Efficient Circular Polarizer Using a Two-layer Nanoparticle Dimer

Subscriber access provided by Kaohsiung Medical University

C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Efficient Circular Polarizer Using a Two-layer Nanoparticle Dimer Array with Designed Chirality Yadong Zhou, Yan Zhao, Jennifer M. Reed, Patricia M Gomez, and Shengli Zou J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02113 • Publication Date (Web): 18 May 2018 Downloaded from http://pubs.acs.org on May 18, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Efficient Circular Polarizer Using a Two-layer Nanoparticle Dimer Array with Designed Chirality Yadong Zhou1, Yan Zhao1,2, Jennifer M. Reed1, Patricia M. Gomez1, and Shengli Zou1* 1. Department of Chemistry, University of Central Florida, 4111 Libra Drive, Orlando, Florida 328162366, United States 2. School of Life Sciences, Qufu Normal University, Qufu, 273165, P. R. China *Corresponding Author: [email protected] Phone number: (+1) 407-823-4123

Abstract

Using a two-layer metal nanoparticle dimer array, we numerically show that the array can act as an efficient circular polarizer. Linearly polarized incident light can be completely split into right and left circularly polarized light. The simulation results show that the efficiency of the polarizer depends on the size of the nanoparticles, the gap distance between the two particles in the dimers, the distance between the two layers, and the relative orientation between the dimer axes in the two layers. The periodic distance between two neighboring dimers in one layer is also a crucial factor in affecting the splitting efficiency. The simulation results demonstrate a simple route of using plasmonic nano-materials for designing efficient circular polarizers.

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 28

1. Introduction

A photon can be in two polarization states, which carry its spin angular momentum. The two polarization states are classically called left-handed or right-handed circularly polarized light (CPL) or simply left or right circularly polarized light. CPL can be treated as a liner combination of two linearly polarized waves of equal amplitude but differing in phase by 90◦. Linearly polarized light can also be decomposed into two circularly polarized waves of opposite polarities with the same amplitude. Both the electric and magnetic field vectors of a CPL travel along a helical path.1 CPL has been applied in different applications including circularly polarized antenna,2,3 circular dichroism (CD) spectroscopy,4 optical techniques (optical information processing, display and storage),5,6 as well as working as asymmetric photolysis in photochemical synthesis.7,8 Quarter-wave plate is commonly used to generate CPL from linearly polarized light. However, the widespread use of the quarter-wave plate is limited by the feasibility of integration and complexity of the devices and systems.9 Another approach in generating CPL is to use cholesteric liquid crystals,10-12 where the photonic crystals are formed by rodlike molecules.13 Nevertheless, both methods are restricted to very narrow frequency ranges. New routes to produce broadband and highly efficient circular polarizers have been discovered thanks to the recent advances in synthesizing metamaterials.14-19 With these advancements, metamaterials with extreme and unusual values of permittivity and permeability including those non-existing in nature can be fabricated. One of the notable features of the new metamaterials is their capability to manipulate the polarization states of electromagnetic


Page 3 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


waves.20-22 Gansel et al.23,24 designed a 3-dimensional gold single-helix photonic metamaterial working as a broadband circular polarizer, in which the circular polarization with the same handedness of the helices was blocked and the other one could be transmitted. In the study, the splitting of left and right CPL can be achieved in the wavelengths ranging from 3 to 7.5 µm. The underlying mechanism is believed to be the phase matching between the electric field vector of the circularly polarized light and the surface plasmons of the 3D helical photonic nanowires along the spiral direction.9 Following Gansel et al.’s work, Yang et al.13 proposed a similar nanowire metamaterials with double-helical structure, in which a much broader operation band was achieved, thus extending the wavelength bands to Visible-light region. Multi-helical nanowire metamaterials were also proposed by Yang et al.25 in order to achieve higher signal-tonoise (S/N) ratios. Both single- or multi-helix photonic metamaterials offer excellent performance as circular polarizers, the only downside of those materials is the complicated fabrication process. In addition, planar metamaterials26,27 with multiple layers can also be used as circular polarizers. Ma et al.28 reported a multi-band circular polarizer, which is composed of a multi-layer planar spiral structure with a twisted angle between particles in two neighboring layers. The structure can transform linearly polarized incident light into left/right CPL by the plasmonic coupling between different layers at different resonant frequencies. Nevertheless, even with the recent advancements in fabricating new metamaterials, producing practical circular polarizers with low profile and larger operation bandwidths remains a challenge. Recently, plasmonic nanosystems and nanostructures have attracted more and more attentions from different groups due to the newly developed techniques in manipulating individual nanoparticles using bio-method, such as those using DNA, peptides or other scaffolds.29,30 In a recent work, Liu et al. used programmable DNA surface adapters to self-



