Light-powered nano drones

Abstract

The present invention relates to a nanodrone, a method of operating a nanodrone, and a system for operating a nanodrone. The nanodrone comprises a substrate extending perpendicular to a normal direction and two or more nanoantennas disposed on and / or within the substrate, each of the two or more nanoantennas exhibiting an optically addressable resonance at a respective resonant wavelength. The two or more nanoantennas comprise a first nanoantenna and a second nanoantenna, each of which has a mean wave vector in a plane perpendicular to the normal direction for left-handed and right-handed circularly polarized light, i=1 for the first nanoantenna and i=2 for the second nanoantenna, respectively. [0010] The nanoantennas are configured to scatter circularly polarized light at their respective resonant wavelengths incident on the nanoantennas along the normal direction, such that the nanoantennas have a TIFF2025504621000204.tif6161. i = L or R [0025] TIFF2025504621000205.tif6161 is non-zero. j i In the case of =R [0030] JPEG2025504621000206.jpg6130, j i In the case of =L [0045] JPEG2025504621000207.jpg7130 is the average wave vector [0050] TIFF2025504621000208.tif6161 is essentially zero, or [006] It is essentially anti-parallel to TIFF2025504621000209.tif6160. [0070] At least one of the files, TIFF2025504621000210.tif6160, [0080] TIFF2025504621000211.tif6161.

Description

[Technical field]

[0001] The present invention is in the field of optomechanics, in particular, the present invention relates to a nanodrone, a method for operating a nanodrone, and a system for operating a nanodrone. [Background technology]

[0002] Light can be used to manipulate the degrees of freedom of motion of microscopic objects via light-induced forces. The latter can result, for example, from dispersive interactions between the electromagnetic field and the dipole moment induced in the object by the electromagnetic field and / or from the deflection of light due to refraction at the object. This allows the trapping of objects ranging from single atoms to biological cells in tightly focused laser beams, also known as optical tweezers or dipole traps. Such optical tweezers can also be used to perform translation of the trapped object by moving the focus of the laser beam, but optical tweezers, due to their non-resonant nature, require very high light intensities to generate sufficiently strong electric potentials. This makes them unsuitable for many applications, especially those involving biological objects such as cells or other objects that absorb only very little light at the wavelengths of the optical tweezers. Furthermore, the rotational degrees of freedom of the trapped object can only be addressed under special circumstances, for objects with specific shapes, such as objects with large handles that can be selectively trapped in a multi-beam optical trap.

[0003] In addition to the dispersive dipole force, light can also exert a force on an object by absorbing or scattering photons. Each photon carries a linear momentum that is transferred to the object when the photon is absorbed or scattered by the object, thereby creating a radiation pressure that acts on the object. This allows for the generation of directional longitudinal forces, for example, via the absorption or scattering of a propagating laser beam. Photon scattering has also been used to generate transverse optical forces, for example, using plasmonic nanoantennas with linearly polarized asymmetric radiation patterns, as reported by YY Tanaka et al., Science Advances 6, eabc3726 (2020), or using asymmetric diffraction gratings, as reported by D. Andren et al., Nat. Nanotech. 16, 970-974 (2021).

[0004] However, approaches proposed so far only allow limited control over some, but not all, degrees of motion of the manipulated object because they only allow linear motion or rotation in a single fixed direction, such as the nanoantenna used by YY Tanaka et al., and / or because the rotational and translational degrees of freedom are coupled for the diffraction grating used by D. Andren et al. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Science Advances 6, eabc3726(2020), YYTanaka [Non-Patent Document 2] Nat.Nanotech.16,970-974(2021),D.Andren Summary of the Invention [Problem to be solved by the invention]

[0006] It is therefore an object of the present invention to provide a means for independently controlling the degrees of freedom of motion of microscopic objects using light. [Means for solving the problem]

[0007] This object is achieved by a nanodrone according to claim 1, a method for operating a nanodrone according to claim 20 and a system for operating a nanodrone according to claim 26. Embodiments of the invention are detailed in the dependent claims.

[0008] A nanodrone according to the invention comprises a substrate extending perpendicular to the normal direction and two or more nanoantennas, each of which is disposed on and / or within the substrate and exhibits an optically addressable resonance at a respective resonant wavelength. The two or more nanoantennas comprise at least a first nanoantenna and a second nanoantenna, each of which is configured to scatter circularly polarized light at a respective resonant wavelength incident on the nanoantenna along the normal direction. Photons of the scattered light have an average wave vector in a plane perpendicular to the normal direction, i=1 for the first nanoantenna and i=2 for the second nanoantenna, for left and right circular polarization, respectively.

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[0009] In the present disclosure, a nanodrone may be any nanoscale or microscale object that can have at least one degree of freedom of motion controlled by light. For example, the physical dimensions of the nanodrone, which may correspond to the physical dimensions of the nanodrone's substrate, may range from, for example, 50 nm to 1 mm, and in some embodiments, 200 nm to 100 μm.

[0010] The substrate may be, for example, a planar substrate having one or more flat surfaces, for example, one or more flat surfaces perpendicular or substantially perpendicular to the normal direction. In other embodiments, some or all of the surfaces of the substrate may be curved, for example, such that the respective surfaces extend parallel to the normal direction. In the following, the normal direction may also be referred to as the Z direction, and the plane perpendicular to the normal direction may also be referred to as the XY plane. In some embodiments, the substrate is at least partially optically transparent, in particular at the resonant wavelength of the two or more nanoantennas. The substrate may be at least partially optically transparent, for example, in the infrared, near infrared, visible and / or ultraviolet spectrum. The substrate may, for example, comprise or consist of one or more optically transparent layers, and the two or more nanoantennas may, for example, be disposed on and / or in one of the optically transparent layers. Additionally or alternatively, the substrate may comprise or consist of one or more opaque layers, for example, one or more absorbing layers, and the two or more nanoantennas may, for example, be disposed on one of the opaque layers.

[0011] Each of the two or more nanoantennas is configured to resonantly scatter light at a respective resonant wavelength, i.e., at a scattering cross section of a given one of the two or more nanoantennas, such that the scattering rate of light incident on the nanoantenna may exhibit a maximum value at the respective resonant wavelength. Scattering may occur via any type of resonant light-matter interaction. The nanoantenna may, for example, comprise or be composed of a material that supports one or more polariton modes, i.e., modes resulting from coupling between the light incident on the material and one or more excitations in the material, such as phonon modes, i.e., collective excitations of atoms in the material, or plasmon modes, i.e., collective excitations of charge carriers such as electrons in the material. The excitations may be related to electric and / or magnetic multipole moments to which the electromagnetic field of the light may couple. The excitations may, for example, be related to electric and / or magnetic dipole moments and / or electric and / or magnetic quadrupole moments. The coupling may be resonant at one or more resonant wavelengths, resulting in a strong interaction between the light and the respective nanoantenna, thus resulting in an increased scattering cross section and an increased scattering rate. Additionally or alternatively, scattering can occur, for example, via Mie scattering. The resonant wavelength can be controlled, for example, by tailoring the physical dimensions, shape, configuration, and / or materials of each nanoantenna structure such that the resonant wavelength is in the infrared, near infrared, visible, and / or ultraviolet spectrum.

[0012] Each of the two or more nanoantennas may comprise one or more structures that may be, for example, embedded in the substrate and / or disposed on a top and / or bottom surface of the substrate extending perpendicular to the normal direction. Some or all of the structures may be conductive, and the conductive structures may include or consist of, for example, metals such as gold, silver, aluminum, and / or copper. The conductive structures may support, for example, one or more plasmon modes and / or one or more phonon modes. Additionally or alternatively, some or all of the structures may be semiconductive and / or dielectric structures. The dielectric structures may include or consist of, for example, a material having a refractive index different from adjacent portions of the substrate, and may be configured to scatter incident light via, for example, Mie scattering. In some embodiments, the dielectric structures may include or consist of a transparent material, in particular glass.

[0013] The two or more nanoantennas comprise at least a first nanoantenna and a second nanoantenna. In some embodiments, the two or more nanoantennas may comprise further antennas, such as a third and a fourth nanoantenna, as described in more detail below. The two or more nanoantennas may in particular comprise an even number of nanoantennas, such as two, four, six or eight nanoantennas. In other embodiments, the two or more nanoantennas may comprise an odd number of nanoantennas, such as three nanoantennas, where two of the three nanoantennas may be used, for example, to move the nanodrone back and forth, and the remaining nanoantenna may be used, for example, to rotate the nanodrone. Preferably, each of the two or more nanoantennas is arranged on a concentric circle around the center of the nanodrone, in particular the center of mass of the nanodrone.

[0014] Each of the first and second nanoantennas may be configured to scatter circularly polarized light at a respective resonant wavelength incident on the respective nanoantenna along the normal direction by absorbing and re-emitting a photon. The absorption of the photon may create, for example, phonons or plasmons within the structure of the nanoantenna, which may then decay by emitting another photon. Additionally or alternatively, the first and second nanoantennas may be configured to scatter circularly polarized light at their respective resonant wavelengths by Mie scattering. The resonant nature of the light-matter interaction with the first and second nanoantennas may allow for selective addressing of the first nanoantenna and / or the second nanoantenna by selecting the wavelength of the incident light accordingly, for example to match the respective resonant wavelengths. Additionally or alternatively, individual nanoantennas may be selectively addressed by appropriate selection of the polarization of the incident light, for example, as described in more detail below. Thus, it is not necessary to selectively direct the incident light to a particular nanoantenna, but the entire nanodrone may be uniformly illuminated, for example, using unfocused light.

[0015] The first and second nanoantennas are configured to asymmetrically scatter circularly polarized light with respect to at least one circular polarization, e.g., such that the far-field scattering pattern of the scattered light is not rotationally symmetric with respect to the normal direction. The average wave vector of the photons of the scattered light in a plane perpendicular to the normal direction, i.e., the expectation value of the wave vector of the scattered photons projected onto the XY plane perpendicular to the normal or Z direction, is given by:

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[0016] The average wave vector of a given nanoantenna i for a given polarization j

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[0017] Each of the first nanoantenna and the second nanoantenna has a mean wave vector of at least one of left-handed and right-handed circularly polarized light incident along a normal direction.

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[0018] The Z component of the mean wave vector of the scattered photons can be zero for one or both circular polarizations in some embodiments (e.g., such that only the optical pressure generated by the incident light acts on each nanoantenna along the normal direction), while in other embodiments it can be non-zero for one or both circular polarizations for some or all of the nanoantennas (e.g., such that the scattered / emitted light generates a recoil along the normal direction in addition to the optical pressure generated by the incident light, thus enhancing the optical pressure or at least partially compensating the optical pressure).

[0019] Asymmetric scattering of the incoming light reduces, on average, the linear momentum transferred to the nanodrone per scattered / emitted photon.

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[0020] Each of the first and second nanoantennas emits opposite circularly polarized light.

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[0021] The first and second nanoantennas further include

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[0022] In this way, the present invention allows for control of the fundamental degrees of freedom of motion, namely translation and rotation. By combining pairs of nanoantennas, each of the degrees of freedom of motion can be accessed, for example, translation along one axis in 1D, translation along two axes, and rotation about a perpendicular axis in 2D, and translation along three axes, as well as rotation about three axes in 3D. Furthermore, due to the polarization dependence of the momentum transferred, each individual degree of freedom can be independently controlled by adjusting the polarization. In some embodiments, the resonant wavelengths of some or all of two or more nanoantennas may be different, which further allows for addressing each individual nanoantenna independently based on the wavelength of the incident light. This can allow, for example, independent control over all three degrees of freedom in 2D or all six degrees of freedom in 3D. Furthermore, the nanodrone can be illuminated with unfocused light, e.g., a collimated light beam, since each individual nanoantenna can be selectively addressed by appropriate selection of the polarization and / or wavelength of the light, rather than requiring the light to be selectively focused on each nanoantenna.

[0023] In a preferred embodiment, the first and second nanoantennas have a scattering cross section A of the first nanoantenna at the resonant wavelength of the first nanoantenna. sc、1 and,

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[0024] In some embodiments, the first and second nanoantennas include:

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[0025] Preferably, the scattering cross section of the second nanoantenna is similar to the scattering cross section of the first nanoantenna for left and / or right circularly polarized light. The scattering cross section of the second nanoantenna can be, for example, 30% to 300%, and in some examples 50% to 200%, of the scattering cross section of the first nanoantenna for one or both polarizations. In some embodiments, the scattering cross sections of the first and second nanoantennas can be substantially equal for one or both polarizations, such that, for example, the scattering cross sections of the nanoantennas differ by less than 30%, in some examples less than 20%, preferably less than 10%, and in one example less than 5%. In some embodiments, the scattering cross sections of some or all of two or more nanoantennas can be similar and / or substantially equal.

