Letter Cite This: ACS Photonics 2018, 5, 734−740
Interaction of Structured Light with a Chiral Plasmonic Metasurface: Giant Enhancement of Chiro-Optic Response Innem V.A.K. Reddy,† Alexander Baev,‡ Edward P. Furlani,*,†,‡,§ Paras N. Prasad,*,†,‡,∥ and Joseph W. Haus⊥ †
Department of Electrical Engineering, ‡Institute for Lasers, Photonics and Biophotonics, §Department of Chemical and Biological Engineering, and ∥Department of Chemistry, University at Buffalo SUNY, Buffalo, New York 14260, United States ⊥ Department of Electro-Optics and Photonics, University of Dayton, 300 College Park, Dayton, Ohio 45469, United States S Supporting Information *
ABSTRACT: We propose an approach to achieve giant enhancement and broad spectral tunability of the chiro-optic response of plasmonic metasurfaces by exploiting interaction with complex light, endowed with both spin and orbital angular momentum. As a proof of principle, we employ fullwave computational analysis to investigate the response of a structured, circularly polarized transverse Laguerre-Gaussian beam incident on a chiral metasurface composed of a twodimensional array of gold nanohelix meta-atoms. Our analysis reveals for the first time unprecedented amplification of circular dichroism that is a manifestation of the total angular momentum of the incident light being enantioselectively transferred to the medium. We also demonstrate that the spectral response of the meta-atoms can be designed to produce a rich manifold of narrow spectral lines with steep gradients. The approach proposed here opens up opportunities for new spectroscopic modalities to probe fundamental molecular structure and behavior, as well as unique, multiplexed biochemical sensing technologies, and a new class of engineered chiral metamaterials in the form of versatile ultrathin media with unmatched optical performance for a gamut of applications, including a new direction for spin photonics, exploiting high reflection contrast between opposite spins. KEYWORDS: structured light, chiral metasurfaces, plasmonics, circular dichroism, biosensing
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means of specially designed spiral wave plates.10 Recently, a light beam with orbital angular momentum was generated by engineering the wavefront with a metasurface, a subwavelength patterned two-dimensional medium.11 The notable advantage of this method is the availability of compact ultrathin devices, albeit with complex two-dimensional topologies. The use of structured light carrying both SAM and OAM with custom designed metasurfaces enables exploitation of extraordinary optical phenomena,12,13 as well as for selective enhancement of well-known phenomena, such as optical activity.14 Potential applications of such metasurfaces include: integrated photonic circuitry in spin-controlled photonics (the optical analogue of solid-state spintronics), examples of which would be spincontrolled gates and optical diodes, spin-controlled beam steering; as well as photonic sensing technologies, precision metrology, myriad optofluidic technologies, and general optical manipulations at the nanoscale. In this paper, we introduce a radically different concept to greatly enhance the intrinsic coupling of circularly polarized light with plasmonic chiral media by endowing the incident
xplorations that merge the concepts of structured light and structured matter have accelerated during the past decade.1−6 Light with orbital angular momentum (OAM) or optical vortices, has generated a great deal of interest, since unusual optical phenomena are revealed that are analogous to effects exclusively associated with the field of electronics. In particular, spin−orbit interaction of nonparaxial (focused) light beams is manifest in the so-called Photon Spin Hall effect (PSHE).3,4 PSHE is a transverse spatial shift between light beams with opposite spin angular momenta (SAM; i.e., right and left circular polarization), which occurs when these beams possess OAM. This effect has a direct analogy with the spin Hall effect in semiconductor physics, when an electric currentcarrying wire becomes electron spin polarized at opposing boundaries, perpendicular to the charge current direction. Practical realization of the PSHE includes preparing tightly focused light beams with opposite circular polarizations (intrinsic spins −1 and +1) and passing them through a device to generate orbital angular momentum. OAM beams can be obtained either via smooth gradient-index media or total internal reflection in a waveguide. Light carrying both SAM and OAM can also be generated by means of a polarization preserving axicon in combination with a biaxial crystal,7,8 or via interaction with liquid crystal spatial light modulators,9 or by © 2018 American Chemical Society