Page 4 of 28

assemble gold nanorods into various chiral supramolecular architectures with distinct configurations and handedness.31 The optical properties of single nanoparticles, nanoparticle clusters, as well as 1D and 2D nanoparticle arrays that can support surface plasmons have been extensively studied.32 Among different plasmonic materials, dimer nanoparticles attracted substantial interest from many groups33-35 due to the highly enhanced electric fields between the gap of the two nanoparticles in the dimer36 and the excited different plasmonic modes (bonding dipole plasmon mode and charge transfer plasmon mode).37-39 According to the plasmon hybridization theory, a bonding mode is excited when the incident polarization direction is parallel to the axis of the dimer, while an antibonding mode occurs when the polarization direction is perpendicular to the dimer axis. When the dimer pairs are delicately arranged into a chiral structure, the interaction between light and the structure should be similar with that of helix metamaterials. Compared with complicated helical photonic metamaterials, the designed plamonic chiral structure will be easier to fabricate if we consider the progressively mature biotechnology. We believe that if the dimer nanoparticles are arranged in a designed pattern, the structure can act as an efficient circular polarizer where one handedness of circular polarization can be blocked whereas the other can be transmitted, and vice versa. In this work, we propose a two-layer silver nanoparticle dimer array, where the dimers in the two layers are arranged with a twisted dihedral angle to achieve a chiral structure. The simulations show that an efficient circular polarizer working at different wavelengths can be generated using the two-layer dimer array. Due to the strong coupling between the two nanoparticles in the dimer and interaction among dimers, one handedness of CPL (either left or right) will be completely blocked whereas the other one will transmit through the array at given wavelengths in an optimal configuration. The working wavelengths can be readily tuned by


Page 5 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


varying parameters in the arrays including the gap distance between the two nanoparticles in the dimer, distance between the two layers and the neighboring distance between dimers in one layer. The particle size is also an important factor in the design.

2. Method The discrete dipole approximation (DDA) method40,41 is used to calculate the optical properties of the designed structures. The DDA method is an efficient yet accurate computational method in calculating the optical properties of particles with arbitrary materials and shapes. The method can also be used to calculate the scattering, adsorption, extinction, and transmission spectra for particles arranged in a periodic pattern. Briefly, in the DDA method, the target particle is divided into N small cubes and each cube represents a polarizable dipole. After solving 3N linear equations, the transmission spectrum for the two-layered dimer nanoparticle array can be calculated. The spectra of circularly polarized light can be obtained using Stokes parameters and Mueller matrices.42 The detailed introduction of the DDA method have been presented in the original literatures40,43,44 and our previous papers.45,46 The dielectric constants of silver are taken from Palik’s handbook.47

3. Results and Discussion



Page 6 of 28

Figure 1. Schematics of (a) a two-layer nanoparticle dimer array. A single unit is composed of two dimers in the top and bottom layers and each dimer includes one core sphere and one satellite sphere. The diameters of the two core spheres are the same and are represented with Dc and the diameters of the two satellite ones are also the same and are labeled as Ds. The centers of core and satellite spheres in each layer are in the same plane. The dimer units are arranged in a periodic array in the YZ plane. The distance between the top and bottom layers (or the center to center distance between the two core spheres in one unit) is denoted as d. The periodicities along the Y and Z axes are represented with Dy and Dz, respectively. (b) Top view of the unit cell composed of two dimers (The core spheres in the top and bottom layers overlap with each other). The axes of the dimers in the two layers are arranged with a twisted dihedral angle, α. s denotes the surface to surface distance between the core and the satellite spheres in a dimer and it is kept the same for dimers in the two layers.


Page 7 of 28

The schematic of the two-layer nanoparticle dimer array is shown in Figure 1a. Each unit in the array is composed of four spheres, where two of them are core spheres and the other two are satellite spheres. Please note that the two core spheres will overlap with each other in the top view as shown in Figure 1b. Both the top and bottom nanoparticle arrays are arranged in a square pattern. In each layer, the centers of the core and satellite spheres are placed in the same plane to guarantee strong coupling between the spheres. The diameters of the core and satellite spheres are denoted as Dc and Ds, respectively. The spacing between the core and satellite spheres in one dimer is represented with s, which is the same for dimers in both the top and bottom layers. α is defined as the twisted dihedral angle of the dimer pairs in one unit in the two layers, as shown in Figure 1b. The center to center distance between the top and bottom layers is expressed as d. The center to center distances between the neighboring units along the Y and Z axes are the same for the top and bottom layers and are expressed as Dy and Dz, respectively. The incident light propagates along the X axis.

