Abstract

The capability to distinguish the handedness of circularly polarized light is a well-known intrinsic property of a chiral nanostructure. It is a long-standing controversial debate, however, whether a chiral object can also sense the vorticity, or the orbital angular momentum (OAM), of a light field. Since OAM is a spatial property, it seems rather counterintuitive that a point-like chiral object could be able to distinguish the sense of the wave-front of light carrying OAM. Here, we show that a dipolar chiral nanostructure is indeed capable of distinguishing the sign of the phase vortex of the incoming light beam. To this end, we take advantage of the conversion of the sign of OAM, carried by a linearly polarized Laguerre–Gaussian beam, into the sign of optical chirality upon tight focusing. Our study provides for a deeper insight into the discussion of chiral light–matter interactions and the respective role of OAM.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Chiral molecules or artificial chiral nanostructures exhibit the inherent property of interacting differently with left-handed and right-handed circularly polarized light [16]. One of the possible manifestations of this spin-dependent interaction is circular dichroism (CD), i.e., the differential absorption of circular polarization states of opposite handedness, which is also utilized as an enabling feature in CD spectroscopy for enantiomeric distinction. This differential light–matter interaction is a direct consequence of the chiral geometry of the involved scatterers and a spinning light field. Artificial chiral structures have also been utilized for the conversion of incoming spin angular momentum (SAM) of light into orbital angular momentum (OAM) [7]. In a 3D chiral nanostructure or molecule, this phenomenon is caused by the excited chiral dipole [6,8], consisting of parallely aligned electric and magnetic dipole moments oscillating with a phase delay of ±π/2, and directly resulting from the geometry of the system. Yet, a chiral dipole and a chiral light–matter interaction can be mimicked by an achiral scatterer under structured illumination [9,10]. The vorticity of the OAM-carrying light generated by a chiral entity illuminated with circularly polarized light depends on the relative phase between the aforementioned electric and magnetic dipoles, and hence, on the handedness of the chiral object itself [6]. Along the same line, it sounds reasonable that also the inversion of this scheme might be applicable. In other words, a chiral object illuminated with a light beam exhibiting a helical phase front (or equivalently, carrying OAM) may be able to couple to a chiral nanostructure based on the sign of the vorticity, partially converting OAM back into SAM with the helicity depending on the vorticity of the illuminating beam and the handedness of the structure. Although this concept appears consequential, it has been a common understanding that chiral media, especially when treated on the level of a pure dipolar response, are not capable of distinguishing the vorticity of the impinging light, and hence, structural chirality cannot couple to OAM on the dipolar level [1115]. For a very insightful review on the interaction of atoms with twisted light, please refer to [16] and references therein. As a consequence, chiral media illuminated with linearly polarized Laguerre–Gaussian (LG) beams with an azimuthal index l=1 or l=1 would show the same transmission, reflection, and absorption spectra, as opposed to the differential absorption (i.e., CD) observed for illumination with left- and right-handed circularly polarized light. A simple argument for this conclusion is the fact that OAM originates from the spatial phase distribution of a light beam or field. Thus, OAM could be labeled as a spatial property of a light beam, in contrast to SAM, which is a local feature related to the polarization [17]. This poses an apparent contradiction with the simple idea of inverting the spin-to-orbit conversion mediated by a chiral nanostructure as described above.

Here, we show that a chiral dipolar nanostructure, when excited resonantly, is in fact capable of sensing the vorticity of the impinging light beam. It can distinguish between light beams carrying phase vortices of opposite charges similar to its capability of sensing the handedness or sign of the SAM of a circularly polarized light beam (see, e.g., [6] and references therein).

In the scheme discussed here, we take advantage of non-paraxial propagation to create non-zero optical chirality or helicity density [18] from a linearly polarized LG beam of charge l=1 or l=1, which possesses no SAM before being focused (see Fig. 1). Thus, a chiral nanostructure placed in the focal field indirectly interacts with the field’s OAM through the relative phase between the electric and magnetic longitudinal field components. Specifically, we show that the sign of the phase charge of an OAM-carrying light beam gets encoded in the phase delay between the longitudinal electric and magnetic field components on the optical axis in the focal plane and, equivalently, in the sign of the optical chirality of the field [18] formed there. In turn, the dipole-like chiral nanostructure can interact differently with this optical chirality, depending on its own geometrical handedness and the chiral dipole it supports at the fundamental resonance. In contrast to the well-known spin-to-orbit coupling in tightly focused circularly polarized light beams [19,20], we convert OAM to local non-zero optical chirality.

 

Fig. 1. LG0±1 beams and their field components upon tight focusing. (a) Intensity and phase distributions of the input LG0±1 beams. (b) Calculated distributions of focal electric (|E|2) and magnetic (|H|2) field intensities (and relative phases) of tightly focused (NA=0.9) beams. The distributions are normalized to the maximum value of the total energy density (ϵ02|E|2+μ02|H|2). The on-axis focal field comprises longitudinal electric and magnetic fields oscillating with a phase difference ±π/2, which corresponds to the vorticity sense of the incoming beam. (c) Linear and dephased oscillation of Ez±iHz generates optical chirality C of opposite sign for both input beams, but no zero spin density s on the optical axis. The dashed circles in first line of (b) (left column) outline the top view of the nanohelix drawn to scale.

