- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Applied

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Helicity Conservation for Mie Optical Cavities

Jorge Olmos-Trigo1,* and Xavier Zambrana-Puyalto2,†

  • 1Donostia International Physics Center (DIPC), Donostia-San Sebastián 20018, Spain
  • 2Istituto Italiano di Tecnologia, Via Morego 30, Genova 16163, Italy

  • *jolmostrigo@gmail.com
  • †xavislow@protonmail.ch
PDF

Phys. Rev. Applied 18, 044007 – Published 4 October, 2022

DOI: https://doi.org/10.1103/PhysRevApplied.18.044007

Abstract

The study of helicity in the context of light-matter interactions is an increasing area of research. However, some fundamental aspects of the helicity content of light fields inside scatterers have been overlooked. In this work, we demonstrate that the helicity of light fields inside lossless spherical cavities cannot be either conserved or sign flipped as a result of a scattering event. The underlying reason is that the internal electric and magnetic Mie coefficients cannot simultaneously oscillate with equal amplitude and equal or opposite phase. Our analytical demonstration is fulfilled regardless of the refractive index, sphere size, and multipolar order. In addition, we show that the helicity of light fields inside lossy spheres can be conserved. This fact is in striking contrast to the behavior of the scattered field, whose helicity content cannot be conserved precisely when the sphere has losses. Finally, we show that the helicity content of internal fields can be flipped for materials with gain.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (48)