(a)

(b)

1

0.6

Transmission

L-150 R-150 L-200 R-200 L-250 R-250

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.2 0

500

700

900

1 L-150 R-150 L-200 R-200 L-250 R-250

0.6

0.2 0

Wavelength/nm

500

700

900

Wavelength/nm

Figure 2. Transmission spectra for the two-layer dimer arrays with (a) varying Dc from 150 to 250 nm while keeping Ds as constant 200 nm and (b) varying Ds from 150 to 250 nm while 7 ACS Paragon Plus Environment


Page 8 of 28

keeping Dc as constant 200 nm. In the simulations, α = 135◦, d =310 nm, Dy = Dz = 600 nm. The surface to surface distance, s, between the two spheres in each dimer is maintained at constant 10 nm. (L: left CPL, R: right CPL).

We start with examining the effect of the relative size of the core and satellite spheres on the splitting efficiency of the polarizer. Previously, both theoretical and experimental studies have shown that the plasmonic coupling between the nanoparticle dimer strongly depends on the relative size of the two nanoparticles.48,49 The calculated spectra for the proposed structures with varying relative core and sitellate particle size in dimers are shown in Figure 2. In Figure 2a, the diameter of the core sphere, Dc, is varied from 150 to 250 nm while the diamter of the satellite sphere is kept at 200 nm. In Figure 2b, Ds is varied from 150 to 250 nm while Dc is fixed at constant 200 nm. In the inset of the figures, L represents the left CPL and R the right CPL. In all the calculations, s is fixed at 10 nm to guarantee relatviely strong coupling between them.33 The periodic distance along the Y and Z axes are kept at 600 nm. d is chosen as 310 nm and α = 135°. Under the illumination of linearly polarized light, the strongest coupling between the two particles in a dimer will occur when the electric field vector of the incident wave is parallel to the axis of the dimer. When the two-layer array is under illumination of left or right CPL, the strongest coupling can be expected when the incident polarization is parallel to the dimer axis at the bottom layer and subsequently parallel to the dimer axis at the top layer. Considering the rotation of the incident polarization, the resonance wavelength, λ, the distance between the two layers, d, and the dihedral angle, α, should follow equation (1)

± ° =

(1),


Page 9 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Where n is an integer. The factor ½ in n is due to the C2 symmetry of the oscillating electric field of the light and +/- sign corresponds to the left/right circularly polarized incident light. When the incident light is linearly polarized, under the condition of the strongest coupling following equation 1, either its left or right CPL component will be absorbed or reflected, and only the rest component will be tranmitted. Consequently, effective splitting can be obtained. According to equation (1), the resonance wavelength for the effective splitting should occur at the wavelengths of around 354, 496 and 827 nm when d =310 nm and α = 135°. However, the calculated resonance wavelengths are at wavelengths between 600 and 700 nm which are quite different from the results predicted using equation (1). We attribute the difference to the phase change of the propagating light ray when interacting with the metal nanoparticles and the strong coupling between two particles in the dimer, among dimers in one layer, and in the bottom and top layers. We used linearly polarized rather than circularly polarized incident light in the simulations which might also be one of the reasons leading to the difference. In both Figure 2a and b, the effective splitting occurs at wavelengths ranging from 600 to 700 nm and the right CPL (dashed curves) are almost completely blocked at around wavelengths of 670 nm. Figure 2a demonstrates that the splitting between left and right CPL in the wavelenghths around 670 nm becomes weak when either the size of core sphere is larger or smaller than that of the satellite sphere. Figure 2b also shows that the relative particle size in a dimer is an important factor in affecting the splitting efficiency of the circular polarizer. We also calculated the transmission spectra of the two-layer arrays when the diameters of both the core and satellite spheres were 100 nm, only very weak splitting efficiency was obtained. The results indicate that not only does the relative size of the two particles in the dimers matter, but also the



absolute size of the particles. In short, plasmonic coupling between two spheres in the dimer needs to be strong enough to guarantee the effective splitting between the right and left CPL.

1

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 28

L-45 R-45 L-90 R-90 L-120 R-120 L-135 R-135

0.6

0.2 0

500

700

Wavelength/nm

900

Figure 3. Transmission spectra for the two-layer nanoparticle dimer arrays with different dihedral angles between the top and bottom dimers in the units. The other parameters: d = 310 nm, s = 10 nm, Dc = Ds = 200 nm, Dy = Dz = 600 nm.

