rus
Issue #5/2023
P. A. Khorin, S. A. Degtyarev, S. N. Khonina
Application Study of a Refractive Biconical Axicon for Azimuthal and Radial Polarization Detection
Application Study of a Refractive Biconical Axicon for Azimuthal and Radial Polarization Detection
DOI: 10.22184/1993-7296.FRos.2023.17.5.394.406
The paper presents the study results of the effect of a biconical axicon, a refractive optical element with two conical surfaces, on illumination by radiation of various polarization states, including inhomogeneous one (with azimuthal and radial polarization). The biconical axicon was previously proposed for converting a beam with circular polarization into a azimuthal polarized beam due to the beam reflection and refraction at the Brewster angle on one conical surface, followed by the beam collimation due to the second conical surface. The polarization transformations performed during diffraction of beams with various polarizations by a biconical axicon are calculated using the finite difference method in the time domain. Based on the numerical simulations, it is shown that the biconical axicon made of K14 glass (with the refractive index n = 1.4958) can be used as a detector for azimuthal and radially polarized beams based on the intensity pattern in one plane.
The paper presents the study results of the effect of a biconical axicon, a refractive optical element with two conical surfaces, on illumination by radiation of various polarization states, including inhomogeneous one (with azimuthal and radial polarization). The biconical axicon was previously proposed for converting a beam with circular polarization into a azimuthal polarized beam due to the beam reflection and refraction at the Brewster angle on one conical surface, followed by the beam collimation due to the second conical surface. The polarization transformations performed during diffraction of beams with various polarizations by a biconical axicon are calculated using the finite difference method in the time domain. Based on the numerical simulations, it is shown that the biconical axicon made of K14 glass (with the refractive index n = 1.4958) can be used as a detector for azimuthal and radially polarized beams based on the intensity pattern in one plane.
Теги: biconical axicon fdtd method fdtd-метод polarization transformations биконический аксикон поляризационные преобразования
Application Study
of a Refractive
Biconical Axicon
for Azimuthal
and Radial Polarization
Detection
P. A. Khorin 1, 2, S. A. Degtyarev 1, 2, S. N. Khonina 1,2
Samara National Research University,
Samara, Russia
Image Processing Systems Institute Russian Academy of Sciences – branch of the Federal Research Center “Crystallography and Photonics” of the Russian Academy of Sciences, Samara, Russia
The paper presents the study results of the effect of a biconical axicon, a refractive optical element with two conical surfaces, on illumination by radiation of various polarization states, including inhomogeneous one (with azimuthal and radial polarization). The biconical axicon was previously proposed for converting a beam with circular polarization into a azimuthal polarized beam due to the beam reflection and refraction at the Brewster angle on one conical surface, followed by the beam collimation due to the second conical surface. The polarization transformations performed during diffraction of beams with various polarizations by a biconical axicon are calculated using the finite difference method in the time domain. Based on the numerical simulations, it is shown that the biconical axicon made of K14 glass (with the refractive index n = 1.4958) can be used as a detector for azimuthal and radially polarized beams based on the intensity pattern in one plane.
Keywords: biconical axicon, polarization transformations, FDTD method
Article received: July 05, 2023
Article accepted: August 16, 2023
Introduction
In the field of modern optics, polarization recognition detection of the optical beams is one of the most important issues [1] that has many practical applications. For example, polarization detection can be used to improve the performance of optical data transmission systems [2–5], to develop new methods of data processing [6, 7] and optical diagnostics [8–9], as well as to structure the material surfaces [10, 11].
There are a lot of methods for recognizing the optical beam polarization, including various approaches based on the interference methods [12–14], application of diffractive optical elements (DOE) [15–17], spatial light modulators (SLMs) [18–20], subwavelength gratings, metasurfaces, anisotropic crystals and films [21–26]. Each of these methods has its own advantages and disadvantages. The use of SLMs is limited by the fact that they convert only part of the light that can lead to a decrease in the polarization contrast. The subwavelength gratings change the polarization contrast depending on the rotation angle of the polarization plane. To compensate for this effect, a combination of polarization and focusing elements is required [26]. It shall also be noted that the production of subwavelength gratings for the visible wavelength range is a comprehensive process. When using the multichannel DOEs, a necessary factor for recognizing the optical beam polarization is the computer processing of correlation patterns [27].
