WO2016154657A1

WO2016154657A1 - Optical nanoantennas

Info

Publication number: WO2016154657A1
Application number: PCT/AU2015/050140
Authority: WO
Inventors: Debabrata SIKDAR; Malin PREMARATNE; Wenlong Cheng
Original assignee: Monash University
Priority date: 2015-03-31
Filing date: 2015-03-31
Publication date: 2016-10-06

Abstract

Optical nanoantennas (100, 800, 1100) are configured to exhibit highly-directional scattering of light, and comprise one or more cubic dielectric nanoparticles (100). The cubic dielectric nanoparticles may be defined by a characteristic dimension (102), such as an edge length, along with a permittivity of the material from which they are composed. These characteristics may be selected such that constructive interference of electric and magnetic resonances results in enhanced scattering in one direction of light comprising at least one predetermined wavelength. An optical nanoantenna (1100) may be coupled to a light emitter (1302) in order to form a directional light source (1300). Such sources may have many applications in sensing, medical diagnosis and treatment, micro-mechanical devices, optical data storage, and on-chip interconnects.

Description

OPTICAL NANOANTENNAS

FIELD OF THE INVENTION

[0001 ] The present invention relates to optical nanostructures, and particularly to nanoparticle structures that exhibit strong directional scattering capabilities, also known as nanoantennas.

BACKGROUND TO THE INVENTION

[0002] The ability to precisely control and engineer the scattering of electromagnetic waves by sub-wavelength nanostructures is of great utility in the emerging field of nanophotonics. For example, metallic nanoparticles have shown great promise in capturing, focusing and manipulating light at nanoscale dimensions by virtue of their surface plasmon resonances.

[0003] The development of such nanostructures paves the way for

miniaturisation of plasmonic devices and nanophotonic circuits by enabling the manipulation of light on scales below the traditional diffraction limit. For example, many novel light scattering phenomena at nanoscale, such as super-scattering, cloaking, and enhanced directional scattering, can now be realised. Many applications for these phenomena are emerging, including in biomedical therapeutics and imaging.

[0004] To date, the most interesting properties of sub-wavelength

nanostructures have been observed using particles possessing both electrical and magnetic resonances. In such particles the optical scattering pattern can exhibit superior directionality, which contrasts with conventional scattering that is symmetrical in forward and backward directions. Superior directionality is achieved as a result of constructive interference of resonances enhancing scattering in one direction, along with destructive interference minimising the scattered intensity in the opposite direction. [0005] However, to date no natural optical materials are known that exhibit strong magnetic resonances within the visible and infrared ranges. These wavelengths are, of course, of great interest in many practical applications. As a result, various optically driven resonating meta-materials, usually based on metallic nanostructures, have been engineered to exhibit artificial magnetism along with their intrinsic electrical response in order to obtain unidirectional scattering patterns. However, the intrinsic metallic losses in these plasmonic nanostructures in the visible and near-infrared regions strongly dilute the response, and limit performances at nanoscale.

[0006] It has been found that large permittivity dielectric nanoparticles may also support electric and optically induced magnetic resonances, while being lossless. The unusual radiation patterns resulting from cancellation of scattering in either the forward or backward direction in such dielectric nanoparticles were first theoretically predicted by Kerker ef a/ for magneto dielectric nanospheres in the small particle limit. (M Kerker, DS Wang and CL Giles, 'Electromagnetic scattering by magnetic spheres,' Journal Optical Society of America, Volume 73, pages 765 to 767, 1983). However, the nanoparticles considered to date mostly operate away from the visible and infrared ranges. More recent theoretical investigations suggest that spherical silicon or germanium nanoparticles may exhibit strong magnetic responses in the visible or infrared range, thus potentially achieving directional scattering patterns in the spectral ranges of interest (see, e.g., R Gomez-Medina et al 'Electric and magnetic di-polar response of germanium nanospheres: Interference effect, scattering and isotropy, and optical forces,' Journal of Nanophotonics, Volume 5, 053512, 201 1 ).

[0007] The first directional light-scattering patterns resembling Kerker's-type scattering in the visible and infrared range from single nanoparticles have been experimentally observed using silicon nanospheres (YH Fu et al, 'Directional visible light scattering by silicon nanoparticles,' Nature Communications, Volume 4, page 1527, 2013) and in gallium arsenide nanopillars (S Person et al,

'Demonstration of zero optical backscattering from single nanoparticles,' Nano Letters, Volume 13, pages 1806 to 1809, 2013). [0008] In other work, a core (metal)-shell (dielectric) nanosphere has been engineered to possess spectrally overlapping electric and magnetic dipole resonances of equal strength, and azimuthally symmetric, unidirectional, enhanced forward scattering with completely suppressed backward scattering has been theoretically reported (W Liu et al, 'Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,' ACS Nano, Volume 6, pages 5489 to 5497, 2012). It was also shown that directionality may be improved by using a chain, or even by a random ensemble, of such core-shell nanoparticles.

