Optical Orbital Angular Momentum Read-Out Using a Self-Assembled

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Optical Orbital Angular Momentum Read-Out Using a Self-Assembled Plasmonic Nanowire Deepak K. Sharma, vijay kumar, Adarsh B. Vasista, Diptabrata Paul, Shailendra Kumar Chaubey, and G V Pavan Kumar ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01220 • Publication Date (Web): 18 Dec 2018 Downloaded from http://pubs.acs.org on December 19, 2018

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Optical Orbital Angular Momentum Read-Out Using a Self-Assembled Plasmonic Nanowire †

Deepak K. Sharma,

†

Vijay Kumar,

†

Shailendra K. Chaubey,

†Department

†

Adarsh B. Vasista,

†

Diptabrata Paul,

∗,†,‡

and G. V. Pavan Kumar

of Physics, Indian Institute of Science Education and Research(IISER) Pune-411008, India

‡Center

for Energy Science, Indian Institute of Science Education and Research(IISER) Pune-411008, India

E-mail: [email protected]

Abstract Orbital angular momentum (OAM) has emerged as an important parameter to store, control and transport information using light. Recognizing optical beams that carry OAM at the nanoscale and their interaction with sub-wavelength nanostructures has turned out to be a vital task in nanophotonic signal processing and communication. The current platforms to decode information from dierent OAM modes are mainly based on bulk optics and/or requires sophisticated nanofabrication procedures. Motivated by these issues, herein we report on the utility of chemically prepared, individual plasmonic nanowire for OAM read-out. Our method is based on pattern recognition of coherent light scattering from individual nanowire that can be used as direct read-outs of two parameters of an OAM beam: magnitude of topological charge and its sign. All the experimental observations related to pattern formation are corroborated by three dimensional numerical simulations. Given that pattern formation and recognition are 1

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exhaustively utilized in various computational domains, we envisage that our results can be interfaced with machine-learning methods, wherein direct read-out of OAM signals can be performed without human intervention. Such methods may have direct implication on chip-scale robotics and chiral nano-photonic interfaces. Vortices are ubiquitous in nature. They form one of the most intriguing physical phenomena, and are observed from galactic to atomic length scales. Laser beams too can carry vortices and have emerged as one of the interesting topics in optical communication and light-matter interaction. 13 The study of interaction of optical vortices with nanoscale matter has turned out to be not only of fundamental importance, but also with implications in chip-scale nanophotonics and optical communication. Laguerre-Gaussian beams carrying orbital angular momentum (OAM) are widely used optical vortex beams. The beams are termed as LG

l m

beams, where l represents the azimuthal index (topological charge / Mode

number of OAM) and m represents the radial index. Topological charge l also means that vortex beam carries lh ¯ OAM per photon. 4 An azimuthally varying phase term ei φ (where l

φ is the azimuthal coordinate) in vortex beam makes the wavefront of these beams to trace a helical path with a phase singularity at its center. Conventionally, vortex beams have been extensively studied in the context of optical communication. 57 They also nd applications in stellar vortex coronagraphy, 8,9 sensing 10 etc. Use of these beams are not limited to macroscale; they have been harnessed at micron and sub-micron scale for quantum memory device, 11 optical tweezers, 1214 nonlinear optics, 1517 and many more. Accessibility to innite orthogonal states of OAM makes vortex beam an unparalleled optical carrier for large information transfer. It has been observed that multiplexing of OAM can enhance information transfer by many folds. 5 But this capability leads to the challenge of reading dierent OAM modes at the detection end, especially at scales comparable to wavelength of light. Identication of dierent OAM modes has been studied and realized at larger scales using conventional interferometric 18,19 and diraction 20 measurements. Recent development in the nanofabrication has made the detection of OAM possible at even much 2