Another method for the generation of heterogeneously polarized beams is the application of special structures [28], as well as the refractive optical elements, for example, with the refracting or reflecting axicons that convert the radiation polarization when light is incident at the Brewster angle [29–34].
In this work, we consider the possible application of a refractive biaxicon [34] for detecting the azimuthal and radially polarized optical beams. A refractive biaxicon is an optical element that has two working conical surfaces (polarization is converted on the inner surface of the element due to the beam reflection and refraction at the Brewster angle, and the outer surface provides collimation of the converted beam) and is used to convert an optical beam with circular polarization to the azimuthal polarized beam.
We use the FDTD method in our paper to calculate the diffraction on an optical element, then we analyze the obtained data in the form of intensity patterns to recognize the type of polarization. In previous papers [33, 34], the polarization transformations occurring on the conical surfaces were studied in an approximate way using the geometric optics. However, these studies were limited to the far diffraction field. It is important to note that in the up-to-date applications of microelements, including microaxicons [35–37], the emphasis is on the near diffraction field. Therefore, it becomes necessary to study the developed element in the electromagnetic approximation in order not only to clarify the results of geometric and optical calculations, but also to study the polarization transformations and possible detection of the polarization state in the near diffraction field.
1. Theoretical background
In [34], a refractive biconical axicon was proposed for generation of an azimuthal polarized vortex beam from a beam with circular polarization. The element is made by two conical surfaces in such a way that it forms a rotation figure resembling a volcano (Fig. 1). The projections and 3D-shape of the biconical axicon with its physical dimensions are shown in Fig. 1.
It is assumed that a collimated circularly polarized beam is incident from bottom to top on the inner conical surface relevant to the Brewster angle. The refracted part of the beam has azimuthal polarization. The second conical surface reflects the developed beam further outward so that it is collimated. The detailed results of the basic formulas describing an optical element shape with a refractive index of the material n = 1,4958is given in [33, 34].
The type of light beam polarization depends on the components of the electric and magnetic field vectors. Let us consider several well-known types of a light source polarization. Let a Gaussian beam with circular polarization fall on a refracting biconical axicon. The Jones vector of the incident beam shall be as follows:
. (1)
When the initial beam is incident on the “crater” of the biconical axicon, a completely s-polarized beam is reflected. Thus, the element is operated as a polaroid filter that transmits polarization along the polar vector ϕ.
The Jones matrix of a linear polaroid filter shall be as follows:
. (2)
Let’s use the matrix (2) to influence the vector (1):
. (3)
It can be seen from the formula (3) that the output beam has azimuthal polarization with a first-order vortex phase.
We will consider the case when the incident beam has radial polarization, then the Jones vector shall have the following form:
. (4)
Let’s use the matrix (2) to influence the vector (4):
. (5)
It can be seen from the formula (5) that the element under consideration actually reflects the incident beam with radial polarization.
If the incident beam has an azimuthal polarization described by the Jones vector of the following form:
, (6)
then the output field shall take the following polarization state:
. (7)
It can be seen from the formula (7) that the output beam retains azimuthal polarization that indicates that the biconical axicon is invariant to the azimuthal polarized light.
2. Numerical simulation
Based on the presented model of a biconical axicon and a Gaussian beam with a wavelength λ = 1,5 a radius of neck σ = 3λ and various polarization types, it is proposed to perform a numerical calculation of diffraction based on the FDTD method. Having considered the theoretical analysis performed, it is assumed that a biconical axicon made of K14 glass with a refractive index n = 1.4958 can be used to detect the azimuthal and radially polarized beams.