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2. INTERACTION OF A DIPOLAR CHIRAL SCATTERER WITH TIGHTLY FOCUSED LG0±1 BEAMS

We start by analyzing the above-mentioned phenomenon of OAM generation by a chiral object. In the interaction of circularly polarized light with a sub-wavelength-sized chiral structure [see Fig. 2(a)], a chiral dipole is excited as a consequence of the chiral geometry of the illuminated structure. A chiral dipole is formed by parallely aligned electric and magnetic dipole moments oscillating with a phase delay [6,8,9]. The emission of a chiral dipole is, therefore, ruled by the radiation of an out-of-phase superposition of parallel electric and magnetic dipole moments. The emission of an electric and a magnetic dipole moment observed around the dipole axis is radially and azimuthally polarized light [21], respectively. Hence, the aforementioned superposition is equivalent to a circularly polarized LG beam of charge |l|=1 with the sign of the spin and OAM depending on the relative phase between the dipoles and the handedness of the chiral dipole. We consider tight focusing of linearly x-polarized LG beams of zero radial order and azimuthal order l=±1 to exclude any possible influence of SAM from the input beam on the interaction between the field and the chiral nanostructure. We therefore start with a paraxial beam (propagating along the z axis) carrying OAM only. The electric field distribution in the back focal plane of the focusing lens can be expressed as (see Fig. 1)

E=E0rw0er2w02e±ilϕe^x,
where r and ϕ are the radial and azimuthal coordinates, respectively, and w0 is the equivalent beam waist. The focal fields can be calculated using vectorial diffraction theory [22,23]. Figure 1 shows the focal fields calculated for the parameters used in the experiment: w0=2mm, NA=0.9 f=2mm, and λ=1450nm, with f and λ the focal lengths of the focusing system and the wavelength of the beam, respectively. In the following, we are interested mainly in the structure of the focal field on and near the optical axis in the focal plane. On the optical axis, the electromagnetic field is purely longitudinal (transverse components cross zero), with these axial electric and magnetic field components being dephased by exactly ±π/2. A sub-wavelength-sized nanostructure placed at this position in the focal plane will be excited by these field components. This configuration resembles the structure of a chiral dipole as discussed above. We therefore expect efficient coupling to a chiral nanostructure, if the relative phase between the electric and magnetic field components matches the relative phase of the electric and magnetic dipole moments forming the chiral dipole mode. The latter is dictated by the geometrical handedness of the chiral nanostructure.

 

Fig. 2. Measurement scheme and the results. (a) Simplified sketch of the experimental setup [6,24] for probing the vorticity of the incoming beam with a chiral scatterer and scanning-electron micrograph of the utilized nanostructure. (b) Dimensions of the nanohelix. The strength of its chiroptical response can be described by the chiral dipole oscillating along the z direction (helix axis). (c) Experimental and simulation spectra of the fundamental resonance of the nanohelix as a function of the vorticity of the incoming beam. The insets depict the focal optical chirality and the relative size and position of the nanohelix in the focal plane.

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The aforementioned focal fields give rise to non-zero optical chirality, defined as [see Fig. 1(c)] [18,25]

C=ω2c2I[E*·H],
providing for a quantitative measure of how strongly chiral an electromagnetic field is. Importantly, the sign of the vorticity of the input beam is manifested by the phase relation between the longitudinal electric and magnetic fields, as shown in Fig. 1(b). Thus, for incoming beams of opposite charge l=±1, C+1=C10. In addition, the SAM (density) defining the local degree of circular polarization is zero on the optical axis, owing to the chosen symmetry (see Fig. 1). It should be stressed here that the input beam [Eq. (1)] possesses neither a non-zero optical chirality nor SAM at any point in the back focal plane. Hence, the observed non-zero optical chirality on the optical axis in the focus can be solely attributed to the formation of electric and magnetic longitudinal fields with their relative phase ruled by the sign of the OAM.

In previous studies [1215], it was shown that a dipolar chiral object (e.g., a molecule) cannot show differential interaction with linearly polarized LG beams of opposite azimuthal indices. More recently, it was proposed that the OAM of paraxially propagating LG modes can engage in chiral light–matter interactions via quadrupolar responses [2629]. Also, the role of longitudinal fields in chiral interactions was emphasized recently [26,30].

With our scheme, we now show experimentally and theoretically that tightly focused linearly polarized LG0±1 beams provide the necessary condition for a dipole-like chiral particle to scatter differently for different vorticities of the input beam via the creation of longitudinal field components on the optical axis and the resulting optical chirality. Hence, we take advantage of non-paraxial propagation of structured light and the corresponding longitudinal field components created at the focal plane [9,30].

In our experiment, we utilize a plasmonic nanohelix as a prototypical chiral scatterer [see Fig. 2(a)]. In our previous study [6], it was shown that the fundamental resonance of this single-loop (right-handed) plasmonic nanohelix could be approximated by the dominating longitudinal components of the electric and magnetic dipoles pzimz. In this context, pz and mz refer to the real- and positive-valued amplitudes of the z components of the electric and magnetic dipoles, respectively [see Fig. 2(a)]. It can be therefore treated as a dipole-like chiral nanostructure. Since the nanohelix is optically chiral, it features a non-zero cross polarizability GI[p*·m]0 [8,31]. We note that the phase delay of i and thereby also the handedness of the chiral dipole at the fundamental resonance are defined by the right-handed geometry of the structure studied here. Therefore, only one of the tightly focused LG0±1 beams will be able to interact with the helix by exciting the corresponding chiral dipole.

3. EXPERIMENTAL RESULTS

To experimentally (and numerically) verify the concept outlined above, we use a gold nanohelix as a sub-wavelength-sized chiral dipolar scatterer [see Figs. 2(a) and 2(b)]. It was fabricated by electron-beam-induced deposition [32] combined with a subsequent grazing incidence metal coating process, resulting in a core–shell gold nanohelix. Using plane-wave-like circularly polarized excitation, the fundamental optical properties of this nanostructure were studied in detail in an article published recently [6]. The resonance wavelength of the fundamental resonance is 1450 nm. To prove differential interaction of the nanohelix with the incoming light field featuring opposite vorticities, we measured the transmittance spectra around the fundamental resonance using a custom-built optical setup {see simplified sketch in Fig. 2(b), and more details in Refs.  [6,24]}. The helix was excited with tightly focused linearly x-polarized LG0±1 beams (NA=0.9 and w0/f=1). The linearly polarized LG modes were generated using right- and left-handed circularly polarized Gaussian beams transmitted through a q-plate of charge 1/2 [33,34] and a linear polarizer. Subsequently, the spatial modes were cleaned with a Fourier filter and focused onto the sample. The nanohelix fabricated on a glass substrate was placed on a 3D piezo-stage, which allowed for precise positioning of the structure on the optical axis in the focal plane. The transmitted and forward-scattered light was collected by a second high-NA (1.3) objective and detected using a photo-diode. We note that for a proof-of-principle experimental demonstration, we measured only the total transmitted power, which should differ for different signs of OAM of the input beams (see Supplement 1).

