rus
Issue #3/2022
V. Yu. Venediktov, K. N. Gavril’eva, Yu. S. Gudin, V. D. Nenadovich, A. A. Ryzhaya, A. A. Sevruygin, A. L. Sokolov, E. V. Shalymov
Polarization Interferometer and Structured Light
Polarization Interferometer and Structured Light
DOI: 10.22184/1993-7296.FRos.2022.16.3.226.234
This article describes an experimental study of the optical vortex formation using beams reflected from a combination of two cube-corner reflectors with a special interference phase-shifting coating. As predicted earlier, if arranged properly, these cube-corner reflectors create a spatial polarization structure, that can be called an optical vortex, since the plane of oscillations of thе vector E rotates with azimuth variation in the transverse plane. This enables an easy way of creating such vortices, albeit with some difficulties due to the need for precise optical path control and vortices themselves created in far field.
This article describes an experimental study of the optical vortex formation using beams reflected from a combination of two cube-corner reflectors with a special interference phase-shifting coating. As predicted earlier, if arranged properly, these cube-corner reflectors create a spatial polarization structure, that can be called an optical vortex, since the plane of oscillations of thе vector E rotates with azimuth variation in the transverse plane. This enables an easy way of creating such vortices, albeit with some difficulties due to the need for precise optical path control and vortices themselves created in far field.
Теги: cube-corner reflectors optical vortex polarization of light retroreflective spatial-polarization interferometer spatial polarization structure поляризация света пространственная поляризационная структура световозвращающий пространственно-поляризационный интерферометр уголковые отражатели
Polarization Interferometer and Structured Light
V. Yu. Venediktov 1, K. N. Gavril’eva 1, Yu. S. Gudin 1, V. D. Nenadovich 2, A. A. Ryzhaya 1, A. A. Sevruygin 1, A. L. Sokolov 2, E. V. Shalymov 1
Laser Measurement and Navigation Systems department, Saint Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia
Research-and-Production Corporation, Precision Systems and Instruments (RPC PSI), Moscow, Russia
This article describes an experimental study of the optical vortex formation using beams reflected from a combination of two cube-corner reflectors with a special interference phase-shifting coating. As predicted earlier, if arranged properly, these cube-corner reflectors create a spatial polarization structure, that can be called an optical vortex, since the plane of oscillations of thе vector E rotates with azimuth variation in the transverse plane. This enables an easy way of creating such vortices, albeit with some difficulties due to the need for precise optical path control and vortices themselves created in far field.
Keywords: optical vortex, cube-corner reflectors, spatial polarization structure, polarization of light, retroreflective spatial-polarization interferometer
Received on: 12.04.2022
Accepted on: 26.04.2022
INTRODUCTION
Optical vortices have many different potential applications – communications, optical testing, optical manipulation of small particles, and so on. Several methods exist to create an optical vortex, including computer-generated holograms. spiral phase plates, mode conversion and so on. However, new methods of creating optical vortices are welcomed to increase the area of their application.
Previously, lots of work was done on creating of the cube-corner reflectors (CCR) with a certain far-field diffraction pattern, with one of the effective ways to optimize it was using a special phase-shifting interference coating to create the required phase shift of the light is reflected on the cube-corner reflectors faces. [1–6] The primary goal of developing such cube-corner prisms was related to the task of measuring the distance from the ground to satellites. Today all GPS satellites, all Glonass satellites and many other satellites are equipped by the panels, containing several dozens or even several hundreds of special CCR elements. When compared with the “usual” CCR, easily available from numerous commercial companies, such CCR reveal two special features, namely:
The angle between the edges at the top of the prism is slightly more than the standard 90°.
Hence, instead of the single beam with the hexagonal pattern in its section such CCR reflects the incoming plane wave as the combination of six separate beams, propagating along the conical surface.
“Usual” CCRs employ the total internal reflection from the edges. Hence, after each reflection the P- and S- linearly polarized components of radiation accumulate mutual phase shift, depending upon the reflection geometry. The reflecting faces of the prisms, which we consider here, are coated by the special polarization coatings, providing either preservation of the linear polarization or its turn in 90°.