2.1. Inhomogeneous light polarization
Let us simulate the propagation of a heterogeneously polarized beam (with radial and azimuthal polarization) in free space. Table 1 shows a cross section of the intensity and phase of the electric field vector components. The total intensity that is detected in free space at a distance z = 20 μm from the input plane, is a ring distribution regardless of the polarization type (the last column of Table 1). Thus, there is no opportunity to distinguish radial polarization from azimuthal one only by the intensity pattern. As a rule, in this case, additional polarizing devices are required, for example, the polarizing analyzers that single out the linear component at a certain angle. Moreover, in this case, an additional location analysis of the distinguished part of intensity is required [38].
Based on the data obtained as a result of the diffraction calculation in the near field (distance z up to 20 μm), it is possible to plot the Jones vector. Table 2 shows distribution of the Jones vector in the OXY plane at various distances for a radially and azimuthal polarized beam. It can be seen from Fig. 2 that the Jones vector direction for different types of inhomogeneous polarization has a significant difference. However, plotting of such a diagram based on the experimental data requires additional optical elements and subsequent digital processing [19, 20].
Thus, to recognize the type of polarization, additional elements or devices are required, while it would be most convenient to use such instruments that are applied as a sensor: availability or absence of a signal (intensity) in a certain detection area. It is proposed to use a biconical axicon as such a sensor [34].
2.2. Action of the biconical axicon
Let us consider a biconical axicon as a refractive optical element for detection of an azimuthal and radially polarized beam. For this purpose, we will compare the action of a biconical axicon when radiation with various polarization types is incident on it. Table 3 shows the field diffraction calculation results at the output after passing through the optical element. The transverse intensity distribution shows that the total energy is distributed over the rings. It should be noted that in the case of azimuthal polarization there is no central peak compared to the x-polarization, circular and radial ones that is an immediate sign for determining this type of polarization. In addition, it is possible to distinguish radial polarization from homogeneous one (linear and circular) by the actual energy absence on the ring, the radius of which corresponds to the “crater” of the biconical axicon. As for the intensity level in the central peak, it is approximately the same for homogenous polarization, and 3.5 times higher for radial polarization.
It should be noted that the intensity in the near field obtained by the FDTD method coordinates with the results of geometric-optical approach and the results of a full-scale experiment [34] up to the reversibility of the beam path.
Let us consider in more detail the influence of a biconical axicon on the Gaussian beam with inhomogeneous polarization (see Table 4). Based on the data on the electric field vector components for radial polarization (top line in Table 4), it can be concluded that the vortex phase is absent in all components, and the intensity distribution in the x and y components is represented by the open rings rotated by 90 degrees relative to each other. The z-component intensity almost completely corresponds to the total intensity and is a significant central peak.
As for the azimuthal polarization, it can be seen on the basis of the obtained data (bottom line in Table 4) that the intensity distribution in the x and y components also represents the open rings up to the angle of rotation. The sum of intensities in the X-component and the Y-component corresponds to the total intensity and is shown by the concentric rings. It should be noted that the longitudinal component has a comprehensive structure in the form of eight bright dots located along the ring; there is no central peak.
It is also worth noting that the distribution symmetry of the transverse electric field components in Table 4 correspond to the similar distributions in Table 1 while confirming the theoretical assumptions about the selective effect of biconical axicon on radial and azimuthal polarization.
Thus, the numerical simulation shows that, based on the use of a biconical axicon, it is possible to recognize the azimuthal and radial beam polarization only from the intensity distribution in one plane.
The criterion for radial polarization is detection of a bright correlation peak in the center (Fig. 2a) and, in fact, the absence of intensity on the ring, the radius of which corresponds to the “crater” of the biconical axicon. For the azimuthal polarization, the criterion is absence of a central correlation peak (Fig. 2b).