Figure 2(c) shows the transmittance (T) spectra of the nanohelix measured wavelength by wavelength in the vicinity of its fundamental resonance. As explained, the strength of the interaction depends critically on the vorticity of the incoming beam. The recorded spectra show that the tightly focused LG01 beam can couple more efficiently to the chiral dipole mode of the nanohelix at the fundamental resonance. This is a direct consequence of the longitudinal field components and their relative phase (EziHz) matching the chiral dipole handedness [pzimz; see Fig. 2(b)] of the right-handed structure investigated here. The corresponding simulations (based on finite-difference time-domain method) resemble the experimental results very well [see Fig. 2(c)]. The presented spectra provide experimental and numerical evidence that a dipolar chiral scatterer can distinguish the vorticity of an incoming beam carrying OAM via the generation of non-zero optical chirality by tight focusing.

Additional simulations (not shown here) verify that by changing the handedness of the nanohelix, also the transmission properties change accordingly, and stronger coupling is observed for an LG01 beam. To make sure that the observed differential transmission is indeed a direct consequence of the sign of the on-axis optical chirality, and, hence, the OAM of the input beams, we also checked the influence of the rotation angle of the helix about the optical axis. We found that the relative orientation of the incoming linear polarization state (and corresponding off-axis transverse field components in the focus) with respect to the nanohelix of finite length twisting around the z axis did not play an important role. Rotating the nanohelix about the z axis change only slightly the strength of the observed differential transmission (see Supplement 1).

It is interesting to note here that also the first higher-order resonance of the nanohelix (at λ=840nm) can be described as a system of coupled electric and magnetic dipoles with G0 [6]. In this case, however, the chiroptical response of the helix, in first approximation, is dominated by transverse dipole moments px+imx aligned orthogonal to the optical axis of the system. For the excitation scheme based on the on-axis longitudinal fields presented above, no efficient coupling at the wavelength of the first higher-order resonance can be achieved (see Supplement 1 for details). This is contrary to the response of the helix to plane-wave-like circularly polarized excitation, which has a better overlap with the x-polarized chiral dipole at the first higher-order resonance.

4. CONCLUSION

In summary, we have studied the role of OAM in chiral light–matter interactions on the level of an individual dipolar chiral nanostructure. The tight focusing of linearly polarized LG0±1 modes carrying no SAM but only OAM (of charge |l|=1) results in the creation of non-zero optical chirality peaking on the optical axis in the focal plane. The twisting sense of phase fronts and, equivalently, the sign of the OAM of the incoming light field define the sign of the focal optical chirality. The corresponding field couples preferentially to the nanohelix’s fundamental chiral mode if the sign of the optical chirality in the focal field (dictated by the vorticity of the input field) matches that of the relative phase between the electric and magnetic components of the nanohelix’s chiral mode (dictated by the helix’s handedness). In contrast to recent studies [27,28], the vorticity of the incoming beam was sensed via dipolar interactions not involving any higher-order multipoles. To prove our concept experimentally, we investigated the differential transmission of LG0±1 beams tightly focused onto a single plasmonic nanohelix. Due to the sign relation between the incoming OAM and the focal optical chirality, the nanostructure was able to unambiguously recognize the vorticity of the incoming light field. Our study constitutes a new route for tailoring the chiral light–matter interactions at the nanoscale. In addition, this study sheds new light on the discussion of the role of OAM in chiral light–matter interactions. The polarization rearrangement of the focal fields caused by non-paraxial propagation is a straightforward way of engineering focal fields and optical chirality at the nanoscale, and for studying selectively the individual chiral modes of an arbitrary structure.

Funding

Helmholtz Association (PD140); Consejo Nacional de Ciencia y Tecnología (CONACYT) (267735); Deutscher Akademischer Austauschdienst (DAAD) (57274178); Max Planck–University of Ottawa Centre for Extreme and Quantum Photonics.

Acknowledgment

The authors thank Sergey Nechayev and Martin Neugebauer for fruitful discussion.

 

See Supplement 1 for supporting content.

REFERENCES

1. L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge University, 2009).

2. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009). [CrossRef]  

3. V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25, 2517–2534 (2013). [CrossRef]  

4. B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3d chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013). [CrossRef]  

5. M. Esposito, V. Tasco, M. Cuscunà, F. Todisco, A. Benedetti, I. Tarantini, M. De Giorgi, D. Sanvitto, and A. Passaseo, “Nanoscale 3D chiral plasmonic helices with circular dichroism at visible frequencies,” ACS Photon. 2, 105–114 (2015). [CrossRef]  

6. P. Woźniak, I. De Leon, K. Höflich, C. Haverkamp, S. Christiansen, G. Leuchs, and P. Banzer, “Chiroptical response of a single plasmonic nanohelix,” Opt. Express 26, 19275–19293 (2018). [CrossRef]  

7. Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013). [CrossRef]  

8. L. Hu, Y. Huang, L. Pan, and Y. Fang, “Analyzing intrinsic plasmonic chirality by tracking the interplay of electric and magnetic dipole modes,” Sci. Rep. 7, 11151 (2017). [CrossRef]  

