Effects of Dipole and Quadrupole Modes on the Switchable Total

May 18, 2016 - While the change from total transmission to total reflection can be obtained relatively easier when the dipole mode is excited, the dif...
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Effects of Dipole and Quadrupole Modes on the Switchable Total Transmission and Reflection in an Array of Rectangular Silver Prisms Yadong Zhou and Shengli Zou* Department of Chemistry, University of Central Florida, 4111 Libra Drive, Orlando, Florida 32816-2366, United States ABSTRACT: Using an array of rectangular silver prisms, we numerically demonstrated that close to 100% transmission and reflection of the electromagnetic wave can be switched by slightly changing the incident wavelengths of less than 10 nm. The calculations showed that the resonance wavelengths are associated with the coherent dipole coupling among nanoparticles, and similar phenomena can also be achieved when the quadrupole mode of the metal nanoparticles is excited. While the change from total transmission to total reflection can be obtained relatively easier when the dipole mode is excited, the difference of the resonance wavelengths between the total transmission and reflection is larger. At the resonance wavelength of quadrupole excitation, the change between the total transmission and the reflection is very sharp and shows a Fano-shaped spectral profile; however, achieving close to 100% transmission and reflection is challenging. We studied the effects of prism width, height, and interparticle distance on the resonance wavelength and the efficiencies of the total transmission and reflection. The mechanisms leading to the total transmission and reflection were also investigated. The calculated data can provide guidance in designing optical devices with effectively switchable transmission and reflection.

1. INTRODUCTION Noble metals with nanostructure exhibit many unique properties associated with their size and shape in comparison to their bulk counterparts. Among the many unique properties, the optical properties of metal nanoclusters have been studied extensively both in experimental and theoretical approaches.1−6 The optical properties of metal nanoclusters are associated with the excitation of surface plasmons including both the localized and propagating ones. Due to the tunable optical properties, metal nanoclusters have been applied to many different fields including sensing,5,7,8 imaging,2,9,10 solar energy harvesting,11−14 waveguide,15,16 artificial materials with negative index of refraction,17−20 and optical devices.21−23 The optical properties of a one- or two-dimensional metal nanostructure array can be totally different in comparison to those of an individual one with the same size and shape. For instance, a metal film perforated with periodic holes will produce dramatically enhanced transmission at wavelengths larger than the diameters of the holes, which is impossible in an isolated hole due to diffraction limit.24 The coherent coupling among nanoclusters will generate other interesting features, such as a Fano-shaped resonance line shape, which has also been studied in metallic or dielectric grating,25 disk/ring,26 plasmonic nanoparticle clusters,27,28 and hole array systems.29 A Fano resonance is generated by the coupling between two modes of broad and narrow widths and usually exhibits as an asymmetric line shape in the transmission/reflection spectra with a sharp efficiency change.30 The Fano resonance produced by a two-dimensional (2D) nanoparticle array is believed to be due to the interference among scattered light rays or the interference between the scattered and transmitted light rays.31 Because of the coherent coupling among excited nanoparticles in a periodic array, the scattering (mainly the reflection) will be © 2016 American Chemical Society

enhanced. The coherent coupling is due to the dipole coupling of the excited metal nanoparticles and shows a transverse electric (TE) mode character where the resonance wavelength depends on the neighboring distance between metal nanoparticles perpendicular to the incident polarization direction.32,33 Nikitin et al. studied the excitation of plasmonic resonance of a 2D gold nanoparticle array in a uniform refractive index environment, they found two different configurations of optical states: Rayleigh anomaly and lattice plasmon mode.34 Zhou et al. demonstrated that the narrow outof-plane dipolar interaction can be supported by a 2D nanoparticle array, where the sharp Fano-shaped spectral profile was explained as the interference between the narrow (subradiant) out-of-plane plasmon resonance and broad (superradiant) in-plane plasmon resonance.35 However, they mainly focused on the optical properties when the array is illuminated by a transverse magnetic (TM)-polarized light. The goal of the work is to design a film with switchable total transmission/reflection by slightly changing the incident wavelength and understand the mechanism leading to the phenomenon. In this work, we not only demonstrated the Fano resonance spectral profile, which is consistent with Zhou’s report,35 but also the switchable total transmission and reflection under the TE mode condition. Using a free-standing array of rectangular silver prisms, we numerically showed that both the enhanced transmission and reflection can be obtained, and the exchange between the total transmission and reflection Special Issue: Richard P. Van Duyne Festschrift Received: February 25, 2016 Revised: May 17, 2016 Published: May 18, 2016 20743