Conclusion
In this paper, we study the action of a biconical axicon when it is illuminated by radiation with various polarization states based on the finite difference method in the time domain. The selective action of the considered optical element in relation to two types of cylindrical polarization (radial and azimuthal) is shown on an analytical and numerical level. Possible application of a biconical axicon as a polarization analyzer, namely, a radial and azimuthal polarization sensor/detector by availability or absence of a central intensity peak, is shown. This factor is easily measurable and informative.
The results obtained open up new opportunities for the development of technologies related to the lasers and optics, and can also be used in various branches of science and technology, such as medicine, space research, nanotechnology, etc. It is assumed that the results of this paper can be used to improve the performance of optical data transmission systems, as well as to develop new methods of data processing and optical recognition. In the future, it is planned to perform more detailed studies aimed at expanding the capabilities of the refractive biaxicon and improving the recognition accuracy of various polarization states of the optical beams.
Acknowledgement
The paper was prepared as a part of R&D “Research for development of a multifunctional analog photonic computing device based on the Fourier correlator circuit and dynamic spatial light modulators” of the Russian Federal Nuclear Center – All-Russian Research Institute of Experimental Physics (in the Introduction part), at the expense of the strategic academic leadership program “Priority 2030” (in the part of numerical simulation), as well as a part of the state task of the Federal Research Center “Crystallography and Photonics” of the Russian Academy of Sciences (in the theoretical part).
AUTHORS
Khorin Pavel Alekseevich, Ph.D. in Physical and Mathematical Sciences, Senior Researcher in the Research Laboratory of Automated Systems for Scientific Research (NIL‑35) of Samara National Research University; Senior Researcher, Image Processing Systems Institute Russian Academy of Sciences – Branch of the Federal Scientific Research Center “Crystallography and Photonics” of the Russian Academy of Sciences, Samara, Russia. Research interests: mathematical modeling, diffractive optics, optical and digital image processing. E-mail: paul.95.de@gmail.com, khorin.pa@ssau.ru.
ORCID: 0000-0002-2248-614X
Degtyarev Sergey Aleksandrovich, Ph.D. in Physical and Mathematical Sciences, Associate Professor of Samara National Research University; Researcher, Image Processing Systems Institute Russian Academy of Sciences – Branch of the Federal Scientific Research Center “Crystallography and Photonics” of the Russian Academy of Sciences, Samara, Russia. Research interests: wave and singular optics.
ORCID: 0000-0002-0874-005X
Khonina Svetlana Nikolaevna, Doctor of Physical and Mathematical Sciences, Professor of Samara National Research University; Main Researcher, Image Processing Systems Institute Russian Academy of Sciences – Branch of the Federal Scientific Research Center “Crystallography and Photonics” of the Russian Academy of Sciences, Samara, Russia. Research interests: diffractive optics, singular optics, mode and polarization transformations, optical manipulation, optical and digital image processing.
ORCID: 0000-0001-6765-4373
CONFLICT OF INTEREST
The authors claim that they have no conflict of interest. All authors took part in writing the article and supplemented the manuscript in part of their work.
of a Refractive
Biconical Axicon
for Azimuthal
and Radial Polarization
Detection
P. A. Khorin 1, 2, S. A. Degtyarev 1, 2, S. N. Khonina 1,2
Samara National Research University,
Samara, Russia
Image Processing Systems Institute Russian Academy of Sciences – branch of the Federal Research Center “Crystallography and Photonics” of the Russian Academy of Sciences, Samara, Russia
The paper presents the study results of the effect of a biconical axicon, a refractive optical element with two conical surfaces, on illumination by radiation of various polarization states, including inhomogeneous one (with azimuthal and radial polarization). The biconical axicon was previously proposed for converting a beam with circular polarization into a azimuthal polarized beam due to the beam reflection and refraction at the Brewster angle on one conical surface, followed by the beam collimation due to the second conical surface. The polarization transformations performed during diffraction of beams with various polarizations by a biconical axicon are calculated using the finite difference method in the time domain. Based on the numerical simulations, it is shown that the biconical axicon made of K14 glass (with the refractive index n = 1.4958) can be used as a detector for azimuthal and radially polarized beams based on the intensity pattern in one plane.