In the following studies, we examine the effect of the dihedral angle, α, on the splitting efficiency of the polarizer. The diameters of both core and satellite spheres will be kept at 200 nm in all the following calculations based on the results in Figure 2. The dihedral angle will affect the relative directions between the incident electric field polarization in CPL and the axis of dimers in the bottom and top layers, and consequently affect the splitting efficiency between the left and right CPL. As indicated in equation (1), the angle that works the best for optical 10 ACS Paragon Plus Environment

Page 11 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


splitting at studied wavelengths should be predictable at a given dihedral angle once the distance between the top and bottom layer, d, has been selected. However, the prediction will not exactly follow the equation due to the complex interaction between the incident light and metal nonaparticles. Due to the C2 symmetry of the oscillating electric field in the incident light, the transmission efficiencies of the right and left CPL will be switched when the dihedral angle α is changed to (360°- α) or (180°- α). In the study, we only show the calculation results when α is smaller than 180°. Figure 3 shows the transmission spectra for the two-layer arrays when the dihedral angle, , is varied from 45° to 135°. In the simulations, we find that the dihedral angle has only slight effect on changing the resonance wavelength. For example, the resonance wavelengths should occur at 930 nm and 827 nm when the dihedral angle is 120° and 135°, respectively, if they follow equation (1). However, Figure 3 shows that the resonance wavelengths can always be found between 600 to 700 nm in both conditions, which are quite different from the predicted values. When α = 90°, the right and left CPL are almost overlapped which should be due to the C2 symmetry of the oscillating electric field. We also notice that the spectrum of the right CPL when angle is α almost overlap with that of the left CPL when angle is (180° - α), although discrepancy happens at some wavelengths because of the complex interaction between incident light and the two-layer system. In the wavelengths ranging from 600 to 750 nm, the transmission efficiency of the left CPL is smaller than that of the right CPL when α < 90°, whereas they are switched when α > 90°. The switchable transmission efficiency shows that the polarizer can be easily manipulated to determine which handedness of CPL will be blocked by simply changing the twisted dihedral angle. There are oscillations in the obtained spectra; we attribute those oscillating features to the complex coupling between the two spheres in a dimer, among dimers in the array, and the coupling among spheres at different layers. The 11 ACS Paragon Plus Environment


calculations show that the most efficient splitting happens when α = 135° where the right CPL can be totally blocked and only the left CPL will be transmitted. We fix α = 135° in all the following simulations.

1

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 28

0.6

L-0 R-0 L-10 R-10 L-20 R-20 L-30 R-30

0.2 0

500

700

900

Wavelength/nm Figure 4. Transmission spectra for the two-layer dimer arrays with varying s from 0 to 30 nm. α = 135°, d = 310 nm, Dc = Ds = 200 nm, Dy = Dz = 600 nm.

Since the interparticle distance in the dimer will significantly affect the plasmonic coupling between them and the absorption efficiency of the dimer,36,39 we also vary the distance between the core and satellite particles, s. The other parameters are chosen as follows: d = 310 nm, α = 135°, Dc = Ds = 200 nm, Dy = Dz = 600 nm. The transmission spectra are shown in Figure 4 where s is varied from 0 to 30 nm. When the core and satellite spheres are touching (s = 0 nm), a relatively broad feature is obtained, as shown in Figure 4 (two red curves). Even though the 12 ACS Paragon Plus Environment

Page 13 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


transmission efficiency of the left CPL is pretty high in the wavelengths between 600 to 800 nm, the value of the right CPL is also over 20%, indicating a weak splitting effect. When the two spheres touch each other, they evolve into a big peanut shaped particle and the strong coupling between the two particles is significantly reduced. The calcuations indicate that the strong coupling between the two particles in the dimer is pretty crucial in obtaining the effective right and left CPL splitting. When s is increased to 10 nm, the effective splitting can be obtained as indicated by the two green curves. In the meanwhile, the broadband becomes narrower, the lowest transmission efficiency of the right CPL drops and is close to zero at around 680 nm resulting in an effective splitting. When s is further increased, the transmission efficiency of the left CPL keeps dropping and the broadband keeps narrowing, however, effective splitting can still be obtained at around wavelengths of 650 nm. The blue and magenta curves show that further increasing s has only slight change on the splitting efficiency of the array when the interparticle distance in a dimer is large enough, i.e. s ≥ 20 nm. The results further demonstrate that a strong coupling between the two particles in the dimers is essential to produce an efficient circular polarizer. In the meanwhile, the wavelengths of the effective splitting slightly shift to blue with increasing s.



1

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 28

L-260 R-260 L-310 R-310 L-360 R-360 L-410 R-410

0.6

0.2 0

500

700

900

Wavelength/nm Figure 5. Transmission spectra for the two-layer dimer arrays with different distances between two layers, d, from 260 to 410 nm. The other parameters: Dc = Ds = 200 nm, Dy = Dz = 600 nm , s = 10 nm, α = 135°.