[0026] Wave vector

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[0027] In some embodiments,

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[0028] The resonant wavelengths of some or all of the two or more nanoantennas may be equal, e.g., to address some or all of the two or more nanoantennas with a single light source. In other embodiments, the resonant wavelengths of some or all of the two or more nanoantennas may be different from the resonant wavelengths of the other nanoantennas, e.g., to address individual nanoantennas or subsets of nanoantennas with a particular wavelength of light. For example, a first subset of nanoantennas may have a first resonant wavelength and a second subset of nanoantennas may have a second resonant wavelength that is different from the first resonant wavelength. The resonant wavelengths of the first and second nanoantennas may be equal in some embodiments and different in other embodiments. The resonant wavelengths of two nanoantennas may be considered equal, for example, if the scattering cross section of a given one of the two nanoantennas and / or the scattering efficiency by this nanoantenna for circularly polarized light incident along the normal direction at the resonant wavelength of the other nanoantenna is at least 50%, in some instances at least 75%, preferably at least 90%, and in one instance at least 95% of the scattering cross section and scattering efficiency at the resonant wavelength of the given nanoantenna, respectively, or vice versa. Otherwise, the resonant wavelengths of the two nanoantennas may be considered different. The resonant wavelengths of the first and second nanoantennas may differ, for example, by more than 50 nm, preferably more than 100 nm, and in one instance by more than 200 nm. In some embodiments, the difference in the resonant wavelengths of the first and second nanoantennas may be greater than the half-width at half maximum of one or both of the resonances.

[0029] In a preferred embodiment, the intensity-normalized in-plane force imparted to a first nanoantenna by scattering of circularly polarized light incident along the normal direction at the resonant wavelength of the second nanoantenna is

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[0030] In some embodiments,

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[0031] Additionally or alternatively,

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[0032] In one embodiment,

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[0033] In some embodiments, the two or more nanoantennas further comprise, in addition to the first and second nanoantennas, a third nanoantenna and a fourth nanoantenna, each of the third and fourth nanoantennas also disposed on and / or within the substrate and exhibiting optically addressable resonance at a respective resonant wavelength. Each of the third and fourth nanoantennas can also include one or more structures, in particular one or more conductive structures, for example as described above for the first and second nanoantennas. Similar to the first and second nanoantennas, each of the third and fourth nanoantennas is configured to scatter circularly polarized light at a respective resonant wavelength incident on the respective nanoantenna along a normal direction, such that photons of the scattered light have a mean wave vector in a plane perpendicular to the normal direction for left and right circularly polarized light, respectively.

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[0034] Each of the third and fourth nanoantennas has a mean wave vector in the XY plane

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[0035] Wave vectors for the first to fourth nanoantennas

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[0036] Wave vectors for the first to fourth nanoantennas

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[0037] In some embodiments, for each nanoantenna of a first pair of nanoantennas selected from the first, second, third, and fourth nanoantennas, e.g., for each of the first and second nanoantennas, j=L or R.

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[0038] In some embodiments, the first nanoantenna pair may be composed of a first and a second nanoantenna, and the second nanoantenna pair may be composed of a third and a fourth nanoantenna. Linear momentum may be transferred to the nanodrone by light having a given circular polarization (either L or R) using either one of the first and second nanoantennas, and by light of the opposite circular polarization using either one of the third and fourth nanoantennas, but linear momentum is not transferred via either one of the first and second nanoantennas in the case of the opposite circular polarization, and via either one of the third and fourth nanoantennas in the case of the given circular polarization.

[0039] Preferably,

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[0040] In a preferred embodiment, the non-zero wave vector for the i-th nanoantenna

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[0041] In some embodiments, the resonant wavelengths of a third nanoantenna pair selected from the first, second, third, and fourth nanoantennas are equal, and the resonant wavelengths of a fourth nanoantenna pair consisting of two nanoantennas among the first, second, third, and fourth nanoantennas that do not overlap with the third nanoantenna pair, i.e., are not included in the third nanoantenna pair, are equal. The resonant wavelengths of the third pair may be different from each of the resonant wavelengths of the fourth pair. This may allow selective addressing of either the third nanoantenna pair or the fourth nanoantenna pair by selecting the wavelength of light accordingly, without the need to focus the incident light on a particular nanoantenna.

[0042] Preferably, the third nanoantenna pair is composed of a nanoantenna selected from the first nanoantenna pair and a nanoantenna selected from the second nanoantenna pair, e.g., the first and third nanoantennas. Correspondingly, the fourth nanoantenna pair may be composed of another nanoantenna from the first and second nanoantenna pair, e.g., the second and fourth nanoantennas. This may allow selective addressing of each of the four nanoantennas by selecting the wavelength and polarization of the light accordingly, without the need to focus the incident light on a particular nanoantenna.

[0043] an intensity-normalized in-plane force imparted to a third pair of nanoantennas, e.g., the first nanoantenna and / or the third nanoantenna, by scattering of circularly polarized light incident along a normal direction at a resonant wavelength of one or both nanoantennas of the fourth pair, e.g., the second nanoantenna and / or the fourth nanoantenna.

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[0044] In some embodiments, the optically addressable resonance of some or all of the two or more nanoantennas is a plasmon resonance. In other words, incident light can couple to one or more plasmon modes, i.e., collective excitations of charge carriers such as electrons, within each nanoantenna, e.g., within the conductive structures of each nanoantenna. Plasmon resonance can occur, for example, in the visible spectrum for many metals, especially noble metals such as gold, platinum, palladium, and silver, but also other metals such as aluminum and copper. Additionally or alternatively, the optically addressable resonance of some or all of the two or more nanoantennas can be a phononic resonance. In other words, incident light can couple to one or more phonon modes, i.e., collective vibrational excitations of atoms, within each nanoantenna, e.g., within the conductive structures of each nanoantenna. Phononic resonance can occur, for example, in the near-infrared spectrum. Additionally or alternatively, the optically addressable resonance of some or all of the two or more nanoantennas can also be a resonance involving a different type of resonant light-matter interaction, e.g., a Mie resonance.

[0045] Some or all of the two or more nanoantennas may comprise one or more resonators, e.g., structures supporting one or more resonantly enhanced excitation modes (resonator modes), such as phonon or plasmon modes that couple to optical and / or optical modes. For example, the physical dimensions, e.g., length, of one or more of the structures of the nanoantennas may be selected such that standing waves may form within the respective structures. In this manner, certain modes, e.g., excitation modes of bulk materials, may be resonantly enhanced while other modes may be suppressed. This may result in optically addressable resonance of the respective nanoantennas. Each of the resonators may have a resonator axis, which may correspond, for example, to the axis of an electric or magnetic dipole moment associated with one or more of the resonantly enhanced excitation modes.

[0046] In a preferred embodiment, some or all of the two or more nanoantennas each comprise a pair of coupled resonators. The distance between the pair of resonators may be sufficiently small, for example, so that charge accumulations in the two resonators interact via attractive and / or repulsive forces and / or so that the evanescent electromagnetic field of a resonator mode of one of the resonators leaks into the other resonator and vice versa, thereby coupling the two resonators. Additionally or alternatively, the pair of resonators may be coupled via a coupling element, for example, a conductive and / or dielectric structure connecting the resonators, the width of the coupling element may be, for example, substantially smaller than the width of the resonators. The coupling strength between the pair of resonators may be selected such that the pair of resonators exhibits a common mode, for example a symmetric and antisymmetric superposition of the resonator modes of the two individual resonators.

[0047] The coupling between the resonators may result in a spectral splitting of the common mode, which may therefore also be referred to as a split mode. Preferably, the coupling, and thus the spectral splitting, is small enough so that each common mode (and therefore also a superposition of each common mode) can be excited by light of the same wavelength. The coupling may be small, for example, compared to the width of the resonance of each nanoantenna and / or the width of the resonance of one of the resonators.

[0048] The resonator axes of the pair of resonators may be tilted relative to each other, for example by an angle of 45° to 135°. The resonator axes may in particular be substantially perpendicular to each other. Preferably, the resonator axes are tilted relative to each other by an angle of 80° to 100°, in some examples 85° to 95°, in one example 88° to 92°. Coupled resonators with tilted resonator axes may exhibit a chiral response, where left-handed and right-handed circularly polarized light may couple into different modes, for example symmetric and antisymmetric superpositions of a common mode, respectively. This may result in a polarization-dependent distribution of scattered light. The superposition of the common mode may be at least partially localized in one of the pair of resonators, i.e. the near-field of each superposition of the common mode may be at least partially cancelled in the other resonator. Light of suitable circular polarization may therefore be used, for example, to selectively excite one of the pair of resonators.

[0049] Some or all of the two or more nanoantennas may each further comprise a third resonator. The third resonator may be substantially parallel to the first resonator of the pair of coupled resonators of the respective nanoantenna. This may, for example, facilitate absorption and / or scattering of light emitted from the first resonator by the third resonator. Preferably, the resonator axes of the first and third resonators are tilted relative to each other by an angle of -10° to 10°, in some examples -5° to 5°, and in one example -2° to 2°. The distance between the first and third resonators may be large enough such that the first and third resonators are not coupled by evanescent fields, but may interact with each other, for example, via their electromagnetic far fields.

[0050] A first resonator of a pair of coupled resonators may be disposed, for example, adjacent a first end of a second resonator of the pair, such that a corner of the first resonator faces a corner, an end face of the second resonator, and / or vice versa. The first and second resonators may be disposed, for example, in a V-shaped or L-shaped configuration.

[0051] The third resonator may be disposed adjacent to a second end of the second resonator opposite the first end, for example, such that a corner of the third resonator faces a corner of the second resonator, an end face of the second resonator, and / or vice versa. The first, second, and third resonators may be disposed, for example, in a U-shaped configuration. Thus, a nanoantenna in which the first and third resonators are disposed adjacent both ends of the second resonator may be referred to hereinafter as a U-shaped nanoantenna. In some examples, the first and third resonators may be disposed such that the first and third resonators are mirror symmetric with respect to the second resonator. The third resonator may also be coupled to the second resonator. In some embodiments, the first and third resonators are spaced the same distance from the second resonator.

[0052] Alternatively, the third resonator may be arranged such that the first resonator is disposed between the second end of the second resonator and the third resonator. For example, the first resonator, the second resonator and the third resonator may be arranged in an F-shaped configuration, for example, such that the first resonator is disposed adjacent to the first end of the second resonator and the third resonator is disposed on the far side of the first resonator from the second end of the second resonator, such that the first resonator is disposed between the first end of the second resonator and the third resonator. Thus, a nanoantenna in which the first resonator is disposed adjacent to the first end of the second resonator and between the third resonator and the second end of the second resonator may be referred to hereinafter as an F-shaped nanoantenna.

[0053] Both the F-shaped and U-shaped nanoantennas can exhibit polarization-dependent distributions of scattered light. Interference between the first and third resonators can invert and / or break the rotational symmetry of the distribution of scattered light upon illumination with circularly polarized light, thus resulting in a non-zero mean wave vector in the XY plane for at least one circular polarization.

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[0054] In some embodiments, the arrangement of two or more nanoantennas or a subset thereof exhibits one or more symmetries, in particular symmetries with respect to the center of the nanodrone. The symmetry subset may in particular include or consist of the first and second nanoantennas or the first, second, third and fourth nanoantennas. One of the symmetries may be, for example, a discrete rotational symmetry around the center of the nanodrone, for example a two-fold (180°) or four-fold (90°) rotational symmetry. Additionally or alternatively, one of the symmetries may be a mirror / reflection symmetry with respect to one or more symmetry planes extending through the center of the nanodrone. The one or more symmetry planes may be spanned by a normal vector parallel to the normal direction and respective in-plane vectors perpendicular to the normal direction. The one or more symmetry planes may in particular include a plane perpendicular to the connection vector between adjacent nanoantennas, for example between the first nanoantenna and the third nanoantenna and / or between the first nanoantenna and the fourth nanoantenna. In one example, the symmetry includes two-fold rotational symmetry (corresponding to inversion / point symmetry) and mirror symmetry.