  1. B. E. Saleh and M. C. Teich Fundamentals of Photonics (Wiley, New York, 1991), Vol. 22.
  2. M. Calkin, An invariance property of the free electromagnetic field, Am. J. Phys. 33, 958 (1965).
  3. I. Fernandez-Corbaton, X. Zambrana-Puyalto, and G. Molina-Terriza, Helicity and angular momentum: A symmetry-based framework for the study of light-matter interactions, Phys. Rev. A 86, 042103 (2012).
  4. D. Zwanziger, Quantum field theory of particles with both electric and magnetic charges, Phys. Rev. 176, 1489 (1968).
  5. I. Białynicki-Birula, On the wave function of the photon, Acta Phys. Pol. A 1, 97 (1994).
  6. I. Bialynicki-Birula, E. Newman, J. Porter, J. Winicour, B. Lukacs, Z. Perjes, and A. Sebestyen, A note on helicity, J. Math. Phys. 22, 2530 (1981).
  7. I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, X. Vidal, M. L. Juan, and G. Molina-Terriza, Electromagnetic Duality Symmetry and Helicity Conservation for the Macroscopic Maxwell’s Equations, Phys. Rev. Lett. 111, 060401 (2013).
  8. X. Zambrana-Puyalto, X. Vidal, M. L. Juan, and G. Molina-Terriza, Dual and anti-dual modes in dielectric spheres, Opt. Express 21, 17520 (2013).
  9. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, Strong magnetic response of submicron silicon particles in the infrared, Opt. Express 19, 4815 (2011).
  10. A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, Optically resonant dielectric nanostructures, Science 354, aag2472 (2016).
  11. N. Tischler, I. Fernandez-Corbaton, X. Zambrana-Puyalto, A. Minovich, X. Vidal, M. L. Juan, and G. Molina-Terriza, Experimental control of optical helicity in nanophotonics, Light: Sci. Appl. 3, e183 (2014).
  12. I. Fernandez-Corbaton, M. Fruhnert, and C. Rockstuhl, Objects of Maximum Electromagnetic Chirality, Phys. Rev. X 6, 031013 (2016).
  13. F. Alpeggiani, K. Bliokh, F. Nori, and L. Kuipers, Electromagnetic Helicity in Complex Media, Phys. Rev. Lett. 120, 243605 (2018).
  14. K. A. Forbes and G. A. Jones, Measures of helicity and chirality of optical vortex beams, J. Opt. 23, 115401 (2021).
  15. R. P. Cameron, J. B. Götte, S. M. Barnett, and A. M. Yao, Chirality and the angular momentum of light, Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 375, 20150433 (2017).
  16. M. Hanifeh, M. Albooyeh, and F. Capolino, Optimally chiral light: Upper bound of helicity density of structured light for chirality detection of matter at nanoscale, ACS Photonics 7, 2682 (2020).
  17. G. Mie, Beiträge zur optik trüber medien, speziell kolloidaler metallösungen, Ann. Phys. 330, 377 (1908).
  18. G. Gouesbet, J. Lock, and G. Gréhan, Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: Localized approximations and localized beam models, a review, J. Quant. Spectrosc. Radiat. Transfer 112, 1 (2011).
  19. M. Nieto-Vesperinas, R. Gomez-Medina, and J. J. Saenz, Angle-suppressed scattering and optical forces on submicrometer dielectric particles, J. Opt. Soc. Am. A 28, 54 (2011).
  20. J. Olmos-Trigo, D. R. Abujetas, C. Sanz-Fernández, J. A. Sánchez-Gil, and J. J. Sáenz, Optimal backward light scattering by dipolar particles, Phys. Rev. Res. 2, 013225 (2020).
  21. F. Qin, Z. Zhang, K. Zheng, Y. Xu, S. Fu, Y. Wang, and Y. Qin, Transverse Kerker Effect for Dipole Sources, Phys. Rev. Lett. 128, 193901 (2022).
  22. J. Olmos-Trigo, C. Sanz-Fernández, A. García-Etxarri, G. Molina-Terriza, F. S. Bergeret, and J. J. Sáenz, Enhanced spin-orbit optical mirages from dual nanospheres, Phys. Rev. A 99, 013852 (2019).
  23. G. Labate, A. Alù, and L. Matekovits, Surface-admittance equivalence principle for nonradiating and cloaking problems, Phys. Rev. A 95, 063841 (2017).
  24. C. Sanz-Fernández, M. Molezuelas-Ferreras, J. Lasa-Alonso, N. de Sousa, X. Zambrana-Puyalto, and J. Olmos-Trigo, Multiple Kerker anapoles in dielectric microspheres, Laser Photonics Rev. 15, 2100035 (2021).
  25. L. Liu, A. Di Donato, V. Ginis, S. Kheifets, A. Amirzhan, and F. Capasso, Three-Dimensional Measurement of the Helicity-Dependent Forces on a Mie Particle, Phys. Rev. Lett. 120, 223901 (2018).
  26. M. Nieto-Vesperinas and X. Xu, Reactive helicity and reactive power in nanoscale optics: Evanescent waves. Kerker conditions. Optical theorems and reactive dichroism, Phys. Rev. Res. 3, 043080 (2021).