Another important parameter that might be affecting the splitting efficiency is the distance between the top and bottom layers, d, based on equation (1). The effect of d on the splitting efficiency of the array is shown in Figure 5, where d is varied from 260 to 410 nm. The other paremeters are fixed as follows: Dc = Ds = 200 nm, Dy = Dz = 600 nm , s = 10, α = 135°. According to equation (1), the resonance wavelength of the effective splitting should be dramatically changed when d is changed from 260 to 410 nm. For example, the resonance wavelength should be at around 690 nm when d = 260 nm while the wavelength will be changed to about 470 nm when d = 410 nm in the studied wavelengths range. However, the simualtion results show that the distance between the bottom and the top layers has only slight effect on the 14 ACS Paragon Plus Environment

Page 15 of 28

resonance wavelength. The effective splitting can be obtained at wavelengths of 650-700 nm. When d is increased, the transmission efficiency of the left CPL gradually drops while that of the right CPL increases, thus leading to a gradually dwindling splitting effect. The simulations show that smaller layer-layer distances (d = 260 and 310 nm) are preferred to generate better splitting effect which attributes to the stronger coupling among particles in the top and bottom layers.

1

L-500 R-500 L-550 R-550 L-600 R-600 L-650 R-650

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.6

0.2 0

500

700

900

Wavelength/nm Figure 6. Transmission spectra for the nanoparticle dimer arrays with varying periodicity from 500 to 650 nm. The other parameters: Dc = Ds = 200 nm, s = 10 nm, α = 135°, and d = 310 nm.

We also examine the effect of the periodicity of dimers along the Y and Z axes in the array on the splitting efficiency of the polarizer. The neighboring dimer distance will affect the 15 ACS Paragon Plus Environment


Page 16 of 28

coherent coupling among dimers in the arrays which has been studied in several pervious works,33,46,50-53 thus changing the transmission efficiency or the optical splitting effect. The calculated transmission spectra are shown in Figure 6, where the periodic distance is varied from 500 to 650 nm. When the periodicity is 500 nm, the efficient splitting happens at wavelengths around 550 nm. The resonance wavelength is red-shifted to 600 nm when the periodicity is changed to 550 nm. The resonance wavelength is further red-shifted to 650 nm and 700 nm when the periodicity is increased to 600 and 650 nm, respectively. The simulation results show that the resonance wavelength changes almost proportionally to the neighboring distance between dimers in the array indicating the coherent coupling50 among the dimers is very important in generating high splitting efficiency of the array.

4. Conclusion

In conclusion, a two-layer nanoparticle dimer array can generate similar effects as that of well-studied 3D gold helix metamaterials in splitting left and right CPL from linearly polarized incident light and can act as an efficient circular polarizer. Using the designed structure, one handedness of the CPL can be efficiently blocked and the other handedness will be transmitted, thus leading to the splitting between left and right CPL. The calculation results demonstrate that the dihedral angle between the dimers in the top and bottom layers, relative and absolute size of the particles in the dimers, the surface to surface distance between the two particles in a dimer as well as the periodicity of the arrays have significant effects on the splitting efficiency of the polarizer. Quite interestingly, contradictory to the prediction using a simple equation, we find that the distance between the top and bottom layers and the dihedral angle between the dimers in


Page 17 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the top and bottom layers has only slight effect on the resonance wavelengths where the effective splitting occurs. The simulation results show that an efficient polarizer could be obtained when s = 10 nm, Dc = Ds = 200 nm, d = 310 nm, α = 135°, Dy = Dz = 600 nm where the transmission efficiency of the right CPL is close to zero while the transmission efficiency of the left CPL is over 60%. The theoretical simulations and optimized parameters could provide guidance in the future experimental design for efficient circular polarizers.

Acknowledgement We are thankful for the support of this research by the National Science Foundation and the Office of Naval Research Fund. This work used the Extreme Science and Engineering Discovery Environment (XSEDE) Open Science Grid (OSG) at the service-provider through allocation szou.