[0009] However, fabrication of spherical core-shell nanoparticles with sufficient accuracy remains challenging. Furthermore, due to the presence of metallic components, intrinsic material losses in these core-shell nanoparticles cause heating, severely limiting their nanoscale applications.

[0010] Accordingly, there remains an ongoing need for the development of new nanostructures for use in sub-wavelength optical processing which combine a number of the most desirable characteristics, such as low-loss, strong directionality, the ability to operate at wavelengths (e.g. within the infrared and visible spectra) of particular interest in common applications, relative ease of fabrication, and the ability to function effectively when fabricated from materials having low to moderate permittivity. The present invention seeks to address this need.

SUMMARY OF THE INVENTION

[001 1 ] In one aspect, the present invention provides an optical nanoantenna configured to exhibit highly-directional scattering of light, which comprises a cubic dielectric nanoparticle.

[0012] According to embodiments of the invention, simple lossless dielectric nanocubes may be employed to overcome a number of limitations of prior nanostructures, and to address the need for advantageous new types of nanostructures, as identified above.

[0013] According to embodiments of the invention, the cubic dielectric nanoparticle has a characteristic dimension and permittivity selected to achieve the highly-directional scattering of light comprising at least one predetermined wavelength.

[0014] Advantageously, through appropriate engineering of the dimensions of the cubic nanoparticles, and relative permittivity of the materials from which they are composed, operation of the optical nanoantenna may be achieved within the wavelength ranges of particular interest, including infrared and visible ranges.

[0015] According to such embodiments, the cubic dielectric nanoparticle has a characteristic dimension and permittivity selected such that constructive interference of resonances results in enhanced scattering in one direction of light comprising at least one predetermined wavelength.

[0016] According to some embodiments of the invention, the relative permittivity of the material from which the cubic dielectric nanoparticle is composed is less than 50. Advantageously, the relative permittivity may be less than 30. Furthermore, in advantageous embodiments of the invention, the relative permittivity is greater than 5.

[0017] Further, according to embodiments of the invention, the characteristic dimension of the cubic dielectric nanoparticle is less than the predetermined wavelength. In particular, the characteristic dimension may be less than 400 nm, such as being between 100 nm and 300 nm, such as, for example, 200 nm.

[0018] The resonances of the cubic dielectric nanoparticle may comprise magnetic and electric resonances of dipolar modes, and at least one high-order mode. In some embodiments, the resonances principally comprise magnetic and electric dipolar and quadrupolar modes.

[0019] In some arrangements embodying the invention, the optical

nanoantenna comprises two or more dielectric nanoparticles arranged in a linear array which is characterised by an interparticle distance. The linear array may be configured to exhibit the highly-directional scattering of light comprising at least one predetermined wavelength λ.

[0020] In some embodiments the interparticle distance is greater than λ/2 and less than 3λ/2. In particular, the interparticle distance may be greater than λ/2 and less than λ, or greater than λ and less than 3λ/2.

[0021 ] In another aspect, the invention provides a directional light source comprising a light emitter coupled to an optical nanoantenna configured to exhibit highly-directional scattering of light, and which comprises a cubic dielectric nanoparticle. The optical nanoantenna of the directional light source may comprise two or more dielectric nanoparticles arranged in a linear array characterised by an interparticle distance.

[0022] Further features, properties, advantages, benefits and applications of the invention will be apparent from the following description of particular embodiments. It will be appreciated, however, that this description is provided by way of example only, in order to communicate the principles of the invention, and exemplary methods for putting the invention into effect. The detailed description should not, however, be regarded as limiting of the scope of the invention, as defined by the preceding statements, or by the claims appended hereto. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Embodiments of the invention will now be described with reference to the accompanying drawings, in which:

Figure 1 is a schematic diagram of a dielectric nanocube embodying the invention;

Figures 2(a) and (b) are graphs illustrating scattering cross-sections of dielectric nanocubes embodying the invention;

Figure 3 is a graph illustrating a multi-polar decomposition of the scattering profile of a nanocube embodying the invention;

Figure 4 is a graph illustrating wavelength dependence of real and imaginary components of electric and magnetic polarisabilities of a dielectric nanocube embodying the invention;

Figures 5(a) and (b) are far-field scattering patterns corresponding with the dielectric nanocube represented in Figure 4;

Figure 6 is a graph showing multi-polar decomposition of the scattering profile of a low permittivity nanocube embodying the invention;

Figures 7(a) to (c) show far-field scattering patterns corresponding with the dielectric nanocube represented in Figure 6;

Figure 8 is an schematic illustration of an optical nanoantenna comprising two dielectric nanocubes embodying the invention;

