Open Access
Issue
EPJ Appl. Metamat.
Volume 11, 2024
Article Number 3
Number of page(s) 6
DOI https://doi.org/10.1051/epjam/2024004
Published online 09 February 2024

© Y. Liu et al., Published by EDP Sciences, 2024

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 Introduction

The generation of the structured lights with complicated polarization states and phase distributions has attracted intense attention [113], for the promising applications in the next-generation optical communication [14,15] and optical manipulation [16,17]. Information can be encoded into the either the various polarization states or the topological charges of the orbital angular momentum (OAM), which can greatly enlarge the capacity and the security in the optical communication systems [18,19]. Therefore, the ability of demultiplexing the modes and thus decoding the information from the structured light is highly demanded [20]. Traditional ways of sorting vortex are always bulky and complex [21,22]. The emergence of metamaterials or metasurfaces with the artificially designed structures that can be used to achieve various phase or polarization modulation ability makes devices ultra-compact and highly integrated [2325]. However, fabrication is always highly costed, especially in the visible range. Meanwhile, the approachable meta-atom size from the current nanofabrications is still the main reason of the scattering loss [2629]. The idea of structuring real atoms or molecules into certain orders can also bring metamaterials' properties to natural materials such as natural hyperbolic materials with indefinite dielectric tensor [30,31] and the spherulite crystals with cylindrical anisotropy [3234]. Since these materials are homogenous at the atom/molecule level, fabrication challenges and scattering losses can be avoided. Here, by mimicking metamaterials, we designed and fabricated a spherulite prism with azimuthally patterned liquid crystals (LC) that can act as a vector vortices sorter. A cylindrical birefringence originated from the azimuthally arranged molecules separates the radially and azimuthally polarized vortex beams from the incident circularly polarized beam. The designed device of the wedge-like spherulite prism contributes to the advanced complex light manipulation techniques, paving the way to realize the simultaneous control of the polarizations and OAM of light in a compact and efficient way.

2 Design

Here, the spherulite with cylindrically anisotropic refraction indices is designed into a wedge-shaped prism by using the nematic LC (4-pentyl[1,1-biphenyl]-4-carbonitrile, 5CB). The 5CB molecule is intrinsically anisotropic with its refractive index (ne) along the longer axis larger than that (no) along the short axis, as shown in Figure 1. Once these molecules are constructed into a spherulite with the longitudinal axis along the azimuthal direction of the material, the formed spherulite may show cylindrically anisotropic indices with nA = ne and nR = no, which is mimicking the metamaterials consisted of concentric multi-layered structure. If such a spherulite is cut into a prism, cylindrical vector beams passing through the prism experience the cylindrical anisotropy and are thus refracted to two different directions. A left or right circularly polarized beam can be decomposed into radial and azimuthal components, i.e., er and eθ in equation (1) [35]:

(1)

where P(r) and θ are the amplitude profile and the azimuthal angle in the transverse plane of the incident beam. The topological charge l is used to characterize beams' OAM. er and eθ are the unit-vectors at the radial and azimuthal directions. Consequently, once a circularly polarized beam is incident onto such a prism, two OAM beams of the radial and azimuthal polarizations can be obtained due to the different refraction angles, as shown in Figure 1. The acquired output beams contain topological charge of either +1 or −1 depending on the chirality of the input circular polarization.

thumbnail Fig. 1

The schematic of spherulite prism working as a structured light sorter. The 5CB molecule is optically anisotropic with its refractive index ne along the longer axis and no along the short axis. The spherulite is constructed by these molecules with the longitudinal axis along the azimuthaldirection of the material, exhibiting the cylindrically anisotropy: nA = ne and nR = no, which is mimicking the metamaterials consisted of concentric multi-layered structure. Such a spherulite is cut into a prism and can be used to sort two optical vector vortices with radial and azimuthal polarizations from a circularly polarized beam.