References (1) Hu, J.; Zhao, X.; Lin, Y.; Zhu, A.; Zhu, X.; Guo, P.; Cao, B.; Wang, C. AllDielectric Metasurface Circular Dichroism Waveplate. Scientific Reports 2017, 7, 41893. (2) Qing, X.; Chen, Z. N. Compact Asymmetric-Slit Microstrip Antennas for Circular Polarization. IEEE transactions on antennas and propagation 2011, 59, 285-288. (3) Jia-Yi, S.; Kin-Lu, W.; Chieh-Chin, H. Coplanar Waveguide-Fed Square Slot Antenna for Broadband Circularly Polarized Radiation. IEEE Transactions on Antennas and Propagation 2003, 51, 2141-2144. (4) Whitmore, L.; Wallace, B. A. Protein Secondary Structure Analyses from Circular Dichroism Spectroscopy: Methods and Reference Databases. Biopolymers 2008, 89, 392-400. 17 ACS Paragon Plus Environment


Page 18 of 28

(5) Grell, M.; Oda, M.; Whitehead, K.; Asimakis, A.; Neher, D.; Bradley, D. A Compact Device for the Efficient, Electrically Driven Generation of Highly Circularly Polarized Light. Adv. Mater. 2001, 13, 577-580. (6) Wagenknecht, C.; Li, C.-M.; Reingruber, A.; Bao, X.-H.; Goebel, A.; Chen, Y.A.; Zhang, Q.; Chen, K.; Pan, J.-W. Experimental Demonstration of a Heralded Entanglement Source. Nat Photon 2010, 4, 549-552. (7) Matsumoto, A.; Abe, T.; Hara, A.; Tobita, T.; Sasagawa, T.; Kawasaki, T.; Soai, K. Crystal Structure of the Isopropylzinc Alkoxide of Pyrimidyl Alkanol: Mechanistic Insights for Asymmetric Autocatalysis with Amplification of Enantiomeric Excess. Angew. Chem. Int. Ed. 2015, 54, 15218-15221. (8) Kawasaki, T.; Sato, M.; Ishiguro, S.; Saito, T.; Morishita, Y.; Sato, I.; Nishino, H.; Inoue, Y.; Soai, K. Enantioselective Synthesis of near Enantiopure Compound by Asymmetric Autocatalysis Triggered by Asymmetric Photolysis with Circularly Polarized Light. J. Am. Chem. Soc. 2005, 127, 3274-3275. (9) Hu, J.; Zhao, X.; Li, R.; Zhu, A.; Chen, L.; Lin, Y.; Cao, B.; Zhu, X.; Wang, C. Broadband Circularly Polarizing Dichroism with High Efficient Plasmonic Helical Surface. Opt. Express 2016, 24, 11023-11032. (10) Hikmet, R. A. M.; Kemperman, H. Electrically Switchable Mirrors and Optical Components Made from Liquid-Crystal Gels. Nature 1998, 392, 476-479. (11) Mitov, M.; Dessaud, N. Going Beyond the Reflectance Limit of Cholesteric Liquid Crystals. Nat Mater 2006, 5, 361-364. (12) Ha, N. Y.; Ohtsuka, Y.; Jeong, S. M.; Nishimura, S.; Suzaki, G.; Takanishi, Y.; Ishikawa, K.; Takezoe, H. Fabrication of a Simultaneous Red-Green-Blue Reflector Using Single-Pitched Cholesteric Liquid Crystals. Nat Mater 2008, 7, 43-47. (13) Yang, Z. Y.; Zhao, M.; Lu, P. X.; Lu, Y. F. Ultrabroadband Optical Circular Polarizers Consisting of Double-Helical Nanowire Structures. Opt. Lett. 2010, 35, 2588-2590. (14) Huang, Y.; Zhou, Y.; Wu, S.-T. Broadband Circular Polarizer Using Stacked Chiral Polymer Films. Opt. Express 2007, 15, 6414-6419. (15) Shalaev, V. M. Optical Negative-Index Metamaterials. Nat Photon 2007, 1, 4148. (16) Soukoulis, C. M.; Wegener, M. Past Achievements and Future Challenges in the Development of Three-Dimensional Photonic Metamaterials. Nature Photonics 2011, 5, 523530. (17) Liu, N.; Guo, H.; Fu, L.; Kaiser, S.; Schweizer, H.; Giessen, H. ThreeDimensional Photonic Metamaterials at Optical Frequencies. Nat Mater 2008, 7, 31-37. (18) Liu, N.; Liu, H.; Zhu, S.; Giessen, H. Stereometamaterials. Nat Photon 2009, 3, 157-162. (19) Bai, B.; Svirko, Y.; Turunen, J.; Vallius, T. Optical Activity in Planar Chiral Metamaterials: Theoretical Study. Phys. Rev. A 2007, 76, 023811. (20) Bachman, K. A.; Peltzer, J. J.; Flammer, P. D.; Furtak, T. E.; Collins, R. T.; Hollingsworth, R. E. Spiral Plasmonic Nanoantennas as Circular Polarization Transmission Filters. Opt. Express 2012, 20, 1308-1319. (21) Sun, W.; He, Q.; Hao, J.; Zhou, L. A Transparent Metamaterial to Manipulate Electromagnetic Wave Polarizations. Opt. Lett. 2011, 36, 927-929.


