matter waves inside a Mach-Zehnder three-grating interferometer are analyzed. Alternatively to atom-photon entanglement scenarios, the model considered here only relies on the atomic wavefunction and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. Good quantitative agreement is found when comparing the results obtained from our model with the experimental data.",
journal = "Journal of Physics A-Mathematical and Theoretical",
title = "Coherence loss and revivals in atomic interferometry: a quantum-recoil analysis",
number = "16",
volume = "45",
doi = "10.1088/1751-8113/45/16/165303"
}

Davidović, M., Sanz, A. S., Božić, M.,& Arsenović, D.. (2012). Coherence loss and revivals in atomic interferometry: a quantum-recoil analysis. in Journal of Physics A-Mathematical and Theoretical, 45(16).
https://doi.org/10.1088/1751-8113/45/16/165303

Davidović M, Sanz AS, Božić M, Arsenović D. Coherence loss and revivals in atomic interferometry: a quantum-recoil analysis. in Journal of Physics A-Mathematical and Theoretical. 2012;45(16).
doi:10.1088/1751-8113/45/16/165303 .

Davidović, Milena, Sanz, Angel S., Božić, Mirjana, Arsenović, Dušan, "Coherence loss and revivals in atomic interferometry: a quantum-recoil analysis" in Journal of Physics A-Mathematical and Theoretical, 45, no. 16 (2012),
https://doi.org/10.1088/1751-8113/45/16/165303 . .

TY  - JOUR
AU  - Božić, Mirjana
AU  - Vusković, Leposlava
AU  - Davidović, Milena
AU  - Sanz, Angel S.
PY  - 2011
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/402
AB  - We present an analysis and interpretation of the experiment performed by Jacques et al (2007 Science 315 966), which represents a realization of Wheeler's delayed-choice Gedankenexperiment. Our analysis is based on the evolution of the photon state, since the photon enters into the Mach-Zehnder interferometer (MZI) with a removable beam splitter until it exits. Given the same photon state incident on the output beam splitter BS(output), the photon's state at the exit will be very different depending on whether BSoutput is on or off. Hence, the statistics of photon counts collected by the two detectors, positioned along orthogonal directions at the exit of the interferometer, will also be very different for each case. Therefore, it is not that the choice of inserting (on) or removing (off) a beam splitter leads to a delayed influence on the photon behavior before arriving there, but that such a choice influences the photon state at and after BSoutput, i.e. after it has exited the MZI. The random on/off choice at BSoutput has no delayed effect on the photon to behave as a wave or a corpuscle at the entrance and inside the interferometer, but influences the subsequent evolution of the photon state incident on BS(output).
T2  - Physica Scripta
T1  - On Wheeler's delayed-choice Gedankenexperiment and its laboratory realization
DO  - 10.1088/0031-8949/2011/T143/014007
ER  - 

@article{
author = "Božić, Mirjana and Vusković, Leposlava and Davidović, Milena and Sanz, Angel S.",
year = "2011",
abstract = "We present an analysis and interpretation of the experiment performed by Jacques et al (2007 Science 315 966), which represents a realization of Wheeler's delayed-choice Gedankenexperiment. Our analysis is based on the evolution of the photon state, since the photon enters into the Mach-Zehnder interferometer (MZI) with a removable beam splitter until it exits. Given the same photon state incident on the output beam splitter BS(output), the photon's state at the exit will be very different depending on whether BSoutput is on or off. Hence, the statistics of photon counts collected by the two detectors, positioned along orthogonal directions at the exit of the interferometer, will also be very different for each case. Therefore, it is not that the choice of inserting (on) or removing (off) a beam splitter leads to a delayed influence on the photon behavior before arriving there, but that such a choice influences the photon state at and after BSoutput, i.e. after it has exited the MZI. The random on/off choice at BSoutput has no delayed effect on the photon to behave as a wave or a corpuscle at the entrance and inside the interferometer, but influences the subsequent evolution of the photon state incident on BS(output).",
journal = "Physica Scripta",
title = "On Wheeler's delayed-choice Gedankenexperiment and its laboratory realization",
doi = "10.1088/0031-8949/2011/T143/014007"
}

Božić, M., Vusković, L., Davidović, M.,& Sanz, A. S.. (2011). On Wheeler's delayed-choice Gedankenexperiment and its laboratory realization. in Physica Scripta.
https://doi.org/10.1088/0031-8949/2011/T143/014007

Božić M, Vusković L, Davidović M, Sanz AS. On Wheeler's delayed-choice Gedankenexperiment and its laboratory realization. in Physica Scripta. 2011;.
doi:10.1088/0031-8949/2011/T143/014007 .