9. J. S. Eismann, M. Neugebauer, and P. Banzer, “Exciting a chiral dipole moment in an achiral nanostructure,” Optica 5, 954–959 (2018). [CrossRef]  

10. S. Nechayev, J. S. Eismann, G. Leuchs, and P. Banzer, “Orbit-to-spin angular momentum conversion employing local helicity,” Phys. Rev. B 99, 075155 (2019). [CrossRef]  

11. M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002). [CrossRef]  

12. D. Andrews, L. Romero, and M. Babiker, “On optical vortex interactions with chiral matter,” Opt. Commun. 237, 133–139 (2004). [CrossRef]  

13. F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005). [CrossRef]  

14. W. Löffler, D. Broer, and J. Woerdman, “Circular dichroism of cholesteric polymers and the orbital angular momentum of light,” Phys. Rev. A 83, 065801 (2011). [CrossRef]  

15. F. Giammanco, A. Perona, P. Marsili, F. Conti, F. Fidecaro, S. Gozzini, and A. Lucchesini, “Influence of the photon orbital angular momentum on electric dipole transitions: negative experimental evidence,” Opt. Lett. 42, 219–222 (2017). [CrossRef]  

16. M. Babiker, D. L. Andrews, and V. E. Lembessis, “Atoms in complex twisted light,” J. Opt. 21, 013001 (2018). [CrossRef]  

17. K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015). [CrossRef]  

18. Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104, 163901 (2010). [CrossRef]  

19. Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99, 073901 (2007). [CrossRef]  

20. K. Y. Bliokh, F. J. Rodrguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796 (2015). [CrossRef]  

21. P. Woźniak, P. Banzer, and G. Leuchs, "Selective switching of individual multipole resonances in single dielectric nanoparticles," Laser & Photon. Rev. 9, 231–240 (2015).

22. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358–379 (1959). [CrossRef]  

23. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

24. P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, “On the experimental investigation of the electric and magnetic response of a single nano-structure,” Opt. Express 18, 10905–10923 (2010). [CrossRef]  

25. D. M. Lipkin, “Existence of a new conservation law in electromagnetic theory,” J. Math. Phys. 5, 696–700 (1964). [CrossRef]  

26. G. F. Quinteiro, F. Schmidt-Kaler, and C. T. Schmiegelow, “Twisted-light-ion interaction: the role of longitudinal fields,” Phys. Rev. Lett. 119, 253203 (2017). [CrossRef]  

27. K. A. Forbes and D. L. Andrews, “Optical orbital angular momentum: twisted light and chirality,” Opt. Lett. 43, 435–438 (2018). [CrossRef]  

28. D. L. Andrews, “Quantum formulation for nanoscale optical and material chirality: symmetry issues, space and time parity, and observables,” J. Opt. 20, 033003 (2018). [CrossRef]  

29. R. M. Kerber, J. M. Fitzgerald, S. S. Oh, D. E. Reiter, and O. Hess, “Orbital angular momentum dichroism in nanoantennas,” Commun. Phys. 1, 87 (2018). [CrossRef]  

30. C. Rosales-Guzmán, K. Volke-Sepulveda, and J. P. Torres, “Light with enhanced optical chirality,” Opt. Lett. 37, 3486–3488 (2012). [CrossRef]  

31. F. Crimin, N. Mackinnon, J. B. Götte, and S. M. Barnett, “Optical helicity and chirality: conservation and sources,” Appl. Sci. 9, 828 (2019). [CrossRef]  

32. K. Höflich, R. B. Yang, A. Berger, G. Leuchs, and S. Christiansen, “The direct writing of plasmonic gold nanostructures by electron-beam-induced deposition,” Adv. Mater. 23, 2657–2661 (2011). [CrossRef]  

33. Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam-Berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett. 26, 1 (2001). [CrossRef]  

34. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006). [CrossRef]  