[0055] In some embodiments, the two or more nanoantennas further comprise one or more roll nanoantennas and / or one or more pitch nanoantennas, for example to control the rotational degree of freedom around a rotation axis perpendicular to the normal direction (pitch and / or roll). The one or more roll nanoantennas may be arranged along a pitch axis of the nanodrone, which is substantially perpendicular to the normal direction, for example to control the rotational degree of freedom around the roll axis of the nanodrone, which is substantially perpendicular to each of the normal direction and the pitch axis. The one or more pitch nanoantennas may be arranged along the roll axis, for example to control the rotational degree of freedom around the pitch axis. As with other nanoantennas, each of the roll nanoantennas and pitch nanoantennas is disposed on and / or in a substrate and exhibits optically addressable resonances at respective resonant wavelengths. Each of the roll nanoantennas and pitch nanoantennas may include one or more structures, such as one or more conductive structures, for example as described above for the first and second nanoantennas. Preferably, the pitch axis and / or the roll axis extends through the center of the nanodrone.

[0056] The roll nanoantenna and the pitch nanoantenna may be configured to absorb and / or scatter light, particularly linearly and / or circularly polarized light, at the respective resonant wavelengths incident on the respective nanoantenna along the normal direction. The roll nanoantenna and the pitch nanoantenna may be configured, for example, to absorb the incident light and / or to symmetrically scatter the incident light, for example, such that the three-dimensional average wave vector of the scattered photons is zero (i.e., the scattered / emitted photons do not generate a net recoil and therefore do not transfer a net momentum to the respective nanoantenna). Thus, the momentum carried by the photons of the incident light can generate an optical pressure on the respective nanoantenna along the normal direction, which in turn can generate a torque around the roll axis or the pitch axis, respectively. Some or all of the roll nanoantenna and the pitch nanoantenna may each include a single structure, such as a single conductive structure, for example a single resonator. The single resonator may, for example, exhibit a dipole-like far-field scattering pattern, which is inversion symmetric such that the scattered photons have a zero average wave vector in all three dimensions. In some embodiments, some or all of the roll nano-antennas and pitch nano-antennas can have different resonant wavelengths, e.g., such that each roll nano-antenna and pitch nano-antenna can be individually addressed with light at its respective resonant wavelength.

[0057] In a preferred embodiment, some or all of the roll nanoantennas and pitch nanoantennas each comprise two pairs of coupled resonators, i.e. a first pair of coupled resonators and a second pair of coupled resonators. For each pair of resonators, the axes of the resonators of the respective pair may be inclined with respect to each other, in particular may be substantially perpendicular to each other, for example as described above. One or both resonators of the first pair of coupled resonators are substantially parallel to the respective resonators of the second pair of coupled resonators. In other words, the first resonator of the first pair may be substantially parallel to the first resonator of the second pair and / or the second resonator of the first pair may be substantially parallel to the second resonator of the second pair. This may, for example, facilitate the absorption and / or scattering of light emitted from one pair of resonators by the parallel resonators of the other pair, resulting in interference of light emitted and / or scattered by the two parallel resonators. Interference between these resonators can break the inversion and / or rotational symmetry of the far-field scattering pattern of each roll or pitch nanoantenna when illuminated with circularly polarized light, thus giving rise, for example, to a non-zero mean wavevector normal to at least one of the circularly polarized light.

[0058] The first pair of coupled resonators may be disposed in a first plane on and / or within the substrate that is substantially perpendicular to the normal direction, and the second pair of coupled resonators may be disposed in a second plane on and / or within the substrate that is substantially perpendicular to the normal direction and different from the first plane, e.g., above or below the first pair of resonators.

[0059] In some embodiments, the first resonator of the first pair may at least partially overlap with the first resonator of the second pair. Thus, the first resonator of the first pair and the first resonator of the second pair may hereinafter also be referred to as overlapping resonators. The overlapping resonators may at least partially overlap each other when viewed along the normal direction, e.g., such that at least 50%, in some examples at least 75%, and in one example at least 90% of the cross-sectional area of ​​one or both of the overlapping resonators overlaps with the other overlapping resonator. Preferably, the overlapping resonators fully overlap, e.g., such that the projection of one or both of the overlapping resonators onto the other overlapping resonator along the normal direction is fully contained within the circumference of the other overlapping resonator. The second resonator of the first pair may not overlap with the second resonator of the second pair, e.g., when viewed along the normal direction. Thus, the second resonator of the first pair and the second resonator of the second pair may hereinafter also be referred to as non-overlapping resonators. In some embodiments, one or both of the non-overlapping resonators may not overlap with the resonators of the respective other pair.

[0060] In some embodiments, each of the first and second pairs of coupled resonators includes a central resonator and a distal resonator. The central resonator may be disposed, for example, adjacent to a center of the respective nanoantenna, and the distal resonator may be disposed, for example, at an outer portion of the respective nanoantenna. The distal resonators may be disposed, for example, adjacent both ends of the central resonator. Preferably, the distal resonators extend in opposite directions from the respective ends of the central resonator, in particular in a direction substantially perpendicular to the resonator axis of the central resonator. For example, the proximal end of each distal resonator may be disposed adjacent the respective ends of the central resonator, with the distal ends of the distal resonators facing outward from the central resonator in opposite directions, such that, for example, each of the pair of resonators is disposed in an L-shaped or V-shaped configuration with the two pairs of L-shaped or V-shaped configurations rotated 180° with respect to each other. The central resonators of the first and second pairs of coupled resonators may be substantially parallel to each other, for example, to facilitate interference of light emitted from the two central resonators. In some embodiments, the central resonators may at least partially overlap each other, i.e., the central resonators may be overlapping resonators. The distal resonators may not overlap each other, i.e., the distal resonators may be non-overlapping resonators. In some embodiments, the distal resonators may also be substantially parallel to each other.

[0061] The roll and pitch nanoantennas may be configured to scatter the incident light asymmetrically for at least one circular polarization. The roll and pitch nanoantennas may be configured to scatter the incident light such that the Z component of the mean wave vector of the scattered photons is different for opposite circular polarizations, such that the force on the roll and pitch nanoantennas along the normal direction is polarization dependent. This may be used to generate a torque around the roll or pitch axis. The total force on a given nanoantenna along the normal direction may include the optical pressure generated by the incident light as well as the force generated by the scattered light in case of a non-zero Z component of the mean wave vector of the scattered photons (i.e., in case of asymmetric scattering).

[0062] Some or all of the roll nanoantennas and pitch nanoantennas may be configured to scatter incident light such that, for example, the Z component of the mean wave vector is non-zero for one circular polarization (i.e., asymmetric scattering) but is substantially zero for the opposite circular polarization (e.g., symmetric scattering), e.g., to at least partially compensate for or enhance the optical pressure generated by incident light along the normal direction. Additionally or alternatively, some or all of the roll nanoantennas and pitch nanoantennas may be configured to scatter incident light such that, for example, the Z component of the mean wave vector is non-zero for both circular polarizations but is substantially anti-parallel for the opposite polarizations, e.g., optical pressure is at least partially compensated for one polarization (i.e., the Z component of the mean wave vector is oriented along the normal direction, thus generating a recoil in a direction opposite to the normal direction) and enhanced for the opposite polarization (i.e., the Z component of the mean wave vector is opposite to the normal direction, thus generating a recoil parallel to the normal direction). Thus, the total force on each nanoantenna generated by the incident and scattered light may be smaller for one circular polarization than for the opposite circular polarization, which may generate a torque substantially collinear with the roll or pitch axis, as well as a force substantially collinear with the normal direction.

[0063] Asymmetric scattering due to different Z components of the mean wave vector of scattered photons for opposite polarizations may arise, for example, due to interference between the resonators of the first and second pair of coupled resonators. This can be achieved by choosing an appropriate arrangement of the resonators, in particular by adapting the distance between the resonators, the orientation of the resonators, the resonant wavelengths of the resonators, and / or the overlap between the resonators. The arrangement of the resonators may be selected, for example, such that modes localized in different resonators, for example either the central resonator or the distal resonator, can be excited with left-handed and right-handed circular polarizations, respectively, for one or both of the first and second pairs of resonators. The arrangement of the resonators may further be selected such that, for one or both circular polarizations, the mode excited in the first pair, for example the mode localized in the distal resonator of the first pair, and the mode excited in the second pair, for example the mode localized in the distal resonator of the second pair, destructively interfere in a direction substantially parallel or substantially anti-parallel to the normal direction. Furthermore, the arrangement of the resonators may also be selected such that a first pair of resonators, e.g., the overlap / center resonator of the first pair, at least partially blocks light that would otherwise reach a second pair of resonators, e.g., the overlap / center resonator of the second pair, thereby creating a “shadow” for each resonator of the second pair, and / or vice versa.

[0064] In some embodiments, the roll nanoantenna may comprise a first roll nanoantenna and a second roll nanoantenna arranged on either side of the center of the nanodrone along the pitch axis, in particular symmetrically with respect to the center of the nanodrone, the first roll nanoantenna having a Z component of the mean wave vector of the scattered photons that is non-zero (e.g., to at least partially compensate for or enhance the optical pressure) for circular polarization j=L or j=R;

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[0065] Similarly, the pitch nanoantenna may comprise a first pitch nanoantenna and a second pitch nanoantenna in a corresponding configuration along the roll axis. Preferably, the resonant wavelengths of the first and second pitch nanoantennas are equal but different from the resonant wavelengths of the first and second roll nanoantennas. This may allow the roll nanoantenna and the pitch nanoantenna to be addressed independently using light of the respective resonant wavelengths. In another example, the first roll nanoantenna and the first pitch nanoantenna may have a first resonant wavelength, and the second roll nanoantenna and the second pitch nanoantenna may have a second resonant wavelength different from the first resonant wavelength. To address the roll nanoantenna and the pitch nanoantenna independently, both roll nanoantennas may be configured to receive light of opposite polarizations, e.g., Z components of the mean wave vector of the scattered photons are non-zero, but substantially anti-parallel to each other for polarization j.

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[0066] The present invention further provides a method of operating a nanodrone according to any one of the embodiments described herein, comprising illuminating the nanodrone with light polarized at a resonant wavelength of a first nanoantenna and light polarized at a resonant wavelength of a second nanoantenna substantially along a normal direction, the polarization of light at the resonant wavelength of the first nanoantenna and the polarization of light at the resonant wavelength of the second nanoantenna being selected such that linear momentum transferred to the nanodrone by light scattered by the first and second nanoantennas generates a force acting on the nanodrone that is substantially perpendicular to the normal direction and / or a torque acting on the nanodrone that is substantially collinear with the normal direction.

[0067] The light for illuminating the nanodrone can be generated using an illumination system, such as, for example, one of the systems for operating nanodrones according to any one of the embodiments described below. The nanodrone may be illuminated with unfocused light, for example, one or more collimated light beams, such that, for example, the entire nanodrone is uniformly illuminated. The polarization at the resonant wavelength of the first and second nanoantennas may be, for example, circular, elliptical and / or linear.

[0068] For example, the polarization of the light can be selected such that the average in-plane wave vectors, and therefore the transferred linear momentum, of the photons of the light scattered by the first and second nanoantennas are non-zero and substantially anti-parallel to each other and are substantially collinear with the normal direction, i.e., generate a torque that is substantially parallel or substantially anti-parallel to the normal direction, thereby enabling the nanodrone to rotate, for example, about an axis substantially parallel to the normal direction, which may be referred to as the yaw axis.

[0069] In another example, the polarization of the light can be selected such that the average in-plane wave vectors of the photons of the light scattered by the first and second nanoantennas, and thus the transferred linear momentum, are both non-zero and substantially parallel to each other, generating a force substantially perpendicular to the normal direction. This allows the nanodrone to, for example, move or translate along a direction substantially perpendicular to the normal direction. In addition to the force generated by the scattered light substantially perpendicular to the normal direction, the incident light illuminating the nanodrone can generate an optical pressure on the nanodrone, i.e., an additional force along the incident direction substantially parallel to the normal direction. In some embodiments, the optical pressure may be at least partially compensated by a counteracting force, for example as described in more detail below.

[0070] In yet another example, the polarization of the light can be selected such that the average in-plane wave vector of the photons of the light scattered by one of the first and second nanoantennas is non-zero and the average in-plane wave vector of the photons of the light scattered by the other nanoantenna is substantially zero, e.g., to generate a force and a torque.