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smaller scale. 2123 But complicated structure and large size of these devices may constrain their integration in a compact nanophotonic circuit. At nanoscale, plasmonic structures with large optical scattering cross-section exhibit unique way to read OAM modes and recent eorts have shown great promise. 24,25 Until now, the reported methods utilize complex plasmonic architectures, which are challenging to fabricate on large scale, and require clean room facility. There is an imperative for research on simple plasmonic nanostructures that can read the OAM modes unambiguously. More so, if the said nanostructures can be prepared by bottom-up nanofabrication techniques using chemical synthesis, then they can be functionalized, manipulated and integrated using processes such as self-assembly. Motivated by these issues, herein we report on our experiments that show a new way to read OAM modes at subwavelength scale by analyzing the optical scattering patterns from a self-assembled, individual plasmonic nanostructure. For this purpose, we use a chemically synthesized single plasmonic nanowire (NW) as an OAM sensor at subwavelength scale. Plasmonic nanowire made of sliver and gold has been realized as subwavelength waveguide optical antenna, 2629 sensor, 30 nonlinear optical antennas 31,32 and as a platform to study spin-orbit coupling in light scattering. 33 They are yet to be harnessed as OAM sensor and to this end, we have utilized elastic scattering of light from individual sliver nanowire for the detection of OAM. Importantly, we discriminate the magnitude and sign of the OAM by directly reading scattered patterns in the fareld.

Results and discussions Chemically synthesized Ag nanowires (NWs) 34 are dropcasted on a glass coverslip. Measurements are performed on a sample containing wires with width ranging from 300 nm to 400 nm to conrm the reproducibility of the experiment. But all measurements presented here are from single NW with diameter equal to ∼360 nm. Figure 1(a) shows schematic of the

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system under study. We have used spatial light modulator (SLM) with o-axis blazed holograms to generate LG and HG beams. 35 SLM modulates the phase of the incident Gaussian beam (633 nm wavelength) from He-Ne laser to convert it into LG or HG beam. Operational wavelength (633 nm) falls near to resonance in the broad scattering spectrum of the NW. 36 First diracted order from SLM is ltered and sent to microscopic objective (0.50 NA, 50x) as Gaussian, LG or HG beam for the illumination of individual NW. Forward scattered light was captured with high numerical aperture objective lens (1.49 NA, 100x). Fourier plane (FP) image of the forward scattered light is captured by imaging back focal plane of the collection objective lens on to the charge coupled device (CCD). A pinhole was introduced at the image plane to collect signal only from excitation position on NW and hence to avoid scattering from other parts of the sample. Unscattered light was blocked using a block at the conjugate back focal plane in the collection path. A detailed experimental setup is given in gure S1, Supplementary Material. Inset (Fig. 1(a)) shows real plane bright eld optical image of representative NW illuminated with LG beam. NW is oriented along the x-axis as indicated in bright eld optical image of NW. Figure 1(b) shows a FP image of the transmitted LG10 beam having no NW in the focus of the beam. Figure 1(c) shows the fareld scattering pattern of the LG10 beam in the presence of NW in focal regime of the beam. Presence of OAM in the beam is represented by a unique scattering pattern in the FP image and hence make the NW a good platform to characterize OAM. In what follows, we show how the scattering pattern of LG beam diers from other kind of beams and also utilize the patterns to discriminate the magnitude and sign of the topological charge of OAM carrying beams.

Uniqueness of scattering patterns of LG beams − First we compare how nanowire scattering pattern from LG beam diers from conventional Gaussian beam. Figure 2(a) shows scattered FP image of Gaussian beam with input polarization aligned along y-axis, transverse to the long axis of NW. The direct illumination 4


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Figure 1: (a) Schematic describing Fourier plane (FP) imaging of forward scattering of Laguerre Gaussian (LG) beam from Ag nanowire (NW) placed on a glass coverslip. Back focal plane of the collection objective lens is captured for the analysis of fareld. The inset shows real plan bright eld optical image of NW illuminated with LG beam. FP images (b) without and (c) with NW in the focal region for LG10 beam illumination. Inner dotted circle in FP images represents critical angle of glass. k0 is free space wavevector.