Such cube-corner reflectors form of a six-spot diffraction pattern with each spot having planes of vector E oscillations rotated relative to each other at a certain angle. In [4, 7, 8] there was considered in theory the so-called polarization interferometer. Such an interferometer is similar to the usual cross-like Michelson interferometer, where both plane mirrors are replaced by the said CCRs. In the papers [4, 7, 8] various configurations of such interferometers were considered in theory. It was shown that the most interesting variant is the one in which the equilateral triangles of the input faces of CCRs are rotated in 60o one with respect to another. As we have said already, in the papers [4, 7, 8] these devices were studied in theory. It was shown that it is possible to create different configurations of such devices. In one of such configurations it is possible to produce the so-called vector vortex wave with the azimuthal direction of polarization vector. This article, which is now offered to the attention of readers, presents the first experimental realization of such a device and generation of the vector vortex in it. For the reader’s convenience we present first a brief explanation of such device operation, and after it the experimental results and some discussion. It is interesting to note that, according to the results of [8], other configurations of polarization interferometer can produce the so-called phase vortex of the second order and many other interesting and promising variants of the structured light beams with the axially symmetrical distribution of phase and polarization. Such configurations will be investigated in our next papers.
POLARIZATION INTERFEROMETER FOR VECTOR VORTEX FIORMATION
The rigorous theory of the polarization interferometer performance was given in [8]. Here we present some briefs from the said paper so as to simplify the reader understanding of our experimental setup.
First thing to note – when the beam enters CCR it undergoes three reflections, each of which induces a phase shift between the orthogonal components of the electric vector E. Second – the plane of incidence of the beam on the edge does not coincide. This determines the polarization characteristics of the CCR. The resulting structure of the reflected beam polarization depends on which of the six sectors the beam hits (Fig. 1a), incoming beam polarization and CCR parameters [1–6]. The wavefront of the incoming beam is divided into six parts upon its reflection from the CCR, as mentioned earlier, and these parts have different polarization states and phase shifts. In addition to that due to diffraction and interference between them a complex far-field diffraction pattern (FFDP) will form.
The phase shift of the orthogonal components during reflection has most significant impact, and it depends on the type of the CCR face coating. In our case these CCRs have special interference coating, thus resulting phase shift can be selected during production over a wide range from 0 to π. Such coatings induce phase shift thanks to multiple layers and different transmittances at the media boundary for P- and S- polarized components of the wave. In case of reflection at Brewster angle from a CCR face a P- component travels down to the last layer of the interference coating, almost without reflections, and returns, thanks to total internal reflection, with a certain phase shift that depends on the coating thickness its refractive index, and the number of layers. Meanwhile the S- component undergoes numerous reflections at layer boundaries, and the resulting wave if formed by superposition of the secondary coherent waves with different phase shifts [6]. In our case only CCRs with zero phase shift are considered with the FFDP of a symmetric system of six spots without a central spot.
Let’s assume two CCRs with a special phase-shifting coating, which ensures a zero-phase shift between P- and S- polarization components upon reflection from each of the three faces are placed instead of a mirrors in a Michelson-type interferometer, at a 90° angle as shown on Fig. 2 (a). Depending on phase shift (0 to π) between reflected beams we will get different patterns.
This phase shift can be created either using liquid crystal variable retarder, variable pathlength cell or an adjustable mount, for example with a piezoceramic actuator. The resulting setup works similar to a retroreflective spatial-polarization interferometer (RSPI), based on a Rayleigh interferometer, described in [9]. The polarization properties of the RSPI are described by a spiral polarization rotator, the order and sign of which change depending on the angular distance from the beam axis.
In case of the incoherent superposition the reflected beam can be decomposed into a set of Hermite–Gaussian modes with different polarization. Now we’ll add path difference between two reflected beams (i. e. phase shift) into equation to see how it affects the polarization structure of the reflected light superposition. If the incoming plane wave has linear polarization an axisymmetric polarization structure is observed in the reflected beam. At a high distance, the intensity in the ring becomes uniform. Depending on the phase difference of the reflected beams the polarization structure changes significantly. At zero phase difference, an axisymmetric polarization structure of the second order can be observed, shown in Fig. 2b, with a Jones vector:
.
If a phase difference is π, the beams cancel each other, and a fourth-order beam with the opposite vector E rotation in the transverse plane appears at the periphery, Fig. 2c:
.
