# Recent Advances in Generation and Detection of Orbital Angular Momentum Optical Beams—A Review

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{ilϕ}to EM waves, even though there are numerous models in various categories and appropriate for different application circumstances. They are divided into two groups: those that are independent of wave polarization and those that are dependent on it.

## 2. OAM Emitters Based on Diffractive Optic Elements

^{ilϕ}to EM waves, even though there are numerous models in different types and appropriate for distinct application circumstances. The first scheme makes use of isotropic materials like SPPs [77] and CGHs [78]. An SPP is the simplest device for manipulating OAM modes at millimeter frequencies. An SPP is a dielectric slab of material with an azimuthally reliant on thickness that causes incident radiation to undergo an azimuthal phase change [79,80]. The SPP’s total step height, h, is selected so that the total phase change around the SPP’s center is an integer multiple of 2πl, where l is an integer. The azimuthal mode number l of the incident radiation is modified because of this, such that: $\Delta l=\frac{h\Delta n}{\lambda}$, where Δn is the refractive index difference between the dielectric material and the surrounding medium, and λ is the incident wavelength.

## 3. MSs for Generation of Vector OV Beams

^{ilϕ}. The resonant frequency of the scatterer is modified by changing its geometry, causing the phase shift to differ at the desired frequency. After optimization, a total of 2π phase shift is achieved, and the effective generation of various OAM states has been demonstrated [124]. Tunable scatterers stocked by varactor diodes have recently been suggested as a convenient way to generate multiple OAM modes [125]. Scatterers can also be rendered anisotropic to regulate various polarizations independently. Even if the scatterer’s responses are polarization-dependent, the helicity of the emitted OAM is independent of the incident wave’s polarization state. In other words, the helicity is fixed.

_{x}= +1 and ℓ

_{y}= −2. The MS prototype with 30 × 30 units was fabricated and tested to authenticate the efficacy of the engineered MS for generating dual-polarized dual-mode converged OAM beams. The measurements are carried out in the near-field anechoic chamber using a 3D platform and an open-ended WG probe, as shown in Figure 5a [126]. Figure 5b,c depicts the measured full hemisphere far-field radiation patterns in magnitude and phase for the two orthogonal polarized OAM modes, with the excessive intensity annular tapered patterns, as well as the typical spiral phase fronts and on-axis phase singularities, obviously visible [126].

## 4. OAM Beams Generation with Photonic Integrated Circuits

_{1}(Figure 8(a1)) and Λ

_{2}(Figure 8(a2)) have been superimposed into a ring resonator in the device, resulting in a superimposed grating envelope with numerous beat perturbations, as illustrated in Figure 8(a3). Figure 8b–d shows far-field images of the two-beat grating device recorded at various resonant wavelengths according to the transmission/radiation spectrum, resulting in various topological charge combinations. The near-field pattern (Figure 8e) and the well-defined spiral interference fringes (Figure 8d) show two crescent-shaped lobes positioned in a circular pattern, showing that the radiated beams are truly emitted from the modulated gratings. Because it does not require any extra couplers or MZIs, the suggested device is quite small. Furthermore, by simply adding more gratings, it may construct superposition states in more than two dimensions. Because all modes are emitted from the same source mode via the same superimposed grating, the used methodology is simple and maintains a fairly constant phase between the OAM states.

_{o}(x,y,z) and A

_{t}(x,y,z) are the amplitudes of the obtained and target vortex beams, respectively [152]. Fidelity surges with b until it hits a peak, after which it drops with b. The greatest fidelity is 0.93 for b = 1.8 μm, which is the length of the holographic grating in the accompanying figure. The OV beam is formed based on the grating width d and the fixed length b = 1.8 μm, as shown in Figure 9h–l. The field distribution for d = 1 μm, 1.4 μm, 1.8 μm, and 2.2 μm indicate that d has a moderate effect on phase but a considerable effect on amplitude. The fidelity represented in Figure 9l has an optimal F = 0.93 for d = 1.6 μm.

_{x}) [165,166,167]. Because of the low cost, the high material strength of Si and CMOS compatibility, PICs based on the Si platform are particularly well suited as a medium for integrating with other components. Moreover, in [153,168] a scheme is proposed that uses a hybrid plasmonic WG to produce light beams with selective angular momentum (AM) over a wide wavelength range. AM beams can either propagate through optical WGs or emit into free space. Since it is based on an SOI platform and uses standard CMOS technology, this approach has high fabrication feasibility.