Keywords: biconical axicon, polarization transformations, FDTD method
Article received: July 05, 2023
Article accepted: August 16, 2023
Introduction
In the field of modern optics, polarization recognition detection of the optical beams is one of the most important issues [1] that has many practical applications. For example, polarization detection can be used to improve the performance of optical data transmission systems [2–5], to develop new methods of data processing [6, 7] and optical diagnostics [8–9], as well as to structure the material surfaces [10, 11].
There are a lot of methods for recognizing the optical beam polarization, including various approaches based on the interference methods [12–14], application of diffractive optical elements (DOE) [15–17], spatial light modulators (SLMs) [18–20], subwavelength gratings, metasurfaces, anisotropic crystals and films [21–26]. Each of these methods has its own advantages and disadvantages. The use of SLMs is limited by the fact that they convert only part of the light that can lead to a decrease in the polarization contrast. The subwavelength gratings change the polarization contrast depending on the rotation angle of the polarization plane. To compensate for this effect, a combination of polarization and focusing elements is required [26]. It shall also be noted that the production of subwavelength gratings for the visible wavelength range is a comprehensive process. When using the multichannel DOEs, a necessary factor for recognizing the optical beam polarization is the computer processing of correlation patterns [27].
Another method for the generation of heterogeneously polarized beams is the application of special structures [28], as well as the refractive optical elements, for example, with the refracting or reflecting axicons that convert the radiation polarization when light is incident at the Brewster angle [29–34].
In this work, we consider the possible application of a refractive biaxicon [34] for detecting the azimuthal and radially polarized optical beams. A refractive biaxicon is an optical element that has two working conical surfaces (polarization is converted on the inner surface of the element due to the beam reflection and refraction at the Brewster angle, and the outer surface provides collimation of the converted beam) and is used to convert an optical beam with circular polarization to the azimuthal polarized beam.
We use the FDTD method in our paper to calculate the diffraction on an optical element, then we analyze the obtained data in the form of intensity patterns to recognize the type of polarization. In previous papers [33, 34], the polarization transformations occurring on the conical surfaces were studied in an approximate way using the geometric optics. However, these studies were limited to the far diffraction field. It is important to note that in the up-to-date applications of microelements, including microaxicons [35–37], the emphasis is on the near diffraction field. Therefore, it becomes necessary to study the developed element in the electromagnetic approximation in order not only to clarify the results of geometric and optical calculations, but also to study the polarization transformations and possible detection of the polarization state in the near diffraction field.
1. Theoretical background
In [34], a refractive biconical axicon was proposed for generation of an azimuthal polarized vortex beam from a beam with circular polarization. The element is made by two conical surfaces in such a way that it forms a rotation figure resembling a volcano (Fig. 1). The projections and 3D-shape of the biconical axicon with its physical dimensions are shown in Fig. 1.
It is assumed that a collimated circularly polarized beam is incident from bottom to top on the inner conical surface relevant to the Brewster angle. The refracted part of the beam has azimuthal polarization. The second conical surface reflects the developed beam further outward so that it is collimated. The detailed results of the basic formulas describing an optical element shape with a refractive index of the material n = 1,4958is given in [33, 34].
The type of light beam polarization depends on the components of the electric and magnetic field vectors. Let us consider several well-known types of a light source polarization. Let a Gaussian beam with circular polarization fall on a refracting biconical axicon. The Jones vector of the incident beam shall be as follows:
. (1)
When the initial beam is incident on the “crater” of the biconical axicon, a completely s-polarized beam is reflected. Thus, the element is operated as a polaroid filter that transmits polarization along the polar vector ϕ.
The Jones matrix of a linear polaroid filter shall be as follows:
. (2)
Let’s use the matrix (2) to influence the vector (1):
. (3)
It can be seen from the formula (3) that the output beam has azimuthal polarization with a first-order vortex phase.