Božić, Mirjana, Vusković, Leposlava, Davidović, Milena, Sanz, Angel S., "On Wheeler's delayed-choice Gedankenexperiment and its laboratory realization" in Physica Scripta (2011),
https://doi.org/10.1088/0031-8949/2011/T143/014007 . .

TY  - JOUR
AU  - Sanz, Angel S.
AU  - Davidović, Milena
AU  - Božić, Mirjana
AU  - Miret-Artes, Salvador
PY  - 2010
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/294
AB  - Bohmian mechanics allows to visualize and understand the quantum-mechanical behavior of massive particles in terms of trajectories. As shown by Bialynicki-Birula, Electromagnetism also admits a hydrodynamical formulation when the existence of a wave function for photons (properly defined) is assumed. This formulation thus provides an alternative interpretation of optical phenomena in terms of photon trajectories, whose flow yields a pictorial view of the evolution of the electromagnetic energy density in configuration space. This trajectory-based theoretical framework is considered here to study and analyze the outcome from Young-type diffraction experiments within the context of the Arago-Fresnel laws. More specifically, photon trajectories in the region behind the two slits are obtained in the case where the slits are illuminated by a polarized monochromatic plane wave. Expressions to determine electromagnetic energy flow lines and photon trajectories within this scenario are provided, as well as a procedure to compute them in the particular case of gratings totally transparent inside the slits and completely absorbing outside them. As is shown, the electromagnetic energy flow lines obtained allow to monitor at each point of space the behavior of the electromagnetic energy flow and, therefore, to evaluate the effects caused on it by the presence (right behind each slit) of polarizers with the same or different polarization axes. This leads to a trajectory-based picture of the Arago-Fresnel laws for the interference of polarized light.
T2  - Annals of Physics
T1  - Understanding interference experiments with polarized light through photon trajectories
EP  - 784
IS  - 4
SP  - 763
VL  - 325
DO  - 10.1016/j.aop.2009.12.005
ER  - 

@article{
author = "Sanz, Angel S. and Davidović, Milena and Božić, Mirjana and Miret-Artes, Salvador",
year = "2010",
abstract = "Bohmian mechanics allows to visualize and understand the quantum-mechanical behavior of massive particles in terms of trajectories. As shown by Bialynicki-Birula, Electromagnetism also admits a hydrodynamical formulation when the existence of a wave function for photons (properly defined) is assumed. This formulation thus provides an alternative interpretation of optical phenomena in terms of photon trajectories, whose flow yields a pictorial view of the evolution of the electromagnetic energy density in configuration space. This trajectory-based theoretical framework is considered here to study and analyze the outcome from Young-type diffraction experiments within the context of the Arago-Fresnel laws. More specifically, photon trajectories in the region behind the two slits are obtained in the case where the slits are illuminated by a polarized monochromatic plane wave. Expressions to determine electromagnetic energy flow lines and photon trajectories within this scenario are provided, as well as a procedure to compute them in the particular case of gratings totally transparent inside the slits and completely absorbing outside them. As is shown, the electromagnetic energy flow lines obtained allow to monitor at each point of space the behavior of the electromagnetic energy flow and, therefore, to evaluate the effects caused on it by the presence (right behind each slit) of polarizers with the same or different polarization axes. This leads to a trajectory-based picture of the Arago-Fresnel laws for the interference of polarized light.",
journal = "Annals of Physics",
title = "Understanding interference experiments with polarized light through photon trajectories",
pages = "784-763",
number = "4",
volume = "325",
doi = "10.1016/j.aop.2009.12.005"
}

Sanz, A. S., Davidović, M., Božić, M.,& Miret-Artes, S.. (2010). Understanding interference experiments with polarized light through photon trajectories. in Annals of Physics, 325(4), 763-784.
https://doi.org/10.1016/j.aop.2009.12.005

Sanz AS, Davidović M, Božić M, Miret-Artes S. Understanding interference experiments with polarized light through photon trajectories. in Annals of Physics. 2010;325(4):763-784.
doi:10.1016/j.aop.2009.12.005 .