3 Experiment

The spherulite prism is formed by injecting the 5CB LC into a wedged shape cell, as shown in Figure 2. The top part is a glass mold of 20 × 20 mm side by side and an oblique surface of 5°, and is then put on a glass substrate. Both the top and below surfaces are spin-coated with a 30 nm thick layer of photoalignment agent (sulfonic azo dye, sodium 4,4-bis (4-hydroxy-3-carboxy-phenylazo) benzidine-2,2-disulphonate, SD1) for the molecular arrangement. Subsequently, the light irradiation on the SD1 layer is carried out by using a radially polarized vortex laser at 405 nm for 15 min to supply the photo-alignment, which is used in turn to align the molecules azimuthally. Under the polarized optical microscope, the illuminating white light is linearly polarized. After the sample, we put a linear polarizer with its transmittance direction perpendicular to the linear polarization of the incidence. Then we can see the Maltese dark cross, which is the signature of the cylindrical anisotropy [36,37].

A circularly polarized beam at 532 nm is incident on to the prism from the substrate side normally, which means the incident angle θi at the top oblique surface is 5°. The anisotropic refractive indices of the 5CB LC are no =1.55 and ne = 1.75 along the short and long-axis of the molecule [38], respectively. In our case, the no and ne are corresponding to indices along the radial and azimuthal directions of the spherulite. Based on Snell's law, we calculate the refraction angle of the beams at radial (θR) and azimuthal polarization (θA) as below:

(2)

where ng = 1.5 is the refractive index of the glass.

The theoretical calculation results are shown in Figure 2b. The separation of the two beams in angle Δθ = |θAθR| reaches to the maximum at 58° in Figure 3c. The horizontal line at θ = 90° indicates the occurring of the total refraction of the two beams. In principle, a large separation means a high efficiency of the sorter. However, the refraction angle of θR and θA are also very large, which may bring in a serious deviation of the intensity distribution around the azimuthal angle θ and thus greatly affect the purity of the vortex beams. In the experiment, the incident angle θi is just 5° and the distortion to the intensity is almost negligible, as shown in Figure 3. It should be noted that the value of Δθ at the magnitude of 1° is large enough to spatially split the two output beams of the orthogonal polarizations at the far field.

The output beams are characterized by a Mach−Zehnder interference setup, as shown in Figure 4. A linearly polarized laser beam at 532 nm is transformed into circular polarization by a quarter waveplate and then imported into the Mach−Zehnder interference setup by a beam splitter (BS). The spherulite prism sample is put in one arm of the Mach−Zehnder interference setup while the beam in the other arm is transformed into left or right circular polarization by using a linear polarizer (LP) and a quarter wave plate (λ/4 WP). After the sample, the circularly polarized incidence is split into two beams with radial and azimuthal polarizations. We extract either one of the two output beams which is realigned by the two mirrors (M1 and M2) and then interfered with the reference beam after the second BS. According to equation (1), we can obtain the expressions of the radial and azimuthal polarizations as:

(3)

which imply that a radially or azimuthally polarized vortex beam with topological charge l is a superposition of right and left circularly polarized vortex beams with l ± 1. Therefore, by rotating the quarter wave plate, we can use the reference beam with two opposite circular polarizations to detect the left or the right circular polarized components in the output structured light beams through the inference pattern and the results are shown in Figure 5.

thumbnail Fig. 2

Wedge-shape cell to form the spherulite prism. (a) The schematic diagram of the prism. The dimension of the wedge-shape is 20 × 20 mm side (L) by side (L) and with a height (h) of 1.75 mm, which forms an oblique surface of 5°. (b) The refraction angles of the two polarizations at different incident angles.

thumbnail Fig. 3

Intensity distortion due to the refraction. (a) The dependence of the azimuthally polarized output beam intensity distribution along the azimuthal direction θ with respect to different incidence angle θi. (b) The dependence of the radially polarized output beam intensity distribution along the azimuthal direction θ with respect to different incidence angle θi. (c) Intensity variations of output beams at incident angles of 5° (the upper panel) extracted from the (a) and (b) along the left dashed lines and the intensity variations of output beams at incident angles of 57°, which is a little below the critical angle (the lower panel) extracted along the right dashed lines in (a) and (b).