Figures 9(a) to (c) show far-field scattering patterns corresponding with an optical nanoantenna according to the embodiment of Figure 8;

Figure 1 0(a) and (b) show graphs of main-lobe angular width and side lobe level as a function of interparticle distance for a two-particle optical nanoantenna;

Figure 1 1 is a schematic illustration of an optical nanoantenna comprising a plurality of dielectric nanocubes embodying the invention;

Figures 12(a) to (c) show graphs of main-lobe angular width, main-lobe magnitude and maximum side lobe level for an optical nanoantenna according to the embodiment of Figure 1 1 , as a function of the number of nanocubes; and

Figure 1 3 is a schematic illustration of a directed light source embodying the invention. DETAILED DESCRIPTION OF EMBODIMENTS

[0024] Figure 1 shows a schematic diagram of a dielectric nanocube 100 embodying the invention. The nanocube 100 has a characteristic dimension W (102). The characteristic dimension W may be understood as the length of each edge of the nanocube 100. In practice, optical nanoantennas comprising nanocubes embodying the invention may include nanoparticles that are not perfectly cubic. Accordingly, the terms 'cube', 'cubic', 'nanocube' and 'cubic nanoparticle', when used in this specification, should be understood as referring to particles that are substantially cubic in form, to within normal fabrication tolerances and to the extent required in order to achieve the functionality of the corresponding optical nanoantennas.

[0025] The use of pure dielectric nanocubes provides a number of advantages over the prior art, e.g. metal composite core-shell nanospheres, including:

• no heating at nanoscale due to lossless nature of dielectric materials;

• larger packing density in nanoscale devices; and

• ease of fabrication.

[0026] Furthermore, it is also known that a cubic nanoparticle has larger optical coefficients when compared to a spherical nanoparticle of comparable volume and/or linear dimension.

[0027] In general, the dielectric nanocube 100 has both a characteristic dimension 102, and a permittivity associated with the material from which it is fabricated. The permittivity is represented by relative permittivity ε_Γ, which is a property of the material itself, and of photon energy (i.e. frequency or wavelength of incident light). In Figure 1 , an incident plane wave 104 is represented by its corresponding electric, magnetic and propagation vectors. [0028] Extensive numerical simulations have been conducted, resulting in the identification of an approximate lower bound on the relative permittivity and on the characteristic dimensions of nanocubes advantageously embodying the invention. In particular, simulations have identified that the scattering cross-section spectrum of a nanocube with dimension W=200 nm and ε_Γ = 5 features spectrally overlapping electric and magnetic quadrupolar resonances at around 385 nm, approximately on the edge of the visible spectrum.

[0029] Nanocubes with lower permittivity (i.e. ε_Γ<5) will have quadrupolar resonances at higher frequencies, outside the spectral range of primary interest. Increasing the characteristic dimension may enable the scattering spectrum to be shifted towards lower energy for nanocubes having ε_Γ<5, however it has also been found that the scattering peaks become weaker with lowering of the material permittivity. Accordingly, in the exemplary embodiments here-described the characteristic dimension has been set to a value of W=200 nm, and analysis has been conducted for materials having ε_Γ > 5.

[0030] Silicon provides one suitable material from which nanocubes

embodying the invention may be fabricated. Close to the visible light range around 400 nm, silicon has ε_Γ approximately equal to 30. Silicon fabrication technologies are also mature, enabling simple and cost-effective fabrication of silicon nanocubes.

[0031 ] Figure 2(a) shows a graph illustrating scattering cross-sections of silicon nanoparticles, including silicon nanocubes embodying the invention. The graph 200 shows wavelength on the horizontal axis 202, and scattering

cross-section on the vertical axis 204. Three curves are shown on the graph 200.

[0032] A first curve 206 shows the scattering cross-section of a silicon nanocube embodying the invention, and having a characteristic dimension

W=200 nm. This is compared with the corresponding scattering cross-section cross-section 210 of a silicon nanosphere having an equivalent linear dimension, i.e. diameter of 200 nm. The results shown in the graph 200 clearly illustrate that a nanoantenna comprising a cubic silicon nanoparticle can achieve higher scattering cross-sections when compared to equal volume and equal dimensional nanospheres.

[0033] Figure 2(b) shows a graph 220 illustrating scattering cross-sections for silicon nanocubes embodying the invention and having a number of different values of relative permittivity of the constituent material. The horizontal axis 222 shows wavelength, while the vertical axis 224 shows the scattering cross-section in arbitrary units. Rather then being plotted on a common vertical axis, the spectra 226, spanning relative permittivity from 5 to 30, have been vertically offset for easier comparison.

[0034] The scattering spectra in the graph 220 incorporate energies up to that of the electric quadrupole. In the case of nanocubes with relatively large permittivity (e.g. ε_Γ=12.5 and above), there are four distinct resonance peaks in each scattering spectrum. All of these peaks exhibit a common trend of blueshift in wavelength with decreasing permittivity, resulting in spectral overlap (or merging) of the first two low-energy peaks and also for the next two higher-energy peaks at relatively smaller permittivities of ε_Γ=7.5 and ε_Γ=5.

[0035] While the graph 220 shows scattering cross-sections for different materials having a fixed characteristic dimension of the nanocube, it is anticipated that increasing the size of the nanocube will result in a redshift in the scattering spectrum. However, the general trend (i.e. blueshift in wavelength with

decreasing permittivity) for any fixed characteristic dimension of the nanocube will remain the same.

[0036] Figure 3 shows a graph 300 illustrating a multi-polar decomposition of the scattering profile of a nanocube with characteristic dimension W=200 nm and ε_Γ=20 along with the corresponding total cross-section. The horizontal axis 302 shows wavelength, while the vertical axis 304 shows the scattering cross-section. In order to obtain theoretical scattering cross-sections, the total electric field E and the corresponding polarisation vector P can be obtained from FEM

simulations using COMSOL Multiphysics, or may be computed using other known numerical multipole techniques. The multipolar decomposition enables the total scattering cross-section 306 to be broken down into contributions from different multipoles, i.e. magnetic dipole (MD) 308, electric dipole (ED) 31 0, magnetic quadrupole (MQ) 31 2 and electric quadrupole (EQ) 314. Each of these has a corresponding peak wavelength AMD, AED, AMQ, AEQ.

[0037] Through numerical (FEM) simulations, it has been found that nanocubes with relatively large permittivity, for which the resonant peaks of each multipole are spectrally well separated (see graph 220), the far-field scattering patterns of these modes tend to become symmetrically aligned along both forward and backward directions in the manner of pure dipole/quadrupoles. As a result, there is a reduction in interference, and a diminishing unidirectionality in scattering. Therefore, in order to obtain strongly unidirectional scattering patterns, it may be preferred to employ materials with relatively small permittivity which feature resonant peaks originating from spectrally overlapping and interfering dipolar/quadrupolar resonances.

[0038] In particular, when interfering electric and magnetic dipoles satisfy the generalised Kerker's (GK) conditions, strongly unidirectional scattering by the nanoparticle can be observed. The GK conditions are given by the following relation:

[0039] Here, a_e is the electric polarisability of the material, a_m is the magnetic polarisability, and s_s and μ₃ are the relative permittivity and permeability of the surrounding medium. [0040] The above relation is, in general, satisfied by two GK conditions, as follows:

[0041 ] The first GK condition corresponds with unidirectional forward scattering, in which the backward scattering is completely suppressed. The second GK condition provides strongly directional backward scattering, with a corresponding minimum residual forward-scattering intensity.

[0042] Based on the above relations, and simulations of the response of a nanocube having W=200 nm and ε_Γ= 20 (see Figure 3), it is possible to determine the wavelengths at which each of the first and second GK conditions are satisfied. Figure 4 is a graph 400 illustrating wavelength dependence of real and imaginary components of the electric and magnetic dipolar polarisabilities, in which wavelength is shown on the horizontal axis 402, and the polarisability on the vertical axis 404. The four curves show, respectively, the real part 406 of the magnetic polarisability, the imaginary part 408 of the magnetic polarisability, the real part 410 of the electric polarisability, and the imaginary part 412 of the electric polarisability. The desired wavelengths, satisfying the first and second GK conditions, are those at which the imaginary parts of the electric and magnetic polarisabilities are equal. As indicated by the markers 414, 416, these occur for unidirectional forward scattering at 1 195 nm (λ₀) and predominantly backward scattering at 1025 nm (λ-ι). At these wavelengths, the scattering cross-sections of electric and magnetic dipolar modes are also equal, as indicated by points 316, 318 in the graph 300 of Figure 3.

[0043] Figure 5(a) and Figure 5(b) show far-field scattering patterns

corresponding with unidirectional forward scattering (λ₀) and dominantly backward scattering (λ-ι) respectively. These scattering patterns have been obtained based upon three-dimensional FEM simulations at λ₀ and λ-ι , the results of which have been 'sliced' through the y-z and x-z planes in order to assess the azimuthal symmetry of the scattering patterns. Additional simulations were also performed, as a check, using filtered coupled dipole approximations (FCDA), which produced substantially identical results.

[0044] The chart 500 shows the forward-scattering pattern 502, in which it can be seen that backward scattering has been completely suppressed. Furthermore, symmetric scattering is observed along the two orthogonal scattering planes, such that the corresponding scattering patterns are indistinguishable from one another. By comparison, the chart 504 shows the backward-scattering pattern at λ-ι , in which a slight asymmetry is observable between the two orthogonal scattering planes in the corresponding patterns 506, 508. Additionally, the backward-scattering patterns 506, 508 show a residual forward scattering, as predicted. Nonetheless, it can be noted that the relatively large permittivity nanocube can exhibit the unidirectional scattering properties of both a Huygens' source and Huygens' reflector.

