# Wavelength-Tunable Vortex Beam Emitter Based on Silicon Micro-Ring with PN Depletion Diode

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## Abstract

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## 1. Introduction

## 2. Principle of Operation

## 3. Simulation Results

## 4. Analysis of the Emitted Field Propagation

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Allen, L.; Beijersbergen, M.W.; Spreeuw, R.J.C.; Woerdman, J.P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A
**1992**, 45, 8185. [Google Scholar] [CrossRef] [PubMed] - He, H.; Friese, M.E.J.; Heckenberg, N.R.; Rubinsztein-Dunlop, H. Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity. Phys. Rev. Lett.
**1995**, 75, 826–829. [Google Scholar] [CrossRef] [Green Version] - Grier, D.G. A revolution in optical manipulation. Nature
**2003**, 424, 810–816. [Google Scholar] [CrossRef] [PubMed] - Chapin, S.C.; Germain, V.; Dufresne, E.R. Automated trapping, assembly, and sorting with holographic optical tweezers. Opt. Express
**2006**, 14, 13095–13100. [Google Scholar] [CrossRef] [Green Version] - Padgett, M.; Bowman, R. Tweezers with a twist. Nat. Photonics
**2011**, 5, 343–348. [Google Scholar] [CrossRef] - Vicente, O.C.; Caloz, C. Bessel beams: A unified and extended perspective. Optica
**2021**, 8, 451–457. [Google Scholar] [CrossRef] - Forbes, A.; Nape, I. Quantum mechanics with patterns of light: Progress in high dimensional and multidimensional entanglement with structured light. AVS Quantum Sci.
**2019**, 1, 011701. [Google Scholar] [CrossRef] [Green Version] - Ndagano, B.; Nape, I.; Cox, M.A.; Rosales-Guzman, C.; Forbes, A. Creation and Detection of Vector Vortex Modes for Classical and Quantum Communication. J. Light. Technol.
**2018**, 36, 292–301. [Google Scholar] [CrossRef] [Green Version] - Mafu, M.; Dudley, A.; Goyal, S.; Giovannini, D.; McLaren, M.; Padgett, M.J.; Konrad, T.; Petruccione, F.; Lütkenhaus, N.; Forbes, A. Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases. Phys. Rev. A
**2013**, 88, 032305. [Google Scholar] [CrossRef] [Green Version] - Zhang, Y.; Agnew, M.; Roger, T.; Roux, F.S.; Konrad, T.; Faccio, D.; Leach, J.; Forbes, A. Simultaneous entanglement swapping of multiple orbital angular momentum states of light. Nat. Commun.
**2017**, 8, 632. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Liu, J.; Nape, I.; Wang, Q.; Vallés, A.; Wang, J.; Forbes, A. Multidimensional entanglement transport through single-mode fiber. Sci. Adv.
**2020**, 6, eaay0837. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Richardson, D.J.; Fini, J.M.; Nelson, L.E. Space-division multiplexing in optical fibres. Nat. Photonics
**2013**, 7, 354–362. [Google Scholar] [CrossRef] [Green Version] - Ellis, A.D.; Suibhne, N.M.; Saad, D.; Payne, D.N. Communication networks beyond the capacity crunch. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**2016**, 374, 20150191. [Google Scholar] [CrossRef] [Green Version] - Turitsyn, K.S.; Turitsyn, S.K. Nonlinear communication channels with capacity above the linear Shannon limit. Opt. Lett.
**2012**, 37, 3600–3602. [Google Scholar] [CrossRef] [Green Version] - Sakaguchi, J.; Awaji, Y.; Wada, N.; Kanno, A.; Kawanishi, T.; Hayashi, T.; Taru, T.; Kobayashi, T.; Watanabe, M. Space Division Multiplexed Transmission of 109-Tb/s Data Signals Using Homogeneous Seven-Core Fiber. J. Light. Technol.
**2012**, 30, 658–665. [Google Scholar] [CrossRef] - Nakajima, K.; Sillard, P.; Richardson, D.; Li, M.J.; Essiambre, R.J.; Matsuo, S. Transmission media for an SDM-based optical communication system. IEEE Commun. Mag.
**2015**, 53, 44–51. [Google Scholar] [CrossRef] - Mizuno, T.; Takara, H.; Shibahara, K.; Sano, A.; Miyamoto, Y. Dense space division multiplexed transmission over multicore and multimode fiber for long-haul transport systems. J. Light. Technol.
**2016**, 34, 1484–1493. [Google Scholar] [CrossRef] - Wang, J.; Padgett, M.J.; Ramachandran, S.; Lavery, M.P.; Huang, H.; Yue, Y.; Yan, Y.; Bozinovic, N.; Golowich, S.E.; Willner, A.E. Multimode Communications Using Orbital Angular Momentum. In Optical Fiber Telecommunications; Elsevier: Amsterdam, The Netherlands, 2013. [Google Scholar] [CrossRef]
- Berdagué, S.; Facq, P. Mode division multiplexing in optical fibers. Appl. Opt.