thumbnail Fig. 4

The Mach−Zehnder interference setup used to characterize the output structured light beams.

thumbnail Fig. 5

Polarization characterizations and the OAM determination of the two output beams. (a) The doughnut-shaped intensity profile of the output beam with a large refraction angle. (b) Intensity profiles of the output beam after a rotating linear polarizer. (c) The interference pattern of the output beam and the reference of left/right circular polarization. (d) The doughnut-shaped intensity profile of the output beam with the small refraction angle. (e) Intensity profiles of the output beam after a rotating linear polarizer. (f) The interference pattern of the output beam and the reference of left/right circular polarization.

4 Results and discussion

Figure 5a shows the output beam with a large refraction angle, whose intensity profile is in a doughnut shape with a dark center. After a linear polarizer, the doughnut is split into two bright lobes. The central dark line is always along the polarizer when it is rotated, which proves the beam to be at the azimuthal polarization, as shown in Figure 5b. Figure 5c illustrates the interference patterns obtained by using left and right circularly polarized beams. The upper one shows no fork while the lower one shows a spiral fork with two tines, which demonstrates the topological charge to be 1. Figure 5d shows the output beam with the small refraction angle, which is also in a doughnut shape. After a linear polarizer, the doughnut is split into two bright lobes while the central dark line is always normal to the polarizer when it is rotated, as shown in Figure 5e. Therefore, the polarization state of this beam is radial. In Figure 5f, the interference patterns of the radially polarized beam with the left and right circularly polarized beams show non fork and a spiral fork of two tines, which also demonstrates the topological charge of the radial polarization to be 1.

To further demonstrate the sorting performance, we used a right circularly polarized vortex beam with a topological charge l = 1 as the incident beam. According to equation (1), the output beams are two non-OAM (l−1 = 0) beams at radial and azimuthal polarizations after the spherulite prism. Meanwhile, each non-OAM radial or azimuthal polarization contains left and right circular polarization components with ±1 charge OAM. Therefore, the interference with left and right circularly polarized beams in each case show opposite one fold spiral patterns for both the two output beams, as shown in Figure 6. Accordingly, incident left or right circularly polarized beam with any l OAM can be separated into two beams according to the cylindrical polarization states while with OAM l + 1 and l−1. In addition to birefringence, the anisotropy also causes the spin-orbital angular momentum conversion, which provides the modulation ability to the topological charge.

thumbnail Fig. 6

The interference patterns of the output beams from a charge 1 circularly polarized beam interfered with the referenced beams of left/right circular polarizations. (a) The interference pattern of the output radial polarization and the reference of left circular polarization. (b) The interference pattern of the output radial polarization and the reference of right circular polarization. (c) The interference pattern of the output azimuthal polarization and the reference of left circular polarization. (d) The interference pattern of the output azimuthal polarization and the reference of right circular polarization.

5 Conclusion

In summary, we design and experimentally demonstrate a structured light sorter by using a spherulite prism consisted of 5CB molecules, which are azimuthally aligned to produce the cylindrical birefringence. In the experiment, a circularly polarized beam with or without OAM can be separated into two beams with radial and azimuthal polarization states at 532 nm. Since the optical vortex beams with helical wave fronts carry an orbital angular momentum with unlimited range of the topological charge, it provides an unbounded state space, and hence a large potential information capacity. Also, orbital angular momentum modes are the candidate for free-space quantum key distribution systems, where the ability to efficiently sort single photons based on their OAM mode number is very important. Therefore, the proposed device may find applications of the future high-capacity optical communications and quantum communications [3945].

Supplementary Material

Fig. S1. Comparison of the interferences with incident circularly polarized beam of non-OAM .