[0045] By comparing the scattering patterns in Figures 5(a) and 5(b) it can be said that although in the case of backward scattering the magnitude of the main scattering lobe is about 1 .6 times larger, forward scattering offers better directionality, superior azimuthal symmetry, and complete suppression of scattering in other directions, thus minimising energy leakage.

[0046] In view of the foregoing results, further analysis of embodiments of the invention focuses on unidirectional forward scattering, in view of its vast practical applications and superior characteristics. An objective of this further analysis is to identify design strategies to improve directionality and/or scattering magnitude. As has been noted, nanocubes embodying the invention and having relatively small permittivity are expected to exhibit enhanced directionality due to the merging of resonant peaks, originating from spectrally overlapping

dipolar/quadrupolar resonances. [0047] Figure 6 is a graph showing a multipolar decomposition of the scattering profile of a relatively low permittivity (ε_Γ=5) nanocube having

characteristic dimension W=200 nm. The horizontal axis 602 shows wavelength, while the vertical axis 604 shows the scattering cross-section. The five curves shown in the graph 600 represent the total scattering cross-section 606, MD cross-section 608, ED cross-section 610, MQ cross section 612, and EQ cross- section 614. In this embodiment, it is possible to obtain forward-scattering patterns at multiple wavelengths within the spectral range of interest, which is not possible with a larger permittivity nanocube. These wavelengths are λ₀ (616), at which the first GK condition is satisfied, λ (618), resulting from the overlap of electric and magnetic dipolar resonances, and λ₂ (620), resulting from the spectral overlap of electric and magnetic quadrupolar resonances.

[0048] Figure 7 shows far-field scattering patterns corresponding with the dielectric nanocube having the characteristics shown in Figure 6. Again, all results have been obtained using FEM simulations at the respective wavelengths. In each case, scattering patterns in two orthogonal planes are plotted, and are specifically identified where distinguishable (i.e. where a sufficient asymmetry is present).

[0049] The chart 700 shows scattering cross-sections 702, 704 at wavelength λ₀, in which electric and magnetic dipoles with equal scattering cross-sections interfere and backward scattering is completely suppressed. However, azimuthal symmetry is not fully preserved due to the minor contribution from the electric quadrupole mode (curve 614 in Figure 6).

[0050] The chart 706 shows scattering patterns 708, 710 at wavelength λ-ι . Forward scattering is slightly enhanced, however backward scattering is not completely suppressed in this case due to imperfect destructive interference of the dipolar modes, as a result of their unequal scattering cross-sections.

Additionally, a greater azimuthal asymmetry is evident. [0051 ] The chart 712 shows the scattering pattern 714 at the quadrupolar peak wavelength λ₂. In this case, the magnitude of the main scattering lobe is significantly enhanced (by a factor greater than 2), azimuthally symmetric scattering pattern is completely restored, and backward scattering is substantially suppressed. The forward-scattering pattern observed in this case is due to interference between spectrally overlapping quadrupolar modes EQ and MQ (curves 612, 614 in Figure 6), and is narrower in comparison to the cases in which dipolar modes interfere (at λ₀ and λ-ι). Around a 50 percent reduction in angular width is observed, indicating superior directionality at λ₂. Alternative computations using FCDA lead to the same conclusions.

[0052] It is notable, however, that the directionality enhancement at λ₂ is obtained at a cost of increasing side-scattering-lobe levels, visible as the peaks 716, 718 in the chart 712. While these lobes are present at λ₀ and λι , they are not visible at levels of -18 dB and -14 dB respectively. At λ₂, however, the relative magnitude of the side lobes 716, 718 is -10 dB. This implies higher energy leakage in undesired directions, which is attributable to the growing presence of non-zero contributions to scattering from modes of different order at that particular wavelength. At λ₂ there is a significant presence of magnetic dipole modes, contributing towards the side lobes 716, 718 at large scattering angles. Nonetheless, for the given dimensions, the relatively small permittivity nanocube provides better tailoring of unidirectional light scattering in the forward direction, when compared to the relatively larger permittivity nanocube having the far-field scattering characteristics illustrated in Figures 5(a) and 5(b).

[0053] It is anticipated that the directionality of the forward-scattering profile may be further improved by deploying a linear chain of identical nanoparticles. Figure 8 is a schematic illustration of an optical nanoantenna 800 comprising two dielectric nanocubes 802, 804 arranged with a linear interparticle distance 806. The interparticle distance 806 is denoted by d. Numerical simulations of the arrangement 800 have been conducted for various values of the interparticle distance d. [0054] The simulations have shown that the nanoantenna 800 exhibits a set of side-scattering lobes represented by indices m' with maxima aligned along the diffraction angles 6_m-. The number and angle of these lobes depends primarily upon the ratio d/λ, as dictated by the diffraction-grating effect. Table I provides a summary of the d/λ dependency of the side-scattering lobes, along with the backscattering suppression.

TABLE ί. ϊηίΐί.κ¾¾ ϊ οΐ d τ> the far -field, scanc-rbia paiiereK .

s!—l i:W. : 1 ^'ΆΥ i , .i.l^'

=0 : ±2

d— 31!2 ¾7-i.i ?\ * K».4V° , - i-. l&O^'"' . i . :. :. .^*. ^': 4

[0055] Note that for d< λ/2, although there is no major side lobe due to no diffraction effect, minor side lobes and non-zero backscattering were still observed which has been ascribed to the fact that d is too small to have sufficient phase delay to ensure complete destructive interference at larger angles. As d is further reduced below λ/2, the undesired scattering lobes grow in magnitude. For larger values of d, diffraction-grating effect provides the major contribution to the side-scattering lobes, substantially determine the angles of side-lobe maxima, as well as whether backscattering is completely suppressed or not.

[0056] In general, if d<nA/2, where n is a positive integer, then 2(n - 1 ) side- scattering lobes are present and backscattering is completely suppressed.

However, when d= ηλ/2, there are still 2(n - 1 ) side-scattering lobes, but at smaller angles than before, and additionally backscattering is not completely suppressed.

[0057] Accordingly, there is a desirable range of A/2<d< λ with just two side lobes, and a secondary desirable range of A<d<3A/2 having four side-scattering lobes, where there is substantially zero backscattering, and substantially suppressed side scattering. In each case, the optical nanoantenna 800 exhibits the unidirectional scattering properties of a Huygens' source.

[0058] Figures 9(a) to (c) show far-field scattering patterns corresponding with embodiments of the optical nanoantenna 800, based on the low permittivity nanocubes having W=200 nm and ε_Γ=5. The scattering patterns have been obtained using FEM simulations at the preferred wavelength λ₂=385 nm.

[0059] The chart 900 shows the main lobe 902 and side lobes 904 for d=1600 nm, the chart 906 shows the main lobe 908 and side lobes 910 for d=3200 nm, and the chart 912 shows the main lobe 914, and side lobes 916, for d=6400. The scattering patterns indicate that the main (forward) scattering lobe becomes significantly narrower as d is increased (from 33° at d=1600 nm to 20° at d=6400 nm). However, energy leakage to side-scattering lobes also grows as a result of increasing phase delay between the nanocubes, thereby supporting more diffraction-grating orders.

[0060] These phenomena are further illustrated in Figures 10(a) and 10(b), which show graphs of main-lobe angular width and side-lobe level, respectively , as a function of interparticle distance d, for a two-particle optical nanoantenna 800. The graph 1000 shows d (in nanometres) on the horizontal axis 1002, and main-lobe angular width (in degrees) on the vertical axis 1004. The group of curves 1006 corresponds with the main lobes in two orthogonal planes at wavelengths λ₀ and λ-ι , while the substantially coincident curves 1008 correspond with the forward-scattering patterns for the two main lobes at λ₂. As can be seen, the main lobe is always narrower at λ₂ than at either λι or λ₀. Furthermore, the main lobe at λ₂ maintains azimuthal symmetry independently of the interparticle distance d. As the interparticle distance is increased, the angular width falls rapidly. However, as shown by the graph 1010, this comes at the cost of increasing the level of the strongest side-scattering lobe. [0061 ] In the graph 1010 the horizontal axis 1012 shows interparticle distance d, while the vertical axis 1014 indicates the relative level (in dB) of the strongest side lobe. The group of curves 1016 corresponds with the side lobes in two orthogonal planes at wavelength λ₀ and λ-ι , while the pair of curves 1018 corresponds with the side lobes in orthogonal planes at wavelength λ₂. It will be noted, firstly, that the side lobes at λ₂ do not exhibit the same azimuthal symmetry as the main lobe. Additionally, as the distance d is increased, the magnitude of the main scattering lobe increases (i.e. the suppression decreases). At all interparticle distances of interest, suppression is greater at λ₂ than at λι or λ₀. Again this indicates that λ₂ is the most beneficial operating wavelength, ensuring minimum energy leakage, as well as improved scattering directionality.