[0071] In some embodiments, the resonant wavelengths of the first and second nanoantennas are different. The intensity of the light at the resonant wavelengths of the first and second nanoantennas can be selected to generate a force but no net torque, or a torque but no net force. For example, the intensity can be adjusted so that the magnitude of the linear momentum transferred by the first and second nanoantennas is substantially equal. If the average wave vectors of the photons scattered by the first and second nanoantennas are substantially antiparallel, the forces generated by the two nanoantennas can cancel out such that the total force (net force) on the nanodrone is substantially zero. If the wave vectors are substantially parallel, the torques generated by the two nanoantennas can cancel out such that the total torque (net torque) on the nanodrone is substantially zero.

[0072] In some embodiments, the method may further include adjusting the polarization, intensity, and / or wavelength of the light to change the direction of the force and / or torque. Additionally or alternatively, the method may include adjusting the polarization, intensity, and / or wavelength of the light to generate a force instead of a torque, or vice versa. The method may further include adjusting the polarization, intensity, and / or wavelength of the light to change the magnitude of the force and / or torque. The polarization, intensity, and / or wavelength of the light may be adjusted, for example, to cause the nanodrone to perform a predetermined motion, for example to move along a predetermined path. In some embodiments, only the polarization and / or intensity of the light is adjusted to perform some or all of the aforementioned operations. All other parameters of the light, such as the direction of incidence, the intensity pattern near the nanodrone, and the wavelength, may not be adjusted, i.e., may remain constant.

[0073] Tuning the polarization and intensity of the light, respectively, can include tuning the respective parameters of the light at the resonant wavelengths of one or both of the first and second nanoantennas. The nanodrones can be manipulated, for example, by tuning the Stokes parameters S0 and S3 of the incident light, i.e., the total power of the incident light and the power difference between the left and right circularly polarized components of the light, at one or both of the resonant wavelengths. In some examples, only the Stokes parameters S0 and S3 of the incident light may be tuned, and all other parameters of the light may remain constant.

[0074] The polarization of the light at the resonant wavelength of one or both of the first and second nanoantennas can be inverted (e.g., left-handed instead of right-handed) or changed to a linear polarization, e.g., such that the respective transferred linear momentum is substantially zero or substantially antiparallel to its previous orientation. Similarly, the polarization of the light at the resonant wavelength of one or both of the first and second nanoantennas can be changed to an elliptical polarization, e.g., to adjust the respective mean wave vectors of the scattered photons and thus the magnitude of the transferred linear momentum.

[0075] The intensity of the light at the resonant wavelength of one of the first and second nanoantennas may be reduced, in particular reduced to zero, for example, to address only one of the first and second nanoantennas, and in some examples, the polarization of the light may be adjusted simultaneously while adjusting the intensity.

[0076] Tuning the wavelength of the light may include tuning the wavelength from a resonant wavelength of one nanoantenna to a resonant wavelength of another nanoantenna, for example, by increasing the intensity at the resonant wavelength of one nanoantenna from zero while decreasing the intensity at the resonant wavelength of the other nanoantenna to zero, or by continuously shifting the wavelength from the resonant wavelength of one nanoantenna to the resonant wavelength of the other nanoantenna. The wavelength of the light may be tuned, for example, such that the light resonates with another nanoantenna different from the first and second nanoantennas.

[0077] In some embodiments, the nanodrone may comprise a third nanoantenna and a fourth nanoantenna in addition to the first and second nanoantennas, e.g., as described above. The polarization, intensity and / or wavelength of the light may be selected such that, for example, the linear momentum transferred by the third nanoantenna is substantially zero, whereas the linear momentum transferred by the first nanoantenna is initially non-zero, e.g., to generate a torque in combination with one of the other nanoantennas, e.g., the second nanoantenna. The polarization, intensity and / or wavelength of the light may then be adjusted such that, whereas the linear momentum transferred by the first nanoantenna is substantially zero, the linear momentum transferred by the third nanoantenna is non-zero, e.g., to generate a force instead of a torque. Similarly, the polarization, intensity and / or wavelength of the light may be adjusted to switch between the second and fourth nanoantennas, e.g., to reverse the direction of the torque or force, or to generate a force in the vertical direction.

[0078] In a preferred embodiment, the method may further include determining the orientation of the nanodrone in a plane substantially perpendicular to the normal direction, for example, in the XY plane. The orientation of the nanodrone may be determined, for example, by imaging the drone with an imaging system such as a microscope and / or by observing the intensity distribution of light scattered by the nanoantenna. The direction of the linear momentum transmitted by the nanoantenna may be determined by the orientation of the nanoantenna and may therefore be fixed in the nanodrone's reference frame, but may depend on the orientation of the nanodrone in an external reference frame.

[0079] The method may further include adjusting the polarization, intensity and / or wavelength of the light based on the determined orientation of the nanodrone. In particular, the aforementioned parameters may be adjusted so that the direction of the force acting on the nanodrone is maintained, e.g., to maintain the direction of motion of the nanodrone by taking into account the change in the orientation of the nanodrone. For example, the ellipticity of the polarization of the light at the resonant wavelength of one or both of the one or more nanoantennas, e.g., the first and second nanoantennas, may be adjusted to account for the change in the orientation of the nanodrone, e.g., by increasing or decreasing the ellipticity accordingly. Additionally or alternatively, the intensity of the light at the resonant wavelength of one or both of the one or more nanoantennas, e.g., the first and second nanoantennas, may be adjusted to account for the change in the orientation of the nanodrone, e.g., by increasing the intensity at the resonant wavelength of one of the first and second nanoantennas while decreasing the intensity at the resonant wavelength of the other of the first and second nanoantennas, or vice versa.

[0080] In some embodiments, the method may further include providing a bottom surface on which the nanodrone is operated. The bottom surface extends perpendicular to the normal direction and may be, for example, a flat surface perpendicular or substantially perpendicular to the normal direction. In other embodiments, the bottom surface may be a curved surface. The bottom surface may be optically transparent, particularly at the resonant wavelength of the nanoantenna. In some embodiments, the bottom surface may be formed by a bottom wall of a chamber or cell or a bottom wall of a well or recess in which the nanodrone is operated. The chamber or well may be at least partially filled with a liquid, such as water or an aqueous solution.

[0081] The method can include generating a repulsive force between the bottom surface and the nanodrone to counteract the optical pressure generated by the illuminating light, e.g., to at least partially compensate for the linear momentum along the normal direction transferred to the nanodrone by the absorption and / or scattering of photons from the incident light. This can, for example, prevent the nanodrone from being pushed downward by the illuminating light into contact with the bottom surface. The repulsive force can, for example, be such that the nanodrone hovers above the bottom surface at a substantially constant distance, which can, for example, be on the order of hundreds of nanometers.

[0082] The repulsive force may be, in particular, an electrostatic force, generated by charging the bottom surface and the nanodrones with the same polarity. This may be achieved, for example, by providing an electrolyte in contact with the bottom surface and the nanodrones. The electrolyte may, for example, contain an anionic or cationic surfactant, such as sodium chloride and / or sodium dodecyl sulfate, ammonium lauryl sulfate, sodium laureth sulfate, sodium lauroyl sarcosinate, cetrimonium bromide and / or benzalkonium chloride. In another example, the repulsive force may, for example, be a magnetic force, i.e., the nanodrones may float above the bottom surface by magnetic levitation. In some embodiments, the optical pressure generated by the illumination light may additionally or alternatively be countered by an optically induced force. The nanodrones may, for example, be confined along the vertical direction within a focused light sheet.

[0083] The present invention further provides a method of operating a nanodrone according to any one of the embodiments described herein. The system comprises an illumination system configured to generate polarized light at a resonant wavelength of a first nanoantenna and at a resonant wavelength of a second nanoantenna. The illumination system is configured to adjust the polarization and intensity of the light at the resonant wavelengths of the first and second nanoantennas. The system further comprises an imaging system for imaging the nanodrone and a controller for controlling the illumination system. The controller is configured to obtain a motion command specifying a movement to be performed by the nanodrone. The controller is further configured to determine an orientation of the nanodrone from an image obtained from the imaging system and determine the polarization and intensity of the light generated by the illumination system at the resonant wavelengths of the first and second nanoantennas based on the motion command and the determined orientation. The controller is also configured to use the illumination system to illuminate the nanodrone with light at the resonant wavelengths of the first and second nanoantennas having the determined polarization and intensity to perform the movement specified by the motion command.

[0084] The illumination system may comprise one or more light sources, in particular coherent light sources such as lasers for generating light at the resonant wavelengths of the first and second nanoantennas. In some embodiments, the output power of some or all of the one or more light sources may be adjustable, for example to adjust the intensity of the light. The illumination system may further comprise polarization optics, such as one or more polarizers and / or one or more wave plates for controlling the polarization of the light. The illumination system may also comprise one or more means for controlling the intensity of the light, which may comprise elements with adjustable transmittance, such as, for example, acousto-optical modulators, electro-optical modulators, adjustable wave plates in combination with polarizers, and / or variable neutral density filters. In some embodiments, the illumination system may be further configured to generate light at wavelengths other than the resonant wavelengths of the first and second nanoantennas, for example at one or more resonant wavelengths of other nanoantennas, and adjust its polarization and intensity.

[0085] The illumination system may be configured to illuminate the nanodrone along the normal direction and / or substantially along the normal direction, for example, using a pair of beams including a first light beam at the resonant wavelength of the first nanoantenna and a second light beam at the resonant wavelength of the second nanoantenna. The illumination system may include one or more focusing elements, such as lenses, for generating one or more collimated light beams. In some embodiments, the illumination system may further be configured to illuminate the nanodrone in a direction opposite to the normal direction, for example, using a pair of counter-propagating beams including a third light beam at the resonant wavelength of the first nanoantenna and a fourth light beam at the resonant wavelength of the second nanoantenna. The illumination system may be configured to independently control the polarization and intensity of each of the beams.

[0086] The imaging system may be configured to take images of the nanodrones during operation, in particular along the normal direction and / or substantially along the normal direction. The imaging system may comprise, for example, a microscope, which may be configured to image, for example, a plane perpendicular or substantially perpendicular to the normal direction. The imaging system may be configured to image the nanodrones at a wavelength not resonant with any of the nanoantennas and / or using unpolarized or linearly polarized light, for example to reduce light scattering by the nanoantennas and / or forces acting on the nanodrones. To this end, the imaging system may comprise, for example, an additional light source. Additionally or alternatively, the imaging system may also be configured to image the nanodrones at a wavelength resonant with one or more of the nanoantennas and / or using circularly polarized light, for example to determine the position of each nanoantenna. To this end, the imaging system may use, for example, light generated by an illumination system.

[0087] The controller may be implemented in hardware, software, or a combination thereof. The controller may comprise, for example, a processor and a storage medium including instructions executed by the processor to provide the functionality described herein. In some embodiments, the controller may be configured to perform some or all of the steps of a method of operating a nanodrone according to any one of the embodiments described herein.

[0088] The motion command may, for example, specify a translation and / or rotation to be performed with the nanodrone, e.g., a direction and distance for a linear translation of the nanodrone and / or a direction and angle for a rotation of the nanodrone. The motion command may further specify a speed and / or an angular velocity at which the nanodrone is moved. The motion command may also specify more complex operations that may include, for example, translations and rotations performed simultaneously and / or a sequence of one or more translations and / or one or more rotations. The motion command may, among other things, specify a path along which the nanodrone is moved. The motion command may also specify a speed profile along which the nanodrone is moved along the specified path. The motion command may, for example, be received from a user or another device. In some embodiments, the motion command may also be generated and / or modified by the controller itself, e.g., as part of a feedback control loop. In one example, the motion command may specify, for example, a position and / or an orientation at which the nanodrone is held.