DOI: 10.1021/acs.jpcc.6b01972 J. Phys. Chem. C 2016, 120, 20743−20748

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The Journal of Physical Chemistry C can be achieved by slightly changing the incident wavelengths of less than 10 nm. The coupling among the rectangular prisms can be either due to TM or TE modes depending on the size and resonance wavelength of the prism, as well as the distance between the neighboring prisms. We demonstrated that the TE mode is associated with the excited dipole of the prism and the TM mode is accompanied by the excited quadrupole of the prism. The TE mode coupling among prisms shows a broad Fano resonance shaped peak (dip) where the transition from the total transmission to the total reflection can be easily obtained, the two resonance wavelengths are, however, quite far away from each other with a difference over 100 nm. The appearance of the Fano spectral profile can be explained by the interference that occurs between the broad resonance profile of an individual particle and the narrow resonance peak produced by the radiative coupling among nanoparticles. However, the TM mode coupling among nanoparticles gives a very sharp Fano resonance peak (dip). Different from the case in the TE mode coupling, the two resonance wavelengths associated with the total transmission and reflection are very close to each other, while the efficiency difference between the peak transmission and reflection is not as great as that in the TE mode case. It is worth noting that the enhanced transmission and reflection can appear with an opposite order in the two situations. In the TE mode coupling, the enhanced transmission typically appears at shorter wavelengths in comparison to the enhanced reflection. However, the enhanced reflection shows up at either shorter or longer wavelengths in the TM mode coupling.

Figure 1. Schematic of (a) a free-standing two-dimensional rectangular silver prism array and (b) an individual rectangular silver prism in the array. The array is arranged in the YZ plane, the neighboring center to center distances along the Y and Z axes are expressed as dy and dz, respectively. Rectangular prism is used with a height, h, and a width of the square bottom, w. The incident light propagates along the X axis, the polarization direction is either along the Y or Z axis.

2. METHODS In the calculations, we used the discrete dipole approximation (DDA) method to calculate the transmission and reflection spectra of the free-standing 2D prism array.36,37 The detailed descriptions of the DDA method had been introduced in the previous literature.38 In short, a target of arbitrary shape can be represented with an array of polarizable cubes. Since the target particle is represented with multiple dipoles, higher order excitations of the particle are also included, and the calculations are accurate as long as the length of the polarizable cube is small enough. When particles are arranged in a periodic array as discussed in the article, one individual target particle will be treated as a unit cell and periodic boundary conditions will be applied. In addition to the DDA method, the coupled dipole (CD) method was also used to assist us in explaining the obtained transmission spectra. In the CD method, each metal nanoparticle is treated as a single dipole, which excludes any higher order excitations.39

Figure 2. Transmission spectra for the rectangular silver prism arrays when the incident polarization is parallel to (a,b) the Y axis and (c,d) the Z axis. h = 150 nm, w is (a,c) 100 nm, and (b,d) 300 nm. dy is fixed at 500 nm, dz is varied from 500 to 900 nm. The numbers in each figure represent the interparticle distances along the Z axis in nm, similarly hereinafter.