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Figure 2: Fourier plane (FP) images highlighting orbital angular momentum (OAM) induced preferential scattering (indicated by white arrows) from NW for incident LG beam in comparison to symmetric scattering for Gaussian and HG beams. Top insets show beams after the SLM. Experimentally measured FP images showing fareld scattering from NW (aligned along the x-axis) for transversely polarized incident (a) Gaussian beam, (b) LG−1 0 beam, and (c) HG10 beam. (d)-(f) are corresponding simulated FP images corroborating experimental observations of scattering from dierent beams. Input powers used at the back aperture of illumination objective lens were 70 nW (Gaussian Beam), 68 nW (LG−1 0 beam) and 60 nW (HG10 beam). Simulated scattered near-eld electric eld (SNFEF) distributions are shown for (g) Gaussian beam, (h) LG−1 0 beam and (i) HG10 beam. Schematics in these gures show positions of cross-sectional planes (y-z planes) of SNFEF distribution across NW for dierent 6distribution for LG−1 beam in comparison to beam illuminations. SNFEF has ACS asymmetric 0 Paragon Plus Environment symmetric distributions for Gaussian and HG10 beams across NW.

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near kx /k0 = ky /k0 = 0 is blocked and appears as black disk corresponding to a region of NA of illumination objective lens (0.50 NA) in the FP image. Scattered light spreads along ky /k0 wave vectors with small distribution along kx /k0 axis. Scattering along kx /k0 is dependent on focusing of incident beam, and its spread increases with increase in NA of illumination objective. One of the important aspects of scattering for an incident beam with transverse polarization from thick NW is the presence of light in the forbidden region (at super critical angles). Scattering in the forbidden region is negligible for input polarization along NW (Fig. S2 and S3, supporting information). But as width of the NW is further reduced, the scattering intensity in forbidden region increases 37 even for input polarization along the NW. Hence thick NWs have an advantage in polarization controlled angular distribution of scattering over thinner ones. Figure 2(b) shows FP image of forward scattering for transversely polarized LG−1 beam. 0 We get preferential radiation direction (preferential scattering) indicated by white arrows in FP image. Biased scattering can be attributed to OAM in the LG beam. 38 Due to the presence of OAM in LG beams, Poynting Vector circulate around intensity null. This makes Poynting vector directions to be opposite for two interaction positions on both sides of the singularity of the beam on wire. Thus the far-eld scattering pattern is biased as per the OAM characteristics of the beam as shown in Fig2(b). Signature of the OAM in scattered far-eld does not change as a beam moves along the length of the NW (Fig. S4, supporting information). Hence the method is rendered to be robust with respect to positioning. But length of the NW should be greater than the spot size to avoid scattering from ends of the NW

Next, we compare the scattering patterns due to LG beam and Hermite-Guassian (HG) beam that has singularity but no angular momentum. These beams have a nodal line at the center as evident in the image above Fig. 2(c). The scattering pattern is symmetric in FP image for transversely polarized HG10 beam (Fig. 2(c)). The absence of intensity at wave vectors along ky /k0 axis near kx /k0 = 0 is a consequence of singularity and nodal line at the 7


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center of LG and HG beams respectively.