EXPERIMENTAL SETUP AND RESULTS
The experimental setup is shown in Fig. 3, where a He-Ne laser 1 is used as a source. With the help of a tunable beam expander 2, one can obtain either a parallel beam of light or a slightly diverging one. The collimated beam passes through polarizer 3, after which it is divided by non-polarizing beam splitter cube 4 into two waves with equal intensity and polarization. After that, the beams are reflected by retroreflectors 5 and 6, and combined in a beam-splitting cube, creating required polarization distribution. Then the beam was reflected several times using a simple mirrors installed at a certain distances (not shown on the the diagram) to increase the optical path. After that it was recorded using digital camera or observed by a naked eye on the screen 9. In some cases, lens 8 was installed to focus the image, in some cases not. By rotating the polarizer 8, the distribution of polarization was analyzed in the final picture.
Result obtained with only one corner reflector & without polarizer 8 are shown in Fig.4, top left. Top right & bottom row of Fig.4 shows results with only one corner reflector at various orientations of polarizer 8 (top right, bottom left & right).
The image obtained with both corner reflectors without polarizer 8 at some distance is shown in Fig. 5. Fig. 6 shows the images obtained at different angles of the polarizer 8. Due to insufficient distance between the experimental setup and the camera these images does not look like they should (with a donut-shaped intensity distribution) since effects of far-field diffraction haven’t affected intensity distribution well enough. However, one clearly see that intensity distribution changes while rotating the polarizer according to the expectations.
Conclusion
We have presented an experimental study of the polarization-symmetric structure formation of the reflected radiation using beams reflected from a combination of two cube-corner reflectors with a special interference phase-shifting coating. Based on previous theoretical studies, we have created a basic retroreflective spatial-polarization interferometer to obtain a donut-shaped intensity distribution out of linearly polarized light with resulting plane of polarization rotating around the center. Results show that polarization in the resulting image matches theoretical studies. In near future it is planned to continue this experiment with increased optical path to include circular polarization and far-field diffraction in its full extend. Other configurations of polarization interferometer can produce the so-called phase vortex of the second order and many other interesting and promising variants of the structured light beams with the axially symmetrical distribution of phase and polarization. Such configurations will be investigated in our next papers.
Funding
The research was funded by the Russian Government within the Program “Priority‑2030”. K. N. Gavril’eva is grateful to the Russian Foundatuib for Basic Research for funding within the grant 20-32-90140.
ABOUT AUTHORS
V. Yu. Venediktov, Dr. of Sciences (Phys.&Math.), Professor, Chief Researcher, Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0055-1234-5678
K. N. Gavrilieva, Postgraduate Student, Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0001-8946-9558
Yu. S. Gudin, student, Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0002-1061-7261
V. D. Nenadochev, JSC “Research-and-production corporation “Precision system and Instruments” (RPC PSI), Moscow, Russia
ORCID: 0000-0003-2628-0648
A. A. Ryzhaya, student, Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0001-9574-1802
A. A. Sevryugin, Cand. of Sciences (Phys.& Math.), Researcher, Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0002-5982-7892
A. L. Sokolov, Doctor of Technical Sciences, Prof., Head of Department, JSC “Research-and-production corporation “Precision system and Instruments” (RPC PSI), Moscow, Russia.
ORCID: 0000-0001-6164-7615
E. V. Shalymov, Ph.D., Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0002-0731-6978
V. Yu. Venediktov 1, K. N. Gavril’eva 1, Yu. S. Gudin 1, V. D. Nenadovich 2, A. A. Ryzhaya 1, A. A. Sevruygin 1, A. L. Sokolov 2, E. V. Shalymov 1
Laser Measurement and Navigation Systems department, Saint Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia
Research-and-Production Corporation, Precision Systems and Instruments (RPC PSI), Moscow, Russia
This article describes an experimental study of the optical vortex formation using beams reflected from a combination of two cube-corner reflectors with a special interference phase-shifting coating. As predicted earlier, if arranged properly, these cube-corner reflectors create a spatial polarization structure, that can be called an optical vortex, since the plane of oscillations of thе vector E rotates with azimuth variation in the transverse plane. This enables an easy way of creating such vortices, albeit with some difficulties due to the need for precise optical path control and vortices themselves created in far field.
Keywords: optical vortex, cube-corner reflectors, spatial polarization structure, polarization of light, retroreflective spatial-polarization interferometer
Received on: 12.04.2022
Accepted on: 26.04.2022
INTRODUCTION
Optical vortices have many different potential applications – communications, optical testing, optical manipulation of small particles, and so on. Several methods exist to create an optical vortex, including computer-generated holograms. spiral phase plates, mode conversion and so on. However, new methods of creating optical vortices are welcomed to increase the area of their application.