Sanz, Angel S., Davidović, Milena, Božić, Mirjana, Miret-Artes, Salvador, "Understanding interference experiments with polarized light through photon trajectories" in Annals of Physics, 325, no. 4 (2010):763-784,
https://doi.org/10.1016/j.aop.2009.12.005 . .

TY  - JOUR
AU  - Božić, Mirjana
AU  - Davidović, Milena
AU  - Dimitrova, Teodara L.
AU  - Miret-Artes, Salvador
AU  - Sanz, Angel S.
AU  - Weis, Antoine
PY  - 2010
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/297
AB  - We study experimentally and theoretically the influence of light polarization on the interference patterns behind a diffracting grating. Different states of polarization and configurations are considered. The experiments are analyzed in terms of electromagnetic energy (EME) flow lines, which can be eventually identified with the paths followed by photons. This gives rise to a novel trajectory interpretation of the Arago-Fresnel laws for polarized light, which we compare with interpretations based on the concept of "which-way" (or "which-slit") information.
T2  - Journal of Russian Laser Research
T1  - Generalized arago-fresnel laws: the eme-flow-line description
EP  - 128
IS  - 2
SP  - 117
VL  - 31
DO  - 10.1007/s10946-010-9131-9
ER  - 

@article{
author = "Božić, Mirjana and Davidović, Milena and Dimitrova, Teodara L. and Miret-Artes, Salvador and Sanz, Angel S. and Weis, Antoine",
year = "2010",
abstract = "We study experimentally and theoretically the influence of light polarization on the interference patterns behind a diffracting grating. Different states of polarization and configurations are considered. The experiments are analyzed in terms of electromagnetic energy (EME) flow lines, which can be eventually identified with the paths followed by photons. This gives rise to a novel trajectory interpretation of the Arago-Fresnel laws for polarized light, which we compare with interpretations based on the concept of "which-way" (or "which-slit") information.",
journal = "Journal of Russian Laser Research",
title = "Generalized arago-fresnel laws: the eme-flow-line description",
pages = "128-117",
number = "2",
volume = "31",
doi = "10.1007/s10946-010-9131-9"
}

Božić, M., Davidović, M., Dimitrova, T. L., Miret-Artes, S., Sanz, A. S.,& Weis, A.. (2010). Generalized arago-fresnel laws: the eme-flow-line description. in Journal of Russian Laser Research, 31(2), 117-128.
https://doi.org/10.1007/s10946-010-9131-9

Božić M, Davidović M, Dimitrova TL, Miret-Artes S, Sanz AS, Weis A. Generalized arago-fresnel laws: the eme-flow-line description. in Journal of Russian Laser Research. 2010;31(2):117-128.
doi:10.1007/s10946-010-9131-9 .

Božić, Mirjana, Davidović, Milena, Dimitrova, Teodara L., Miret-Artes, Salvador, Sanz, Angel S., Weis, Antoine, "Generalized arago-fresnel laws: the eme-flow-line description" in Journal of Russian Laser Research, 31, no. 2 (2010):117-128,
https://doi.org/10.1007/s10946-010-9131-9 . .

TY  - JOUR
AU  - Božić, Mirjana
AU  - Arsenović, Dušan
AU  - Sanz, Angel S.
AU  - Davidović, Milena
PY  - 2010
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/286
AB  - Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied. It is assumed that the scattering process does not destroy the atomic wave function describing the state of the atom before the scattering process takes place, but only induces a certain shift and change of its phase. We find that the visibility of the interference strongly depends on the statistical distribution of transferred momenta to the atom during the photon-atom scattering event. This also explains the experimentally observed (Chapman et al 1995 Phys. Rev. Lett. 75 2783) dependence of the visibility on the ratio d(p)/lambda(i) = y'(12)(2 pi/kd lambda(i)), where y'(12) is the distance between the place where the scattering event occurs and the first grating, k is the wave number of the atomic centre-of-mass motion, d is the grating constant and lambda(i) is the photon wavelength. Furthermore, it is remarkable that photon-atom scattering events happen experimentally within the Fresnel region, i.e. the near-field region, associated with the first grating, which should be taken into account when drawing conclusions about the relevance of 'which-way' information for the interference visibility.
T2  - Physica Scripta
T1  - On the influence of resonance photon scattering on atom interference
SP  - 014017
VL  - T140
DO  - 10.1088/0031-8949/2010/T140/014017
ER  - 