Page 19 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(22) Silveirinha, M. G. Design of Linear-to-Circular Polarization Transformers Made of Long Densely Packed Metallic Helices. IEEE Transactions on Antennas and Propagation 2008, 56, 390-401. (23) Gansel, J. K.; Thiel, M.; Rill, M. S.; Decker, M.; Bade, K.; Saile, V.; von Freymann, G.; Linden, S.; Wegener, M. Gold Helix Photonic Metamaterial as Broadband Circular Polarizer. Science 2009, 325, 1513-1515. (24) Gansel, J. K.; Wegener, M.; Burger, S.; Linden, S. Gold Helix Photonic Metamaterials: A Numerical Parameter Study. Opt. Express 2010, 18, 1059-1069. (25) Yang, Z.; Zhao, M.; Lu, P. How to Improve the Signal-to-Noise Ratio for Circular Polarizers Consisting of Helical Metamaterials? Opt. Express 2011, 19, 4255-4260. (26) Kuwata-Gonokami, M.; Saito, N.; Ino, Y.; Kauranen, M.; Jefimovs, K.; Vallius, T.; Turunen, J.; Svirko, Y. Giant Optical Activity in Quasi-Two-Dimensional Planar Nanostructures. Phys. Rev. Lett. 2005, 95, 227401. (27) Rogacheva, A. V.; Fedotov, V. A.; Schwanecke, A. S.; Zheludev, N. I. Giant Gyrotropy Due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure. Physical Review Letters 2006, 97. (28) Ma, X.; Huang, C.; Pu, M.; Hu, C.; Feng, Q.; Luo, X. Multi-Band Circular Polarizer Using Planar Spiral Metamaterial Structure. Opt. Express 2012, 20, 16050-16058. (29) Hentschel, M.; Schäferling, M.; Duan, X.; Giessen, H.; Liu, N. Chiral Plasmonics. Science Advances 2017, 3, e1602735. (30) Schreiber, R.,et al. Chiral Plasmonic DNA Nanostructures with Switchable Circular Dichroism. Nat. Commun. 2013, 4, 2948. (31) Lan, X.; Su, Z.; Zhou, Y.; Meyer, T.; Ke, Y.; Wang, Q.; Chiu, W.; Liu, N.; Zou, S.; Yan, H. Programmable Supra‐Assembly of a DNA Surface Adapter for Tunable Chiral Directional Self‐Assembly of Gold Nanorods. Angew. Chem. Int. Ed. 2017, 56, 14632-14636. (32) Ross, M. B.; Mirkin, C. A.; Schatz, G. C. Optical Properties of One-, Two-, and Three-Dimensional Arrays of Plasmonic Nanostructures. J. Phys. Chem. C 2016, 120, 816-830. (33) Bordley, J. A.; Hooshmand, N.; El-Sayed, M. A. The Coupling between Gold or Silver Nanocubes in Their Homo-Dimers: A New Coupling Mechanism at Short Separation Distances. Nano Lett. 2015, 15, 3391-3397. (34) Talley, C. E.; Jackson, J. B.; Oubre, C.; Grady, N. K.; Hollars, C. W.; Lane, S. M.; Huser, T. R.; Nordlander, P.; Halas, N. J. Surface-Enhanced Raman Scattering from Individual Au Nanoparticles and Nanoparticle Dimer Substrates. Nano Lett. 2005, 5, 1569-1574. (35) Sheikholeslami, S.; Jun, Y.-w.; Jain, P. K.; Alivisatos, A. P. Coupling of Optical Resonances in a Compositionally Asymmetric Plasmonic Nanoparticle Dimer. Nano Lett. 2010, 10, 2655-2660. (36) Hao, E.; Schatz, G. C. Electromagnetic Fields around Silver Nanoparticles and Dimers. J. Chem. Phys. 2004, 120, 357-366. (37) Zhao, L. L.; Jensen, L.; Schatz, G. C. Surface-Enhanced Raman Scattering of Pyrazine at the Junction between Two Ag20 Nanoclusters. Nano Lett. 2006, 6, 1229-1234. (38) Lassiter, J. B.; Aizpurua, J.; Hernandez, L. I.; Brandl, D. W.; Romero, I.; Lal, S.; Hafner, J. H.; Nordlander, P.; Halas, N. J. Close Encounters between Two Nanoshells. Nano Lett. 2008, 8, 1212-1218. (39) Nordlander, P.; Oubre, C.; Prodan, E.; Li, K.; Stockman, M. Plasmon Hybridization in Nanoparticle Dimers. Nano Lett. 2004, 4, 899-903.