  27. F. Graf, J. Feis, X. Garcia-Santiago, M. Wegener, C. Rockstuhl, and I. Fernandez-Corbaton, Achiral, helicity preserving, and resonant structures for enhanced sensing of chiral molecules, ACS Photonics 6, 482 (2019).
  28. J. Lasa-Alonso, D. R. Abujetas, Á. Nodar, J. A. Dionne, J. J. Sáenz, G. Molina-Terriza, J. Aizpurua, and A. García-Etxarri, Surface-enhanced circular dichroism spectroscopy on periodic dual nanostructures, ACS Photonics 7, 2978 (2020).
  29. J. Lasa-Alonso, J. Olmos-Trigo, A. García-Etxarri, and G. Molina-Terriza, Correlations between helicity and optical losses within general electromagnetic scattering theory, Mater. Adv. 3, 4179 (2022).
  30. A. Hayat, J. B. Mueller, and F. Capasso, Lateral chirality-sorting optical forces, Proc. Natl. Acad. Sci. 112, 13190 (2015).
  31. K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, Transfer of Light Helicity to Nanostructures, Phys. Rev. Lett. 110, 143603 (2013).
  32. M. Nieto-Vesperinas, Optical theorem for the conservation of electromagnetic helicity: Significance for molecular energy transfer and enantiomeric discrimination by circular dichroism, Phys. Rev. A 92, 023813 (2015).
  33. G. Tkachenko and E. Brasselet, Helicity-dependent three-dimensional optical trapping of chiral microparticles, Nat. Commun. 5, 1 (2014).
  34. R. Ali, F. A. Pinheiro, R. S. Dutra, F. S. Rosa, and P. A. M. Neto, Enantioselective manipulation of single chiral nanoparticles using optical tweezers, Nanoscale 12, 5031 (2020).
  35. J. Feis, D. Beutel, J. Köpfler, X. Garcia-Santiago, C. Rockstuhl, M. Wegener, and I. Fernandez-Corbaton, Helicity-Preserving Optical Cavity Modes for Enhanced Sensing of Chiral Molecules, Phys. Rev. Lett. 124, 033201 (2020).
  36. P. Scott, X. Garcia-Santiago, D. Beutel, C. Rockstuhl, M. Wegener, and I. Fernandez-Corbaton, On enhanced sensing of chiral molecules in optical cavities, Appl. Phys. Rev. 7, 041413 (2020).
  37. K. Voronin, A. S. Taradin, M. V. Gorkunov, and D. G. Baranov, Single-handedness chiral optical cavities, ACS Photonics 9, 2652 (2022).
  38. J. Olmos-Trigo, C. Sanz-Fernández, D. R. Abujetas, J. Lasa-Alonso, N. de Sousa, A. García-Etxarri, J. A. Sánchez-Gil, G. Molina-Terriza, and J. J. Sáenz, Kerker Conditions Upon Lossless, Absorption, and Optical Gain Regimes, Phys. Rev. Lett. 125, 073205 (2020).
  39. J. Olmos-Trigo, D. R. Abujetas, C. Sanz-Fernández, X. Zambrana-Puyalto, N. de Sousa, J. A. Sánchez-Gil, and J. J. Sáenz, Unveiling dipolar spectral regimes of large dielectric Mie spheres from helicity conservation, Phys. Rev. Res. 2, 043021 (2020).
  40. J. Olmos-Trigo, M. Meléndez, R. Delgado-Buscalioni, and J. J. Sáenz, Sectoral multipole focused beams, Opt. Express 27, 16384 (2019).
  41. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, 1999).
  42. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, NY, USA, 2008).
  43. B. Luk’yanchuk, R. Paniagua-Domínguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, Hybrid anapole modes of high-index dielectric nanoparticles, Phys. Rev. A 95, 063820 (2017).
  44. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge, UK, 1995).
  45. Notice that if ψl′(z)=0 then ψl(z)≠0. On the other hand, if ψl(z)=0 then ψl′(z)≠0. Notice that if xl′(z)=0 then xl(z)≠0. On the other hand, if xl(z)=0 then xl′(z)≠0.
  46. X. Zambrana-Puyalto, I. Fernandez-Corbaton, M. Juan, X. Vidal, and G. Molina-Terriza, Duality symmetry and Kerker conditions, Opt. Lett. 38, 1857 (2013).
  47. Notice that the optical size of the sphere is q=ka∼0.65. That is, we are dealing with a dipolar sphere under illumination of either a Gaussian beam of NA=0.15 or a plane wave.
  48. It is worthwhile to notice that we need an engineered incident field such as tightly focused Gaussian beam to excite nonradiating anapoles in spheres. That is, we need to get rid of higher-order multipoles contributing to the scattering efficiency, a phenomenon that would not occur if impinging with a plane wave [24].

Outline

Information

Phys. Rev. Applied 18, 044007– Published 4 October, 2022
  • Received 23 March 2022
  • Revised 6 August 2022
  • Accepted 9 August 2022
Crossmark - Check for updates button

© 2022 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation