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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Dielectric Environment Manipulation toward Versatile Light Scattering of High Refractive Index Nanoparticles Guanqiao Zhang, Chuwen Lan, Rui Gao, Yongzheng Wen, and Ji Zhou J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b09670 • Publication Date (Web): 26 Oct 2018 Downloaded from http://pubs.acs.org on October 29, 2018

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The Journal of Physical Chemistry

Dielectric Environment Manipulation toward Versatile Light Scattering of High Refractive Index Nanoparticles

Guanqiao Zhang1, Chuwen Lan2, Rui Gao3, Yongzheng Wen1, Ji Zhou1,*

1

State Key Lab of New Ceramics and Fine Processing, School of Materials Science and

Engineering, Tsinghua University, Beijing 100084, China 2

Beijing Laboratory of Advanced Information Networks & Beijing Key Laboratory of

Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China 3

High Temperature Thermochemistry Laboratory, Department of Mining and Materials

Engineering, McGill University, Montreal, Quebec H3A 0C5, Canada

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

ABSTRACT Optical scattering process is of fundamental importance for manipulating light-matter interaction at subwavelength scale. Dielectric nanoparticles with high refractive index have been a long-proven candidate for supporting optical Mie resonances, and is recently regaining considerable attention thanks to a combination of their low-loss property as well as the compatibility with modern micro-nano processing technologies. Changing the surrounding environment of nanoparticles can exert great influence on the scattering behaviors, especially in the case of plasmonic particles, whose ability to sensitively detect index change has been well implemented in the field of optical sensing. However, few reports can be found scrutinizing the detailed mechanism concerning dielectric nanoparticles, and the systematic research on how surrounding environment can shape their scattering behaviors remain largely uncharted waters. Therefore, it is necessary to elucidate to what extent can surrounding environment affect the optical responses of high refractive index nanoparticles. In this paper, we theoretically and numerically investigate three representative geometries, namely individual nanosphere, individual nanodisk and twodimensional nanodisk array (metasurfaces). For individual nanosphere, we examine the influence of the surrounding medium by applying well-established analytical solutions. For individual nanodisk, multipole expansion is utilized for unveiling the mode evolutions of the decomposed modes upon altering the surrounding environment. For metasurfaces, we demonstrate mode overlap and split phenomena through dynamically tuning the refractive index of the embedded medium. This work may find applications in sensing and optical switching devices composed of high refractive index dielectric nanoparticles.


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INTRODUCTION The understanding of electromagnetic scattering by subwavelength particles at nanoscale is essential for addressing light-matter interaction in the microscopic physical world. A plethora of natural phenomena, such as the beauty of the clear azure sky and the magnificent flaming sunset, all stem from the fundamental process of light scattering, which naturally arises from the heterogeneity of their systems consisting of both scatterers and the surrounding environment.1 Theoretical researches on the issue of light scattering date back to well a century ago, when Lord Rayleigh studied the scattering behavior of particles smaller than the wavelength.2 Following that milestone, comes the theoretical contributions by Mie3 and Gans4 on spherical and ellipsoidal particles. To this day, the booming field of nanotechnology has paved an efficient path toward the convenient and accurate engineering for light manipulation. However, this does not seal the human ambition for perfection, and quite to the contrary, it is high time researchers explored into novel scattering phenomena, as utilization of their peculiar properties can prove instrumental for the next breakthrough. In fact, for the past decades, a great deal of effort has been devoted to this field with a vast number of accomplishments achieved, including the realization of superscattering,5,6 scattering invisibility,7 arbitrary scattering directionality,8-10 multipolar interference,11 and ideal dipole scattering,12 just to name a few. These results not only render us the powerful means of tailoring electromagnetic interactions, but also give rise to the sprouting of practical applications.13 The modern science and technology have witnessed the burgeoning advancement of plasmonics, a field of research capable of dominating the light-matter interaction through surface plasmon resonance (SPR).14,15 Metal nanoparticles, upon interacting with the electric component of incoming light, can confine electromagnetic field into subwavelength volume, and the conduction electrons of which will oscillate collectively.16,17 The scenario is also referred to as localized surface plasmon resonance (LSPR). Due to their versatility of coupling with light, metal nanoparticles have seen great preference in numerous applications, such as surface-enhanced Raman scattering (SERS),18,19 surface-enhanced fluorescence (SEF),20,21 surface-enhanced infrared absorption (SEIRA),22,23 biomedicine,24,25 solar energy cells,26,27 etc. Another promising domain is the plasmonic metamaterials and metasurfaces, which give birth to a variety of exotic physical properties.28-31 Meanwhile, the optical responses of metal nanoparticles are



affected and can be tuned by virtue of many factors, including the polarization of external light,32 the geometrical parameters of nanoparticles,33 intrinsic properties of constituent plasmonic materials,34,35 nanoparticles’ coupling effect,15 as well as the surrounding dielectric environment.16 The SPR is extremely sensitive to the refractive index change of the host media, which can be explained by the dispersion relation of surface plasmon polariton (SPP) : spp  c  d  m ( d   m )  , where  spp is the propagating constant of SPP mode, c is the speed of light,  d and  m are the dielectric function of the neighboring environment and the metal itself.16 People have paid close attention to plasmonic sensing that can be used to detect the presence of certain chemicals or biological tissues, which in essence relies on the accurate spectral response to the change of dielectric surrounding.36 However, the intrinsic losses of metals remain a non-negligible problem, especially at the case when clusters of metal nanoparticles are gathered, hampering the overall performances and functionalities of the concerning devices.37 An alternative choice is to utilize all-dielectric nanoparticles.38 Unlike their plasmonic counterparts, whose losses are closely associated with free electrons, all-dielectric particles are endowed with electromagnetic responses owing to their bound charges and ensuing displacement currents with inherently low losses.39 It is both theoretically predicted1 and experimentally verified40 that dielectric nanoparticles with high refractive index can support optical resonance, from simple low-order Mie modes to multipolar behaviors,41 injecting vitality into the classical field of light scattering. Furthermore, particles with different shapes and symmetry properties are investigated, which further enriched our understanding and available selection of mode coupling or hybridization.37,42,43 Meanwhile, all-dielectric metamaterials that consist of elaborately designed nanoparticle arrays have gained ever-increasing attention in recent years.44-48 They are able to support resonant behaviors in three dimensions and, as a matter of fact, isotropic responses are more readily achievable.49,50 Optical magnetism,51 perfect reflection,52 magnetic mirrors,53 as well as Huygens’ surfaces,54 are just a tip of the iceberg in this flourishing research field. However, one major setback for current dielectric photonic devices still lies in our limited understanding toward achieving fine tunability, and similar to the aforementioned case of plasmonic particles, adjusting the surrounding dielectric environment for dielectric scatterers also delivers a practical approach toward manipulating basic light scattering process. In fact, some works have already followed this path by combing all-dielectric


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nanoparticles with functional materials, such as liquid crystal,55 magnetic thin film56 and quantum dots,57 so that a state of flexible control could be achieved. Besides, tuning the color of all-dielectric metasurfaces through microfluid injection has also been demonstrated.58 Despite employing various kinds of physical field to externally stimulate changes in physical properties of the functional materials for obtaining tailorable responses from embedded dielectric particles, the essence of such ingenuity lies steadily in the principle of altering the surrounding dielectric environment. To further future innovations, it would be highly opportune to launch a more detailed investigation into the interaction pattern between electromagnetic waves and dielectric scatterers with respect to the role of surrounding environment. General and systematical studies are also welcomed to fulfill the quests for understanding to what extent can surrounding environment affect the light scattering process. In this paper, we theoretically and numerically study the influence of surrounding dielectric environment on the scattering behaviors of high-index dielectric nanoparticles. In order to present a comprehensive analysis, we focus our attention on three different kinds of geometrical configurations, namely individual nanosphere, individual nanodisk, and twodimensional nanodisk array (metasurfaces). Near-infrared is chosen as the operating band and the material properties are set to mimic silicon, which possesses near-zero intrinsic loss within the band and is compatible with present-day micro-nano processing technologies. For individual nanosphere, the electric dipole mode (MD) displays less sensitivity to the variation of surrounding compared to the magnetic quadrupole mode (MQ), while electric dipole mode (ED) characters are relative easily erased by decreasing the refractive index discrepancy between the dielectric nanosphere and the environment. For individual nanodisk, we employ multipole decomposition method in spherical coordinate to elucidate the dynamic change of each mode upon altering the surrounding. It is discovered that the scattering properties of nanodisks with different aspect ratio exhibit distinctive responses. The case of metasurfaces is investigated by means of transmission spectra simulations. We also demonstrate mode overlap and split performances upon altering the refractive index of the environment, where in previous work, similar effects have been realized via geometry engineering.59 This offers a practical approach to switching optical responses of photonic devices between different operative modes accurately and effectively, and has the potential to inspire future designs and applications



related to electromagnetic scattering from a fundamental level.

METHODS For the case of individual nanosphere, we utilize Matlab for generating all corresponding data based on the well-established analytical solutions to the scattering behaviors from one single spherical particle1 (See Section I in Supporting Information for details). For individual nanodisk, we employ a combined approach consisting of numerically solving the scattered field with the aid of COMSOL Multiphysics, followed up by applying multipole expansion in spherical coordinate to the existing field distributions (See Section II in Supporting Information for details). Finally, for metasurfaces, we use CST Microwave Studio for simulating the transmission spectra as well as producing other related results. Unit cell configuration is employed to mimic periodical boundary conditions.

RESULTS AND DISCUSSION Individual Nanosphere.

We start by investigating the scattering behaviors of an

individual nanosphere, where the exact analytical solutions could be readily achieved based on the basic Maxwell Equations, with well-established planar wave expansion method in spherical coordinates.1 Configuration of the parameters is shown in schematic view in Figure 1a, in which a planar wave is propagating in the z-direction, with electric field pointing towards the x-axis, in accordance with the convention. In order to ensure a consistent criterion for result comparison, and to simulate the performance of silicon nanoparticles in actual experiments, we consider an N  3.5 as the refractive index for dielectric scatterers without lossy part, and a target wavelength range from 1000 nm to 2000 nm, as a universal assumption throughout this paper. In the case of spherical particles, whose high geometrical symmetry eliminates all variables but the radius, the scattering spectra are calculated with the radius varying from 100 nm to 300 nm under vacuum conditions, i.e. N  1 for the surrounding environment, as shown in Figure 1b. The color indicates the scattering efficiency ( Qsca ), which is the scattering cross section normalized to  a 2 , a being the radius. The first three local maxima of Qsca , as marked by the dashed lines, stand for MD, ED, and MQ respectively. The ED shows relatively low intensity while the MQ shows relatively narrow linewidth in contrast to the other two modes. One thing


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noteworthy is that the resonance wavelengths of these three modes exhibit approximately linear relation with the sphere radius. This can be easily interpreted by referring to the estimation formula of the first resonance wavelength for spherical particles with relatively large refractive index,   2 N sph a , as deduced by assuming the denominator of the Mie scattering coefficient to approach zero.60 Higher order modes can be predicted in a similar fashion. Based on the analysis above, we select nanosphere radius as 220 nm to further explore its responses to the variation of the environment, due to the convenience that only the first three modes are located within the targeted wavelength range from 1000 nm to 2000 nm. In Figure 1c, color map is also utilized to better illustrate the results, and we extract the resonance positions in Figure 1c for a better close-up view, as shown in Figure 1d. The ED is omitted from discussion here due to its relatively low intensity. As a matter of fact, the local maximum attributed to ED totally disappears when N  1.2 , meaning that this mode is rather easily erased by decreasing the refractive index discrepancy between the nanosphere and the surrounding environment. For N  1.5 , the MD wavelength shows no obvious shift upon altering N while the MQ wavelength is significantly redshifted with the increase of N . This indicates that MQ is more sensitive to the environment than MD. When N  1.5 , the linewidth of MD exhibits substantial broadening, and the scattering strength of MQ surpasses that of MD, indicating that when compared to MD, the MQ displays better robustness to homogenization tendency between the nanosphere and the environment in terms of refractive index. Therefore, from a sensing point of view, MQ is more appropriate for the purpose of detecting small variation of refractive index change in the nanosphere scenario. Note that the scattering intensity employed here is essentially the superposition result of all separated modes. The term ‘MD’, ‘ED’, and ‘MQ’ indicate the modes which contribute the most to the scattering spectra at specific wavelengths. However, it would be premature to assume that the contributions from other modes are simply negligible. In fact, certain measures have been proposed in recent research to specifically address the means through which other modes could be suppressed while the mode of interest is manifested, resulting in, for example, ideal dipole scattering.12 The scattering spectra of nanosphere with higher refractive index upon changing the environment have also been calculated (see Figure S1 in Supporting Information). Note that the dynamic responses of ED could be readily traced under these scenarios, thanks to the relatively high contrast in refractive index.



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Field distributions are important features for characterizing scattering behaviors, as well as revealing the fundamental physical processes. In Figure 1e and 1f, we calculate the

E

absolute-square electric field

2

at the edge and center of the nanosphere with the

same parameters as adopted in Figure 1c.

E

2

is derived by averaging the electric field

over an imaginary spherical shells of constant radius, which can qualitatively characterize near-field distributions (see Section I in Supporting Information for details). The spectral positions of the two hotspots in Figure 1e almost coincide with MD and MQ in Figure 1c, which means that magnetic resonances can effectively attract electric field at the edge of sphere shell. Such two hotspots exhibit redshift behaviors when increasing N , and their magnitudes decline accordingly as a result of lowering refractive index contrast. Notably, the hotspot that coincides with MQ is provided with relatively narrow linewidth and can enhance electric field energy concentration more than tenfold at N =1 . Even at N =1.5 , the enhancement is still noticeable. This further highlights the potential of MQ for sensing, where small variation of index change outside the sphere edge can be detected by virtue of enhanced electric field that facilitates light-matter interaction. The hotspot in Figure 1f, corresponding to electric field at sphere center, experiences slight blueshift upon increasing N , accompanied by an expected depression in magnitude. The spectral position of the

hotspot deviates from ED, a mode often associated with the enhancement of electric field at the particle center. In fact, the ED shows relatively weak intensity, and is strongly affected by the spectrally adjacent MQ mode. Therefore, the electric field at the sphere center is actually shaped by the synergic interaction of multiple modes. In order to elucidate far-field scattering behaviors, we analyze Mie scattering intensities S1

2

2

and S 2 , which

are closely related to the  and  components of the scattered field, respectively (see Section I in Supporting Information for details). Figure 1g shows the plot for the far-field scattering pattern for MD with various values of N . The upper half represents S1 2

2

2

and

the lower half represents S 2 , with  varying from 0 to 180. Both S1 and S 2

2

monotonically decrease with the increase of N . As a result, the forward scattering becomes increasingly dominant over the backward scattering with larger values of N , due to the homogenization in terms of the refractive index, while the absolute scattering magnitude also plummets. Achieving high-level forward scattering magnitude while reducing the proportion of backward scattering requires the skillful balancing of the two opposing effects. Figure 1h plots the results for MQ with the same configuration as Figure


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1g. The S1 2

2

S1 and S 2

shows distinct character of lateral scattering at 90. Unlike the case of MD, 2

do not monotonically decrease when increasing N between 0-45, while

backward scattering almost vanishes at large values of N . For N =1.8 we witness nearperfect forward scattering with relatively high intensity as well as the total suppression of backward scattering. This makes MQ of dielectric nanosphere suitable for directional scattering by adjusting the refractive index of the surrounding medium. Individual Nanodisk.

Next, we consider the scenario of an individual nanodisk with a

refractive index of N dis  3.5 without lossy part, identical as in the case of nanosphere. The nanodisk shape is a superior layout in terms of better compatibility with micro/nanofabrication techniques like electron beam lithography, where precise geometry control could be more readily achieved compared to the nanosphere shape. The nanodisk radius r and nanodisk height h can be tuned synergistically to further amplify the resonant behaviors, or to produce sophisticated and well-tailored electromagnetic responses with greater flexibility. We hereby assume a plane wave excitation propagating along the direction perpendicular to the planar surface of the nanodisk, designated as the z-axis, while polarized along the x-axis in a Cartesian coordinate system, as shown in Figure 2a. In order to investigate the influences of geometrical parameters, we calculate the scattering performances of an individual nanodisk with r  200 nm surrounded by medium with refractive index N  1 . Color map is employed to indicate scattering efficiency Qsca with h varying from 300 nm to 600 nm, as displayed in Figure 2b. It is evident that aspect ratio

(AR), defined as h 2r , plays a crucial part in modelling mode evolutions. For large AR (large h ), three distinct scattering maxima dominate the interested wavelength range, and can be specified as MD, ED, and EQ (electric quadrupole mode), respectively, from regions of longer to shorter wavelength. The resonance wavelengths of all these three modes experience blueshift while decreasing AR. And the ED characters are more prone to be erased when decreasing h in this case. It is also revealed in Figure 2b that no apparent ED scattering maximum can be observed with h  450 nm . In fact, mode characters at smaller h cannot be simply determined based on total scattering efficiency. Mode overlapping along with other complex mode evolutions may arise as a result of altering geometrical parameters. Therefore emerges the necessity to employ the multipole expansion method in spherical coordinate, so that the contribution toward overall scattering



performance from each mode could be well elucidated61 (see Section II in Supporting Information for details). We study the impact of AR on mode properties by examining two scenarios with larger and smaller AR. This serves as a basic guidance for the better understanding of the relationship between surrounding medium and the scattering behaviors for nanodisks with different geometry. In Figure 2c we plot the result of multipole decompositions for a nanodisk with larger AR of r  200 nm and h  500 nm located in vacuum (i.e. N  1 ). ‘Total’ is calculated from integrating energy flux while ‘Multipole Sum’ is the summation of the first four modes --- ED, MD, EQ, and MQ. The two lines are well in line with each other, suggesting a very decent approximation as the contribution from higher-order modes are negligible. The three scattering peaks are identified as ED, MD and EQ from the decomposition results, with Qsca exceeding 14 at MD. It is worth noting that the contribution from MQ is so vanishingly small that it is effectively overwhelmed by the other modes. For comparison, we selected the geometry of r  300 nm and h  200 nm as our subject for analysis, representing nanodisks with

smaller AR. The result is shown in Figure 2d. Two scattering peaks and one scattering dip are observed, with the first peak at around 1540 nm identified as mainly ED contribution, while the second peak at around 1225 nm as a combined contribution from both ED and MD. For simplicity, we label these two modes as ED1 and ED2, resembling the hybrid MieFabry-Perot modes observed in elongated nanobars.37 The scattering dip can be ascribed to the anapole mode, which arises from the destructive interference between electric dipole and toroidal dipole decomposed in the Cartesian coordinate.62 Far-field scattering is possible to be strongly suppressed through carefully designing geometry by utilizing such anapole mode. Here in spherical coordinate expansion the scattering dip is directly caused by the local minimum of ED. Meanwhile, the contribution of MQ remains small in contrast to ED and MQ in the targeted wavelength range. The overall scattering behaviors of nanodisk with smaller AR is vastly different from that with larger AR. Then we investigate the influence of surrounding environment on the scattering performances of individual nanodisk based on preceding analysis. Results are displayed in Figure 3, with the same geometrical parameters as those in Figure 2c (larger AR). Local scattering peaks are highlighted with dash-dotted lines. Figure 3a and 3b plot the evolutions of total scattering efficiency and multipole summation results, respectively. The two plots are in good accordance throughout most parts, except for the region with relatively larger


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N and shorter wavelength, which are distinguished by rectangles with dashed borders.

Higher-order modes such as electric octupole mode (EO) and magnetic octupole mode (MO) must be introduced to account for the discrepancies in this region. The MD is not sensitive to the environment as the resonance wavelength barely moves when altering N . The spectral position shifts for only about 10 nm from N =1 to N =1.7 , above which the scattering peak of MD could not be detected. For ED, the scattering peak persists throughout increasing N and the resonance wavelength blueshifts about 50 nm from N =1 to N =2 . The EQ shows the greatest sensitivity, however, its scattering peak is

totally wiped out when N  1.3 due to its weak intensity. We note here that the mode evolutions regarding total scattering efficiency is a superposition result of all contributing modes. Therefore it is necessary to evaluate how each decomposed mode develops when changing the surrounding medium. The results are displayed in Figure 3c-3f. The MQ is so weak that we can omit the discussion. We label each scattering peak in decomposed modes with an extra prime to discriminate from those in total scattering data. It is clear that MD’ resonance wavelength shifts for less than 20 nm throughout increasing N , which matches the phenomenon observed in Figure 2a and 2b for MD. The spectral position of ED’ also barely moves as seen in Figure 2d. Thus, the resonance shift of ED can be mainly attributed to the varying rate at which different modes are attenuated with the increase of N , or in simple terms, a synergistic process. The EQ’ is sensitive to the environment as

the resonance wavelength redshifts for more than 200 nm from N =1 to N =2 . However, its relatively weak intensity still counts toward a disadvantage, making it vulnerable for detecting drastic change of surrounding medium. We also plot the near-field and far-field scattering patterns of each decomposed mode at different N values, manifesting the evolutions of electric and magnetic fields (see Figure S2 and Figure S3 in Supporting Information). In Figure 4 we illustrate the results of the nanodisk with identical geometrical parameters to that in Figure 2d (with smaller AR). Refer to Figure 3 for tabs and annotations. Here we omit the discussion on MQ and EQ due to their vanishingly weak intensities in the wavelength range of interest. In Figure 4a and 4b, ED1 and ED2 correspond to the local scattering peaks while anapole mode corresponds to the scattering dip. We employ the term ‘anapole mode’ for designating the local minimum here, although this mode can only emerge from multipole expansion in the Cartesian coordinate. It is nothing beyond



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expectations to see that Figure 4a and 4b match well with each other, therefore voiding the necessity to address the participation of higher-order modes without compromising on accuracy. ED1 and anapole mode experience redshifts while increasing N . However, the accurate pinpointing of the scattering peak may be severely hindered by the linewidth broadening of ED1. As a matter of fact, ED1 local maximum is totally wiped out when N  1.6 . Meanwhile, anapole mode with its character of the local minimum persists even

at N  1.9 . As for ED2 mode, the line quickly flattens after N  1.2 , suggesting its vulnerability to the refractive index variation of the surrounding medium. Figure 4c and 4d further illustrate the mode evolutions of decomposed modes. ED1’ redshifts when increasing N , displaying the same tendency as ED1, confirming its major contribution to the total scattering efficiency. The spectral position of the anapole’ mode remains stable with respect to the increase of N . This intriguing character may prompt further search for the dark scattering state insensitive to the environment. The local maximum of MD’ barely moves when N  1.4 and almost coincides with the scattering minimum of ED’, which is the anapole’ mode, making its characters covered by other scattering behaviors. We also plot the near-field and far-field scattering patterns of each decomposed mode at different N values, manifesting the evolutions of electric and magnetic fields (see Figure S4 and

Figure S5 in Supporting Information). Two-dimensional Nanodisk Array (Metasurfaces).

After analyzing individual

nanoparticles, it is time to shed light on the problem about how surrounding environment affects the electromagnetic responses of a cluster of dielectric particles or particle arrays. Thanks to the mutual interaction or coupling among adjacent particles, as well as the lattice resonances for regular arrays, a cornucopia of optical phenomena can be achieved and manipulated compared to the case of individual particle. Here we consider the twodimensional nanodisk array, or the metasurfaces, as schematically shown in Figure 5a. Each nanodisk is assigned with refractive index N dis  3.5 free of lossy part. Lattice constant d along x- and y-axis remains equal, and a y-polarized plane wave propagating along z-axis excites the optical responses of the metasurfaces. We first investigate the influence of geometrical parameters on spectral mode evolution by fixing the lattice constant d as 700 nm and the nanodisk radius r as 200 nm, and continuously varying the nanodisk height h from 200 nm to 600 nm. Vacuum ( N  1 ) is assumed as the


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surrounding medium. Transmission result is displayed in Figure 5b, in which the transmission dips are marked with dash-dotted lines. For metasurfaces, only the first two lowest order modes --- MD and ED are considered for the sake of simplicity. It is observed that mode overlap and split occur when altering the nanodisk height. At h  200 nm , MD and ED overlap and only a single transmission dip is perceived. Then MD and ED are separated by increasing h and the spectral positions of both modes move toward longer wavelength. For h around 400 nm we witness the largest gap between the two resonance wavelengths. When h is increased up to 500 nm ~ 520 nm, the MD and ED merge to form a continuous band with zero transmission. Considering the lossless feature of the system, this region can be utilized to realize perfect reflection. Finally, MD and ED overlap again and gradually merge into one single transmission dip. Altering the nanodisk height opens up the possibility toward the dynamic tuning of such metasurfaces, paving the way for in-depth study into the influence of surrounding environment. We then turn our attention toward how the optical responses of the metasurfaces can be tuned by the change in the refractive index of the surrounding medium. The discussion will be based on a metasurface of an array of nanodisks with r  200 nm , d  700 nm and h  400 nm , around which the resonance wavelength difference between MD and ED

maximized with N  1 . Transmission spectra for different values of N is shown in Figure 6a with each curve vertically displaced by T  1 relative to adjacent curves. Shaded region indicates where diffraction takes place (   N *d ). In Figure 6b we plot the relation between the resonance wavelength and N retrieved from Figure 6a. With the increase of N , the transmission dip of MD first blueshifts slightly and then eventually redshifts, while the transmission dip of ED redshifts throughout the change. The gap between the two dips gradually shrinks, and finally at N  2 , the two modes overlap each other. The ED shows greater sensitivity to the environment than MD, especially at larger values of N . Such mode overlap behavior has been demonstrated previously by tuning geometrical parameters of lattice constant and nanodisk radius,59 and we hereby achieve an alternative approach by altering the dielectric environment in which the metasurfaces are embedded. To further analyze mode properties, we calculate the transmittance-phase and plot the field profiles for each interested mode. Figure 6c depicts the transmittancephase for MD and ED when N  1 where the two modes are totally separated. The transmission spectrum is plotted for reference. It is clear that both modes experience abrupt



phase change of π at resonance, exhibiting distinctive separated responses. Magnetic field is concentrated inside the nanodisk with magnetic field vectors in the xy-plane aligning nearly along the x-axis for MD (Figure 6e), and electric field is concentrated inside the nanodisk with electric field vectors in the xy-plane aligning near along the y-axis for ED (Figure 6f). These are common and typical characters observed in the separated MD and ED. Figure 6d illustrates the transmittance-phase for the overlapped mode when N  2 . And an abrupt phase change of 2π is observed, which can be viewed as a

superposition of the phase responses of separated MD and ED. Figure 6g and 6h plot the field profile for the overlapped mode. The magnetic field hotspot and the electric field hotspot are elongated along the x-axis and y-axis, respectively, in comparison to the field profiles for separated MD and ED. Field vectors are more complicated since the amplitude of the out-of-plane vectors far outweighs that of the in-plane vectors. Another set of parameters investigated is r  200 nm , d  700 nm and h  200 nm , the results of which is shown in Figure 7. From the transmission spectra in Figure 7a, we observe one single transmission dip that can be attributed to mode overlap at smaller values of N . The resonance wavelength of the overlapped mode redshifts from N  1 to

N =1.4 (Figure 7b), while the magnitude of the transmission dip gradually decreases. At N =1.4 the metasurfaces exhibit near-perfect transmission over the entire wavelength range, similar to the Huygens’ surfaces that enable high efficiency forward scattering,54 where both the mode overlap and refractive index match are necessary. When N is further increased to 1.6, the overlapped mode splits into two separated modes. Both modes redshift with the increase of N , with ED being more sensitive to the environment. However, unlike the previous case in Figure 6 where the resonance wavelength of MD exceeds that of ED, here the first resonance is identified as ED. This reminds us of the former case of an individual nanodisk, where the first resonance is identified as MD for larger AR and ED for smaller AR. Therefore these two results confirm each other without contradictory. We also calculate the transmittance-phase spectrum for the overlapped mode at N  1 and separated modes at N  1.7 in Figure 7c and 7d. These results also conform to the data in our previous case that single separated mode experience abrupt phase change of π while overlapped mode experience abrupt phase change of 2π . Field profiles for the overlapped mode are plotted in Figure 7e and 7f while the separated ED and MD are plotted in Figure 7g and 7h, respectively. These results also agree with the


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corresponding data in Figure 6. We envision that tuning the dielectric environment in which the dielectric metasurfaces are embedded serves as an efficient and dependable method for manipulating the electromagnetic responses and light-matter interactions. Mode overlap and split behaviors demonstrated above via altering the refractive index of the surrounding medium may find applications in dynamically controlling beam-steering and beam-shaping. Furthermore, tuning the dielectric properties of the surrounding environment can produce a significant impact on the amplitude of transmission or reflection. This may facilitate researches toward facile and sensitive optical switching devices that could enable high-speed switching between various states including but not limited to total transmission, total reflection and perfect absorption.

CONCLUSIONS We have studied the influence of the surrounding environment on the scattering behaviors and optical responses of dielectric nanoparticles with high refractive index by means of theoretical calculations and numerical simulations. Three typical scenarios: individual nanosphere, individual nanodisk and two-dimensional nanodisk arrays (metasurfaces) have been chosen as our subject of investigation, illustrating the dynamic evolutions of resonant modes and field profiles upon altering the refractive index of the surrounding medium. We have identified MQ as a highly potent candidate for sensing the change in refractive index of the environment in the case of individual nanosphere. In addition, near-perfect forward scattering can be achieved at MQ by tuning the dielectric properties of the environment. For individual nanodisk, we have discovered that the spectral positions of certain decomposed modes remain approximately invariant to the change in refractive index of the environment , which, despite being inapplicable for sensing purposes, offers a potentially viable baseline, whereas other modes can indeed become sensitive to such changes, depending on geometrical size or aspect ratio. The metasurfaces case witnesses mode overlap and split upon altering the embedded medium, which opens up the opportunity for dynamically tuning the spectral responses and scattering properties of metasurfaces with agility. This work may offer fundamental directions for architecting sensing and optical switching devices composed of high refractive index dielectric nanoparticles.



ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Analytical solutions for generating data in the case of individual nanosphere; details of multipole expansion in spherical coordinate for individual nanodisk; additional figures related to the scattering behaviors of nanospheres with other refractive index values, evolutions of near-field distributions and far-field scattering patterns for individual nanodisk (Figures S1-S5) (PDF)

AUTHOR INFORMATION Corresponding Author *Email: [email protected] ORCID Guanqiao Zhang: 0000-0001-9274-9358 Rui Gao: 0000-0002-7619-2382 Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the Basic Science Center Project of NSFC under Grant No. 51788104, as well as National Natural Science Foundation of China under Grant Nos. 51532004 and 11704216.