[0089] The orientation of the nanodrone can be determined, for example, by determining one or more rotation angles, e.g., one or more Euler angles, of the nanodrone relative to a stationary reference axis, such as an axis in a reference frame of the illumination and / or imaging system, e.g., a normal direction or an axis perpendicular to the normal direction. The controller can determine the orientation of the nanodrone by determining the location of one or more reference points on the nanodrone and / or the orientation of one or more reference axes of the nanodrone in an image obtained from the microscope. The one or more reference points can include, for example, one or more nanoantennas, a center of the nanodrone, and / or one or more reference features on the nanodrone, which can include, for example, a notch and / or a protrusion along the circumference of the nanodrone, an opening or hole in the nanodrone, and / or a protrusion and / or a recess on the top or bottom surface of the nanodrone. The one or more reference axes can include, for example, one or more axes of symmetry of the nanodrone, a longitudinal axis along which the nanodrone has a maximum extent, and / or a lateral axis along which the nanodrone has a minimum extent. In some embodiments, the controller may also be configured to determine the position of the nanodrone from images obtained from the imaging system, for example by determining the position of the center of the nanodrone.

[0090] The controller may be configured to determine the polarization and intensity of each beam generated by the illumination system. To determine the polarization and intensity of the light generated by the illumination system, the controller may be configured to transform the motion command into the reference frame of the nanodrone, for example, by applying a rotation to the motion command by the determined rotation angle. The controller may be further configured to determine a magnitude and / or direction of a force and / or a magnitude and / or direction of a torque to be applied to the nanodrone based on the motion command and the determined orientation, for example, based on the transformed motion command. The controller may be further configured to determine the polarization and intensity of the light at the resonant wavelength of the first and second nanoantennas based on the determined force and / or determined torque, for example, by applying a corresponding transformation, which may be based on a mathematical model of the nanodrone and / or a predefined calibration curve.

[0091] The controller may be configured to control some or all of the elements of the illumination system. The controller may be configured in particular to control the output power of some or all of the light sources of the illumination system and / or to control one or more means for controlling the intensity of the light, e.g., to adjust the intensity of the light at the resonant wavelengths of the first and second nanoantennas to a determined value. The controller may further be configured to control one or more wave plates and / or polarizers, e.g., to adjust the polarization of the light at the resonant wavelengths of the first and second nanoantennas to a determined value.

[0092] In some embodiments, a system for operating nanodrones may include one or more nanodrones according to any one of the embodiments described herein. Additionally or alternatively, the system may also include one or more chambers or wells in which the nanodrones are operated.

[0093] In the following, a detailed description of the invention and its exemplary embodiments is given with reference to the drawings. [Brief description of the drawings]

[0094] [Figure 1a] FIG. 2 is a top view of a nanoantenna for a nanodrone according to an exemplary embodiment of the present invention when illuminated with right-hand circularly polarized light. [Figure 1b] FIG. 1b is a side view of the nanoantenna of FIG. [Figure 1c] FIG. 1b is a top view of the nanoantenna of FIG. 1a according to an exemplary embodiment of the present invention when illuminated with left-handed circularly polarized light. [Figure 1d] FIG. 1b is a top view of the nanoantenna of FIG. 1a according to another exemplary embodiment of the present invention when illuminated with left-handed circularly polarized light. [Figure 2a] FIG. 2 is a diagram of a nanodrone equipped with a pair of nanoantennas according to an exemplary embodiment of the present invention when illuminated using a first illumination scheme. [Figure 2b] FIG. 2b is a diagram of the nanodrone of FIG. 2a when illuminated using a second illumination scheme. [Figure 3a] FIG. 2 is a top view of a nanoantenna comprising multiple resonators in accordance with an exemplary embodiment of the present invention. [Figure 3b] FIG. 2 is a top view of a nanoantenna comprising multiple resonators according to another exemplary embodiment of the present invention. [Figure 4] FIG. 3B illustrates the generation of directional forces using the nanoantennas of FIGS. 3a and 3b. [Figure 5a] FIG. 1 is a diagram of a nanodrone having a pair of nanoantennas with resonators according to an exemplary embodiment of the present invention. [Figure 5b] FIG. 1 is a diagram of a nanodrone having four nanoantennas with resonators according to an exemplary embodiment of the present invention. [Figure 6] FIG. 5B is an illumination scheme for addressing the degrees of freedom of movement of the nanodrones of FIGS. 5a and 5b. [Figure 7] FIG. 1 is a diagram of a system for operating a nanodrone, according to an exemplary embodiment of the present invention. [Figure 8] 1 is a flowchart of a method of operating a nanodrone according to an exemplary embodiment of the present invention. [Figure 9] 1A-1D are scanning electron micrographs and optical micrographs of nanodrones according to exemplary embodiments of the present invention. [Figure 10] 13 is experimental data showing independent control of two degrees of freedom of movement in two dimensions for a nanodrone with four nanoantennas, in accordance with an exemplary embodiment of the present invention. [Figure 11a] FIG. 1 is a top view of a roll / pitch nano-antenna for a nanodrone in accordance with an exemplary embodiment of the present invention. [Figure 11b] FIG. 11b is a side view of the roll / pitch nano-antenna of FIG. [Figure 12] FIG. 1 illustrates a top view of a nanodrone with roll and pitch nano-antennas in accordance with an exemplary embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0095] Figures 1a and 1b show schematic diagrams (not to scale) of a nanoantenna 100 for a nanodrone according to an exemplary embodiment of the invention, such as the nanodrone 200 of Figures 2a and 2b. In Figure 1a, the nanoantenna 100 is shown in a top view along the Z axis of Figure 1b, which may hereinafter be referred to as the normal axis. In Figure 1b, the nanoantenna 100 is shown in a side view along the Y axis of Figure 1a.

[0096] The nanoantenna 100 comprises one or more structures (not shown), in particular conductive structures such as nanoscale metallic rods, e.g., as described in more detail below with reference to Figures 3a and 3b. The nanoantenna 100 exhibits an optically addressable resonance at a resonant wavelength where light incident on the nanoantenna is resonantly scattered by resonant coupling to one or more excitation modes, e.g., plasmonic or phononic modes, in the conductive structures of the nanoantenna 100. This can result in an enhanced scattering cross section and therefore an enhanced scattering rate of light at the resonant wavelength, as described below with reference to Figure 4.

[0097] The nanoantenna 100 receives a first circularly polarized light j in= L (left circular polarization / clockwise polarization) or R (right circular polarization / counterclockwise polarization), resulting in a far-field scattering pattern of the nanoantenna 100, i.e., the intensity distribution I of the light scattered by the nanoantenna 100. out is not symmetric when projected onto a plane perpendicular to the normal direction, e.g., the far-field scattering pattern when projected onto this plane is not inversion symmetric. out (θ, φ) ≠ I out (π-θ, φ+π) and I out (θ, φ) ≠ I out (θ, φ+π), where θ and φ are the polar and azimuthal angles, respectively, relative to the normal direction, i.e., the (three-dimensional) far-field scattering pattern is neither inversion-symmetric with respect to the origin nor rotationally-symmetric about the normal direction.

[0098] In the example of Fig. 1a and Fig. 1b, the normal direction corresponds to the Z direction in Fig. 1b, i.e., the incident light has a wave vector k in and the first circular polarization is right-handed circular polarization (j in =R). Due to asymmetric scattering by the nanoantenna 100, in the following, the in-plane wave vector

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[0099] The nanoantenna 100 may be implemented in one of two forms that differ in their response to light of opposite circular polarization:

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[0100] A first shape nanoantenna 100A shown in FIG. 1c has light incident along the normal direction and opposite circular polarizations such that the far-field scattering pattern of the light emitted by the nanoantenna 100 is not symmetric with respect to the normal direction.

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[0101] In contrast, a second shape nanoantenna 100B, shown in FIG. 1d, receives light incident along the normal direction and with the opposite circular polarization.

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[0102] 2a and 2b show schematic diagrams (not to scale) of a nanodrone 200 in a top view according to an exemplary embodiment of the present invention, the nanodrone 200 being illuminated using a first illumination scheme in FIG. 2a and a second illumination scheme in FIG. 2b.

[0103] The nanodrone 200 comprises a substrate 202 extending perpendicular to a normal direction, which may be, for example, anti-parallel to the viewing direction of Figs. 2a and 2b. Preferably, at least a part of the substrate 202 or the entire substrate 202 is optically transparent. The substrate 202 may, for example, comprise or consist of a transparent polymeric material, such as glass and / or a transparent thermoplastic material. Preferably, the substrate 202 comprises or consists of a material suitable for manufacturing by photolithography and / or electron beam lithography and / or 3D nanoprinting, such as a photoresist and / or an electron beam resist. The substrate 202 may, for example, comprise or consist of hydrogen silsesquioxane (HSQ), poly(methyl methacrylate) (PMMA), silicon dioxide (SiO2), SU-8 photoresist, two-photon polymerization resin, polyphenylaldehyde (PPA), and / or AR-N series resists sold by ALLRESIST GmbH. The substrate 202 may be, for example, a circular slab having a substantially flat surface, as in the examples of Figures 2a and 2b, and the diameter of the substrate 202 in the XY plane may be, for example, 0.5 μm to 100 μm, and in some examples 1 μm to 10 μm. The thickness of the substrate 202 along the normal direction may be, for example, 20 nm to 10 μm, and in some examples 50 nm to 1 μm.

[0104] The nanodrone 200 further comprises a pair of nanoantennas 100-1 and 100-2, hereinafter referred to as the first nanoantenna 100-1 and the second nanoantenna 100-2, respectively. In the example of Fig. 2a-b, the first and second nanoantennas 100-1, 100-2 are nanoantennas of a first type, such as the nanoantenna 100A of Fig. 1c, i.e., the in-plane wave vectors of the scattered photons are

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[0105] The first and second nanoantennas 100-1, 100-2 are disposed on and / or within the substrate 202 and are arranged symmetrically with respect to the center of mass 204 of the nanodrone 200, i.e., such that the center of mass 204 is in the middle of the connection vector connecting the center of the first nanoantenna 100-1 and the center of the second nanoantenna 100-2. The first and second nanoantennas 100-1, 100-2 are aligned along the in-plane wave vector

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[0106] The first and second nanoantennas 100-1, 100-2 may have different resonant wavelengths, the difference between which may be, for example, 50 nm to 500 nm, preferably 100 nm to 300 nm, making it possible to selectively address either the first nanoantenna 100-1 or the second nanoantenna 100-2 using light at their respective resonant wavelengths without the need to focus the light on each nanoantenna.

[0107] In the example of FIG. 2a, the nanodrone 200 is illuminated along the normal direction with left-handed circularly polarized light at the resonant wavelength (j1=L) of the first nanoantenna 100-1 and right-handed circularly polarized light at the resonant wavelength (j2=R) of the second nanoantenna 100-2. In this case, the in-plane wave vectors of the photons scattered by the first and second nanoantennas 100-1, 100-2 both point along the negative X direction in FIG. 2a, thereby generating a force F on the nanodrone 200 that points along the X direction. The intensities of the light at the resonant wavelength of the first nanoantenna 100-1 and the light at the resonant wavelength of the second nanoantenna 100-2 can be balanced such that the in-plane force imparted by the scattered light on each nanoantenna (proportional to the sum over the in-plane wave vectors of all photons scattered by each nanoantenna) has substantially the same magnitude for both nanoantennas 100-1, 100-2. In this case, the torques generated by the two nanoantennas 100-1, 100-2 are cancelled out and only a force F is generated, no net torque is generated. In this way, the nanodrone 200 can be moved along the X direction and the direction of motion can be reversed by inverting the polarization of light at both the resonant wavelength of the first nanoantenna 100-1 and the resonant wavelength of the second nanoantenna 100-2 (i.e., j1=R and j2=L).

[0108] In the example of FIG. 2b, the nanodrone 200 is illuminated along the normal direction with left-handed circularly polarized light at both resonant wavelengths (j1=L and j2=L), i.e., the polarization of light at the resonant wavelength of the second nanoantenna 100-2 is inverted with respect to the illumination scheme of FIG. 2a. This causes the in-plane wave vector of the photons scattered by the second nanoantenna 100-2, and therefore the force generated by the second nanoantenna 100-2, to be inverted such that instead of a force F as in FIG. 2a, a torque M acting on the nanodrone 200 is generated, which is collinear with the normal direction. In this way, the nanodrone 200 can be rotated around the normal direction, and the direction of rotation can be inverted by inverting the polarization of light at both the resonant wavelength of the first nanoantenna 100-1 and the resonant wavelength of the second nanoantenna 100-2 (i.e., j1=R and j2=R).

[0109] 3a and 3b show schematic diagrams (not to scale) of nanoantennas 300A and 300B in top view, respectively, according to exemplary embodiments of the present invention. Nanoantenna 300A is a first shape nanoantenna similar to nanoantenna 100A of FIG. 1c, while nanoantenna 300B is a second shape nanoantenna similar to nanoantenna 100B of FIG. 1d.

[0110] Each of the nanoantennas 300A, 300B includes a conductive structure, e.g., three conductive structures 302-1, 302-2, and 302-3 as in the example of Figs. 3a, 3b. Each of the conductive structures 302-1 to 302-3 may include or consist of a metal, e.g., gold, silver, aluminum, and / or copper. In other embodiments, some or all of the structures 302-1, 302-2, and 302-3 may also be dielectric or semiconductive structures and may include or consist of a transparent material, e.g., glass. Each of the conductive structures 302-1 to 302-3 forms a resonator for one or more excitation modes, e.g., plasmon modes or phonon modes, which couple to light, e.g., via electric dipole moments and / or magnetic dipole moments. Thus, an excitation mode may be excited by absorption of one or more photons and may decay by emission of one or more photons, thereby giving rise to one or more optically addressable resonances. Thus, the conductive structures 302-1 to 302-3 may be referred to as resonators. Each of the resonators 302-1, 302-2, and 302-3 may have a resonator axis 304-1, 304-2, and 304-3, respectively, which may be aligned with a direction of an electric dipole moment and / or a magnetic dipole moment associated with a respective excitation mode, which may correspond, for example, to a longitudinal axis of the respective resonator.

[0111] In the example of FIG. 3a and FIG. 3b, each of the resonators 302-1 to 302-3 of the nanoantennas 300A and 300B is a rectangular rod. The resonant wavelength of each of the resonators 302-1 to 302-3 can be tuned by adjusting the physical dimensions of the respective resonators, such as, for example, its length l and / or its width w. The length l of the resonators 302-1 to 302-3 may be, for example, about 50 nm to 2 μm, and in some examples, 100 nm to 400 nm. The width w of the resonators 302-1 to 302-3 may be, for example, about 10 nm to 500 nm, and in some examples, 20 nm to 100 nm. The height of the resonators 302-1 to 302-3 along the normal direction may be, for example, about 10 nm to 500 nm, and in some examples, 20 nm to 100 nm. The resonators 302-1 to 302-3 of a given nanoantenna, e.g., nanoantenna 300A, may have similar shapes and / or similar resonant wavelengths. For example, the width w and / or length l of the resonators 302-1 to 302-3 of each nanoantenna may differ by less than 50%. Preferably, the resonators 302-1 to 302-3 of each nanoantenna have substantially the same shape and / or the same resonant wavelength. For example, the width w and / or length l of the resonators 302-1 to 302-3 of each nanoantenna may differ by less than 20%, in some instances less than 10%, and in one instance less than 5%. The resonant wavelengths of the resonators 302-1 to 302-3 of each nanoantenna may differ by, for example, less than 300 nm, preferably less than 200 nm, in some instances less than 50 nm, and in one instance less than 10 nm.

[0112] 3a, the resonators 302-1-302-3 of the nanoantenna 300A are arranged in a U-shaped configuration, with the first resonator 302-1 and the third resonator 302-3 positioned adjacent opposite ends of the second resonator 302-2, e.g., such that the corners of the respective resonators face each other and are spaced a distance d apart. The first and third resonators 302-1, 302-3 are positioned substantially parallel to each other and substantially perpendicular to the second resonator 302-2, e.g., such that the resonator axes 304-1, 304-3 are substantially parallel to each other and substantially perpendicular to the resonator axis 304-2. The distance d can be selected to be small enough so that the excited modes in the resonators 302-1 to 302-3 are coupled to each other, for example, via evanescent fields leaking from the resonators 302-1 to 302-3 and / or via electric and / or magnetic fields generated by charge accumulation in the resonators 302-1 to 302-3. The distance d may be, for example, between 2 nm and 100 nm, and in some examples between 4 nm and 50 nm. Preferably, the coupling strength between adjacent resonators is greater than the detuning of the respective resonators, i.e. the difference between the resonant wavelengths of the respective resonators, so that the coupling between the resonators 302-1 to 302-3 gives rise to a common mode corresponding to a superposition of the modes of the individual resonators 302-1 to 302-3. The coupling strength may, for example, be at least two times the detuning, preferably at least five times the detuning.

[0113] In the example of FIG. 3b, the resonators 302-1-302-3 of the nanoantenna 300B are arranged in an F-shaped configuration. The first resonator 302-1 is, for example, positioned adjacent to a first end of the second resonator 302-2 such that the corners of each resonator face each other and are separated by a similar distance d as the corresponding resonator of the nanoantenna 300A. The distance d may be selected to be small enough so that the excitation modes in the first resonator 302-1 and the second resonator 302-2 are coupled to each other. The third resonator 302-3 is, for example, positioned on a side of the first resonator 302-1 facing outward from the second resonator 302-2 such that the first resonator 302-1 is positioned between the first end of the second resonator 302-2 and the third resonator 302-3. The distance d3 between the first resonator 302-1 and the third resonator 302-3 may be selected to be large enough so that the modes of the first resonator 302-1 and the third resonator 302-3 are not coupled to each other via the evanescent field. Similar to the configuration of FIG. 3a, the first and third resonators 302-1, 302-3 are substantially parallel to each other and substantially perpendicular to the second resonator 302-2. The first and second resonators 302-1, 302-2 may have substantially the same shape and / or the same resonant wavelength, for example, similar to the nanoantenna 300A. The third resonator 302-3 may be slightly smaller than the first resonator 302-1, for example, such that the resonant wavelength of the third resonator 302-3 is slightly smaller than the resonant wavelength of the first resonator 302-1. The length l3 of the third resonator 302-3 may be, for example, 70% to 95%, and in some examples, 85% to 95%, of the length L of the first resonator 302-1. The resonant wavelength of the third resonator 302-3 may be, for example, 10 nm to 300 nm, and in some examples, 50 nm to 200 nm, which is smaller than the resonant wavelength of the first resonator 302-1.

[0114] FIG. 4 shows the numerically simulated radiation characteristics of a U-shaped nanoantenna (Type I), such as nanoantenna 300A in FIG. 3a, and an F-shaped nanoantenna (Type II), such as nanoantenna 300B in FIG. 3b, illustrating the operating principles of each shape of nanoantenna.

[0115] Panel a shows the results for illumination with left circularly polarized light (clockwise, CW) in the top row and right circularly polarized light (counterclockwise, CCW) in the bottom row. The left column shows the radiation characteristics of a U-shaped nanoantenna, the right column shows the radiation characteristics of an F-shaped nanoantenna, and the center column shows the radiation characteristics of a nanoantenna comprising a pair of coupled resonators in an L-shaped configuration, such as resonators 302-1 and 302-2. The left subplot of each column shows the numerically simulated near-field intensity distribution of the illuminated nanoantenna, and the right subplot of each column shows the numerically simulated far-field intensity distribution of light scattered by the nanoantenna, with the arrows indicating the force on the nanoantenna generated by the scattered light.

[0116] Coupling between two substantially perpendicular resonators, such as resonators 302-1 and 302-2, can give rise to a common mode corresponding to a symmetric and antisymmetric superposition of modes in the individual resonators. Illumination with circularly polarized light can excite a symmetric or antisymmetric superposition of the common mode, thereby resulting in local excitation of only one of the resonators, as shown in the left subplot of the center column of panel a. Each resonator can have a dipole-like emission characteristic, with light emitted primarily in a direction perpendicular to the respective resonator axis. When the two resonators are positioned at an angle to each other, the response of the nanoantenna is chiral, i.e., the nanoantenna exhibits different intensity distributions of emitted light for left- and right-handed circularly polarized illumination, as shown in the right subplot of the center column of panel a.

[0117] The third resonator 302-3 can act as a reflector or directing element to break the inversion symmetry of the radiation intensity distribution, thereby resulting in a non-zero in-plane wave vector of the scattered photons and thus a non-zero in-plane force on the nanoantenna. In other embodiments, instead of or in addition to the third resonator 302-3, a reflective and / or absorptive element can be provided, e.g., a structure configured to absorb light emitted by the first resonator 302-1 and / or the second resonator 302-2 in one direction, e.g., at least partially, in the X direction in Figures 3a, 3b, to break the inversion symmetry.

[0118] In an F-shaped nanoantenna, for example as shown in the right column of panel a, the distance d3 between the first resonator 302-1 and the third resonator 302-3 and / or the resonant wavelength of the third resonator 302-3 can be selected such that the light emitted by the first and third resonators 302-1, 302-3 constructively interferes in a first direction, e.g., the negative X direction in Fig. 3b, and destructively interferes in a second direction opposite to the first direction, e.g., the X direction in Fig. 3b. Thus, when illuminating the nanoantenna such that the first resonator 302-1 is excited (left circular polarization in the example of Fig. 4), the nanoantenna can mainly scatter light in a first direction such that a force is generated in the opposite direction. In contrast, when the nanoantenna is illuminated such that the second resonator 302-2 is excited (right-handed circularly polarized light in the example of FIG. 4), the dipole-like emission characteristics of the second resonator 302-2 and the third resonator 302-3 can result in a substantially inversion-symmetric intensity distribution of the scattered light such that the force on the nanoantenna is substantially zero.

[0119] In a U-shaped nanoantenna such as that shown in the left column of panel a, the coupling of the three resonators 302-1 to 302-3 can give rise to a common mode corresponding to a superposition of modes from each of the three resonators. Illumination with circularly polarized light can excite a superposition of the common mode that is primarily localized in either the first resonator 302-1 or the third resonator 302-3. Interference between the light emitted by the first and third resonators 302-1, 302-3 can result in an asymmetric intensity distribution of the emitted light for both circular polarizations, with the in-plane wave vector, and therefore the generated force, being substantially antiparallel for left- and right-handed circular polarizations. Since the second resonator 302-2 is disposed adjacent to the upper ends of the first and third resonators 302-1, 302-3 along the Y-axis, the in-plane wave vectors for the left-handed and right-handed circularly polarized light do not have to be perfectly anti-parallel, but may be at an angle of, for example, 150° to 210° to each other, in some examples 160° to 200°, and preferably 170° to 190°.

[0120] Panels b and c show the numerically simulated magnitude of the forces generated on a U-shaped and an F-shaped nanoantenna, respectively, upon illumination with circularly polarized light. For both shapes of nanoantennas, results are shown for two nanoantennas with different resonant wavelengths (solid / dotted: 830 nm, dash-dotted / dotted-dotted: 980 nm), which were obtained by appropriately adjusting the resonator dimensions such as length l and width w.

[0121] Each of the nanoantennas exhibits a pronounced resonant peak at its respective resonant wavelength where the force on the nanoantenna is greatest. The difference between the resonant wavelengths of the U-shaped nanoantennas in panel b is selected such that the force on the smaller nanoantenna, with a resonant wavelength of 830 nm, exhibits a zero crossing at the resonant wavelength of the larger nanoantenna, at 980 nm. The force on the U-shaped nanoantenna in panel b may be substantially equal in magnitude for both circularly polarized light. Thus, the response of the nanoantenna is shown only for a single polarization in panel b for illustrative purposes.

[0122] In panel c, the response of the F-shaped nanoantenna is shown for both circular polarizations. With the nanoantenna oriented as shown in Figure 3b, illumination with left-handed circularly polarized light produces a nonzero force, while illumination with right-handed circularly polarized light produces substantially zero force. In contrast, an inverted configuration (i.e., a "mirror image" of the nanoantenna shown in Figure 3b) can show the opposite response, i.e., illumination with right-handed circularly polarized light produces a nonzero force, while illumination with left-handed circularly polarized light produces substantially zero force.

[0123] 5a shows a schematic diagram (not to scale) of a nanodrone 500A in a top view according to an exemplary embodiment of the invention. Similar to the nanodrone 200 of FIGS. 2a-b, the nanodrone 500A comprises a substrate 202 and a pair of nanoantennas 300A-1, 300A-2 disposed on and / or in the substrate 202. The substrate 202 is a circular slab, and reference features, such as notches 502, are disposed along the circumference of the substrate 202, for example to determine the orientation of the nanodrone 500A.

[0124] Each of the nanoantennas 300A-1, 300A-2 is a U-shaped nanoantenna with three coupled resonators similar to the nanoantenna 300A of FIG. 3a. The nanoantennas 300A-1, 300A-2 are inversion symmetric (corresponding to two-fold rotational symmetry around the normal direction) with respect to the center of mass 204 of the nanodrone 500A, i.e., the nanoantennas 300A-1, 300A-2 are mirror images of each other and are located on either side of the center of mass 204 at the same distance from the center of mass 204. The nanoantennas 300A-1, 300A-2 may have different resonant wavelengths. For example, the length l of the resonator of the first nanoantenna 300A-1 may be shorter than the length of the resonator of the second nanoantenna 300A-2, or vice versa (not shown). The resonator width w of the nanoantennas 300A-1, 300A-2 may be selected such that both nanoantennas 300A-1, 300A-2 have the same mass, e.g., if the resonator length l of the first nanoantenna 300A-1 is shorter than the resonator length of the second nanoantenna 300A-2, then the resonator width w of the first nanoantenna 300A-1 is longer than the resonator width of the second nanoantenna 300A-2, or vice versa.

[0125] 5b shows a schematic diagram (not to scale) of a nanodrone 500B in a top view according to another exemplary embodiment of the present invention. Similar to the nanodrone 500A of FIG. 5a, the nanodrone 500B also comprises a substrate 202 having a notch 502. Instead of a pair of U-shaped nanoantennas 300A-1, 300A-2, the nanodrone 500B comprises four F-shaped nanoantennas 300B-1, 300B-2, 300B-3 and 300B-4, each comprising a pair of coupled resonators and a third resonator similar to the nanoantenna 300B of FIG. 3b.

[0126] The four nanoantennas 300B-1 to 300B-4 are arranged in inversion symmetry with respect to the center of mass 204 of the nanodrone 500B, and each has mirror symmetry with respect to a symmetry plane parallel to the XZ plane and the XY plane and including the center of mass 204. In other words, the third and fourth nanoantennas 300B-3, 300B-4 are mirror images of the first nanoantenna 300B-1, and the second nanoantenna 300B-2 corresponds to a copy of the first nanoantenna 300B-1 rotated by 180°. In such an arrangement, the first pair of nanoantennas, i.e., the first and second nanoantennas 300B-1, 300B-2, can scatter circularly polarized light at their respective resonant wavelengths incident along the normal direction, resulting in a mean wave vector for polarization j (e.g., left circular polarization j=L).

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[0127] A third pair of nanoantennas, e.g., the first and third nanoantennas 300B-1, 300B-3, can have the same resonant wavelength, and a fourth pair of nanoantennas, e.g., the second and fourth nanoantennas 300B-2, 300B-4, can have the same resonant wavelength, with the resonant wavelength of the fourth pair of nanoantennas being different from the resonant wavelength of the third pair of nanoantennas. Thus, the third and fourth pairs of nanoantennas can be selectively addressed by selecting the wavelength of the incident light accordingly. In combination with the polarization dependence of the mean wave vector of the scattered photons, this allows each of the nanoantennas to be individually selectively addressed by appropriate selection of the polarization and wavelength of the incident light, e.g., as described in more detail below with reference to FIG. 6. In other embodiments, different arrangements and different resonant wavelengths of the nanoantennas 300B-1 to 300B-4 may be selected, for example, such that the first and third nanoantennas 300B-1, 300B-3 may be addressed with the same polarization but may have different resonant wavelengths, and the second and fourth nanoantennas 300B-2, 300B-4 may be addressed with the same polarization but may have different resonant wavelengths.

[0128] FIG. 6 shows a schematic of how the fundamental motional degrees of freedom of nanodrone 500A of FIG. 5a (top) and nanodrone 500B of FIG. 5b (bottom) can be controlled using a pair of circularly polarized beams at their respective resonant wavelengths.

[0129] The first nanoantenna 300A-1 of the nanodrone 500A is oriented in the nanodrone 500A orientation as shown in Figures 5a and 6, i.e., such that the in-plane wave vector of the scattered photons is substantially parallel to the Y direction of Figure 5a for right-handed circularly polarized illumination and substantially anti-parallel to the Y axis of Figure 5a for left-handed circularly polarized illumination. In contrast, the second nanoantenna 300A-2 of the nanodrone 500A is oriented in the nanodrone 500A orientation as shown in Figures 5a and 6, i.e., such that the in-plane wave vector of the scattered photons is substantially anti-parallel to the Y direction of Figure 5a for right-handed circularly polarized illumination and substantially parallel to the Y axis of Figure 5a for left-handed circularly polarized illumination.

[0130] Thus, for the nanodrone 500A, a torque substantially parallel or antiparallel to the normal direction can be generated by illuminating the nanodrone 500A with right- and left-handed circularly polarized light, respectively, at both resonant wavelengths (top left-most and top right-most panels of FIG. 6). A force substantially perpendicular to the connection vector between the first nanoantenna 300A-1 and the second nanoantenna 300A-2 (i.e., collinear with the Y-axis for the orientation of the nanodrone 500A, as shown in FIG. 5a) can be generated by illuminating the nanodrone 500A with right-handed circularly polarized light at one resonant wavelength and left-handed circularly polarized light at the other resonant wavelength, and the direction of the force can be reversed by reversing the circular polarization (top middle panel of FIG. 6). In this way, two degrees of freedom of motion (rotation around the normal direction and translation in one direction perpendicular to the normal direction) can be controlled independently.

[0131] The nanoantennas 300B-1 to 300B-4 of the nanodrone 500B, in which the in-plane wave vector of the scattered photons is non-zero for one circular polarization but substantially zero for the opposite circular polarization, are arranged such that the in-plane wave vector for the first and second nanoantennas 300B-1, 300B-2 (first pair of nanoantennas) is non-zero and substantially anti-parallel for illumination with left-handed circular polarization (see, for example, the second panel from the left in the bottom row of FIG. 6), and the in-plane wave vector for the third and fourth nanoantennas 300B-3, 300B-4 (second pair of nanoantennas) is non-zero and substantially anti-parallel for illumination with right-handed circular polarization (see, for example, the second panel from the right in the bottom row of FIG. 6). Furthermore, the nanoantennas 300B-1 through 300B-4 are oriented such that their non-zero in-plane wave vectors are substantially perpendicular to the connection vector between the center of mass 204 and the respective nanoantenna, i.e., substantially tangential to the concentric circles around the center of mass 204 on which the nanoantennas 300B-1 through 300B-4 are disposed.

[0132] Thus, for nanodrone 500B, a torque substantially parallel or antiparallel to the normal direction can be generated in the same way as for nanodrone 500A, i.e., by illuminating nanodrone 500B with right- and left-handed circularly polarized light at both resonant wavelengths (second-left and second-right panels in the bottom row of FIG. 6), respectively. A force in a first direction substantially perpendicular to the connection vector between the first nanoantenna 300B-1 and the fourth nanoantenna 300B-4 (i.e., collinear with the X-axis for the orientation of nanodrone 500B, as shown in FIG. 5b) can be generated by illuminating nanodrone 500B with right-handed circularly polarized light at one resonant wavelength and left-handed circularly polarized light at the other resonant wavelength, and the direction of the force can be reversed by reversing the circular polarization (middle panel in the bottom row of FIG. 6). A force in a second direction, substantially perpendicular to the connection vector between the first nanoantenna 300B-1 and the third nanoantenna 300B-3 and thus substantially perpendicular to the first direction (i.e., collinear with the Y-axis for the orientation of the nanodrone 500B, as shown in FIG. 5b), can be generated by illuminating the nanodrone 500B with left and right circularly polarized light at one of the resonant wavelengths (e.g., the resonant wavelength of the third pair of nanoantennas formed by the first and third nanoantennas 300B-1, 300B-3, the rightmost panel in the bottom row of FIG. 6, or the resonant wavelength of the fourth pair of nanoantennas formed by the second and fourth nanoantennas 300B-2, 300B-4, the leftmost panel in the bottom row of FIG. 6), simultaneously with, for example, linearly polarized light, and the direction of the force can be reversed by changing to the other resonant wavelength. In this way, all three degrees of freedom of motion in two dimensions (rotation around the normal direction and translation in two orthogonal directions perpendicular to the normal direction) can be independently controlled.

[0133] 7 shows a schematic diagram (not to scale) of a system 700 for operating a nanodrone in a side view according to an exemplary embodiment of the present invention. The system 700 can be used to operate a nanodrone according to any one of the embodiments described herein, such as the nanodrone 200 of FIG. 2a, 2b as shown in FIG. 7, and is used below as a non-limiting example for illustrative purposes. The system 700 may be configured to operate a nanodrone, for example, by at least partially executing the method 800 of FIG. 8.

[0134] The system 700 comprises an illumination system 702 configured to generate polarized light at two wavelengths, e.g., at the resonant wavelengths of a pair of nanoantennas 100-1, 100-2 of the nanodrone 200. To this end, the illumination system 702 comprises a pair of light sources 704A, 704B, e.g., a pair of lasers, each of which is configured to generate light at each of the two wavelengths and associated with a respective optical path within the system 700. The light generated by the light sources 704A, 704B may already be polarized, e.g., linearly polarized, or may subsequently be polarized using a polarizer (not shown) along each optical path. The light generated by the light sources 704A, 704B can be superimposed and combined into a common optical path using a dichroic mirror 710B.

[0135] The illumination system 702 is further configured to adjust the polarization and intensity of the light at the two wavelengths. Each of the light sources 704A, 704B may be configured, for example, to adjust the output power of the generated light. Additionally or alternatively, the illumination system 702 may comprise a means for adjusting the intensity of the light propagating along the respective optical paths, for example a wave plate in combination with an acousto-optical modulator or a polarizer. The illumination system further comprises a half-wave plate (λ / 2 wave plate) 706A, 706B in the optical paths of each of the light sources 704A, 704B, configured to rotate the linear polarization of the light propagating along the respective optical paths. The illumination system 702 further comprises a quarter-wave plate (λ / 4 wave plate) 712 in the common optical path, the quarter-wave plate being configured to convert the linearly polarized light into an elliptically polarized light, in particular a circularly polarized light, depending on its orientation relative to the slow and fast axes of the quarter-wave plate.

[0136] The system 700 further comprises an imaging system for imaging the nanodrone 200. In the example of FIG. 7, the imaging system is a microscope comprising an objective lens 714 and a photodetector 716, where the objective lens 714 may be, for example, a high NA objective lens, in particular a water or oil immersion objective lens, and may be configured to image the plane in which the nanodrone 200 is operated on the photodetector 716. The photodetector may be, for example, a CCD or CMOS chip configured to record a spatially resolved image. The illumination system 702 may comprise lenses 708A, 708B in the optical path of each of the light sources 704A, 704B, for example, to focus the light propagating along the respective optical paths at the back focal plane of the objective lens 714, so that, for example, the respective beams are collimated at the front focal plane of the objective lens 714, which may coincide with the plane in which the nanodrone 200 is operated. The diameter of the illumination beam at the front focal plane of the objective lens 714 may be, for example, 20 μm to 500 μm, such that the entire nano drone 200 is uniformly illuminated. The illumination system 702 may further include a dichroic mirror 710A for combining the optical path from the light source 704A with the optical path of the imaging system.

[0137] Both the illumination system 702 and the imaging system of system 700 are configured to illuminate and image the nanodrone 200 from above, respectively, although one or both subsystems may be positioned differently. For example, the imaging system may be positioned below the nanodrone 200 to image the nanodrone from below. In some embodiments, the illumination system 702 may be configured to illuminate the nanodrone with two pairs of counter-propagating beams (not shown), each pair including a beam at each of two wavelengths. One pair of beams may, for example, illuminate the nanodrone 200 from above, while the other pair of beams may illuminate the nanodrone 200 from below.

[0138] The system 700 further comprises a controller 718, which may be implemented in hardware, software, or a combination thereof. The controller 718 may comprise a processor, such as a central processing unit (CPU), a graphics processing unit (GPU), an application specific integrated circuit (ASIC) and / or a field programmable gate array (FPGA), and a storage medium, such as a non-volatile memory and / or a volatile memory, that includes instructions for execution by the processor to provide the functionality described herein. The controller 718 is configured to control the illumination system 702 as well as the imaging system of the system 700. The controller 718 is configured, among other things, to operate the nano drone 200 using the illumination system 702 and the imaging system. To this end, the controller 718 may be configured to perform some or all of the steps of a method 800, which will be described below with reference to FIG. 8.