@article{
author = "Božić, Mirjana and Arsenović, Dušan and Sanz, Angel S. and Davidović, Milena",
year = "2010",
abstract = "Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied. It is assumed that the scattering process does not destroy the atomic wave function describing the state of the atom before the scattering process takes place, but only induces a certain shift and change of its phase. We find that the visibility of the interference strongly depends on the statistical distribution of transferred momenta to the atom during the photon-atom scattering event. This also explains the experimentally observed (Chapman et al 1995 Phys. Rev. Lett. 75 2783) dependence of the visibility on the ratio d(p)/lambda(i) = y'(12)(2 pi/kd lambda(i)), where y'(12) is the distance between the place where the scattering event occurs and the first grating, k is the wave number of the atomic centre-of-mass motion, d is the grating constant and lambda(i) is the photon wavelength. Furthermore, it is remarkable that photon-atom scattering events happen experimentally within the Fresnel region, i.e. the near-field region, associated with the first grating, which should be taken into account when drawing conclusions about the relevance of 'which-way' information for the interference visibility.",
journal = "Physica Scripta",
title = "On the influence of resonance photon scattering on atom interference",
pages = "014017",
volume = "T140",
doi = "10.1088/0031-8949/2010/T140/014017"
}

Božić, M., Arsenović, D., Sanz, A. S.,& Davidović, M.. (2010). On the influence of resonance photon scattering on atom interference. in Physica Scripta, T140, 014017.
https://doi.org/10.1088/0031-8949/2010/T140/014017

Božić M, Arsenović D, Sanz AS, Davidović M. On the influence of resonance photon scattering on atom interference. in Physica Scripta. 2010;T140:014017.
doi:10.1088/0031-8949/2010/T140/014017 .

Božić, Mirjana, Arsenović, Dušan, Sanz, Angel S., Davidović, Milena, "On the influence of resonance photon scattering on atom interference" in Physica Scripta, T140 (2010):014017,
https://doi.org/10.1088/0031-8949/2010/T140/014017 . .

TY  - JOUR
AU  - Božić, Mirjana
AU  - Arsenović, Dušan
AU  - Sanz, Angel S.
AU  - Davidović, Milena
PY  - 2010
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1862
AB  - Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied. It is assumed that the scattering process does not destroy the atomic wave function describing the state of the atom before the scattering process takes place, but only induces a certain shift and change of its phase. We find that the visibility of the interference strongly depends on the statistical distribution of transferred momenta to the atom during the photon-atom scattering event. This also explains the experimentally observed (Chapman et al 1995 Phys. Rev. Lett. 75 2783) dependence of the visibility on the ratio d(p)/lambda(i) = y'(12)(2 pi/kd lambda(i)), where y'(12) is the distance between the place where the scattering event occurs and the first grating, k is the wave number of the atomic centre-of-mass motion, d is the grating constant and lambda(i) is the photon wavelength. Furthermore, it is remarkable that photon-atom scattering events happen experimentally within the Fresnel region, i.e. the near-field region, associated with the first grating, which should be taken into account when drawing conclusions about the relevance of 'which-way' information for the interference visibility.
T2  - Physica Scripta
T1  - On the influence of resonance photon scattering on atom interference
DO  - 10.1088/0031-8949/2010/T140/014017
ER  - 

@article{
author = "Božić, Mirjana and Arsenović, Dušan and Sanz, Angel S. and Davidović, Milena",
year = "2010",
abstract = "Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied. It is assumed that the scattering process does not destroy the atomic wave function describing the state of the atom before the scattering process takes place, but only induces a certain shift and change of its phase. We find that the visibility of the interference strongly depends on the statistical distribution of transferred momenta to the atom during the photon-atom scattering event. This also explains the experimentally observed (Chapman et al 1995 Phys. Rev. Lett. 75 2783) dependence of the visibility on the ratio d(p)/lambda(i) = y'(12)(2 pi/kd lambda(i)), where y'(12) is the distance between the place where the scattering event occurs and the first grating, k is the wave number of the atomic centre-of-mass motion, d is the grating constant and lambda(i) is the photon wavelength. Furthermore, it is remarkable that photon-atom scattering events happen experimentally within the Fresnel region, i.e. the near-field region, associated with the first grating, which should be taken into account when drawing conclusions about the relevance of 'which-way' information for the interference visibility.",
journal = "Physica Scripta",
title = "On the influence of resonance photon scattering on atom interference",
doi = "10.1088/0031-8949/2010/T140/014017"
}

Božić, M., Arsenović, D., Sanz, A. S.,& Davidović, M.. (2010). On the influence of resonance photon scattering on atom interference. in Physica Scripta.
https://doi.org/10.1088/0031-8949/2010/T140/014017

Božić M, Arsenović D, Sanz AS, Davidović M. On the influence of resonance photon scattering on atom interference. in Physica Scripta. 2010;.
doi:10.1088/0031-8949/2010/T140/014017 .