Figure 2a,c show the transmission spectra for the prism arrays when w = 100 nm. dy is fixed at 500 nm, and dz is varied from 500 to 900 nm. The incident polarization is along the Y axis in Figure 2a and along the Z axis in Figure 2c. As shown in Figure 2a, the resonance wavelength shifts to red with increasing dz, which is consistent with the previous theoretical and experimental results.41,42 In Figure 2c, significantly reduced transmissions or enhanced reflections are obtained at around the wavelength of 530 nm when the incident polarization is along the Z axis. The reduced transmission is explained as the coherent dipole coupling among the metal nanoparticles.43 The resonance wavelength of 530 nm is close to the neighboring center to center distance of prisms along the Y axis, which is fixed at 500 nm in the calculations. The detailed discussions regarding the coherent dipole coupling among metal nanoparticles had been discussed in the previous literature.16,44 When w is increased to 300 nm, the excited dipoles of the metal nanoparticle become stronger, so is the coupling among them. As shown in Figure 2b, close to zero transmission (total reflection) is obtained when dz ⩾ 600 nm due to the coherent coupling among excited dipoles. Total transmission can be achieved at the wavelength close to dz, while the difference of the resonance wavelengths between the total transmission and

3. RESULTS AND DISCUSSION The schematic of a free-standing rectangular prism array arranged in the YZ plane is shown in Figure 1a. In the calculations, the prism array is placed in air. A rectangular prism is sketched in Figure 1b with a height of h and a square bottom width of w. The neighboring center to center distances of the prisms along the Y and Z axes are expressed as dy and dz, respectively. In all the calculations, the incident light propagates along the X axis and the incident polarization is parallel to either the Y or Z axis. The dielectric constants of silver are taken from Palik’s handbook.40 We start from arrays with prisms of h = 150 nm, the transmission spectra for the arrays are shown in Figure 2. 20744

DOI: 10.1021/acs.jpcc.6b01972 J. Phys. Chem. C 2016, 120, 20743−20748

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efficiencies in the Fano resonances shape becomes larger. The difference of the spectrum profiles in Figure 3c,d implies that the prisms with a higher height are preferred to obtain sharp efficiency transition from total transmission to total reflection. Even though the sharp Fano resonance feature can be obtained in Figure 3d, the largest difference between the highest and the lowest transmission efficiencies is only about 70% when dz = 700 nm, and the magnitude of the difference drops quickly with increasing dz. For example, when dz is 800 nm, the transmission efficiency increases from about 40% to 80% at a resonance wavelength of around 800 nm as shown in Figure 3d, the difference between the two values is dropped from 70% when dz = 700 nm to 40% when dz = 800 nm. In the following calculations, we kept h as a constant of 200 nm and increased the prism width to 300 nm. The results are summarized in Figure 4. Figure 4a implies that the transition

the total reflection is over 100 nm. Even though the widths of the transmission dip in Figure 2a are much narrower, a total reflection however cannot be obtained due to the reduced polarizability of the prism with a smaller size. Interestingly, when the incident polarization is along the Z axis as shown in Figure 2d, instead of the invariable resonance at around a wavelength of 530 nm in Figure 2c, a very sharp Fano-shaped resonance profile at the wavelength close to dz appears. The detailed explanation of the appearance of the Fano-shaped resonance will be introduced in the following paragraphs. Opposite to the spectra shown in Figure 2b where a near total transmission is obtained at wavelengths close to dz, Figure 2d shows that the transmission efficiency is close to zero at the same wavelength, while the efficiency increases sharply over only several nanometers. Similar Fano resonance feature had also been observed experimentally in metal nanoparticle arrays when the angle of incident light was changed.35 To obtain sharper spectrum change from total transmission to total reflection, we also varied the height of the rectangular prism while maintaining its width as a constant. The calculated spectra are shown in Figure 3 where w is fixed at 200 nm, while

Figure 4. Transmission spectra for the rectangular silver prism arrays where h = 200 nm and w = 300 nm when the incident polarization is parallel to (a) the Y axis and (d) the Z axis. dy is fixed at 500 nm, and dz is varied from 500 to 900 nm.