The experimental observations in Fig. 2(a-c) were corroborated by full-wave 3D nite element method (FEM) simulations using COMSOL Multiphysics (version 5.1) commercial software. Ag NW is modeled with a geometry having a pentagonal cross section with diameter 350 nm and length 5µm, placed on a glass substrate. Wavelength dependent refractive index of Ag is taken from. 39 The system is meshed with the free tetrahedral mesh of size 20 nm to ensure accuracy. A single NW on glass is illuminated with beam (Gaussian, LG, and HG) of wavelength 633 nm with beam waist (633 nm) maintained at NW-glass interface to introduce similar focusing conditions as of experiment. The local electric eld is calculated, and the near eld to far eld transformation is performed using reciprocity arguments. 40 Simulated FP images of forward scattering shown in gure 2(d-f) are in good agreement with experimentally observed scattered far-eld for dierent beam illuminations. To further understand the eect of OAM on scattering we have analyzed the simulated scattered electric eld distribution near NW for illumination with dierent beams. OAM present in LG beam results in asymmetric spatial distribution of scattered near eld in comparison to symmetric distribution for Gaussian and HG beam illuminations as shown in Fig2 (g-i). Near eld electric eld calculations also show localized plasmon generation at the excitation position. It should be noted that there is no propagating plasmon mode being excited as interaction of free space photons at the center of NW does not possess enough momentum for the generation of surface plasmon polaritons in NW. We performed scattering simulations to explore the eect of the material of NW on scattering by changing the material to a dielectric (Zinc sulphide (ZnS)) and by making the NW as perfect electric conductor and keeping other properties constant at 633 nm wavelength as shown in gure S5, supporting information. We found method to be robust for working with dierent materials. Directionality values (D) for preferential scattering of LG−1 0 beam calculated according to the procedure shown in gure S6, supporting information are found 8


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to be 0.35 for ZnS and 0.40 for PEC NWs which are near to 0.38 for Ag NW. We also tried to maximize the directionality value by changing various other parameters of the NW such as diameter, position of NW along its short axis (y) with respect to beam focus and its shape as shown in gures S7-S9 respectively, supporting information. Size (diameter) dependence shows increase in directionality value as a function of increase in diameter from 100nm to 500nm. This can be understood as we go higher in diameter, scattering cross-section of the NW increases. Preferential scattering is sensitive to movement of NW along its short axis and have maximum directionality value for parking of NW at the center of beam focus. Presence of OAM induced preferential scattering in scattered fareld from NWs with dierent cross sections makes the present method robust to be used for any one dimensional component of a photonic circuit irrespective of its shape. Working of scattering measurements were tested over a range of operational wavelength. Simulated FP images (gure S10, supporting information) show scattering pattern of LG−1 0 beam for wavelengths from 600 nm to 900 nm. One can clearly observe the eect of OAM in the scattering for dierent wavelengths.

Scattering patterns are sensitive to the mode number − Figure 3(a-c) shows experimentally measured scattering FP images of LG

l m

beams as a

function of varying mode number, l. Scattering FP image for l = -1 has two lobes (indicated by white dots) on both sides of ky /k0 axis with preferential scattering indicated by white arrows (Fig. 3(a)). The number of lobes increases with increment in the number of l in FP images. Figures 3(b and c) shows that l = -2 and l = -3 have three and four lobes, respectively. This suggests number of lobes in FP image is equals to l +1 for a given OAM mode number l. It should be noted that preferential scattering direction for l = -2, -3 remains same as of l = -1 indicated by white arrows in respective gures. Increase in number of lobes with increase in mode number l can be understood from the fact that higher order vortex beams are unstable and split into l number of vortices as shown in insets of gure 3(a-c). 41 As explained in Fig.2, single dark region (singularity) at the center of beam causes absence 9


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Figure 3: Fourier plane (FP) images showing dependence of scattering on the mangitude of OAM. Experimentally measured FP images show unique scattering pattern for (a) l = -1, (b) l = -2 and (c) l = -3. Number of lobes in the scattering pattern along ky /k0 axis increases with increase in OAM mode number l. Number of lobes is indicated by white dots. Insets in gures (a)-(c) show splitting of vortex in l number of vortices in real plane image with no NW in the focal regime. (d) - (f) Simulated FP images corroborating experimental results. of wave vector along ky /k0 axis near kx /k0 = 0 resulting into two lobes in FP image. The cases of l = -2 and -3 modes will contain two and three dark regions inside the beam, respectively. This means vortex with l = -2 mode interacts with nanowire with three bright points (points with nonzero intensity) and hence scattering from these three points results in three lobes in FP image. Similar explanation holds for l = -3 mode and l = +1, +2, +3 modes (data not shown). It should be noted that the input power for dierent modes are not the same. As the mode number increases, the power density of the scattered light decreases. Input power for the scattering of dierent modes of OAM shown in Fig. 3 are 8 nW (LG−1 0 ), 10