Page 20 of 28

(40) Draine, B. T.; Flatau, P. J. Discrete-Dipole Approximation for Scattering Calculations. JOSA A 1994, 11, 1491-1499. (41) Yang, W. H.; Schatz, G. C.; Van Duyne, R. P. Discrete Dipole Approximation for Calculating Extinction and Raman Intensities for Small Particles with Arbitrary Shapes. J. Chem. Phys. 1995, 103, 869-875. (42) Bohren, C. F.; Huffman, D. R., Absorption and Scattering of Light by Small Particles; John Wiley & Sons: New York, N.Y., USA, 2008. (43) Draine, B. T. The Discrete-Dipole Approximation and Its Application to Interstellar Graphite Grains. The Astrophysical Journal 1988, 333, 848-872. (44) Draine, B. T.; Flatau, P. J. Discrete-Dipole Approximation for Periodic Targets: Theory and Tests. JOSA A 2008, 25, 2693-2703. (45) Zhou, Y.; Zhao, Y.; Zou, S. Different Transmission Enhancement Mechanisms in a Sandwiched Nanofilm. Particle & Particle Systems Characterization 2017, 1600327-n/a. (46) Zhou, Y.; Zou, S. Effects of Dipole and Quadrupole Modes on the Switchable Total Transmission and Reflection in an Array of Rectangular Silver Prisms. J. Phys. Chem. C 2016, 120, 20743-20748. (47) Palik, E. D., Handbook of Optical Constants of Solids; Academic press: Cambrige, M.A., USA, 1998; Vol. 3. (48) Njoki, P. N.; Lim, I.-I. S.; Mott, D.; Park, H.-Y.; Khan, B.; Mishra, S.; Sujakumar, R.; Luo, J.; Zhong, C.-J. Size Correlation of Optical and Spectroscopic Properties for Gold Nanoparticles. J. Phys. Chem. C 2007, 111, 14664-14669. (49) Tabor, C.; Murali, R.; Mahmoud, M.; El-Sayed, M. A. On the Use of Plasmonic Nanoparticle Pairs as a Plasmon Ruler: The Dependence of the near-Field Dipole Plasmon Coupling on Nanoparticle Size and Shape. J. Phys. Chem. A 2009, 113, 1946-1953. (50) Zou, S.; Schatz, G. C. Narrow Plasmonic/Photonic Extinction and Scattering Line Shapes for One and Two Dimensional Silver Nanoparticle Arrays. J. Chem. Phys. 2004, 121, 12606-12612. (51) Auguié, B.; Barnes, W. L. Collective Resonances in Gold Nanoparticle Arrays. Phys. Rev. Lett. 2008, 101, 143902. (52) Walsh, G. F.; Forestiere, C.; Dal Negro, L. Plasmon-Enhanced Depolarization of Reflected Light from Arrays of Nanoparticle Dimers. Opt. Express 2011, 19, 21081-21090. (53) Kravets, V. G.; Schedin, F.; Grigorenko, A. N. Extremely Narrow Plasmon Resonances Based on Diffraction Coupling of Localized Plasmons in Arrays of Metallic Nanoparticles. Phys. Rev. Lett. 2008, 101, 087403.


Page 21 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

(a)


X

Top view

Page 22 of 28

(b)

d α Z Dc

Y

s Top view

Ds ACS Paragon Plus Environment

Y

Page 23 of 28

(a) 1

(b) 1

0.6

0.6

0.2 0

L-150 R-150 L-200 R-200 L-250 R-250

Transmission

L-150 R-150 L-200 R-200 L-250 R-250

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.2

500

700

Wavelength/nm

900

0

ACS Paragon Plus Environment

500

700

Wavelength/nm

900


1

L-45 R-45 L-90 R-90 L-120 R-120 L-135 R-135

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 28

0.6

0.2 0

500

700

Wavelength/nm


900

Page 25 of 28

1

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.6

L-0 R-0 L-10 R-10 L-20 R-20 L-30 R-30

0.2 0

500

700

Wavelength/nm


900


1

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 28

L-260 R-260 L-310 R-310 L-360 R-360 L-410 R-410

0.6

0.2 0

500

700

Wavelength/nm


900

Page 27 of 28

1

L-500 R-500 L-550 R-550 L-600 R-600 L-650 R-650

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.6

0.2 0

500

700

Wavelength/nm


900



Page 28 of 28

Efficient Circular Polarizer Using a Two-layer Nanoparticle Dimer

Recommend Documents