from the total transmission to the total reflection can be obtained when the incident polarization is parallel to the Y axis, but the resonance dip is significantly widened in comparison to the spectra in Figure 3b where h = 200 nm and w = 200 nm. Compared with the spectra in Figure 2b, the Fano resonance feature in Figure 4b becomes less sharp when w is increased from 100 to 300 nm; however, the magnitude of the intensity difference between the lowest and the highest transmission efficiencies grows when the incident polarization is parallel to the Z axis. With increasing dz, the magnitude of the intensity difference between the lowest and the highest transmission increases initially and then drops gradually and the Fano resonance feature narrows sharply. In addition, the maximal magnitude of the efficiency difference between the lowest and the highest transmissions can be obtained when dz = 800 nm. So far, we have investigated the effects of prism height, width, neighboring prism distance, and the orientation of incident polarization on the sharp transition between the total transmission and the total reflection for rectangular silver prism arrays. The calculations show that increasing neighboring prism distance will lead to sharp Fano resonance feature. The height of the prism has no significant effect on the spectrum profile; however, a higher particle is preferred to generate sharp transition from a total transmission to a total reflection. Increasing prism width will broaden both the magnitudes between the highest and the lowest transmission efficiencies and the Fano resonance feature. Arrays with prisms of increasing height, width, and neighboring distance will generate spectrum feature with sharp transition and increasing magnitude of difference between the lowest and the highest transmission efficiencies. The calculations show that prisms with h = 200 nm and w = 300 nm are the optimal structure to

Figure 3. Transmission spectra for the rectangular silver prism arrays when the incident polarization is parallel to (a,b) the Y axis and (c,d) the Z axis. w = 200 nm, while (a,c) h = 150 nm and (b,d) h = 200 nm. dy is fixed at 500 nm, and dz is varied from 500 to 900 nm.

h is varied from 150 to 200 nm. Figure 3a,c gives the transmission spectra for arrays with h = 150 nm and Figure 3b,d for arrays with h = 200 nm. dy is also fixed at 500 nm, and dz is changed from 500 to 900 nm. When the incident polarization is parallel to the Y axis, the spectra in Figure 3a,b are pretty similar to each other, which indicates that the prism height has no significant effect on the spectra. Please note that h in Figure 3a,c is the same as that in Figure 2. Although the profiles and trends of spectra in Figure 3a are very similar to those in Figure 2b, the spectra in the former show a much sharper efficiency change from total transmission to total reflection. Figure 3c,d shows the transmission spectra when the incident polarization is along the Z axis. The general trends and profiles of the spectra in both figures are also similar, which further confirms that the h has no significant effect on the resonance wavelength and spectrum profile for the array. Nevertheless, the Fano resonance features are much more obvious in Figure 3d in comparison to those in Figure 3c, and the difference of the magnitudes between the highest and the lowest transmission 20745

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dipoles along each X, Y, or Z axis only can be calculated. The contributions of excited dipoles along three different axes when the incident polarization is along the Y or Z axes are shown in Figure 6a,b, respectively. The total absorption for the array is

obtain sharp transition between the total transmission and the total reflection in the visible wavelengths range. With further increasing prism size, the resonance feature will shift quickly to wavelengths over 1000 nm. After obtaining the optimal conditions in generating the sharp Fano resonance profile in the transmission spectra for the prism array, we are interested in examining the mechanisms leading to the Fano resonance feature as well as the total transmission/reflection when the incident polarization is parallel to the Y or Z axis. When the incident polarization is parallel to the Y axis, the resonance feature is generated by the coherent coupling among excited dipoles, which had been discussed in the previous literature.41,42,45 To verify this conclusion again, we simplified the rectangular silver prism array to an array of spherical silver particles using the CD method, where only dipolar mode of the individual particle is excited.39,41 Arrays composed of rectangular silver prisms with h = 150 nm, w = 300 nm, and dy = 500 nm and dz = 800 nm are used as examples for the comparison between the spectra generated using the DDA and CD methods. The radius of the spherical particle is taken as 180 nm whose polarizability is similar to that of the rectangular prism. The neighboring center to center distances are kept the same as those in the prism arrays. Figure 5a shows that the main feature of the