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Figures

Figure 1. Scattering behaviors of an individual nanosphere. (a) Schematic view of the basic configuration. The refractive index of the nanosphere is set as N sph  3.5 without lossy part. (b) Color map of the scattering efficiency

Qsca with nanosphere radius ranging from 100 nm to 300 nm. The

refractive index of the surrounding medium is set as N  1 . Dashed lines indicate the first three resonant modes. The spectral positions of these modes exhibit approximately linear relation with the sphere radius. (c) Color map of the scattering efficiency

Qsca as a function of the refractive index N in surrounding

medium, with a nanosphere radius of 220 nm. (d) Resonance wavelengths of MD and MQ retrieved from (c). MQ is more sensitive to the environment when N  1.5 . (e)&(f) Absolute-square electric field

E

2

at the edge and the center of the nanosphere as a function of N , with the same parameters in

(c) (see main text for details). These serve as a qualitative means of characterization for the near-fields. (g)&(h) Far-field scattering performances for MD and MQ of the nanosphere with the same parameters in (c). The upper half in each panel represents S1

2

while the lower half represents S 2

text for details).


2

(see main

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Figure 2. Scattering behaviors of an individual nanodisk. (a) Schematic view of the basic configuration. The refractive index of the nanodisk is set as scattering efficiency

N dis  3.5 without lossy part. (b) Color map of the total

Qsca of an individual nanodisk with r  200 nm as a function of wavelength

and nanodisk height h . The refractive index of the surrounding medium is set as N  1 . Three scattering peaks at larger h are marked with arrows. (c)&(d) Multipole expansion results in spherical coordinate for the nanodisk with larger AR of r  200 nm and h  500 nm (c) and smaller AR of r  300 nm and h  200 nm (d).



Figure 3. The influence of the surrounding medium on the scattering behaviors of an individual nanodisk with r  200 nm and h  500 nm . Dash-dotted lines indicate the evolutions of the scattering peaks. (a)&(b)

Qsca as a function of wavelength and N for (a) total scattering efficiency and (b)

multipole summation results. The two figures are in good agreement except for the region enclosed by dashed borders where higher-order multipoles should be taken into consideration to account for the discrepancy. (c)-(f)

Qsca evolutions of the decomposed modes. An extra prime is added to the name of

each scattering maximum to distinguish from those in (a) and (b). MQ is excluded from discussion due to its weak intensity.


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Figure 4. The influence of the surrounding medium on the scattering behaviors of an individual nanodisk with r  300 nm and h  200 nm . Dash-dotted lines indicate the evolutions of the scattering peaks or the scattering dip. (a)&(b)

Qsca as a function of wavelength and N for (a) total scattering

efficiency and (b) multipole summation results. The two figures match well, suggesting negligible contributions from higher-order multipoles. (c)&(d)

Qsca evolutions of the decomposed modes. An

extra prime is added to the name of each scattering maximum or scattering minimum to distinguish from those in (a) and (b). MQ and EQ is excluded from discussion due to their weak intensities.



Figure 5. (a) Schematic view of the basic configuration for the two-dimensional nanodisk array (metasurfaces). The refractive index of each nanodisk is

N dis  3.5 without lossy part. (b)

Transmission spectrum as a function of wavelength and the nanodisk height h . The refractive index of the surrounding medium is set as N  1 with lattice distance d  700 nm and nanodisk radius r  200 nm . Transmission dips are marked with dash-dotted lines.


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Figure 6. Influence of the surrounding environment on the optical responses of the metasurfaces with parameters of

r  200 nm , d  700 nm and h  400 nm . (a) Transmission spectra at

different values of N . Each curve is vertically displaced by T  1 relative to adjacent curves. Shaded region indicates where diffraction takes place. (b) The resonance wavelengths of MD and ED retrieved from (a). (c) Transmittance-phase spectrum at N  1 where MD and ED are totally separated. (d) Transmittance-phase spectrum at N  2 where mode overlap occurs. Transmission spectra are also plotted in (c) and (d) for reference. (e)&(f) Field profiles for the separated MD (e) and ED (f) at N  1 . Arrows indicate the in-plane vectors of the field corresponding to the color bar. (g)&(h) Field profiles for the overlapped mode at N  2 . Vector plots are omitted since the amplitude of the out-of-plane vectors far exceeds that of the in-plane vectors.



Figure 7. Influence of the surrounding environment on the optical responses of the metasurfaces with parameters of

r  200 nm , d  700 nm and h  200 nm . (a) Transmission spectra at

different values of N . Each curve is vertically displaced by T  1 relative to adjacent curves. Shaded region indicates where diffraction takes place. (b) The resonance wavelength of the overlapped mode, MD and ED retrieved from (a). (c) Transmittance-phase spectrum at N  1 where MD and ED are overlapped. (d) Transmittance-phase spectrum at N  1.7 where MD and ED are totally separated. (e)&(f) Field profiles for the overlapped mode at N  1 . (g)&(h) Field profiles for the separated ED (g) and MD (h) at N  1.7 . Arrows indicate the in-plane vectors of the field corresponding to the color bar.


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Dielectric Environment Manipulation toward ... - ACS Publications

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