_{01}and TE

_{10}modes. Due to the transverse confinement, the SAM and OAM of the OV fields are strongly coupled and the whole space of structure variables of the WG can be separated just into three regimes. These results shed light on the correlation between angular momentum and mode confinement, which is useful for applying OVs in PICs. In the case of higher-order OAM modes propagation, the cross-shaped core WG structure was designed in [161]. Two degenerate driven modes of π/2 l-rotation symmetry can assist the l-th order OAM mode. The designed cross-shaped WG supports OAM modes of ±1 and ±2 topological charges concurrently at a wavelength of 1550 nm with high mode purity. The Hermite Gaussian (HG)-similar guided modes are shown in Figure 12a–d. To fulfil the degeneracy of HG

_{01}–HG

_{10}and ${\mathrm{LG}}_{02}^{\mathrm{e}}\u2013{\mathrm{LG}}_{02}^{\mathrm{o}}$, which form OAM modes of ±1 and ±2 topological charges, respectively, the geometric variables denoted as W

_{1}, L

_{1}, W

_{2}and L

_{2}have been optimized (see Figure 12e). The impact of every parameter on n

_{eff}of the modes is shown in Figure 12f. Additionally, such WG structures were designed for l = ±3 and l = ±4 OAM modes guiding individually, but the purity turned out to be lower and it is challenging to design the WG concurrently supporting the l = ±3 and l = ±4 OAM modes. Probably, a more complex transverse composition is required to further increase the topological charge. Anyway, in-plane operation using higher-order OAM modes is a competitive field.

_{l}

_{=1}mode’s two constitutive eigenmodes. The desired device has a coupling length of 670 μm and exhibits little OAM mode purity loss during the optical power transfer procedure. But again, the design of such a device for the higher-order OAM modes coupling is tricky and still competitive. Figure 13 shows the dependences of the coupling coefficient on the length in the case of the usual directional coupler and on the cutout size t in the case of cross shape WG coupler. As can be seen, the coupling coefficient of the TE

_{10}mode is always higher than the TE

_{01}one in the case of a rectangular WG coupler and does not satisfy a requirement for the OAM

_{l}

_{=1}mode directional coupler. But when the directional coupler is made of a cross-shaped WG, there is a cutout size around 490 µm, where TE

_{01}and TE

_{10}modes have the same coupling coefficient. The insertion of the cutoff breaks down the degeneracy between TE

_{10}and TE

_{01}modes in the starting rectangular WG. The particle swarm optimization method can be used to optimize WG’s width and height and the cutoff dimensions of the cross-shaped WG simultaneously [164].

_{01}and TE

_{10}eigenmodes being mixed with π/2 phase shift. The rectangular WGs assisting multiple transverse modes and keeping symmetry in two orthogonal transverse directions are also proposed in [171].

_{01}mode at the input of a trench WG. Figure 14b shows a cross-section of a WG. The distributions of eigenmodes of a trench WG are shown in Figure 14c and its combination evolutions are presented in Figure 14d. Moreover, the structure of an on-chip OAM modes (de)multiplexer for x-polarization, utilizing the trench WGs was demonstrated.

_{3}N

_{4}WG represents the MS. MS simultaneously realizes OAM excitation and light coupling. The device also generates and adds two high-order TE

_{01}and TE

_{10}modes with π/2 phase difference. The convenience of the MS in simultaneous excitation and mixing of modes at the required phase ratio.

## 5. Detection of Light with OAM

^{3}at a repetition rate of 5 MHz, assuming detector noise does not restrict measurement precision. High-order OAM states can be added to this design. A schematic of the OAM detector system reported in [212] is shown in Figure 16. As shown in Figure 16a,b, it comprises of a center suspended pad connected to one side of a slot-mode photonic crystal nanobeam cavity [212].

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The number of papers related to the “Orbital angular momentum” topic searched in the Scopus database for the years 2000–2021.

**Figure 2.**Methods to generate light with OAM: (

**a**) Shift in the OAM order by illuminating a 3D element with the laser light of different wavelengths [58]; (

**b**) OAM generator via CGH [59]; (

**c**) Schematic of the OV beam generator from MS [60]; and (

**d**) The schematic illustration of the OV beam generator on the embedded multi-WG [61].

**Figure 3.**Elements of singular optics: (

**a**) SPP. Reprinted with permission from ref. [36]. Copyright 1994, Elsevier; (

**b**) spiral axicon; (

**c**) spiral zone plate; (

**d**) OV autofocusing optical element; (

**e**) fork grating; (

**f**) curved fork grating; and (

**g**) grating for OV hyper-geometric laser beams generation.

**Figure 4.**Optical system for generation of vector OV beams by a combination of DOEs and anisotropic crystals: a He-Ne laser emitting linearly polarized light which was expanded using an objective (L1), a quarter-wave plate (QWP) was utilized to alter the linearly polarized beam into the circularly polarized beam, the diffractive optical element (DOE) generates OV Laguerre-Gaussian modes which are focusing by a lens (L2) into a c-cut CaCO

_{3}crystal, cylindrically polarized beams (with radial or azimuthal polarization) are imaging by a lens (L3) at CCD array and analyzed by a polarizer (P). Reprinted with permission from ref. [115]. Copyright 2017, Elsevier.

**Figure 6.**(

**a**) Graphical design of all-fiber focused OV beam generator [141], (

**b**) SEM image of the nanoimprinted KSZP microstructure with topological charge l = −1 [141], and (

**c**) focal spot profiles acquired from FDTD simulation (top row), experimental measurement (middle row), and the measured coaxial interference forms (bottom row) [141].

