# Tailoring Polarization Conversion in Achiral All-Dielectric Metasurfaces by Using Quasi-Bound States in the Continuum

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Calculation of the Stokes Parameters

#### 2.2. Nanodisk Array Implementation

## 3. Results and Discussion

#### 3.1. Single BICs

#### 3.2. Double Accidental BIC

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MTS | Metasurfaces |

BIC | Bound state in the continuum |

aBIC | Accidental BIC |

CEMD | Coupled electric & magnetic dipole |

TE | Transversal electric |

TM | Transversal magnetic |

RCP | Right-handed polarization |

LCP | Left-handed polarization |

## References

- Chen, H.T.; Taylor, A.J.; Yu, N. A review of metasurfaces: Physics and applications. Rep. Prog. Phys.
**2016**, 79, 76401. [Google Scholar] [CrossRef] [PubMed][Green Version] - Cheben, P.; Halir, R.; Schmid, J.H.; Atwater, H.A.; Smith, D.R. Subwavelength integrated photonics. Nature
**2018**, 560, 565–572. [Google Scholar] [CrossRef] [PubMed] - Brongersma, M.L.; Cui, Y.; Fan, S. Light management for photovoltaics using high-index nanostructures. Nat. Mater.
**2014**, 13, 451–460. [Google Scholar] [CrossRef] - Zhu, A.Y.; Chen, W.T.; Zaidi, A.; Huang, Y.W.; Khorasaninejad, M.; Sanjeev, V.; Qiu, C.W.; Capasso, F. Giant intrinsic chiro-optical activity in planar dielectric nanostructures. Light Sci. Appl.
**2018**, 7, 17158. [Google Scholar] [CrossRef] [PubMed] - Zhang, F.; Pu, M.; Li, X.; Gao, P.; Ma, X.; Luo, J.; Yu, H.; Luo, X. All-Dielectric Metasurfaces for Simultaneous Giant Circular Asymmetric Transmission and Wavefront Shaping Based on Asymmetric Photonic Spin–Orbit Interactions. Adv. Funct. Mater.
**2017**, 27, 1704295. [Google Scholar] [CrossRef] - Ma, Z.; Li, Y.; Li, Y.; Gong, Y.; Maier, S.A.; Hong, M. All-dielectric planar chiral metasurface with gradient geometric phase. Opt. Express
**2018**, 26, 6067–6078. [Google Scholar] [CrossRef][Green Version] - Yang, Q.; Liu, M.; Kruk, S.; Xu, Y.; Srivastava, Y.K.; Singh, R.; Han, J.; Kivshar, Y.; Shadrivov, I.V. Polarization-Sensitive Dielectric Membrane Metasurfaces. Adv. Opt. Mater.
**2020**, 8, 2000555. [Google Scholar] [CrossRef] - Kim, J.; Choudhury, S.; DeVault, C.; Zhao, Y.; Kildishev, A.V.; Shalaev, V.M.; Alù, A.; Boltasseva, A. Controlling the Polarization State of Light with Plasmonic Metal Oxide Metasurface. ACS Nano
**2016**, 10, 9326–9333. [Google Scholar] [CrossRef] - Zhang, Q.; Li, M.; Liao, T.; Cui, X. Design of beam deflector, splitters, wave plates and metalens using photonic elements with dielectric metasurface. Opt. Commun.
**2018**, 411, 93–100. [Google Scholar] [CrossRef] - Wei, S.; Yang, Z.; Zhao, M. Design of ultracompact polarimeters based on dielectric metasurfaces. Opt. Lett.
**2017**, 42, 1580–1583. [Google Scholar] [CrossRef] - Guo, K.; Xu, H.; Peng, Z.; Liu, X.; Guo, Z. High-Efficiency Full-Vector Polarization Analyzer Based on GaN Metasurface. IEEE Sens. J.
**2019**, 19, 3654–3659. [Google Scholar] [CrossRef] - Khorasaninejad, M.; Crozier, K.B. Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter. Nat. Commun.
**2014**, 5, 1–6. [Google Scholar] [CrossRef] [PubMed][Green Version] - Zhou, J.; Qian, H.; Chen, C.F.; Zhao, J.; Li, G.; Wu, Q.; Luo, H.; Wen, S.; Liu, Z. Optical edge detection based on high-efficiency dielectric metasurface. Proc. Natl. Acad. Sci. USA
**2019**, 166, 11137–11140. [Google Scholar] [CrossRef] [PubMed][Green Version] - He, Y.; Li, Y.; Liu, J.; Zhang, X.; Cai, Y.; Chen, Y.; Chen, S.; Fan, D. Switchable phase and polarization singular beams generation using dielectric metasurfaces. Sci. Rep.