Božić, Mirjana, Arsenović, Dušan, Sanz, Angel S., Davidović, Milena, "On the influence of resonance photon scattering on atom interference" in Physica Scripta (2010),
https://doi.org/10.1088/0031-8949/2010/T140/014017 . .

TY  - JOUR
AU  - Arsenović, Dušan
AU  - Božić, Mirjana
AU  - Sanz, Angel S.
AU  - Davidović, Milena
PY  - 2009
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/220
AB  - In 1995, Chapman et al (1995 Phys. Rev. Lett. 75 2783) showed experimentally that the interference contrast in a three-grating atom interferometer does not vanish in the presence of scattering events with photons, as required by the complementarity principle. In this work, we present an analytical study of this experiment by determining the evolution of an atom's wave function along the three-grating Mach-Zehnder interferometer under the assumption that the atom is hit by a photon after passing through the first grating. The consideration of a transverse wave function in momentum representation is essential in this study. As is shown, the number of atoms transmitted through the third grating is given by a simple periodic function of the lateral shift along this grating, both in the absence and in the presence of photon scattering. Moreover, the relative contrast (laser on/laser off) is shown to be a simple analytical function of the ratio d(p)/lambda(i), where d(p) is the distance between atomic paths at the scattering locus and lambda(i) the scattered photon wavelength. We argue that this dependence, being in agreement with experimental results, can be considered as showing compatibility between the wave and corpuscle properties of atoms.
T2  - Physica Scripta
T1  - Evolution of the wave function of an atom hit by a photon in a three-grating interferometer
DO  - 10.1088/0031-8949/2009/135/014025
ER  - 

@article{
author = "Arsenović, Dušan and Božić, Mirjana and Sanz, Angel S. and Davidović, Milena",
year = "2009",
abstract = "In 1995, Chapman et al (1995 Phys. Rev. Lett. 75 2783) showed experimentally that the interference contrast in a three-grating atom interferometer does not vanish in the presence of scattering events with photons, as required by the complementarity principle. In this work, we present an analytical study of this experiment by determining the evolution of an atom's wave function along the three-grating Mach-Zehnder interferometer under the assumption that the atom is hit by a photon after passing through the first grating. The consideration of a transverse wave function in momentum representation is essential in this study. As is shown, the number of atoms transmitted through the third grating is given by a simple periodic function of the lateral shift along this grating, both in the absence and in the presence of photon scattering. Moreover, the relative contrast (laser on/laser off) is shown to be a simple analytical function of the ratio d(p)/lambda(i), where d(p) is the distance between atomic paths at the scattering locus and lambda(i) the scattered photon wavelength. We argue that this dependence, being in agreement with experimental results, can be considered as showing compatibility between the wave and corpuscle properties of atoms.",
journal = "Physica Scripta",
title = "Evolution of the wave function of an atom hit by a photon in a three-grating interferometer",
doi = "10.1088/0031-8949/2009/135/014025"
}

Arsenović, D., Božić, M., Sanz, A. S.,& Davidović, M.. (2009). Evolution of the wave function of an atom hit by a photon in a three-grating interferometer. in Physica Scripta.
https://doi.org/10.1088/0031-8949/2009/135/014025

Arsenović D, Božić M, Sanz AS, Davidović M. Evolution of the wave function of an atom hit by a photon in a three-grating interferometer. in Physica Scripta. 2009;.
doi:10.1088/0031-8949/2009/135/014025 .

Arsenović, Dušan, Božić, Mirjana, Sanz, Angel S., Davidović, Milena, "Evolution of the wave function of an atom hit by a photon in a three-grating interferometer" in Physica Scripta (2009),
https://doi.org/10.1088/0031-8949/2009/135/014025 . .