**1982**, 21, 1950–1955. [Google Scholar] [CrossRef] [PubMed] - Bozinovic, N.; Yue, Y.; Ren, Y.; Tur, M.; Kristensen, P.; Huang, H.; Willner, A.E.; Ramachandran, S. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science
**2013**, 340, 1545–1548. [Google Scholar] [CrossRef] [Green Version] - Qu, Z.; Djordjevic, I.B. 500 Gb/s free-space optical transmission over strong atmospheric turbulence channels. Opt. Lett.
**2016**, 41, 3285. [Google Scholar] [CrossRef] - Willner, A.E.; Zhao, Z.; Liu, C.; Zhang, R.; Song, H.; Pang, K.; Manukyan, K.; Song, H.; Su, X.; Xie, G.; et al. Perspectives on advances in high-capacity, free-space communications using multiplexing of orbital-angular-momentum beams. APL Photonics
**2021**, 6, 030901. [Google Scholar] [CrossRef] - Zhao, Z.; Zhang, R.; Song, H.; Pang, K.; Almaiman, A.; Zhou, H.; Song, H.; Liu, C.; Hu, N.; Su, X.; et al. Modal coupling and crosstalk due to turbulence and divergence on free space THz links using multiple orbital angular momentum beams. Sci. Rep.
**2021**, 11, 2110. [Google Scholar] [CrossRef] [PubMed] - Khonina, S.; Kazanskiy, N.; Soifer, V. Optical Vortices in a Fiber: Mode Division Multiplexing and Multimode Self-Imaging. In Recent Progress in Optical Fiber Research; InTech: London, UK, 2012. [Google Scholar] [CrossRef] [Green Version]
- Wang, J.; Yang, J.Y.; Fazal, I.M.; Ahmed, N.; Yan, Y.; Huang, H.; Ren, Y.; Yue, Y.; Dolinar, S.; Tur, M.; et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photonics
**2012**, 6, 488–496. [Google Scholar] [CrossRef] - Zhao, Y.; Askarpour, A.N.; Sun, L.; Shi, J.; Li, X.; Alù, A. Chirality detection of enantiomers using twisted optical metamaterials. Nat. Commun.
**2017**, 8, 1–8. [Google Scholar] [CrossRef] - Tamburini, F.; Anzolin, G.; Umbriaco, G.; Bianchini, A.; Barbieri, C. Overcoming the Rayleigh criterion limit with optical vortices. Phys. Rev. Lett.
**2006**, 97, 163903. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kozawa, Y.; Matsunaga, D.; Sato, S. Superresolution imaging via superoscillation focusing of a radially polarized beam. Optica
**2018**, 5, 86–92. [Google Scholar] [CrossRef] - Fu, H.; Wang, S.; Chang, H.; You, Y. A high resolution and large range fiber Bragg grating temperature sensor with vortex beams. Opt. Fiber Technol.
**2020**, 60, 102369. [Google Scholar] [CrossRef] - Yue, Z.; Ren, H.; Wei, S.; Lin, J.; Gu, M. Angular-momentum nanometrology in an ultrathin plasmonic topological insulator film. Nat. Commun.
**2018**, 9, 1–7. [Google Scholar] [CrossRef] [Green Version] - Fang, J.; Zhou, C.; Mou, Z.; Wang, S.; Yu, J.; Yang, Y.; Gbur, G.J.; Teng, S.; Cai, Y. High order plasmonic vortex generation based on spiral nanoslits. New J. Phys.
**2021**, 23, 033013. [Google Scholar] [CrossRef] - Liu, E.; Yan, B.; Zhou, H.; Liu, Y.; Liu, G.; Liu, J. OAM mode-excited surface plasmon resonance for refractive index sensing based on a photonic quasi-crystal fiber. J. Opt. Soc. Am. B
**2021**, 38, F16–F22. [Google Scholar] [CrossRef] - Vahala, K.J. Optical microcavities. Nature
**2003**, 424, 839–846. [Google Scholar] [CrossRef] - Cai, X.; Wang, J.; Strain, M.J.; Johnson-Morris, B.; Zhu, J.; Sorel, M.; O’Brien, J.L.; Thompson, M.G.; Yu, S. Integrated Compact Optical Vortex Beam Emitters. Science
**2012**, 338, 363–366. [Google Scholar] [CrossRef] - Strain, M.J.; Cai, X.; Wang, J.; Zhu, J.; Phillips, D.B.; Chen, L.; Lopez-Garcia, M.; O’Brien, J.L.; Thompson, M.G.; Sorel, M.; et al. Fast electrical switching of orbital angular momentum modes using ultra-compact integrated vortex emitters. Nat. Commun.