References

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  1. L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge University, 2009).
  2. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
    [Crossref]
  3. V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25, 2517–2534 (2013).
    [Crossref]
  4. B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3d chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
    [Crossref]
  5. M. Esposito, V. Tasco, M. Cuscunà, F. Todisco, A. Benedetti, I. Tarantini, M. De Giorgi, D. Sanvitto, and A. Passaseo, “Nanoscale 3D chiral plasmonic helices with circular dichroism at visible frequencies,” ACS Photon. 2, 105–114 (2015).
    [Crossref]
  6. P. Woźniak, I. De Leon, K. Höflich, C. Haverkamp, S. Christiansen, G. Leuchs, and P. Banzer, “Chiroptical response of a single plasmonic nanohelix,” Opt. Express 26, 19275–19293 (2018).
    [Crossref]
  7. Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
    [Crossref]
  8. L. Hu, Y. Huang, L. Pan, and Y. Fang, “Analyzing intrinsic plasmonic chirality by tracking the interplay of electric and magnetic dipole modes,” Sci. Rep. 7, 11151 (2017).
    [Crossref]
  9. J. S. Eismann, M. Neugebauer, and P. Banzer, “Exciting a chiral dipole moment in an achiral nanostructure,” Optica 5, 954–959 (2018).
    [Crossref]
  10. S. Nechayev, J. S. Eismann, G. Leuchs, and P. Banzer, “Orbit-to-spin angular momentum conversion employing local helicity,” Phys. Rev. B 99, 075155 (2019).
    [Crossref]
  11. M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
    [Crossref]
  12. D. Andrews, L. Romero, and M. Babiker, “On optical vortex interactions with chiral matter,” Opt. Commun. 237, 133–139 (2004).
    [Crossref]
  13. F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
    [Crossref]
  14. W. Löffler, D. Broer, and J. Woerdman, “Circular dichroism of cholesteric polymers and the orbital angular momentum of light,” Phys. Rev. A 83, 065801 (2011).
    [Crossref]
  15. F. Giammanco, A. Perona, P. Marsili, F. Conti, F. Fidecaro, S. Gozzini, and A. Lucchesini, “Influence of the photon orbital angular momentum on electric dipole transitions: negative experimental evidence,” Opt. Lett. 42, 219–222 (2017).
    [Crossref]
  16. M. Babiker, D. L. Andrews, and V. E. Lembessis, “Atoms in complex twisted light,” J. Opt. 21, 013001 (2018).
    [Crossref]
  17. K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
    [Crossref]
  18. Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104, 163901 (2010).
    [Crossref]
  19. Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99, 073901 (2007).
    [Crossref]
  20. K. Y. Bliokh, F. J. Rodrguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796 (2015).
    [Crossref]
  21. P. Woźniak, P. Banzer, and G. Leuchs, "Selective switching of individual multipole resonances in single dielectric nanoparticles," Laser & Photon. Rev. 9, 231–240 (2015).
  22. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358–379 (1959).
    [Crossref]
  23. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
  24. P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, “On the experimental investigation of the electric and magnetic response of a single nano-structure,” Opt. Express 18, 10905–10923 (2010).
    [Crossref]
  25. D. M. Lipkin, “Existence of a new conservation law in electromagnetic theory,” J. Math. Phys. 5, 696–700 (1964).
    [Crossref]
  26. G. F. Quinteiro, F. Schmidt-Kaler, and C. T. Schmiegelow, “Twisted-light-ion interaction: the role of longitudinal fields,” Phys. Rev. Lett. 119, 253203 (2017).
    [Crossref]
  27. K. A. Forbes and D. L. Andrews, “Optical orbital angular momentum: twisted light and chirality,” Opt. Lett. 43, 435–438 (2018).
    [Crossref]
  28. D. L. Andrews, “Quantum formulation for nanoscale optical and material chirality: symmetry issues, space and time parity, and observables,” J. Opt. 20, 033003 (2018).
    [Crossref]
  29. R. M. Kerber, J. M. Fitzgerald, S. S. Oh, D. E. Reiter, and O. Hess, “Orbital angular momentum dichroism in nanoantennas,” Commun. Phys. 1, 87 (2018).
    [Crossref]
  30. C. Rosales-Guzmán, K. Volke-Sepulveda, and J. P. Torres, “Light with enhanced optical chirality,” Opt. Lett. 37, 3486–3488 (2012).
    [Crossref]
  31. F. Crimin, N. Mackinnon, J. B. Götte, and S. M. Barnett, “Optical helicity and chirality: conservation and sources,” Appl. Sci. 9, 828 (2019).
    [Crossref]
  32. K. Höflich, R. B. Yang, A. Berger, G. Leuchs, and S. Christiansen, “The direct writing of plasmonic gold nanostructures by electron-beam-induced deposition,” Adv. Mater. 23, 2657–2661 (2011).
    [Crossref]
  33. Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam-Berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett. 26, 1 (2001).
    [Crossref]
  34. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
    [Crossref]

2019 (2)

S. Nechayev, J. S. Eismann, G. Leuchs, and P. Banzer, “Orbit-to-spin angular momentum conversion employing local helicity,” Phys. Rev. B 99, 075155 (2019).
[Crossref]

F. Crimin, N. Mackinnon, J. B. Götte, and S. M. Barnett, “Optical helicity and chirality: conservation and sources,” Appl. Sci. 9, 828 (2019).
[Crossref]

2018 (6)

K. A. Forbes and D. L. Andrews, “Optical orbital angular momentum: twisted light and chirality,” Opt. Lett. 43, 435–438 (2018).
[Crossref]

D. L. Andrews, “Quantum formulation for nanoscale optical and material chirality: symmetry issues, space and time parity, and observables,” J. Opt. 20, 033003 (2018).
[Crossref]

R. M. Kerber, J. M. Fitzgerald, S. S. Oh, D. E. Reiter, and O. Hess, “Orbital angular momentum dichroism in nanoantennas,” Commun. Phys. 1, 87 (2018).
[Crossref]

M. Babiker, D. L. Andrews, and V. E. Lembessis, “Atoms in complex twisted light,” J. Opt. 21, 013001 (2018).
[Crossref]

P. Woźniak, I. De Leon, K. Höflich, C. Haverkamp, S. Christiansen, G. Leuchs, and P. Banzer, “Chiroptical response of a single plasmonic nanohelix,” Opt. Express 26, 19275–19293 (2018).
[Crossref]

J. S. Eismann, M. Neugebauer, and P. Banzer, “Exciting a chiral dipole moment in an achiral nanostructure,” Optica 5, 954–959 (2018).
[Crossref]

2017 (3)

L. Hu, Y. Huang, L. Pan, and Y. Fang, “Analyzing intrinsic plasmonic chirality by tracking the interplay of electric and magnetic dipole modes,” Sci. Rep. 7, 11151 (2017).
[Crossref]

F. Giammanco, A. Perona, P. Marsili, F. Conti, F. Fidecaro, S. Gozzini, and A. Lucchesini, “Influence of the photon orbital angular momentum on electric dipole transitions: negative experimental evidence,” Opt. Lett. 42, 219–222 (2017).
[Crossref]

G. F. Quinteiro, F. Schmidt-Kaler, and C. T. Schmiegelow, “Twisted-light-ion interaction: the role of longitudinal fields,” Phys. Rev. Lett. 119, 253203 (2017).
[Crossref]

2015 (4)

K. Y. Bliokh, F. J. Rodrguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796 (2015).
[Crossref]

P. Woźniak, P. Banzer, and G. Leuchs, "Selective switching of individual multipole resonances in single dielectric nanoparticles," Laser & Photon. Rev. 9, 231–240 (2015).