Fig. S2. Comparison of the interferences with incident circularly polarized vortex beam of charge 1.

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Funding

This work was supported by the National Key R&D Program of China (Grant No. 2022YFB3806000). The Basic Science Center Project of NSFC (Grant No. 52388201). National Natural Science Foundation of China (Grant No. 11974203).

Conflicts of Interest

The authors have no conflict of interest to disclose.

Data availability statement

This article has no associated data generated and/or analyzed / Data associated with this article cannot be disclosed due to legal/ethical/other reason.

Author contribution statement

Conceptualization, J.S.; Methodology, Y.L and L. Z.; Validation, Y.S., J.Z. and J.S.; Formal Analysis, Y.L.; Investigation, Y.L.; Resources, Y.L.; Data Curation, Y.L.; Writing – Original Draft Preparation, J.S. and Y.L; Writing – Review & Editing, J.Z.; Visualization, Y.W.; Supervision, Y.S., J.Z. and J.S.; Funding Acquisition, J.S.

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Cite this article as: Yuanfeng Liu, Le Zhou, Yongzheng Wen, Yang Shen, Jingbo Sun, Ji Zhou, Structuring light sorter based on a cylindrically anisotropic spherulite prism, EPJ Appl. Metamat. 11, 3 (2024)

All Figures

thumbnail Fig. 1

The schematic of spherulite prism working as a structured light sorter. The 5CB molecule is optically anisotropic with its refractive index ne along the longer axis and no along the short axis. The spherulite is constructed by these molecules with the longitudinal axis along the azimuthaldirection of the material, exhibiting the cylindrically anisotropy: nA = ne and nR = no, which is mimicking the metamaterials consisted of concentric multi-layered structure. Such a spherulite is cut into a prism and can be used to sort two optical vector vortices with radial and azimuthal polarizations from a circularly polarized beam.

In the text
thumbnail Fig. 2

Wedge-shape cell to form the spherulite prism. (a) The schematic diagram of the prism. The dimension of the wedge-shape is 20 × 20 mm side (L) by side (L) and with a height (h) of 1.75 mm, which forms an oblique surface of 5°. (b) The refraction angles of the two polarizations at different incident angles.

In the text
thumbnail Fig. 3

Intensity distortion due to the refraction. (a) The dependence of the azimuthally polarized output beam intensity distribution along the azimuthal direction θ with respect to different incidence angle θi. (b) The dependence of the radially polarized output beam intensity distribution along the azimuthal direction θ with respect to different incidence angle θi. (c) Intensity variations of output beams at incident angles of 5° (the upper panel) extracted from the (a) and (b) along the left dashed lines and the intensity variations of output beams at incident angles of 57°, which is a little below the critical angle (the lower panel) extracted along the right dashed lines in (a) and (b).

In the text
thumbnail Fig. 4

The Mach−Zehnder interference setup used to characterize the output structured light beams.

In the text
thumbnail Fig. 5

Polarization characterizations and the OAM determination of the two output beams. (a) The doughnut-shaped intensity profile of the output beam with a large refraction angle. (b) Intensity profiles of the output beam after a rotating linear polarizer. (c) The interference pattern of the output beam and the reference of left/right circular polarization. (d) The doughnut-shaped intensity profile of the output beam with the small refraction angle. (e) Intensity profiles of the output beam after a rotating linear polarizer. (f) The interference pattern of the output beam and the reference of left/right circular polarization.

In the text
thumbnail Fig. 6

The interference patterns of the output beams from a charge 1 circularly polarized beam interfered with the referenced beams of left/right circular polarizations. (a) The interference pattern of the output radial polarization and the reference of left circular polarization. (b) The interference pattern of the output radial polarization and the reference of right circular polarization. (c) The interference pattern of the output azimuthal polarization and the reference of left circular polarization. (d) The interference pattern of the output azimuthal polarization and the reference of right circular polarization.

In the text

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