**2014**, 5, 4856. [Google Scholar] [CrossRef] [Green Version] - Kim, Y.; Han, J.H.; Ahn, D.; Kim, S. Heterogeneously-Integrated Optical Phase Shifters for Next-Generation Modulators and Switches on a Silicon Photonics Platform: A Review. Micromachines
**2021**, 12, 625. [Google Scholar] [CrossRef] [PubMed] - Li, R.; Feng, X.; Zhang, D.; Cui, K.; Liu, F.; Huang, Y. Radially Polarized Orbital Angular Momentum Beam Emitter Based on Shallow-Ridge Silicon Microring Cavity. IEEE Photonics J.
**2014**, 6, 1–10. [Google Scholar] [CrossRef] - Soref, R. Tutorial: Integrated-photonic switching structures. APL Photonics
**2018**, 3, 021101. [Google Scholar] [CrossRef] [Green Version] - Soref, R.; Bennett, B. Electrooptical effects in silicon. IEEE J. Quantum Electron.
**1987**, 23, 123–129. [Google Scholar] [CrossRef] [Green Version] - Nedeljkovic, M.; Soref, R.; Mashanovich, G.Z. Free-Carrier Electrorefraction and Electroabsorption Modulation Predictions for Silicon Over the 1–14-µm Infrared Wavelength Range. IEEE Photonics J.
**2011**, 3, 1171–1180. [Google Scholar] [CrossRef] - Bogaerts, W.; De Heyn, P.; Van Vaerenbergh, T.; De Vos, K.; Kumar Selvaraja, S.; Claes, T.; Dumon, P.; Bienstman, P.; Van Thourhout, D.; Baets, R. Silicon microring resonators. Laser Photonics Rev.
**2012**, 6, 47–73. [Google Scholar] [CrossRef] - Hao, B.; Leger, J. Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam. Opt. Express
**2007**, 15, 3550. [Google Scholar] [CrossRef] - Lerman, G.M.; Levy, U. Effect of radial polarization and apodization on spot size under tight focusing conditions. Opt. Express
**2008**, 16, 4567. [Google Scholar] [CrossRef] [PubMed] - Khonina, S.N.; Degtyarev, S.A. Analysis of the formation of a longitudinally polarized optical needle by a lens and axicon under tightly focused conditions. J. Opt. Technol.
**2016**, 83, 197. [Google Scholar] [CrossRef] - Helseth, L. Optical vortices in focal regions. Opt. Commun.
**2004**, 229, 85–91. [Google Scholar] [CrossRef] - Rashid, M.; Maragò, O.M.; Jones, P.H. Focusing of high order cylindrical vector beams. J. Opt. A Pure Appl. Opt.
**2009**, 11, 065204. [Google Scholar] [CrossRef] - Khonina, S.N. Vortex beams with high-order cylindrical polarization: Features of focal distributions. Appl. Phys. B
**2019**, 125, 100. [Google Scholar] [CrossRef] - Almazov, A.A.; Khonina, S.N.; Kotlyar, V.V. Using phase diffraction optical elements to shape and select laser beams consisting of a superposition of an arbitrary number of angular harmonics. J. Opt. Technol.
**2005**, 72, 391. [Google Scholar] [CrossRef] - Khonina, S.N.; Podlipnov, V.V.; Karpeev, S.V.; Ustinov, A.V.; Volotovsky, S.G.; Ganchevskaya, S.V. Spectral control of the orbital angular momentum of a laser beam based on 3D properties of spiral phase plates fabricated for an infrared wavelength. Opt. Express
**2020**, 28, 18407. [Google Scholar] [CrossRef] [PubMed] - Lavery, M.P.J.; Speirits, F.C.; Barnett, S.M.; Padgett, M.J. Detection of a Spinning Object Using Light’s Orbital Angular Momentum. Science
**2013**, 341, 537–540. [Google Scholar] [CrossRef] [Green Version] - Cvijetic, N.; Milione, G.; Ip, E.; Wang, T. Detecting Lateral Motion using Light’s Orbital Angular Momentum. Sci. Rep.
**2015**, 5, 15422. [Google Scholar] [CrossRef] [PubMed] - Ren, H.; Wang, X.; Li, C.; He, C.; Wang, Y.; Pan, A.; Maier, S.A. Orbital-Angular-Momentum-Controlled Hybrid Nanowire Circuit. Nano Lett.
**2021**, 21, 6220–6227. [Google Scholar] [CrossRef] - Li, S.; Ding, Y.; Guan, X.; Tan, H.; Nong, Z.; Wang, L.; Liu, L.; Zhou, L.; Yang, C.; Yvind, K.; et al. Compact high-efficiency vortex beam emitter based on a silicon photonics micro-ring. Opt. Lett.
**2018**, 43, 1319. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**3D view of the proposed device. The pn-depletion diode follows the Si rib bent waveguide. The different shades of blue and red represent the different electron (blue) and hole (red) concentrations where darker shades correspond to higher concentrations.