We will consider the case when the incident beam has radial polarization, then the Jones vector shall have the following form:
. (4)
Let’s use the matrix (2) to influence the vector (4):
. (5)
It can be seen from the formula (5) that the element under consideration actually reflects the incident beam with radial polarization.
If the incident beam has an azimuthal polarization described by the Jones vector of the following form:
, (6)
then the output field shall take the following polarization state:
. (7)
It can be seen from the formula (7) that the output beam retains azimuthal polarization that indicates that the biconical axicon is invariant to the azimuthal polarized light.
2. Numerical simulation
Based on the presented model of a biconical axicon and a Gaussian beam with a wavelength λ = 1,5 a radius of neck σ = 3λ and various polarization types, it is proposed to perform a numerical calculation of diffraction based on the FDTD method. Having considered the theoretical analysis performed, it is assumed that a biconical axicon made of K14 glass with a refractive index n = 1.4958 can be used to detect the azimuthal and radially polarized beams.
2.1. Inhomogeneous light polarization
Let us simulate the propagation of a heterogeneously polarized beam (with radial and azimuthal polarization) in free space. Table 1 shows a cross section of the intensity and phase of the electric field vector components. The total intensity that is detected in free space at a distance z = 20 μm from the input plane, is a ring distribution regardless of the polarization type (the last column of Table 1). Thus, there is no opportunity to distinguish radial polarization from azimuthal one only by the intensity pattern. As a rule, in this case, additional polarizing devices are required, for example, the polarizing analyzers that single out the linear component at a certain angle. Moreover, in this case, an additional location analysis of the distinguished part of intensity is required [38].
Based on the data obtained as a result of the diffraction calculation in the near field (distance z up to 20 μm), it is possible to plot the Jones vector. Table 2 shows distribution of the Jones vector in the OXY plane at various distances for a radially and azimuthal polarized beam. It can be seen from Fig. 2 that the Jones vector direction for different types of inhomogeneous polarization has a significant difference. However, plotting of such a diagram based on the experimental data requires additional optical elements and subsequent digital processing [19, 20].
Thus, to recognize the type of polarization, additional elements or devices are required, while it would be most convenient to use such instruments that are applied as a sensor: availability or absence of a signal (intensity) in a certain detection area. It is proposed to use a biconical axicon as such a sensor [34].
2.2. Action of the biconical axicon
Let us consider a biconical axicon as a refractive optical element for detection of an azimuthal and radially polarized beam. For this purpose, we will compare the action of a biconical axicon when radiation with various polarization types is incident on it. Table 3 shows the field diffraction calculation results at the output after passing through the optical element. The transverse intensity distribution shows that the total energy is distributed over the rings. It should be noted that in the case of azimuthal polarization there is no central peak compared to the x-polarization, circular and radial ones that is an immediate sign for determining this type of polarization. In addition, it is possible to distinguish radial polarization from homogeneous one (linear and circular) by the actual energy absence on the ring, the radius of which corresponds to the “crater” of the biconical axicon. As for the intensity level in the central peak, it is approximately the same for homogenous polarization, and 3.5 times higher for radial polarization.
It should be noted that the intensity in the near field obtained by the FDTD method coordinates with the results of geometric-optical approach and the results of a full-scale experiment [34] up to the reversibility of the beam path.
Let us consider in more detail the influence of a biconical axicon on the Gaussian beam with inhomogeneous polarization (see Table 4). Based on the data on the electric field vector components for radial polarization (top line in Table 4), it can be concluded that the vortex phase is absent in all components, and the intensity distribution in the x and y components is represented by the open rings rotated by 90 degrees relative to each other. The z-component intensity almost completely corresponds to the total intensity and is a significant central peak.