Received: November 3, 2017 Published: January 8, 2018 734
DOI: 10.1021/acsphotonics.7b01321 ACS Photonics 2018, 5, 734−740
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A circularly polarized transverse LG beam carries both SAM and OAM. When light carrying SAM interacts with a chiral medium, the SAM is transferred to the internal electronic degrees of freedom, resulting in an enantioselective absorption (so-called circular dichroism, CD). When OAM is transferred to a particle or a molecule, a torque is generated and the particle revolves around the beam axis. In this case, the transfer takes place between the OAM and the center of mass motion.25 It has been shown both theoretically25 and experimentally26 that the lowest electric multipole allowing for transfer of OAM to the internal electronic motion (electronic degrees of freedom) is a quadrupole. Since higher multipole interactions are much weaker than dipole interactions, in practice we observe no difference in the CD signal for chiral molecules in a solution phase, when probed by an optical beam with either l = 0 or l = ±1. We show here, for the first time, that there is strong coupling between OAM beams and chiral plasmonic media; our simulations show that an enhanced coupling of light with total angular momentum ±2 can be observed at plasmon resonances. When helical plasmonic nanoparticles interact with circularly polarized light, a resonant transfer of energy from the field to the nanoparticles occurs, which depends on the photon spin coupled to the surface electron density, that is, driving it inphase or out-of-phase. Invoking a classical electron model, the resonant coupling can be understood as an in-phase generation of an electric current that is manifest by an enhanced absorption rate. In a helical structure the electron current induces a magnetic dipole moment along with an electric dipole moment due to charge displacements and build-up at the boundaries. The mutual orientation of these two dipoles depends on the field spin and helicity of the structure and their dot product determines the CD value. There can be one or more resonances depending on the geometry of the nanohelix structure and its placement with respect to the wave vector. Furthermore, placing multiple nanohelices in the beam path will lead to dipole−dipole coupling between these structures and as a consequence, multiple hybridized resonances. All the above-discussed phenomena play an important role in shaping the spectral response of a material. In the framework of the full-wave analysis, the absorption rate can be calculated by evaluating the surface averaged resistive loss. The difference between resistive loss induced by RCP/LG and LCP/LG modes provides a measure of the CD. In this study, we investigate how the combination of OAM with circularly polarized light changes the spectral response of the system. Since OAM results in the wavefront of the light being spatially distributed, this can have a profound effect on how the field drives the surface charges in a three-dimensional (3D) nonhomogenous chiral structure. The helical wavefront, when in-phase with the induced current, generates an enhanced coupling and a corresponding increase in the dipole field.
light with orbital angular momentum. Past work has shown that such media can be designed using helical chiral polymers15 with tethered gold nanoparticles.16 There has been significant progress in the recent years in the development of chiral polymers with enhanced optical activity.16,17 The introduction of gold nanoparticles, which bond/tether to the chiral polymer, or helical DNA strand enhances the optical activity because of plasmonic coupling.16,18 Tethered gold nanoparticles form a regular helical structure around the helical backbone of the polymer or DNA strand. The helical structure can be approximated by a solid gold nanohelix for numerical analysis, due to the dipole−dipole and near-field coupling between the separate nanoparticles. One alternative approach is low temperature, directional shadow deposition with nanopatterning14,19 to fabricate nanohelix arrays with the feature sizes as small as 20 nm. There are also other comparable state-of-the-art fabrication techniques to create nanohelix arrays.20 In these media many optical phenomena can be enhanced by orders of magnitude. In the following, we demonstrate a versatile tunability of enhanced coupling between structured light, carrying both SAM and OAM, and plamonic nanohelix metamaterial. We also discuss relevant applications that can leverage this coupling.