Previously, lots of work was done on creating of the cube-corner reflectors (CCR) with a certain far-field diffraction pattern, with one of the effective ways to optimize it was using a special phase-shifting interference coating to create the required phase shift of the light is reflected on the cube-corner reflectors faces. [1–6] The primary goal of developing such cube-corner prisms was related to the task of measuring the distance from the ground to satellites. Today all GPS satellites, all Glonass satellites and many other satellites are equipped by the panels, containing several dozens or even several hundreds of special CCR elements. When compared with the “usual” CCR, easily available from numerous commercial companies, such CCR reveal two special features, namely:
The angle between the edges at the top of the prism is slightly more than the standard 90°.
Hence, instead of the single beam with the hexagonal pattern in its section such CCR reflects the incoming plane wave as the combination of six separate beams, propagating along the conical surface.
“Usual” CCRs employ the total internal reflection from the edges. Hence, after each reflection the P- and S- linearly polarized components of radiation accumulate mutual phase shift, depending upon the reflection geometry. The reflecting faces of the prisms, which we consider here, are coated by the special polarization coatings, providing either preservation of the linear polarization or its turn in 90°.
Such cube-corner reflectors form of a six-spot diffraction pattern with each spot having planes of vector E oscillations rotated relative to each other at a certain angle. In [4, 7, 8] there was considered in theory the so-called polarization interferometer. Such an interferometer is similar to the usual cross-like Michelson interferometer, where both plane mirrors are replaced by the said CCRs. In the papers [4, 7, 8] various configurations of such interferometers were considered in theory. It was shown that the most interesting variant is the one in which the equilateral triangles of the input faces of CCRs are rotated in 60o one with respect to another. As we have said already, in the papers [4, 7, 8] these devices were studied in theory. It was shown that it is possible to create different configurations of such devices. In one of such configurations it is possible to produce the so-called vector vortex wave with the azimuthal direction of polarization vector. This article, which is now offered to the attention of readers, presents the first experimental realization of such a device and generation of the vector vortex in it. For the reader’s convenience we present first a brief explanation of such device operation, and after it the experimental results and some discussion. It is interesting to note that, according to the results of [8], other configurations of polarization interferometer can produce the so-called phase vortex of the second order and many other interesting and promising variants of the structured light beams with the axially symmetrical distribution of phase and polarization. Such configurations will be investigated in our next papers.
POLARIZATION INTERFEROMETER FOR VECTOR VORTEX FIORMATION
The rigorous theory of the polarization interferometer performance was given in [8]. Here we present some briefs from the said paper so as to simplify the reader understanding of our experimental setup.
First thing to note – when the beam enters CCR it undergoes three reflections, each of which induces a phase shift between the orthogonal components of the electric vector E. Second – the plane of incidence of the beam on the edge does not coincide. This determines the polarization characteristics of the CCR. The resulting structure of the reflected beam polarization depends on which of the six sectors the beam hits (Fig. 1a), incoming beam polarization and CCR parameters [1–6]. The wavefront of the incoming beam is divided into six parts upon its reflection from the CCR, as mentioned earlier, and these parts have different polarization states and phase shifts. In addition to that due to diffraction and interference between them a complex far-field diffraction pattern (FFDP) will form.
The phase shift of the orthogonal components during reflection has most significant impact, and it depends on the type of the CCR face coating. In our case these CCRs have special interference coating, thus resulting phase shift can be selected during production over a wide range from 0 to π. Such coatings induce phase shift thanks to multiple layers and different transmittances at the media boundary for P- and S- polarized components of the wave. In case of reflection at Brewster angle from a CCR face a P- component travels down to the last layer of the interference coating, almost without reflections, and returns, thanks to total internal reflection, with a certain phase shift that depends on the coating thickness its refractive index, and the number of layers. Meanwhile the S- component undergoes numerous reflections at layer boundaries, and the resulting wave if formed by superposition of the secondary coherent waves with different phase shifts [6]. In our case only CCRs with zero phase shift are considered with the FFDP of a symmetric system of six spots without a central spot.
Let’s assume two CCRs with a special phase-shifting coating, which ensures a zero-phase shift between P- and S- polarization components upon reflection from each of the three faces are placed instead of a mirrors in a Michelson-type interferometer, at a 90° angle as shown on Fig. 2 (a). Depending on phase shift (0 to π) between reflected beams we will get different patterns.