**2017**, 7, 1–10. [Google Scholar] [CrossRef] - Yoon, G.; Lee, D.; Nam, K.T.; Rho, J. “Crypto-Display” in Dual-Mode Metasurfaces by Simultaneous Control of Phase and Spectral Responses. ACS Nano
**2018**, 12, 6421–6428. [Google Scholar] [CrossRef] - Gao, S.; Park, C.S.; Lee, S.S.; Choi, D.Y. A Highly Efficient Bifunctional Dielectric Metasurface Enabling Polarization-Tuned Focusing and Deflection for Visible Light. Adv. Opt. Mater.
**2019**, 7, 1801337. [Google Scholar] [CrossRef] - Hu, Y.; Wang, X.; Luo, X.; Ou, X.; Li, L.; Chen, Y.; Yang, P.; Wang, S.; Duan, H. All-dielectric metasurfaces for polarization manipulation: Principles and emerging applications. Nanophotonics
**2020**, 9, 3755–3780. [Google Scholar] [CrossRef] - Marinica, D.C.; Borisov, A.G.; Shabanov, S.V. Bound States in the Continuum in Photonics. Phys. Rev. Lett.
**2008**, 100, 183902. [Google Scholar] [CrossRef] - Bulgakov, E.N.; Maksimov, D.N. Topological Bound States in the Continuum in Arrays of Dielectric Spheres. Phys. Rev. Lett.
**2017**, 118, 267401. [Google Scholar] [CrossRef] - Ha, S.T.; Fu, Y.H.; Emani, N.K.; Pan, Z.; Bakker, R.M.; Paniagua-Domínguez, R.; Kuznetsov, A.I. Directional lasing in resonant semiconductor nanoantenna arrays. Nat. Nanotechnol.
**2018**, 13, 1042–1047. [Google Scholar] [CrossRef] - Doeleman, H.M.; Monticone, F.; den Hollander, W.; Alù, A.; Koenderink, A.F. Experimental observation of a polarization vortex at an optical bound state in the continuum. Nat. Photonics
**2018**, 12, 397–401. [Google Scholar] [CrossRef] - Abujetas, D.R.; van Hoof, N.; ter Huurne, S.; Gómez Rivas, J.; Sánchez-Gil, J.A. Spectral and temporal evidence of robust photonic bound states in the continuum on terahertz metasurfaces. Optica
**2019**, 6, 996. [Google Scholar] [CrossRef][Green Version] - Koshelev, K.L.; Bogdanov, A.; Kivshar, Y.S. Meta-optics and bound states in the continuum. Sci. Bull.
**2019**, 64, 836–842. [Google Scholar] [CrossRef][Green Version] - Hsu, C.W.; Zhen, B.; Stone, A.D.; Joannopoulos, J.D.; Soljačić, M. Bound states in the continuum. Nat. Rev. Mater.
**2016**, 1, 16048. [Google Scholar] [CrossRef][Green Version] - Han, S.; Pitchappa, P.; Wang, W.; Srivastava, Y.K.; Rybin, M.V.; Singh, R. Extended Bound States in the Continuum with Symmetry-Broken Terahertz Dielectric Metasurfaces. Adv. Opt. Mater.
**2021**, 9, 2002001. [Google Scholar] [CrossRef] - Kang, M.; Zhang, S.; Xiao, M.; Xu, H. Merging Bound States in the Continuum at Off-High Symmetry Points. Phys. Rev. Lett.
**2021**, 126, 117402. [Google Scholar] [CrossRef] - Abujetas, D.R.; Olmos-Trigo, J.; Sánchez-Gil, J.A. Tailoring Accidental Double Bound States in the Continuum in All-Dielectric Metasurfaces. Adv. Opt. Mater.
**2022**, 2200301. [Google Scholar] [CrossRef] - Taghizadeh, A.; Chung, I.S. Quasi bound states in the continuum with few unit cells of photonic crystal slab. Appl. Phys. Lett.
**2017**, 111, 031114. [Google Scholar] [CrossRef][Green Version] - Koshelev, K.L.; Lepeshov, S.; Liu, M.; Bogdanov, A.A.; Kivshar, Y.S. Asymmetric Metasurfaces with High-Q Resonances Governed by Bound States in the Continuum. Phys. Rev. Lett.
**2018**, 121, 193903. [Google Scholar] [CrossRef][Green Version] - Li, S.; Zhou, C.; Liu, T.; Xiao, S. Symmetry-protected bound states in the continuum supported by all-dielectric metasurfaces. Phys. Rev. A
**2019**, 100, 063803. [Google Scholar] [CrossRef] - Cong, L.; Singh, R. Symmetry-Protected Dual Bound States in the Continuum in Metamaterials. Adv. Opt. Mater.
**2019**, 7, 1900383. [Google Scholar] [CrossRef] - Abujetas, D.R.; Barreda, Á.; Moreno, F.; Sáenz, J.J.; Litman, A.; Geffrin, J.M.; Sánchez-Gil, J.A. Brewster quasi bound states in the continuum in all-dielectric metasurfaces from single magnetic-dipole resonance meta-atoms. Sci. Rep.
**2019**, 9, 16048. [Google Scholar] [CrossRef] [PubMed][Green Version] - Gorkunov, M.V.; Antonov, A.A.; Kivshar, Y.S. Metasurfaces with Maximum Chirality Empowered by Bound States in the Continuum. Phys. Rev. Lett.
**2020**, 125, 093903. [Google Scholar] [CrossRef] - Overvig, A.; Yu, N.; Alù, A. Chiral Quasi-Bound States in the Continuum. Phys. Rev. Lett.
**2021**, 126, 073001. [Google Scholar] [CrossRef] [PubMed] - Wang, B.; Liu, W.; Zhao, M.; Wang, J.; Zhang, Y.; Chen, A.; Guan, F.; Liu, X.; Shi, L.; Zi, J. Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum. Nat. Photonics
**2020**, 14, 623–628. [Google Scholar] [CrossRef] - Chen, X.; Zhou, Y.; Ma, X.; Fang, W.; Zhang, W.; Gao, W. Polarization conversion in anisotropic dielectric metasurfaces originating from bound states in the continuum. Opt. Lett.
**2021**, 46, 4120. [Google Scholar] [CrossRef] - Abujetas, D.R.; Sánchez-Gil, J.A.; Sáenz, J.J. Generalized Brewster effect in high-refractive-index nanorod-based metasurfaces. Opt. Express
**2018**, 26, 31523. [Google Scholar] [CrossRef] - Abujetas, D.R.; Olmos-Trigo, J.; Sáenz, J.J.; Sánchez-Gil, J.A. Coupled electric and magnetic dipole formulation for planar arrays of particles: Resonances and bound states in the continuum for all-dielectric metasurfaces. Phys. Rev. B Condens. Matter Mater. Phys.
**2020**, 102, 125411. [Google Scholar] [CrossRef] - Abujetas, D.R.; Sánchez-Gil, J.A. Near-Field Excitation of Bound States in the Continuum in All-Dielectric Metasurfaces through a Coupled Electric/Magnetic Dipole Model. Nanomaterials
**2021**, 11, 998. [Google Scholar] [CrossRef] - Evlyukhin, A.B.; Reinhardt, C.; Seidel, A.; Luk’yanchuk, B.S.; Chichkov, B.N. Optical response features of Si-nanoparticle arrays. Phys. Rev. B Condens. Matter Mater. Phys.
**2010**, 82, 45404. [Google Scholar] [CrossRef][Green Version] - Sersic, I.; van de Haar, M.A.; Arango, F.B.; Koenderink, A.F. Ubiquity of Optical Activity in Planar Metamaterial Scatterers. Phys. Rev. Lett.
**2012**, 108, 223903. [Google Scholar] [CrossRef] [PubMed][Green Version] - Swiecicki, S.D.; Sipe, J.E. Surface-lattice resonances in two-dimensional arrays of spheres: Multipolar interactions and a mode analysis. Phys. Rev. B Condens. Matter Mater. Phys.
**2017**, 95, 195406. [Google Scholar] [CrossRef][Green Version] - Babicheva, V.E.; Evlyukhin, A.B. Resonant Lattice Kerker Effect in Metasurfaces With Electric and Magnetic Optical Responses. Laser Photon. Rev.
**2017**, 11, 1700132. [Google Scholar] [CrossRef][Green Version] - Chen, Y.; Zhang, Y.; Femius Koenderink, A. General point dipole theory for periodic metasurfaces: Magnetoelectric scattering lattices coupled to planar photonic structures. Opt. Express
**2017**, 25, 21358. [Google Scholar] [CrossRef][Green Version] - Baur, S.; Sanders, S.; Manjavacas, A. Hybridization of Lattice Resonances. ACS Nano
**2018**, 12, 1618–1629. [Google Scholar] [CrossRef] - Murai, S.; Abujetas, D.R.; Castellanos, G.W.; Sánchez-Gil, J.A.; Zhang, F.; Rivas, J.G. Bound States in the Continuum in the Visible Emerging from out-of-Plane Magnetic Dipoles. ACS Photonics
**2020**, 7, 2204–2210. [Google Scholar] [CrossRef] - Reid, M.T.H.; Johnson, S.G. Efficient Computation of Power, Force, and Torque in BEM Scattering Calculations. IEEE Trans. Antennas Propag.
**2015**, 63, 3588–3598. [Google Scholar] [CrossRef][Green Version] - Babicheva, V.E.; Evlyukhin, A.B. Metasurfaces with Electric Quadrupole and Magnetic Dipole Resonant Coupling. ACS Photonics
**2018**, 5, 2022–2033. [Google Scholar] [CrossRef][Green Version] - Babicheva, V.E.; Evlyukhin, A.B. Analytical model of resonant electromagnetic dipole-quadrupole coupling in nanoparticle arrays. Phys. Rev. B
**2019**, 99, 195444. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**(