As for the azimuthal polarization, it can be seen on the basis of the obtained data (bottom line in Table 4) that the intensity distribution in the x and y components also represents the open rings up to the angle of rotation. The sum of intensities in the X-component and the Y-component corresponds to the total intensity and is shown by the concentric rings. It should be noted that the longitudinal component has a comprehensive structure in the form of eight bright dots located along the ring; there is no central peak.
It is also worth noting that the distribution symmetry of the transverse electric field components in Table 4 correspond to the similar distributions in Table 1 while confirming the theoretical assumptions about the selective effect of biconical axicon on radial and azimuthal polarization.
Thus, the numerical simulation shows that, based on the use of a biconical axicon, it is possible to recognize the azimuthal and radial beam polarization only from the intensity distribution in one plane.
The criterion for radial polarization is detection of a bright correlation peak in the center (Fig. 2a) and, in fact, the absence of intensity on the ring, the radius of which corresponds to the “crater” of the biconical axicon. For the azimuthal polarization, the criterion is absence of a central correlation peak (Fig. 2b).
Conclusion
In this paper, we study the action of a biconical axicon when it is illuminated by radiation with various polarization states based on the finite difference method in the time domain. The selective action of the considered optical element in relation to two types of cylindrical polarization (radial and azimuthal) is shown on an analytical and numerical level. Possible application of a biconical axicon as a polarization analyzer, namely, a radial and azimuthal polarization sensor/detector by availability or absence of a central intensity peak, is shown. This factor is easily measurable and informative.
The results obtained open up new opportunities for the development of technologies related to the lasers and optics, and can also be used in various branches of science and technology, such as medicine, space research, nanotechnology, etc. It is assumed that the results of this paper can be used to improve the performance of optical data transmission systems, as well as to develop new methods of data processing and optical recognition. In the future, it is planned to perform more detailed studies aimed at expanding the capabilities of the refractive biaxicon and improving the recognition accuracy of various polarization states of the optical beams.
Acknowledgement
The paper was prepared as a part of R&D “Research for development of a multifunctional analog photonic computing device based on the Fourier correlator circuit and dynamic spatial light modulators” of the Russian Federal Nuclear Center – All-Russian Research Institute of Experimental Physics (in the Introduction part), at the expense of the strategic academic leadership program “Priority 2030” (in the part of numerical simulation), as well as a part of the state task of the Federal Research Center “Crystallography and Photonics” of the Russian Academy of Sciences (in the theoretical part).
AUTHORS
Khorin Pavel Alekseevich, Ph.D. in Physical and Mathematical Sciences, Senior Researcher in the Research Laboratory of Automated Systems for Scientific Research (NIL‑35) of Samara National Research University; Senior Researcher, Image Processing Systems Institute Russian Academy of Sciences – Branch of the Federal Scientific Research Center “Crystallography and Photonics” of the Russian Academy of Sciences, Samara, Russia. Research interests: mathematical modeling, diffractive optics, optical and digital image processing. E-mail: paul.95.de@gmail.com, khorin.pa@ssau.ru.
ORCID: 0000-0002-2248-614X
Degtyarev Sergey Aleksandrovich, Ph.D. in Physical and Mathematical Sciences, Associate Professor of Samara National Research University; Researcher, Image Processing Systems Institute Russian Academy of Sciences – Branch of the Federal Scientific Research Center “Crystallography and Photonics” of the Russian Academy of Sciences, Samara, Russia. Research interests: wave and singular optics.
ORCID: 0000-0002-0874-005X
Khonina Svetlana Nikolaevna, Doctor of Physical and Mathematical Sciences, Professor of Samara National Research University; Main Researcher, Image Processing Systems Institute Russian Academy of Sciences – Branch of the Federal Scientific Research Center “Crystallography and Photonics” of the Russian Academy of Sciences, Samara, Russia. Research interests: diffractive optics, singular optics, mode and polarization transformations, optical manipulation, optical and digital image processing.
ORCID: 0000-0001-6765-4373
CONFLICT OF INTEREST
The authors claim that they have no conflict of interest. All authors took part in writing the article and supplemented the manuscript in part of their work.
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