Figure 6. Absorption spectra for the rectangular silver prism arrays from contributions of excited dipoles along the (black) X, (red) Y, or (green) Z axis only as well as (blue) the total absorption for the array when the incident polarization is along (a) the Z axis and (b) the Y axis. h = 150 nm, w = 300 nm, and dy = 500 nm and dz = 800 nm.

also included for comparison. Figure 6a shows that the total absorption for the array is dominant by the contribution from excited dipoles along the Y axis. The results further support the conclusion that the obtained transmission spectrum profile when the polarization is parallel to the Y axis is due to the coherent coupling of excited dipoles. Dipoles along the X axis also contribute to the total absorption; however, no resonance peak appears at wavelengths around 950 nm. Figure 6b shows that excited dipoles along the Z axis contribute dominantly to the total absorption of the array at the resonance wavelength of around 800 nm; however, the absorption contribution from dipoles along the X axis shows a similar resonance peak at the same wavelength indicating the quadrupole characteristic of the excited mode.

Figure 5. Transmission spectra calculated using the discrete dipole approximation (DDA) method (solid line) and the coupled dipole (CD) method (dash line) when the incident polarization is along (a) the Y axis and (b) the Z axis. The prism of h = 150 nm and w = 300 nm is used, and dy = 500 nm and dz = 800 nm. In the coupled dipole method, the radius of the spherical silver particles is taken as 180 nm, which has a similar polarizability as that of the rectangular prism.

4. CONCLUSIONS We numerically examined the transmission spectra for a 2D array composed of rectangular silver prisms under TE- and TM-polarized incident light conditions. The effects of prism heights, widths, and neighboring prism distances on the resonance feature of the spectra were investigated. The calculations showed that the switch between total transmission and total reflection can be easily achieved under TE mode condition. Using the CD method, we found that the coupling among excited dipoles attributes to the resonance feature where the resonance wavelength is determined by the neighboring prism distance perpendicular to the incident polarization direction. Under the TM mode condition, the resonance wavelength is determined by the neighboring prism distance parallel to the incident polarization direction and the generated Fano resonance shape is due to the coupling between the narrow resonance peak from excited quadrupoles and the broad resonance peak of excited dipoles. The transition from the total transmission to the total reflection is sharper, while the magnitude of the change is reduced in comparison to that in the TE mode case. We also demonstrated that prisms with a 200 nm height and a 300 nm width will generate desired sharp transition from total transmission to total reflection in the visible wavelengths.

transmission spectra at wavelengths around 800 nm generated by using the DDA method can be qualitatively reproduced by using the CD method when the incident polarization is along the Y axis. This consistency demonstrates that the total transmission/reflection is mainly due to the coherent dipole coupling among nanoparticles when the polarization is along the Y axis. However, the sharp Fano resonance feature at wavelengths around 800 nm obtained from the DDA method totally disappeared in the spectrum calculated using the CD method when the incident polarization is along the Z axis, as shown in Figure 5b. The calculations further confirm that the broad resonance feature at around 800 nm in Figure 5a is caused by the dipole coupling among rectangular prisms, while the sharp Fano resonance feature in Figure 5b cannot be explained by the same mechanism. To understand the origin of the Fano resonance feature that appears when the incident polarization is along the Z or Y axes, we calculated the absorption contributions of the excited dipoles whose orientations are only along the X, Y, or Z axis, respectively. The calculations are finished by a modified DDA program, where the separated absorption contribution of

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*E-mail: [email protected]. Phone: (+1) 407-823-4123. 20746

DOI: 10.1021/acs.jpcc.6b01972 J. Phys. Chem. C 2016, 120, 20743−20748

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The Journal of Physical Chemistry C Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are thankful for the support of this research by the National Science Foundation and the Office of Naval Research Fund.

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