M. Esposito, V. Tasco, M. Cuscunà, F. Todisco, A. Benedetti, I. Tarantini, M. De Giorgi, D. Sanvitto, and A. Passaseo, “Nanoscale 3D chiral plasmonic helices with circular dichroism at visible frequencies,” ACS Photon. 2, 105–114 (2015).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

2013 (3)

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25, 2517–2534 (2013).
[Crossref]

B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3d chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
[Crossref]

Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
[Crossref]

2012 (1)

2011 (2)

W. Löffler, D. Broer, and J. Woerdman, “Circular dichroism of cholesteric polymers and the orbital angular momentum of light,” Phys. Rev. A 83, 065801 (2011).
[Crossref]

K. Höflich, R. B. Yang, A. Berger, G. Leuchs, and S. Christiansen, “The direct writing of plasmonic gold nanostructures by electron-beam-induced deposition,” Adv. Mater. 23, 2657–2661 (2011).
[Crossref]

2010 (2)

2009 (1)

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[Crossref]

2007 (1)

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99, 073901 (2007).
[Crossref]

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

2005 (1)

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
[Crossref]

2004 (1)

D. Andrews, L. Romero, and M. Babiker, “On optical vortex interactions with chiral matter,” Opt. Commun. 237, 133–139 (2004).
[Crossref]

2002 (1)

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[Crossref]

2001 (1)

1964 (1)

D. M. Lipkin, “Existence of a new conservation law in electromagnetic theory,” J. Math. Phys. 5, 696–700 (1964).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358–379 (1959).
[Crossref]

Andrews, D.

D. Andrews, L. Romero, and M. Babiker, “On optical vortex interactions with chiral matter,” Opt. Commun. 237, 133–139 (2004).
[Crossref]

Andrews, D. L.

M. Babiker, D. L. Andrews, and V. E. Lembessis, “Atoms in complex twisted light,” J. Opt. 21, 013001 (2018).
[Crossref]

K. A. Forbes and D. L. Andrews, “Optical orbital angular momentum: twisted light and chirality,” Opt. Lett. 43, 435–438 (2018).
[Crossref]

D. L. Andrews, “Quantum formulation for nanoscale optical and material chirality: symmetry issues, space and time parity, and observables,” J. Opt. 20, 033003 (2018).
[Crossref]

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[Crossref]

Araoka, F.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
[Crossref]

Babiker, M.

M. Babiker, D. L. Andrews, and V. E. Lembessis, “Atoms in complex twisted light,” J. Opt. 21, 013001 (2018).
[Crossref]

D. Andrews, L. Romero, and M. Babiker, “On optical vortex interactions with chiral matter,” Opt. Commun. 237, 133–139 (2004).
[Crossref]

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[Crossref]

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[Crossref]

Banzer, P.

Barnett, S. M.

F. Crimin, N. Mackinnon, J. B. Götte, and S. M. Barnett, “Optical helicity and chirality: conservation and sources,” Appl. Sci. 9, 828 (2019).
[Crossref]

Barron, L. D.

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge University, 2009).

Baumberg, J. J.

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25, 2517–2534 (2013).
[Crossref]

Benedetti, A.

M. Esposito, V. Tasco, M. Cuscunà, F. Todisco, A. Benedetti, I. Tarantini, M. De Giorgi, D. Sanvitto, and A. Passaseo, “Nanoscale 3D chiral plasmonic helices with circular dichroism at visible frequencies,” ACS Photon. 2, 105–114 (2015).
[Crossref]

Bennett, C. R.

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[Crossref]

Berger, A.

K. Höflich, R. B. Yang, A. Berger, G. Leuchs, and S. Christiansen, “The direct writing of plasmonic gold nanostructures by electron-beam-induced deposition,” Adv. Mater. 23, 2657–2661 (2011).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh, F. J. Rodrguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796 (2015).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

Bomzon, Z.

Braun, P. V.

B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3d chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
[Crossref]

Broer, D.

W. Löffler, D. Broer, and J. Woerdman, “Circular dichroism of cholesteric polymers and the orbital angular momentum of light,” Phys. Rev. A 83, 065801 (2011).
[Crossref]

Chiu, D.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99, 073901 (2007).
[Crossref]

Christiansen, S.

P. Woźniak, I. De Leon, K. Höflich, C. Haverkamp, S. Christiansen, G. Leuchs, and P. Banzer, “Chiroptical response of a single plasmonic nanohelix,” Opt. Express 26, 19275–19293 (2018).
[Crossref]

K. Höflich, R. B. Yang, A. Berger, G. Leuchs, and S. Christiansen, “The direct writing of plasmonic gold nanostructures by electron-beam-induced deposition,” Adv. Mater. 23, 2657–2661 (2011).
[Crossref]

Clays, K.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
[Crossref]

Cohen, A. E.

Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104, 163901 (2010).
[Crossref]

Conti, F.

Crimin, F.

F. Crimin, N. Mackinnon, J. B. Götte, and S. M. Barnett, “Optical helicity and chirality: conservation and sources,” Appl. Sci. 9, 828 (2019).
[Crossref]

Cuscunà, M.

M. Esposito, V. Tasco, M. Cuscunà, F. Todisco, A. Benedetti, I. Tarantini, M. De Giorgi, D. Sanvitto, and A. Passaseo, “Nanoscale 3D chiral plasmonic helices with circular dichroism at visible frequencies,” ACS Photon. 2, 105–114 (2015).
[Crossref]

De Giorgi, M.

M. Esposito, V. Tasco, M. Cuscunà, F. Todisco, A. Benedetti, I. Tarantini, M. De Giorgi, D. Sanvitto, and A. Passaseo, “Nanoscale 3D chiral plasmonic helices with circular dichroism at visible frequencies,” ACS Photon. 2, 105–114 (2015).
[Crossref]

De Leon, I.

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[Crossref]

Drezet, A.

Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
[Crossref]

Ebbesen, T. W.

Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
[Crossref]

Edgar, J. S.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99, 073901 (2007).
[Crossref]

Eismann, J. S.