[0062] Figure 1 1 is a schematic illustration of an optical nanoantenna 1 100 comprising a plurality of dielectric nanocubes, e.g. 1 102, 1 104, 1 106, arranged in a linear array. The interparticle distance between adjacent particles 1 108 is denoted by d, while the interparticle distance between first and last particles in the array 1 1 10 is denoted by D. Theoretical calculations of far-field scattering patterns have been performed using FEM simulations for two nanoparticles (i.e. the arrangement 800) with d=1600 nm, and for five nanoparticles in the arrangement 1 100 with D=1600 nm, i.e. d=400 nm. Note that the total separation between the end nanocubes in both cases is maintained at 1600 nm for fair comparison (i.e. each arrangement can be contained within the same physical space).

[0063] For the two-particle arrangement, d<9A₂/2 gives rise to 16 side- scattering lobes, with the strongest lobes at +40.59° and -40.59°. However, for the five-particle array, d<3A₂/2 contributes to only four side lobes, with the strongest lobes at +87.85° and -87.85°.

[0064] Table II below summarises the parameters of the far-field scattering patterns for these two exemplary cases. TABLE- B, FuomeKf 'i se ii '*iv ekl s atSssriKg p aSlsrss for tfse two ases shown its K site 8,

φ = 9i <·> = () φ = 90"

Sfctetote ievel (dB) -3.6 -4 -9,5 - 01.9

6.43 6.43 9.91 9.91

J itteg) Si 15

[0065] It can be clearly seen in Table II that for shorter interparticle spacing, the energy leakage significantly reduces, with the strongest side-lobe magnitude being around -10 dB for the five-particle array, as compared with -4 dB for the two-particle arrangement. The linear chain of five nanocubes also leads to 1 .5 times increase in forward-scattering cross-section, while preserving

backward-scattering suppression and azimuthal symmetry. However, the beam width of the main scattering lobe is slightly higher (35°, as compared with 33°) in the five nanocube array, which may be attributed to reduced destructive interference for larger scattering angle, and relatively stronger near-field coupling at smaller d.

[0066] Figures 12(a) to (c) show graphs of main-lobe angular width 1200, main-lobe magnitude 1210 and maximum side-lobe level 1230, for an optical nanoantenna according to the arrangement 1 100, as a function of the number of nanocubes. In each case, there is a fixed interparticle spacing, between adjacent particles, of d=400 nm. In all three graphs 1200, 1210, 1230 the horizontal axes 1202, 1212, 1232 show the number of nanocubes in the array, while the vertical axes 1204, 1214, 1234 show the main-lobe angular width (in degrees), the main- lobe scattering magnitude (in metres squared), and the relative maximum side-lobe level (in dB) respectively.

[0067] In the graph of main-lobe angular width 1200, the pair of curves 1206 represent far-field scattering at A₀ and λ _; while the curve 1208 represents main- lobe width at λ₂. Significant reduction in angular width is observed with increasing number of nanocubes, while keeping backscattering totally suppressed, and maintaining perfect azimuthal symmetry. Operating at the wavelength of λ₂ offers the best directionality, with angular width as low as 12.7° for an array of 60 nanocubes.

[0068] In the graph 1210, the curve 1216 represents the main-lobe magnitude at wavelength λ₀, the curve 1218 represents the main-lobe magnitude at λ-ι, and the curve 1220 represents the main-lobe magnitude at wavelength λ₂. Notably, the greatest scattering enhancement is observed at λ₀, followed by λ and finally λ₂. The lower scattering enhancement at λ₂ can be ascribed to comparatively higher-scattering losses along undesired side-scattering lobes, resulting from the largest d/λ ratio. This can be better understood from the graph 1230, in which the curve 1236 represents maximum relative side-lobe level at λ₀, the curve 1238 represents maximum relative side-lobe level at λ-ι, and the curve 1240 represents maximum relative side-lobe level at λ₂. Noticeable differences in scattering enhancement are observed for nanocube arrays of 20 or greater particles.

Although side lobes are significantly suppressed (by a factor of eight or more), they are relatively stronger at A₂ due to the stronger presence of the extrinsic modes of other orders. By numerical simulation, it has been established that for an array of nanocubes, the strongest suppression of backward scattering and side lobes is achieved at λ₀. This is attributed to the fact that at λ₀, scattering from the electric and magnetic dipoles is of equal strength, with minimal presence of higher-order modes (as can be seen in the graph 600 of Figure 6). Overall, therefore, optimal directionality is observed at the peak wavelength of spectrally overlapping higher-order resonances with equal scattering cross-sections of the electric and magnetic quadrupoles (i.e. at λ₂), whereas the optimal scattering enhancement can be obtained at the wavelength at which the first GK condition is met, with equal scattering from electric and magnetic dipoles (i.e. at λ₀).

[0069] Optical nanoantennas embodying the invention may have numerous applications, particularly when coupled with light-emitting structures, in order to form nanoscale-directed light sources. An arrangement 1300 of such a directed light source is illustrated schematically in Figure 1 3. The light source 1300 comprises a light-emitting element 1302, which may be, for example, a microlaser, a nanolaser, a spaser, a quantum dot or other suitable structure. The light emitter 1302 is coupled to a nanoparticle array 1 100. The nanoparticle array 1 100 forms an optical nanoantenna that scatters light from the non-directional emitter 1302 into a directional beam 1304.