**a**) Scheme of the geometrical parameter of the considered MTS and the possible field polarizations. (

**b**) Reflectance map of a square array of poly-Si disks ($h=80$ nm, $D=220$ nm), the lattice parameter being $a=340$ nm. There are two high reflectivity regions associated to two different BICs. The first BIC (symmetry-protected) is located at normal incidence $\theta =0$° and it is associated to a TE mode. The second one is an aBIC located close to 37° and 800 nm and presents TM polarization.

**Figure 2.**Stokes parameters of the reflected light as a function of the incident wavelength for (

**a**) the TE quasi-BIC at $\theta $ = 10°, and (

**b**) the TM quasi-BIC at $\theta $ = 30° for incident light polarized at 45°. The line intensity is proportional to the I parameter (i.e., reflected light intensity). The behavior is notably similar, presenting opposite signs for the Q parameter, which is positive for TE and negative for TM. However, the V parameter is always negative and maximum in absolute value at the BIC location, which implies the attaining of LCP light regardless of the TE/TM nature of the considered BIC. Figures (

**c**,

**d**) represent a polar plot of the ${V}_{n}$ parameter as a function of the incident polarization angle and wavelength (radial axis) for the TE and TM quasi-BICs.

**Figure 3.**(

**a**) Reflectance map of the TE aBIC. (

**b**) Idem for the TM aBIC. (

**c**) Representation of the normalized V stokes parameter ${V}_{n}$ as a function of the wavelength and incident angle for the double aBIC. The plot is an expansion of the parallelogram region on Figures (

**a**,

**b**) to allow a better visualization. As a result, the x-axis changes as a linear function of the incident angle.

**Figure 4.**(

**a**) Stokes parameters of the reflected light as a function of the incident wavelength for the double aBIC ($\theta =68.7$°). The line intensity is proportional to the I parameter (i.e., reflectance). (

**b**) Polar plot of the ${V}_{n}$ parameter in reflection as a function of the incident polarization angle and wavelength (radial axis) for the double aBIC ($\theta =68.7$°).

**Table 1.**Polarization and spectral parameters of all the studied cases. The values of the Stokes parameters are calculated for linearly polarized light at 45°.

R | ${\mathit{L}}_{\mathit{n}}^{2}$ | ${\mathit{V}}_{\mathit{n}}^{2}$ | $\mathit{\lambda}$/nm | $\mathsf{\Delta}\mathit{\lambda}$/nm | Q-Factor | |
---|---|---|---|---|---|---|

TE (10°) | 0.145 | 0.567 | 0.433 | 747.588 | 0.139 | 5375 |

TM (30°) | 0.397 | 0.490 | 0.510 | 751.795 | 0.314 | 2391 |

aBIC RCP | 0.410 | 5 × 10${}^{-6}$ | 0.999995 | 911.119 | 0.006 | 158,016 |

aBIC LCP | 0.375 | 10 × 10${}^{-6}$ | 0.999990 | 909.339 | 0.008 | 113,667 |

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**MDPI and ACS Style**

Pura, J.L.; Kabonire, R.; Abujetas, D.R.; Sánchez-Gil, J.A. Tailoring Polarization Conversion in Achiral All-Dielectric Metasurfaces by Using Quasi-Bound States in the Continuum. *Nanomaterials* **2022**, *12*, 2252.
https://doi.org/10.3390/nano12132252

**AMA Style**

Pura JL, Kabonire R, Abujetas DR, Sánchez-Gil JA. Tailoring Polarization Conversion in Achiral All-Dielectric Metasurfaces by Using Quasi-Bound States in the Continuum. *Nanomaterials*. 2022; 12(13):2252.
https://doi.org/10.3390/nano12132252

**Chicago/Turabian Style**

Pura, Jose Luis, Ruhinda Kabonire, Diego R. Abujetas, and José A. Sánchez-Gil. 2022. "Tailoring Polarization Conversion in Achiral All-Dielectric Metasurfaces by Using Quasi-Bound States in the Continuum" *Nanomaterials* 12, no. 13: 2252.
https://doi.org/10.3390/nano12132252