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THEORY In general, light can have two types of angular momentum: spin and orbital (SAM and OAM), each one of them can be either longitudinal (plane wave or paraxial beam) or transverse (nonparaxial, focused beams, evanescent waves). Light with longitudinal SAM is circularly polarized. By convention, the spin quantum number, σ, is equal +1 for right circular polarization (RCP), whereas it is −1 for left circular polarization (LCP). Light with OAM (orbital angular momentum quantum number l) has a helical wavefront with an axial singularity that represents an optical vortex. The quantum number l can take integer21 or sometimes half-integer values.22 Laguerre-Gaussian (LG) beams are known to possess OAM.23,24 The equation for a scalar Laguerre-Gaussian beam in cylindrical coordinates (r,ϕ,z) reads: LGnl(r , ϕ , z) =
|l| w0 ⎛ 2 r ⎞ |l|⎛ 2r 2 ⎞ 2n! ⎜ ⎟ Ln ⎜ 2 ⎟ π(n + |l|)! wz ⎝ wz ⎠ ⎝ wz ⎠
⎡ 2 ⎛ r kr 2 × exp⎢− 2 − i⎜⎜lϕ + − (2n + |l| + 1) ⎢⎣ wz 2R z ⎝ ⎡ 2z ⎤⎞⎤ × tan−1⎢ 2 ⎥⎟⎟⎥ ⎣ kw0 ⎦⎠⎥⎦
Here, Lln is the generalized Laguerre polynomial of order n and degree |l|, while n,l are radial and OAM quantum numbers, respectively. wz and Rz are the beam’s waist and radius of curvature that are given by
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RESULTS AND DISCUSSION To investigate the coupling of light with OAM to plasmonic nanohelices, we applied incident light consisting of circularly polarized Laguerre-Gaussian modes, LG0,0 ± 1 (OAM (l) of 0, +1, and −1), and with a beam waist radius of 500 nm. To understand the interactions of matter with light, that carries SAM (σ) and OAM (l), we designed our numerical experiment in such a way, that the volume average of the electric field norm in an empty computational domain stays the same, that is, independent of the spin and orbital quantum number. Differences arise only because of the field pattern. The LG0
⎛ 4z 2 ⎞ wz = w0 ⎜1 + 2 4 ⎟ k w0 ⎠ ⎝
Rz = z +
k 2w04 4z
respectively, where w0 is the beam waist radius at z = 0, and 2π k = λ is the wavenumber in the host medium. 735
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Figure 1. (a) Computational domain. S is Poynting vector, representing the direction of energy flow (b) Surface average of the electric field norm vs incident wavelength for a single Au helix suspended in air, water and PVC, and illuminated by a LCP Gaussian beam, l = 0. The results for a sphere in PVC are shown for comparison.
mode with l = 0 and σ = ±1 represents a circularly polarized Gaussian wave. A circularly polarized transverse LG beam has a Jones vector of the form ±1i , where +i will generate right circularly polarized light (σ = 1) and −i will generate left circularly polarized light (σ = −1). The total angular momentum is defined as j = (σ + l). For light with just SAM, the total angular momentum equals j = ±1, while for the light with OAM, the total angular momentum takes integer values in the range j = ±2. Single Helix. A two-turn right-handed gold27,28 nanohelix with a 30 nm major radius, an axial pitch of 60 nm, and wire radius of 20 nm is placed inside a spherical computational domain with a radius of 200 nm (Figure 1a), that is capped by a 100 nm thick shell for the perfectly matched layer (PML) condition. The geometric center of the helix is aligned with the origin of coordinates. A scattering boundary condition is imposed on the outer (nonreflecting) boundary of the domain. The rotational axis of the helix is parallel to the z-axis, that is, to the beam propagation direction. The relative permittivity inside the domain is variable with 1 for air, 1.77 for water, and 2.25, which is a typical value for an organic host polymer material, polyvinyl chloride, PVC. Our wavelength range spans 600 nm, that is, from 500 nm at the blue edge of the spectrum to 1100 nm at the infrared edge. The spectrum of the electric field norm, averaged along the surface of an isolated Au nanohelix is shown in Figure 1b. The nanohelix is excited by a left circularly polarized Gaussian beam. Sharp spectral resonances are observed and their spectral position depends on the specific ambient media: air, water and PVC, in which the nanohelix is suspended. By way of comparison the spectrum of a single 50 nm Au sphere suspended in PVC has a single, broad resonance at approximately 548 nm.29 Note that the two-turn-helix exhibits a much richer manifold of transverse, longitudinal and hybridized resonances, the latter originating from dipolar coupling between the turns of the helix.30,31 When the incident light carries OAM, the local field, generated by the oscillating surface electrons, changes in response to the value of the total angular momentum (Figure 2a,b). The host medium is PVC in the figure. The coupling of the field to the elementary transverse surface plasma oscillations