S. Nechayev, J. S. Eismann, G. Leuchs, and P. Banzer, “Orbit-to-spin angular momentum conversion employing local helicity,” Phys. Rev. B 99, 075155 (2019).
[Crossref]

J. S. Eismann, M. Neugebauer, and P. Banzer, “Exciting a chiral dipole moment in an achiral nanostructure,” Optica 5, 954–959 (2018).
[Crossref]

Esposito, M.

M. Esposito, V. Tasco, M. Cuscunà, F. Todisco, A. Benedetti, I. Tarantini, M. De Giorgi, D. Sanvitto, and A. Passaseo, “Nanoscale 3D chiral plasmonic helices with circular dichroism at visible frequencies,” ACS Photon. 2, 105–114 (2015).
[Crossref]

Fang, Y.

L. Hu, Y. Huang, L. Pan, and Y. Fang, “Analyzing intrinsic plasmonic chirality by tracking the interplay of electric and magnetic dipole modes,” Sci. Rep. 7, 11151 (2017).
[Crossref]

Fidecaro, F.

Fitzgerald, J. M.

R. M. Kerber, J. M. Fitzgerald, S. S. Oh, D. E. Reiter, and O. Hess, “Orbital angular momentum dichroism in nanoantennas,” Commun. Phys. 1, 87 (2018).
[Crossref]

Forbes, K. A.

Frank, B.

B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3d chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
[Crossref]

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[Crossref]

Genet, C.

Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
[Crossref]

Giammanco, F.

Giessen, H.

B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3d chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
[Crossref]

Gorodetski, Y.

Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
[Crossref]

Götte, J. B.

F. Crimin, N. Mackinnon, J. B. Götte, and S. M. Barnett, “Optical helicity and chirality: conservation and sources,” Appl. Sci. 9, 828 (2019).
[Crossref]

Gozzini, S.

Hasman, E.

Haverkamp, C.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Hein, S. M.

B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3d chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
[Crossref]

Hess, O.

R. M. Kerber, J. M. Fitzgerald, S. S. Oh, D. E. Reiter, and O. Hess, “Orbital angular momentum dichroism in nanoantennas,” Commun. Phys. 1, 87 (2018).
[Crossref]

Höflich, K.

P. Woźniak, I. De Leon, K. Höflich, C. Haverkamp, S. Christiansen, G. Leuchs, and P. Banzer, “Chiroptical response of a single plasmonic nanohelix,” Opt. Express 26, 19275–19293 (2018).
[Crossref]

K. Höflich, R. B. Yang, A. Berger, G. Leuchs, and S. Christiansen, “The direct writing of plasmonic gold nanostructures by electron-beam-induced deposition,” Adv. Mater. 23, 2657–2661 (2011).
[Crossref]

Hu, L.

L. Hu, Y. Huang, L. Pan, and Y. Fang, “Analyzing intrinsic plasmonic chirality by tracking the interplay of electric and magnetic dipole modes,” Sci. Rep. 7, 11151 (2017).
[Crossref]

Huang, Y.

L. Hu, Y. Huang, L. Pan, and Y. Fang, “Analyzing intrinsic plasmonic chirality by tracking the interplay of electric and magnetic dipole modes,” Sci. Rep. 7, 11151 (2017).
[Crossref]

Jeffries, G. D. M.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99, 073901 (2007).
[Crossref]

Kerber, R. M.

R. M. Kerber, J. M. Fitzgerald, S. S. Oh, D. E. Reiter, and O. Hess, “Orbital angular momentum dichroism in nanoantennas,” Commun. Phys. 1, 87 (2018).
[Crossref]

Kleiner, V.

Lembessis, V. E.

M. Babiker, D. L. Andrews, and V. E. Lembessis, “Atoms in complex twisted light,” J. Opt. 21, 013001 (2018).
[Crossref]

Leuchs, G.

S. Nechayev, J. S. Eismann, G. Leuchs, and P. Banzer, “Orbit-to-spin angular momentum conversion employing local helicity,” Phys. Rev. B 99, 075155 (2019).
[Crossref]

P. Woźniak, I. De Leon, K. Höflich, C. Haverkamp, S. Christiansen, G. Leuchs, and P. Banzer, “Chiroptical response of a single plasmonic nanohelix,” Opt. Express 26, 19275–19293 (2018).
[Crossref]

P. Woźniak, P. Banzer, and G. Leuchs, "Selective switching of individual multipole resonances in single dielectric nanoparticles," Laser & Photon. Rev. 9, 231–240 (2015).

K. Höflich, R. B. Yang, A. Berger, G. Leuchs, and S. Christiansen, “The direct writing of plasmonic gold nanostructures by electron-beam-induced deposition,” Adv. Mater. 23, 2657–2661 (2011).
[Crossref]

P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, “On the experimental investigation of the electric and magnetic response of a single nano-structure,” Opt. Express 18, 10905–10923 (2010).
[Crossref]

Linden, S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[Crossref]

Lipkin, D. M.

D. M. Lipkin, “Existence of a new conservation law in electromagnetic theory,” J. Math. Phys. 5, 696–700 (1964).
[Crossref]

Löffler, W.

W. Löffler, D. Broer, and J. Woerdman, “Circular dichroism of cholesteric polymers and the orbital angular momentum of light,” Phys. Rev. A 83, 065801 (2011).
[Crossref]

Lucchesini, A.

Mackinnon, N.

F. Crimin, N. Mackinnon, J. B. Götte, and S. M. Barnett, “Optical helicity and chirality: conservation and sources,” Appl. Sci. 9, 828 (2019).
[Crossref]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

Marsili, P.

McGloin, D.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99, 073901 (2007).
[Crossref]

Nechayev, S.

S. Nechayev, J. S. Eismann, G. Leuchs, and P. Banzer, “Orbit-to-spin angular momentum conversion employing local helicity,” Phys. Rev. B 99, 075155 (2019).
[Crossref]

Neugebauer, M.