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−3 66 nW (LG−2 0 ) and 780 nW (LG0 ). Numerically simulated FP images (gures 3d-f) show

similar pattern for l = -1 (Fig. 3(d)), l = -2 (Fig. 3(e)) and l = -3 (Fig. 3(f)) and hence corroborate experimental ndings. Increase in width of the scattered pattern along kx /k0 for higher mode numbers can be accounted for increase in divergence of higher order vortex. 42 This procedure becomes more useful for higher order modes of OAM as splitting of vortex at focus plane is not distinguishable as shown in magnied real plane images in Fig. S11, supporting information. In this case far-eld scattering pattern provides clear distinction in the higher OAM modes as shown for l =-4 to -7 in Fig. S12, supporting information.

Figure 4: Discriminating the sign of topological charge. Scattering FP images of LG Beam (a) l = +1 and (b) l = -1 from plasmonic nanowire discriminating between sign of OAM mode l = |1|. (c) - (d) Simulated scattering FP images corroborating experimental results.

Scattering patterns are sensitive to sign of the topological charge − Vortex beams have positive or negative value of OAM. So it is crucial to identify the sign of particular mode number of OAM along with its magnitude. Figure 4 (a and b) show FP images of scattering for LG beam with l = +1 and l = -1 with same illumination power (8 nW). As indicated by white arrows in experimentally measured FP images, it is evident that preferential scattering inverts its direction as sign of OAM changes from l = +1 to -1. This 11


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is consistent with higher order OAM modes also (See Fig. S13, Supporting Information). Change in the direction of preferential scattering can be understood from the fact that as sign of OAM changes, the Poynting vector direction inverts which guides scattering wave vectors accordingly. 38 Asymmetric distribution in scattering FP image for dierent signs of a particular OAM mode is well corroborated by numerical simulations (Fig. 4(c-d)).

Conclusion To conclude, we have experimentally shown that coherent light scattering pattern from a chemically prepared plasmonic nanowire, self-assembled on a glass substrate can be utilized to read-out the magnitude and sign of the topological charge of an optical vortex beam. A clear distinction between vortex beam scattering patterns and other beams that do not carry orbital angular momentum was established, which was further corroborated by three dimensional numerical simulations. Our work introduces a platform for OAM characteristics read-out at the chip-scale. By further combining techniques based on pattern recognition and machine learning, one can possibly automate the read-out procedure without human intervention. Such methodologies are of high interest in optical communication channels, and the fact that we use a simple, chemically synthesized plasmonic nanowire structures may bring down the cost of such devices for future developments.

Acknowledgement This research work was partially funded by DST-Nano mission Grant (SR/NM/NS-1141/2012(G)), Center For Energy Science (DST Nano mission project), INSA research grant and IndoFrench grant (IFCPAR), project - 5504-3. VK acknowledges DST-SERB India for National Post-Doctoral Fellowship reference no. PDF/2016/002037. DKS acknowledges Infosys foundation, India, for the nancial aid. Authors thank Ms. Kanchan Sharma for the help in the drawing of schematic of the experiment. DKS thanks Dr Rohit Chikkaraddy, Ms. Vandana 12


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Sharma and Mr. Sunny Tiwari for fruitful discussions.

Supporting Information Available Supplementary material containing following details is available free of cost.

• Detailed experimental setup • Polarization controlled scattering of Gaussian beam • OAM detection at dierent positions along the length of NW • Eect of dierent parameters such as size, shape, operational wavelength and NW position with respect to beam focus on scattering from NW

• Detection of higher order modes of OAM

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Optical Orbital Angular Momentum Read-Out Using a Self-Assembled

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