(i.e., collective oscillations of the surface electrons in the crosssectional plane of the helix wire) is enhanced when the absolute value of the total angular momentum of the incident light equals 2. The resonance near 534 nm reaches a maximum value −1 for an RCP LG+1 0 mode and for an LCP LG0 mode. At the same time, this resonance gets strongly suppressed when j = 0, +1 corresponding to either RCP LG−1 0 or LCP LG0 excitation. However, the effect of the OAM on the elementary longitudinal resonance near 640 nm, that is, collective oscillations of surface electrons parallel to the axis of the helix wire (not to be confused with the rotational axis of the helix itself), is the complete opposite. This resonance is almost totally suppressed for j = 0, +2, −2 compared to when the beam does not carry any orbital angular momentum (l = 0, j = ±1). The broad hybrid resonance near 730 nm follows the same trend, whereas the red-most hybrid resonance near 972 nm shows a moderate effect. It should be noted that the local field generated by an achiral Au sphere of 50 nm radius is not influenced by either the polarization or the shape of the incident beam’s wavefront, as expected, and is evidenced by its spectrum presented in Figure 2b. This spectrum remains the same for all different values of the total angular momentum, j = 0, ±1, ±2. Resistive energy dissipation in the conducting nanohelix changes in accordance with the strength of the absorbance. Circular dichroism characterizes the differential absorption of light with different senses of circular polarization. The results of our numerical analysis clearly reveal that enhancing or suppressing the coupling of incident light to the medium via assigning an OAM to the former leads to an enhancement of the CD signal (Figure 2c). The OAM-assisted CD shows about 200-fold enhancement compared to the regular CD at 534 nm. In terms of the total angular momentum, the largest value of the CD is observed when the coupling of light with the given sense of the circular polarization to the medium is enhanced by OAM (j = ±2) and the coupling of the light with the opposite sense of the circular polarization is inhibited (j = 0). In a control experiment with the Au sphere, no CD signal was observed. It is important to note that numerical orientational averaging, together with calculations, performed for an offcenter helix, confirmed that the observed enhancement of the CD signal is neither a result of the alignment of the helix with the respect to the beam axis (see SI, section S3, for discussion),
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Figure 2. (a) (b) Surface average of the electric field norm vs wavelength for a single Au nanohelix suspended in PVC, and illuminated by (a) an LCP Gaussian beam with l = 0, +1, −1; (b) an RCP Gaussian beam with l = 0, +1, −1, (c) Resistive loss difference (surface average) vs incident wavelength for a single Au nanohelix suspended in PVC, (d, e) Resistive loss difference (surface average) vs incident wavelength for an array of 12 Au helices suspended in PVC and separated center-to-center by (d) 50 and (e) 30 nm.
nor a computational artifact (SI, section S4). We hypothesize that the OAM transfer to electronic degrees of freedom (the oscillations of the surface electrons), which occurs via the quadrupole term of the multipole expansion of light−matter interaction Hamiltonian,25 is greatly enhanced due to the plasmon resonance of the gold helix. For more detailed analysis of this coupling the reader is referred to section S5 of the SI. Array of Nanohelices. Dipole−dipole coupling between the meta-atoms of a metasurface provides a means to engineer the spectral response via precise tuning of the spectral position and strength of separate plasmon resonances. To further investigate the interaction of structured light with a chiral plasmonic metasurface we constructed a symmetric array of 12 nanohelices with center-to-center separation of 30 and 50 nm. The results of our numerical analysis are presented in Figure 2d,e (see SI for detailed discussion). Overall, the complex
pattern of the coupling is highly dependent on the mutual relationship between the helical phase of the LG mode and the resonant wavelength of a particular plasmon resonance. The coupling between the elements of the array produces particularly strong and sharp resonance features in the spectra that can be manipulated in a switch-on/switch-off manner by changing the value of the total angular momentum quantum number. The extent of the coupling between helices is greatly affected by the value of the total angular momentum. The CD spectra for the analyzed array (Figure 2d,e) demonstrate a great advantage of OAM-based light−matter coupling, in accord with the above analysis of an array of noninteracting helices, that is, isolated helix case in Figure 2c. The amplitude of the CD signal near 509 nm for the more closely spaced array, that is, with 30 nm center-to-center nanohelix spacing, exceeds that of the array of noninteracting helices by almost 1 order of magnitude 737
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ACS Photonics (Figure 2e). Interestingly, the CD spectrum has a richer structure for the more spaced apart array, that is, center-tocenter separation of 50 nm, which exhibits two strong and relatively narrow resonances at 523 and 640 nm. This might be due to the dominance of the strong 509 nm resonance, leaving a much weaker resonance in the longer wavelength portion of the spectrum.