This phase shift can be created either using liquid crystal variable retarder, variable pathlength cell or an adjustable mount, for example with a piezoceramic actuator. The resulting setup works similar to a retroreflective spatial-polarization interferometer (RSPI), based on a Rayleigh interferometer, described in [9]. The polarization properties of the RSPI are described by a spiral polarization rotator, the order and sign of which change depending on the angular distance from the beam axis.
In case of the incoherent superposition the reflected beam can be decomposed into a set of Hermite–Gaussian modes with different polarization. Now we’ll add path difference between two reflected beams (i. e. phase shift) into equation to see how it affects the polarization structure of the reflected light superposition. If the incoming plane wave has linear polarization an axisymmetric polarization structure is observed in the reflected beam. At a high distance, the intensity in the ring becomes uniform. Depending on the phase difference of the reflected beams the polarization structure changes significantly. At zero phase difference, an axisymmetric polarization structure of the second order can be observed, shown in Fig. 2b, with a Jones vector:
.
If a phase difference is π, the beams cancel each other, and a fourth-order beam with the opposite vector E rotation in the transverse plane appears at the periphery, Fig. 2c:
.
EXPERIMENTAL SETUP AND RESULTS
The experimental setup is shown in Fig. 3, where a He-Ne laser 1 is used as a source. With the help of a tunable beam expander 2, one can obtain either a parallel beam of light or a slightly diverging one. The collimated beam passes through polarizer 3, after which it is divided by non-polarizing beam splitter cube 4 into two waves with equal intensity and polarization. After that, the beams are reflected by retroreflectors 5 and 6, and combined in a beam-splitting cube, creating required polarization distribution. Then the beam was reflected several times using a simple mirrors installed at a certain distances (not shown on the the diagram) to increase the optical path. After that it was recorded using digital camera or observed by a naked eye on the screen 9. In some cases, lens 8 was installed to focus the image, in some cases not. By rotating the polarizer 8, the distribution of polarization was analyzed in the final picture.
Result obtained with only one corner reflector & without polarizer 8 are shown in Fig.4, top left. Top right & bottom row of Fig.4 shows results with only one corner reflector at various orientations of polarizer 8 (top right, bottom left & right).
The image obtained with both corner reflectors without polarizer 8 at some distance is shown in Fig. 5. Fig. 6 shows the images obtained at different angles of the polarizer 8. Due to insufficient distance between the experimental setup and the camera these images does not look like they should (with a donut-shaped intensity distribution) since effects of far-field diffraction haven’t affected intensity distribution well enough. However, one clearly see that intensity distribution changes while rotating the polarizer according to the expectations.
Conclusion
We have presented an experimental study of the polarization-symmetric structure formation of the reflected radiation using beams reflected from a combination of two cube-corner reflectors with a special interference phase-shifting coating. Based on previous theoretical studies, we have created a basic retroreflective spatial-polarization interferometer to obtain a donut-shaped intensity distribution out of linearly polarized light with resulting plane of polarization rotating around the center. Results show that polarization in the resulting image matches theoretical studies. In near future it is planned to continue this experiment with increased optical path to include circular polarization and far-field diffraction in its full extend. Other configurations of polarization interferometer can produce the so-called phase vortex of the second order and many other interesting and promising variants of the structured light beams with the axially symmetrical distribution of phase and polarization. Such configurations will be investigated in our next papers.
Funding
The research was funded by the Russian Government within the Program “Priority‑2030”. K. N. Gavril’eva is grateful to the Russian Foundatuib for Basic Research for funding within the grant 20-32-90140.
ABOUT AUTHORS
V. Yu. Venediktov, Dr. of Sciences (Phys.&Math.), Professor, Chief Researcher, Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0055-1234-5678
K. N. Gavrilieva, Postgraduate Student, Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0001-8946-9558
Yu. S. Gudin, student, Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0002-1061-7261
V. D. Nenadochev, JSC “Research-and-production corporation “Precision system and Instruments” (RPC PSI), Moscow, Russia
ORCID: 0000-0003-2628-0648
A. A. Ryzhaya, student, Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0001-9574-1802
A. A. Sevryugin, Cand. of Sciences (Phys.& Math.), Researcher, Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0002-5982-7892
A. L. Sokolov, Doctor of Technical Sciences, Prof., Head of Department, JSC “Research-and-production corporation “Precision system and Instruments” (RPC PSI), Moscow, Russia.
ORCID: 0000-0001-6164-7615
E. V. Shalymov, Ph.D., Department of Laser Measurement and Navigation Systems, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia.
ORCID: 0000-0002-0731-6978
Readers feedback