[0070] Directed light sources comprising unidirectional nanoantennas may be suitable for integrated optics-based biosensors, which may be employed to detect proteins, DNA, antibodies, enzymes, and so forth. These may be integrated into 'lab-on-a-chip' platforms. Such biosensors may enable quick and accurate measurement of microorganisms in consumables and in the environment, fast identification of airborne pollutants or toxic gases, fast detection of acute illness, such as heart attacks, and rapid tracking of urgent treatment procedures such as drug activation, and may even be employed for targeted cancer treatment using focused light rays.

[0071 ] As well as being used as an illumination source in microfluidic analysis, directed light sources embodying the invention may find application in other NEMS mechanisms, such as in the minute deflection registers of ultrasensitive force detectors, or as an analog for 'phased array antennas' at nanoscale, with multiple antennas being aligned for better resolution or focusing. Furthermore, by altering the alignment of nanocubes, it may be possible to steer the direction of the forward-scattering light beam.

[0072] Directed light sources employing unidirectional nanoantennas embodying the invention may also find application as Optical nanoscanners' for targeting specific molecules, and may be fixed to nano/micro rotors (NEMS devices) for scanning of three-dimensional areas. As described in detail above, beam width and intensity of the directional radiation are programmable by forming nanocube arrays with tuneable interparticle separation, enabling super resolution and nanoscale focusing. [0073] Other potential applications include nanofocusing of light in high- density multidimensional optical data storage systems, in which data can be manipulated by selectively focusing light onto a small portion of the memory elements. With the addition of modulation means, directed light sources may be employed as on-chip integrated circuit interconnects, allowing optical signals to be transmitted within and between circuits, providing fast data processing with reduced device heating and power consumption.

[0074] It will therefore be appreciated that, while particular embodiments of the invention have been described in order to illustrate the applicable principles, and a range of potential applications, these should not be regarded as limiting the scope of the invention, and numerous variations will be apparent to persons skilled in the relevant arts. It will be appreciated, therefore, that the scope or the invention is as defined in the following claims.

Claims

CLAIMS:

1 . An optical nanoantenna configured to exhibit highly-directional scattering of light, which comprises a cubic dielectric nanoparticle.

2. The optical nanoantenna of claim 1 wherein the cubic dielectric nanoparticle has a characteristic dimension and permittivity selected to achieve the highly-directional scattering of light comprising at least one predetermined wavelength.

3. The optical nanoantenna of claim 1 wherein the cubic dielectric nanoparticle has a characteristic dimension and permittivity selected such that constructive interference of resonances results in enhanced scattering in one direction of light comprising at least one predetermined wavelength.

4. The optical nanoantenna of claim 2 wherein the predetermined wavelength lies within a visible range, or within an infrared range.

5. The optical nanoantenna of claim 2 wherein relative permittivity of the material comprising the cubic dielectric nanoparticle is less than 50.

6. The optical nanoantenna of claim 5 wherein the relative permittivity is less than 30.

7. The optical nanoantenna of claim 5 wherein the relative permittivity is greater than 5.

8. The optical nanoantenna of claim 2 wherein the characteristic dimension is less than the predetermined wavelength.

9. The optical nanoantenna of claim 8 wherein the characteristic dimension is less than 400 nm.

10. The optical nanoantenna of claim 8 wherein the characteristic dimension is between 100 nm and 300 nm.

1 1 . The optical nanoantenna of claim 8 wherein the characteristic dimension is approximately 200 nm.

12. The optical nanoantenna of claim 3 wherein the resonances comprise magnetic and electric resonances of dipolar modes, and at least one higher-order mode.

13. The optical nanoantenna of claim 12 wherein the resonances further comprise magnetic and electric quadrupolar modes.

14. The optical nanoantenna of claim 1 which comprises two or more dielectric nanoparticles arranged in an array characterised by an interparticle distance.

15. The optical nanoantenna of claim 14 which is configured to exhibit the highly-directional scattering of light comprising at least one predetermined wavelength λ.

16. The optical nanoantenna of claim 15 wherein the interparticle distance is greater than λ/2 and less than 3λ/2.

17. The optical nanoantenna of claim 16 wherein the interparticle distance is greater than λ/2 and less than λ.

18. The optical nanoantenna of claim 1 6 wherein the interparticle distance is greater than λ and less than 3λ/2.

19. A directed light source comprising a light emitter which is coupled to a nanoantenna according to claim 1 .

20. A directed light source comprising a light emitter which is coupled to an optical nanoantenna according to claim 14.