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APPLICATIONS In the recent years, fundamental phenomena and many diverse applications have been demonstrated using light carrying OAM,1,32−38 such as photon spin Hall effect, free-space optical communications, imaging, and so on. Here, we will briefly discuss a few key potential applications based on our analysis of the interactions of OAM carrying light with chiral plasmonic metasurfaces. A key feature of this interaction is the ability to manipulate the coupling of light that has a spatially structured wavefront with these metasurfaces to achieve a manifold of sharp and significantly enhanced hybridized plasmon resonances.39 This capability can be leveraged for applications in (i) biosensing, (ii) surface enhanced Raman spectroscopy (SERS), (iii) surface enhanced infrared absorption (SEIRA) spectroscopy, (iv) laser communicaton detection and modulation devices, (v) optical computing, and (vi) near-zero and negative refractive index metamaterials. The growth of plasmon enabled biosensing has been exponential since the Kretschmann coupling configuration was introduced over 4 decades ago.40−42 The use of light with OAM can further enhance sensitivity and selectivity. SERS and SEIRA also benefit from using structured light. Optical computing with structured light, which is a potential future application, requires elementary building blocks, that is, modulators, switches and gates that can function in the optical range of frequencies. Ultrathin chiral metasurfaces that can filter OAM carrying light at select optical frequencies, as demonstrated here, are well suited for integrated electro-optic and photonic applications. The difference generated between the resonance amplitudes by changing the SAM and OAM values can be exploited to design spin controlled plasmonic switches and gates that function in the optical range. Metasurfaces may revolutionize the world of science and technology with cutting-edge applications like metamaterial antennae,43 subwavelength photolithography,44 and so on. Using quasi-resonant coupling between an optically nonlinear chiral polymer and a chiral plasmonic metasurface opens up more exciting possibilities for photon spin controlled optical signal processing and beam steering. Thus, combining nanostructured chiral matter (metamaterials) with structured light (light with OAM) can bring about a synergy required for transformative advances in this area. Design of Proof-of-Concept Experiment. Given a metasurface, consisting of an array of gold nanohelices suspended in a host matrix, an experimental design can be devised (Figure 3), where two equivalent samples are illuminated by a beam, carrying SAM and OAM. The wavelength has to match one of the plasmon resonances of the metasurface. A beam splitter ensures both samples are equally illuminated. An opaque plate with two pin holes is then placed on the transmitted beam path. When circular polarizations of the two parts of the split beam are kept the same, the double slit diffraction pattern can be observed (Figure 3A) on the screen in case when the coupling of the beam with OAM to the
Figure 3. Experimental design sketch.
metasurface is inhibited, corresponding to the zero total value of angular momentum, j = 0 (see Figure 2a,b). When a wave plate, switching the circular polarization to the opposite sense, is placed on the path of one of the parts of the split beam, the coupling of light to the metasurface is enhanced at j = 2 and transmission is inhibited. In this case the observed interference pattern is that of single slit diffraction (Figure 3B). This conceptual experiment can in principle be further developed to devise an elementary block for optical computing, like a switch or a gate.
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CONCLUSION We have demonstrated that interactions between structured light and structured media facilitates unique spectral features. The synergy between them will lead to new and fundamental understanding of light-matter interactions and spur disruptive advances in myriad related technologies. While this field is still emerging, there is a proliferation of novel applications based on these complex phenomena. For the first time we have simulated the interaction of light carrying SAM and OAM with a chiral plasmonic metasurface composed of subwavelength plasmonic gold nanohelix meta-atoms. This system provides an extraordinary CD response, more than an order of magnitude greater than that obtained using conventional circularly polarized light. It also provides unprecedented resonant tuning of the CD spectral response. The selective enhancement of the resonant coupling holds promise for a gamut of applications, from enhanced biosensing to optical communications. Moreover, while we have considered a specific chiral metasurface configuration, the approach demonstrated here applies to a broad range of 2D and 3D plasmonic chiral media. Finally, the modeling approach that we employed can be generalized for the rational design of such media and innovative applications thereof.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.7b01321. (1) Calculations in an enlarged computational domain; (2) Calculations with a defocused beam; (3) Orientational averaging; (4) Calculations with nanohelix moved around the computational domain; (5) Coupling analysis; (6) Field vector plots; (7) Arrays of helices (PDF). 738
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AUTHOR INFORMATION
Corresponding Authors
*E-mail: efurlani@buffalo.edu. *E-mail: pnprasad@buffalo.edu. ORCID
Edward P. Furlani: 0000-0003-1164-5923 Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of manuscript. All the authors contributed to this manuscript equally. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS J.W.H. acknowledges support from Army Research Office Grant No. W911NF-15-1-0178.
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DOI: 10.1021/acsphotonics.7b01321 ACS Photonics 2018, 5, 734−740
Letter
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DOI: 10.1021/acsphotonics.7b01321 ACS Photonics 2018, 5, 734−740