Nori, F.

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodrguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796 (2015).
[Crossref]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Oh, S. S.

R. M. Kerber, J. M. Fitzgerald, S. S. Oh, D. E. Reiter, and O. Hess, “Orbital angular momentum dichroism in nanoantennas,” Commun. Phys. 1, 87 (2018).
[Crossref]

Pan, L.

L. Hu, Y. Huang, L. Pan, and Y. Fang, “Analyzing intrinsic plasmonic chirality by tracking the interplay of electric and magnetic dipole modes,” Sci. Rep. 7, 11151 (2017).
[Crossref]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

Passaseo, A.

M. Esposito, V. Tasco, M. Cuscunà, F. Todisco, A. Benedetti, I. Tarantini, M. De Giorgi, D. Sanvitto, and A. Passaseo, “Nanoscale 3D chiral plasmonic helices with circular dichroism at visible frequencies,” ACS Photon. 2, 105–114 (2015).
[Crossref]

Perona, A.

Persoons, A.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
[Crossref]

Peschel, U.

Quabis, S.

Quinteiro, G. F.

G. F. Quinteiro, F. Schmidt-Kaler, and C. T. Schmiegelow, “Twisted-light-ion interaction: the role of longitudinal fields,” Phys. Rev. Lett. 119, 253203 (2017).
[Crossref]

Reiter, D. E.

R. M. Kerber, J. M. Fitzgerald, S. S. Oh, D. E. Reiter, and O. Hess, “Orbital angular momentum dichroism in nanoantennas,” Commun. Phys. 1, 87 (2018).
[Crossref]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358–379 (1959).
[Crossref]

Rill, M. S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[Crossref]

Rodrguez-Fortuño, F. J.

K. Y. Bliokh, F. J. Rodrguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796 (2015).
[Crossref]

Romero, L.

D. Andrews, L. Romero, and M. Babiker, “On optical vortex interactions with chiral matter,” Opt. Commun. 237, 133–139 (2004).
[Crossref]

Romero, L. C. D.

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[Crossref]

Rosales-Guzmán, C.

Saile, V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[Crossref]

Sanvitto, D.

M. Esposito, V. Tasco, M. Cuscunà, F. Todisco, A. Benedetti, I. Tarantini, M. De Giorgi, D. Sanvitto, and A. Passaseo, “Nanoscale 3D chiral plasmonic helices with circular dichroism at visible frequencies,” ACS Photon. 2, 105–114 (2015).
[Crossref]

Schäferling, M.

B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3d chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
[Crossref]

Schmidt-Kaler, F.

G. F. Quinteiro, F. Schmidt-Kaler, and C. T. Schmiegelow, “Twisted-light-ion interaction: the role of longitudinal fields,” Phys. Rev. Lett. 119, 253203 (2017).
[Crossref]

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ACS Nano (1)

B. Frank, X. Yin, M. Schäferling, J. Zhao, S. M. Hein, P. V. Braun, and H. Giessen, “Large-area 3d chiral plasmonic structures,” ACS Nano 7, 6321–6329 (2013).
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ACS Photon. (1)

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P. Woźniak, P. Banzer, and G. Leuchs, "Selective switching of individual multipole resonances in single dielectric nanoparticles," Laser & Photon. Rev. 9, 231–240 (2015).

Nat. Photonics (1)

K. Y. Bliokh, F. J. Rodrguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796 (2015).
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Optica (1)

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Phys. Rev. A (2)

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
[Crossref]

W. Löffler, D. Broer, and J. Woerdman, “Circular dichroism of cholesteric polymers and the orbital angular momentum of light,” Phys. Rev. A 83, 065801 (2011).
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Phys. Rev. B (1)

S. Nechayev, J. S. Eismann, G. Leuchs, and P. Banzer, “Orbit-to-spin angular momentum conversion employing local helicity,” Phys. Rev. B 99, 075155 (2019).
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Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104, 163901 (2010).
[Crossref]

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99, 073901 (2007).
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Proc. R. Soc. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358–379 (1959).
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L. Hu, Y. Huang, L. Pan, and Y. Fang, “Analyzing intrinsic plasmonic chirality by tracking the interplay of electric and magnetic dipole modes,” Sci. Rep. 7, 11151 (2017).
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Science (1)

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
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Supplementary Material (1)

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Figures (2)

Fig. 1.
Fig. 1. LG0±1 beams and their field components upon tight focusing. (a) Intensity and phase distributions of the input LG0±1 beams. (b) Calculated distributions of focal electric (|E|2) and magnetic (|H|2) field intensities (and relative phases) of tightly focused (NA=0.9) beams. The distributions are normalized to the maximum value of the total energy density (ϵ02|E|2+μ02|H|2). The on-axis focal field comprises longitudinal electric and magnetic fields oscillating with a phase difference ±π/2, which corresponds to the vorticity sense of the incoming beam. (c) Linear and dephased oscillation of Ez±iHz generates optical chirality C of opposite sign for both input beams, but no zero spin density s on the optical axis. The dashed circles in first line of (b) (left column) outline the top view of the nanohelix drawn to scale.
Fig. 2.
Fig. 2. Measurement scheme and the results. (a) Simplified sketch of the experimental setup [6,24] for probing the vorticity of the incoming beam with a chiral scatterer and scanning-electron micrograph of the utilized nanostructure. (b) Dimensions of the nanohelix. The strength of its chiroptical response can be described by the chiral dipole oscillating along the z direction (helix axis). (c) Experimental and simulation spectra of the fundamental resonance of the nanohelix as a function of the vorticity of the incoming beam. The insets depict the focal optical chirality and the relative size and position of the nanohelix in the focal plane.

Equations (2)

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E=E0rw0er2w02e±ilϕe^x,
C=ω2c2I[E*·H],

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