**Figure 2.**Cross-section of the doped part of the ring. N and P are for the electrons and holes concentrations, respectively: ++ is ${10}^{20}$ ${\mathrm{cm}}^{-3}$, + is ${10}^{19}$ ${\mathrm{cm}}^{-3}$, and without sign is $5\times {10}^{18}$ ${\mathrm{cm}}^{-3}$. d and h3 denote the hole diameter and height, respectively.

**Figure 3.**Distributions of electrons in the cross-section of the rib waveguide for different applied voltage values.

**Figure 5.**Intensity and phase distributions of the emitted fields from the ring with radius 5.5 µm. (

**a1**–

**a3**) is an intensity, $arg\left({E}_{x}\right)$ and $arg\left({E}_{y}\right)$ at a given resonant wavelength, respectively. Phase distributions are obtained after passing the field through the quarter-wave plate, so its x-component’s azimuthal order is above by one, and its y-component’s azimuthal order is below by one than the actual order of the generated vector vortex beam. Distribution patterns (

**b1**–

**b3**)–(

**f1**–

**f3**) are obtained similarly. (

**a1**–

**a3**), (

**b1**–

**b3**), and (

**c1–c3**) refer to the resonances at the voltage of 0.5 V, and (

**d1**–

**d3**), (

**e1**–

**e3**), and (

**f1**–

**f3**) to the resonances at −5 V.

**Figure 7.**Intensity and phase distributions of the emitted fields from the ring with radius 26.5 µm. (

**a1**–

**a3**) is an intensity, $arg\left({E}_{x}\right)$ and $arg\left({E}_{y}\right)$ at a given resonant wavelength, respectively. Phase distributions are obtained after passing the field through the quarter-wave plate, so its x-component’s azimuthal order is above by one, and its y-component’s azimuthal order is below by one than the actual order of the generated vector vortex beam. Distribution patterns (

**b1**–

**b3**)–(

**f1**–

**f3**) are obtained similarly. (

**a1**–

**a3**), (

**b1**–

**b3**), and (

**c1–c3**) refer to the resonances at the voltage of 0.5 V, and (

**d1**–

**d3**), (

**e1**–

**e3**), and (

**f1**–

**f3**) to the resonances at −5 V.

**Figure 8.**Distribution patterns of the emitted field in the near field. Size of the field plots is 26 µm × 26 µm.

**Figure 9.**(

**a**) Distribution patterns of the emitted fields in far-field. The size of the field plots is 2 mm × 2 mm. (

**b**) Normalized intensities of the expansion coefficients in the basis of angular harmonics (OAM spectra) of the components of the electric field 1 (left column) and field 2 (right column): for the incident field ${\left|{c}_{m}^{0t}\right|}^{2}$ (vertical lines) and for far-field ${\left|{c}_{m}^{t}\right|}^{2}$ (envelopes).

**Table 1.**List of geometric values in Figure 2.

Dimension | w1 | w2 | h1 | h2 | h3 | d |
---|---|---|---|---|---|---|

Value | 0.545 | 0.5 | 0.22 | 0.11 | 0.07 | 0.15 |

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**MDPI and ACS Style**

Stepanov, I.V.; Fatkhiev, D.M.; Lyubopytov, V.S.; Kutluyarov, R.V.; Grakhova, E.P.; Neumann, N.; Khonina, S.N.; Sultanov, A.K.
Wavelength-Tunable Vortex Beam Emitter Based on Silicon Micro-Ring with PN Depletion Diode. *Sensors* **2022**, *22*, 929.
https://doi.org/10.3390/s22030929

**AMA Style**

Stepanov IV, Fatkhiev DM, Lyubopytov VS, Kutluyarov RV, Grakhova EP, Neumann N, Khonina SN, Sultanov AK.
Wavelength-Tunable Vortex Beam Emitter Based on Silicon Micro-Ring with PN Depletion Diode. *Sensors*. 2022; 22(3):929.
https://doi.org/10.3390/s22030929

**Chicago/Turabian Style**

Stepanov, Ivan V., Denis M. Fatkhiev, Vladimir S. Lyubopytov, Ruslan V. Kutluyarov, Elizaveta P. Grakhova, Niels Neumann, Svetlana N. Khonina, and Albert K. Sultanov.
2022. "Wavelength-Tunable Vortex Beam Emitter Based on Silicon Micro-Ring with PN Depletion Diode" *Sensors* 22, no. 3: 929.
https://doi.org/10.3390/s22030929