**Figure 8.**(

**a1**,

**a2**) Schematic of two single grating (with period of Λ

_{1}and Λ

_{2}, respectively) superimposed into multiple-beat modulated device [151]. An unfolded view of resulting the three beats device (

**a3**) [151]. The far-field patterns of the two-beat grating device: (

**b**) 1508.1 nm, topological charges combination +1 and −1; (

**c**) 1518.9 nm, topological charges combination 0 and −2; and (

**d**) 1530 nm, topological charges combination −3 and −1 [151]. The near-field pattern is showing in (

**e**), and the well-defined spiral interference fringe existed at appropriate locations is showing in (

**f**) [151].

**Figure 9.**(

**a**) The graphical image of the OV beam generator, (

**b**) (

**b1**–

**b4**), the basis of the holographic grating on WG. The acquired OV beams by the holographic gratings with different sizes. The intensity and phase distributions are shown in the upper row and down row of the figures, (

**c**–

**f**) consistent to the holographic gratings with a constant width d = 1.5 μm but different lengths b = 1, 1.4, 1.8, 2.2 μm, and (

**h**–

**k**) corresponding to the holographic gratings with a constant-length b = 1.8 μm but dissimilar widths d = 1, 1.4, 1.8, and 2.2 μm, respectively, (

**g**,

**l**) are the fidelities of the attained OV beams as the functions of length b and width d, correspondingly. Reprinted with permission from ref. [152]. Copyright 2016, Elsevier.

**Figure 11.**The normalized transversal field component intensity distribution superimposed with polarization map (

**a**,

**d**) [166], Normalized absolute amplitude mapping of dominant E-field component (

**b**,

**e**) and phase distribution of dominant E-field component (

**c**,

**f**) of the quasi-TE (

**a**–

**c**) and quasi-TM (

**d**–

**f**) quasi-degenerate modes of order l = 1 in the symmetric (silica clad) silicon nitride WGs enhanced for phase-matched propagation of the constituent eigenmodes (β

_{01}≈ β

_{10}) [166].

**Figure 13.**Cross-section of rectangular WG coupler (

**a**) [164], the coupling coefficient of TE

_{10}and TE

_{01}modes in case of W = 0.72 µm and H = 0.6 µm (

**b**) [164], the cross-section of cross shape WG coupler (

**c**) [164], the coupling coefficient of TE

_{10}and TE

_{01}modes as a function of t (

**d**) [164].

**Figure 14.**(

**a**) OAM beam generator principle built on a single-trench WG; (

**b**) A single trench WG in cross-section; (

**c**) Two eigenmodes of a single-trench WG’s field distributions; and (

**d**) For x-polarization, intensity and phase evolutions of a combination of eigenmodes [67].

**Figure 15.**Detecting OVs: (

**a**) phase of a 13-channel filter; (

**b**) intensity pattern (negative) in the focal plane and correspondence of diffraction orders to OV values; and (

**c**) results of detecting of different OVs in the beam with co-axial superposition exp(−i2φ) + exp(−iφ) (total OAM μ = −0.5) [194].

**Figure 16.**A diagram of the device’s geometry: (

**a**) Top view of a slot-mode PhC cavity geometry and modeling of the E-field distribution of its fundamental optical mode [212]; and (

**b**) The OAM detector in isometric perspective. The cavity from (

**a**) is attached to the square pad by a hanger whose dimensions w

_{h}and l

_{h}are indicated in (

**c**) [212]. The pad motion is moved to the nanobeam when excited by a source of torque as exhibited by the simulated displacement profile shown in (

**c**) [212].

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## Share and Cite

**MDPI and ACS Style**

Fatkhiev, D.M.; Butt, M.A.; Grakhova, E.P.; Kutluyarov, R.V.; Stepanov, I.V.; Kazanskiy, N.L.; Khonina, S.N.; Lyubopytov, V.S.; Sultanov, A.K.
Recent Advances in Generation and Detection of Orbital Angular Momentum Optical Beams—A Review. *Sensors* **2021**, *21*, 4988.
https://doi.org/10.3390/s21154988

**AMA Style**

Fatkhiev DM, Butt MA, Grakhova EP, Kutluyarov RV, Stepanov IV, Kazanskiy NL, Khonina SN, Lyubopytov VS, Sultanov AK.
Recent Advances in Generation and Detection of Orbital Angular Momentum Optical Beams—A Review. *Sensors*. 2021; 21(15):4988.
https://doi.org/10.3390/s21154988

**Chicago/Turabian Style**

Fatkhiev, Denis M., Muhammad A. Butt, Elizaveta P. Grakhova, Ruslan V. Kutluyarov, Ivan V. Stepanov, Nikolay L. Kazanskiy, Svetlana N. Khonina, Vladimir S. Lyubopytov, and Albert K. Sultanov.
2021. "Recent Advances in Generation and Detection of Orbital Angular Momentum Optical Beams—A Review" *Sensors* 21, no. 15: 4988.
https://doi.org/10.3390/s21154988