TY  - JOUR
AU  - Davidović, Milena
AU  - Sanz, Angel S.
AU  - Arsenović, Dušan
AU  - Božić, Mirjana
AU  - Miret-Artes, Salvador
PY  - 2009
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/221
AB  - Motivated by recent experiments where interference patterns behind a grating are obtained by accumulating single photon events, we provide here an electromagnetic energy flow-line description to explain the emergence of such patterns. We find and discuss an analogy between the equation describing these energy flow lines and the equation of Bohmian trajectories used to describe the motion of massive particles.
T2  - Physica Scripta
T1  - Electromagnetic energy flow lines as possible paths of photons
DO  - 10.1088/0031-8949/2009/T135/014009
ER  - 

@article{
author = "Davidović, Milena and Sanz, Angel S. and Arsenović, Dušan and Božić, Mirjana and Miret-Artes, Salvador",
year = "2009",
abstract = "Motivated by recent experiments where interference patterns behind a grating are obtained by accumulating single photon events, we provide here an electromagnetic energy flow-line description to explain the emergence of such patterns. We find and discuss an analogy between the equation describing these energy flow lines and the equation of Bohmian trajectories used to describe the motion of massive particles.",
journal = "Physica Scripta",
title = "Electromagnetic energy flow lines as possible paths of photons",
doi = "10.1088/0031-8949/2009/T135/014009"
}

Davidović, M., Sanz, A. S., Arsenović, D., Božić, M.,& Miret-Artes, S.. (2009). Electromagnetic energy flow lines as possible paths of photons. in Physica Scripta.
https://doi.org/10.1088/0031-8949/2009/T135/014009

Davidović M, Sanz AS, Arsenović D, Božić M, Miret-Artes S. Electromagnetic energy flow lines as possible paths of photons. in Physica Scripta. 2009;.
doi:10.1088/0031-8949/2009/T135/014009 .

Davidović, Milena, Sanz, Angel S., Arsenović, Dušan, Božić, Mirjana, Miret-Artes, Salvador, "Electromagnetic energy flow lines as possible paths of photons" in Physica Scripta (2009),
https://doi.org/10.1088/0031-8949/2009/T135/014009 . .

TY  - JOUR
AU  - Davidović, Milena
AU  - Arsenović, Dušan
AU  - Božić, Mirjana
AU  - Sanz, Angel S.
AU  - Miret-Artes, Salvador
PY  - 2008
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/187
AB  - The momentum distributions associated with both the wave function of a particle behind a grating and the corresponding Bohmian trajectories are investigated and compared. Near the grating, it is observed that the former does not depend on the distance from the grating, while the latter changes with this distance. However, as one moves further apart from the grating, in the far field, both distributions become identical.
T2  - European Physical Journal-Special Topics
T1  - Should particle trajectories comply with the transverse momentum distribution?
EP  - 104
SP  - 95
VL  - 160
DO  - 10.1140/epjst/e2008-00713-0
ER  - 

@article{
author = "Davidović, Milena and Arsenović, Dušan and Božić, Mirjana and Sanz, Angel S. and Miret-Artes, Salvador",
year = "2008",
abstract = "The momentum distributions associated with both the wave function of a particle behind a grating and the corresponding Bohmian trajectories are investigated and compared. Near the grating, it is observed that the former does not depend on the distance from the grating, while the latter changes with this distance. However, as one moves further apart from the grating, in the far field, both distributions become identical.",
journal = "European Physical Journal-Special Topics",
title = "Should particle trajectories comply with the transverse momentum distribution?",
pages = "104-95",
volume = "160",
doi = "10.1140/epjst/e2008-00713-0"
}

Davidović, M., Arsenović, D., Božić, M., Sanz, A. S.,& Miret-Artes, S.. (2008). Should particle trajectories comply with the transverse momentum distribution?. in European Physical Journal-Special Topics, 160, 95-104.
https://doi.org/10.1140/epjst/e2008-00713-0

Davidović M, Arsenović D, Božić M, Sanz AS, Miret-Artes S. Should particle trajectories comply with the transverse momentum distribution?. in European Physical Journal-Special Topics. 2008;160:95-104.
doi:10.1140/epjst/e2008-00713-0 .

Davidović, Milena, Arsenović, Dušan, Božić, Mirjana, Sanz, Angel S., Miret-Artes, Salvador, "Should particle trajectories comply with the transverse momentum distribution?" in European Physical Journal-Special Topics, 160 (2008):95-104,
https://doi.org/10.1140/epjst/e2008-00713-0 . .