[0139] The system 700 further comprises a chamber or well 720 in which the nanodrone 200 can operate. The well 720 may be disposed in or on an optically transparent substrate, such as a glass plate or a microfluidic chip (not shown). The well 720 is configured to hold a liquid 722, such as water or an aqueous solution, in which the nanodrone 200 operates. The composition of the liquid 722 may be selected to generate surface charges of equal polarity on the nanodrone 200 and on the bottom surface 720A of the well 720 above which the nanodrone 200 operates. This can generate a repulsive electrostatic force between the nanodrone 200 and the bottom surface 720A to prevent the nanodrone 200 from contacting the bottom surface 720A as a result of the optical pressure generated by the light irradiating the nanodrone 200.

[0140] FIG. 8 shows a flowchart of a method 800 for operating a nanodrone according to an exemplary embodiment of the present invention. The method 800 can be used to operate a nanodrone according to any one of the embodiments described herein, such as the nanodrone 500B of FIG. 5b. The method 800 can be performed using a system for operating a nanodrone according to any one of the embodiments disclosed herein, such as the system 700 of FIG. 7. In particular, some or all of the steps of the method 800 can be performed by a controller of a system for operating a nanodrone according to any one of the embodiments described herein, such as the controller 718 of the system 700 of FIG. 7. The nanodrone 500B, the system 700, and the controller 718 are used as non-limiting examples for the following illustrative purposes. The method 800 is not limited to the order of execution shown in the flowchart of FIG. 8. The method 800 may be performed in any order, and some of the steps may be performed at least partially simultaneously, as long as they are technically feasible. For example, in some embodiments, step 804 may be performed before step 802. Furthermore, some or all of the steps of method 800, such as steps 804 through 808 for moving the nanodrone along the path specified by the motion commands obtained in step 802, may be performed repeatedly.

[0141] A nanodrone such as nanodrone 500B can be provided prior to or as part of method 800. Nanodrone 500B may be provided with a bottom surface 720A above which nanodrone 500B operates, in particular by providing a well such as a chamber or well 720. This may include providing a liquid 722, which may be water, in well 720. Sodium dodecyl sulfate, for example, at a molar concentration of 1 mM to 20 mM, for example 10 mM, and sodium chloride, for example, at a molar concentration of 0.5 mM to 10 mM, for example 5 mM, may be added to liquid 722 to generate surface charges of the same polarity on nanodrone 500B and bottom surface 720A such that repulsive electrostatic forces act on bottom surface 720A and nanodrone 500B.

[0142] In step 802, a motion command is obtained, e.g., by controller 718, where the motion command specifies a movement to be performed by nano-drone 500B. The motion command may specify, e.g., a direction and distance for a linear translation of nano-drone 500B and / or a direction and angle for a rotation of nano-drone 500B. The motion command may specifically specify a path along which nano-drone 500B is to be moved, which may include, e.g., multiple straight and curved segments.

[0143] In step 804, an image of the nanodrone 500B in the well 720 is taken using the imaging system of the system 700 and provided to the controller 718. The controller 718 determines the orientation of the nanodrone 500B, for example, by determining the location of the center of mass 204 and the location of the notch 502 in the image. The controller 718 can, for example, determine the azimuth angle of a vector connecting the center of mass 204 and the notch 502 relative to the normal direction in which the nanodrone 500B is illuminated by the illumination system 702. In some examples, the image of the nanodrone 500B may be taken while illuminating the nanodrone in step 808, for example, using light generated by the illumination system 702, particularly the light used to move the nanodrone 500B.

[0144] In step 806, the controller 718 determines the polarization and intensity of light that the nano-drone 500B is illuminated with to execute the motion command, e.g., the polarization and intensity of light at each resonant wavelength of the nano-antennas 300B-1-300B-4. The controller 718 can, for example, determine the Stokes parameters S0 and S3 of the light at the resonant wavelengths of the first and third nano-antennas 300B-1, 300B-3 and the light at the resonant wavelengths of the second and fourth nano-antennas 300B-2, 300B-4. This can include transforming the motion command into the reference frame of the nano-drone 500B for the orientation of the nano-drone 500B determined in step 804, e.g., by performing a corresponding rotation about the normal direction.

[0145] In step 808, the nanodrone 718 is illuminated along the normal direction with light at the resonant wavelength(s) of one or more of the nanoantennas 300B-1-300B-4 at the polarization and intensity determined in step 806 using the illumination system 702 to perform the movement specified by the motion command. This may include adjusting one or more of the waveplates 706A, 706B, and 712 accordingly to generate light having the desired polarization at the respective resonant wavelengths. This may further include adjusting the output power and / or optical power of the light sources 704A, 704B along their respective optical paths, for example using acousto-optic modulators, to generate light having the desired intensity at the respective resonant wavelengths.

[0146] The polarization of light at each resonant wavelength is given by a nonzero in-plane wave vector

number

[0147] Steps 804-808 may be performed repeatedly, for example, to continuously monitor the orientation of the nano-drone 500B to move the nano-drone 500B along a path or position specified by the motion commands and / or to adjust the polarization and intensity of the illuminating light accordingly. This may include, for example, adjusting the polarization and / or intensity of the light to change the direction and / or magnitude of the force and / or torque and / or to generate a force instead of a torque, or vice versa.

[0148] System 700 and method 800 may also be generalized to perform locomotion with a nanodrone in three dimensions, e.g., as described in more detail below with reference to Figures 11a, 11b, and 12. This may include, among other things, illuminating the nanodrone with polarized light at the resonant wavelength of its nanoantenna along two counter-propagating directions, e.g., along the +Z and +Z directions of Figure 7.

[0149] FIG. 9 shows scanning electron micrographs (panels a-e) and optical micrographs (panel f) of nanodrones according to an exemplary embodiment of the invention. Panel a shows a scanning electron micrograph of a central portion of a nanodrone with four F-shaped nanoantennas similar to nanodrone 500B of FIG. 5b in top view (scale bar 200 nm). Panel b shows a scanning electron micrograph of a central portion of a nanodrone with two U-shaped nanoantennas similar to nanodrone 500A of FIG. 5a in top view (scale bar 200 nm). Panel c shows a 40° tilted view of one of the nanoantennas of the nanodrone of panel a (scale bar 50 nm) on an indium tin oxide (ITO) substrate (scale bar 200 nm), and panel d shows a 40° tilted view of the entire nanodrone of panel a. Panel e shows a top view of an array of nanodrones with either two or four nanoantennas similar to nanodrones 500A and 500B in Figures 5a and 5b, respectively, on an ITO substrate (scale bar 1 μm). Panel f shows an optical microscope image of multiple nanodrones with either two or four nanoantennas released into a chamber filled with water (scale bar 2 μm). The inset in panel f shows a microscope image of a human red blood cell at the same scale for comparison.

[0150] A nanoantenna for a nanodrone according to the invention can be manufactured, for example, as follows: An antenna layer, in particular a conductive layer, can be provided on a structured substrate, the conductive layer being in particular a monocrystalline metal layer, for example monocrystalline gold flakes, arranged on the structured substrate. The structured substrate can comprise one or more layers and can for example comprise or consist of glass. The structured substrate can for example be coated with a thin layer of indium tin oxide (ITO) arranged on the glass. A bottom layer of a carrier substrate for the nanoantenna, which can for example be the substrate 202 of the nanodrone, can be provided on the structured substrate, for example by spin coating, before providing the antenna layer thereon. The bottom layer of the carrier substrate can have a thickness of for example 20 nm to 200 nm, in some examples 50 nm to 100 nm, for example 70 nm. The bottom layer of the carrier substrate can for example comprise or consist of hydrogen silsesquioxane (HSQ).

[0151] The antenna layer may be patterned to define one or more nanoantenna structures, e.g., one or more nanoantenna conductive structures. The antenna layer may be patterned, for example, by ion beam milling, e.g., helium ion beam milling. Preferably, the antenna layer is patterned only by milling the contours of the nanoantenna structures, e.g., by forming trenches in the antenna layer around each structure, the trenches having a width of, for example, 5 nm to 30 nm, in some examples 10 nm to 20 nm. The remaining portions of the antenna layer that do not form any of the nanoantenna structures can then be removed, e.g., by peeling off the respective portions of the antenna layer. This can substantially reduce patterning time and can further improve the quality of the resulting structures, e.g., due to reduced proximity effects and reduced redeposition of sputtered material.

[0152] In some embodiments, a top layer of a carrier substrate may be deposited on the nanoantenna structures and the bottom layer of the carrier substrate. The top layer may, for example, comprise or consist of the same material as the bottom layer, in particular HSQ. The thickness of the top layer may be thicker than the thickness of the bottom layer, for example about twice as thick, so that, for example, the top layer can be used as an etch mask for the bottom layer to define the shape of the carrier substrate.

[0153] The carrier substrate may be patterned to define a shape of the carrier substrate, which may be, for example, a shape of the substrate 202 of the nanodrone. The carrier substrate may be patterned, for example, by electron beam lithography and / or etching. In one example, a top layer of the carrier substrate is first patterned, for example, by electron beam lithography, to form an etch mask for the bottom layer. The bottom layer of the carrier substrate may then be patterned, for example, by a buffered oxide etch, using the top layer as a mask. In some examples, the buffered oxide etch may also reduce the thickness of the top layer, for example, so that the thicknesses of the top layer and the bottom layer are substantially equal.

[0154] In some embodiments, the micro-patterning of the carrier substrate may be performed after patterning the bottom layer, for example by electron beam lithography. The micro-patterning may be, for example, a smooth edge of the carrier substrate. In some examples, a third carrier substrate layer may be deposited on the top layer, for example by spin coating, before the micro-patterning, and the third carrier substrate layer may include or consist of the same material as the top layer and / or the bottom layer, in particular HSQ. This may, for example, improve the flatness of the top surface of the carrier substrate.

[0155] To release the nanodrones, the coating of the structured substrate can be etched, for example, using an acid such as hydrochloric acid, which selectively etches the coating of the structured substrate and not the carrier substrate. The nanodrones can then be removed from the structured substrate for transfer to, for example, a chamber or well such as well 720. The nanodrones can be peeled off from the structured substrate using a polymer such as, for example, polyvinyl alcohol (PVA) polyvinylpyrrolidone (PVP) and / or polymethylmethacrylate (PMMA). For example, a drop of a polymer solution, for example, a polymer solution containing polymethylmethacrylate (PMMA), can be placed on the nanodrones on the structured substrate. After drying, a polymer piece is formed above the nanodrone, which can be attached to the nanodrone and used as a handle to peel the nanodrone from the structured substrate. The polymer piece can then be dissolved to release the nanodrones, for example, into the liquid 722. In some examples, this can include placing a drop of another polymer solution, for example, a polymer solution containing a water-soluble polymer such as PVA, on the surface of the polymer piece, particularly the polymer piece to which the nanodrone is attached. This can form a second polymer handle for the nanodrone. The PMMA polymer piece can then be dissolved, for example using acetone, and the second polymer handle can be used to transfer the nanodrone into liquid 722, which can dissolve the second polymer handle, thereby releasing the nanodrone into liquid 722.

[0156] Figure 10 shows experimental data illustrating independent control of the degrees of freedom of motion of a nanodrone in two dimensions according to an exemplary embodiment of the present invention. The nanodrone comprises four F-shaped nanoantennas similar to the nanodrone 500B of Figure 5b and can be controlled using the illumination scheme shown in the bottom row of Figure 6. Adjacent pairs of nanoantennas share a common resonant wavelength, with the first and third nanoantennas 300B-1, 300B-3 having a resonant wavelength of about 830 nm and the second and fourth nanoantennas 300B-2, 300B-4 having a resonant wavelength of about 980 nm (see Figure 5b). The scale bar is 2 μm and is the same for all panels.

[0157] Panels a and b contain a series of images taken while rotating the nanodrone in the clockwise and counterclockwise directions, respectively. For this, the nanodrone is illuminated with circularly polarized light of the same polarization at both resonant wavelengths, and the direction of rotation can be inverted by inverting the polarization, i.e., by using left circularly polarized light instead of right circularly polarized light at both resonant wavelengths, and vice versa.

[0158] Panel c shows the traces of the nanodrone during linear movement in directions substantially parallel and substantially anti-parallel to the Y-axis. For this, the nanodrone is illuminated with light of only one of the resonant wavelengths, which has both left-handed and right-handed circularly polarized components, and may be, for example, linearly polarized. The direction of motion of the nanodrone can be reversed by switching between the resonant wavelengths, i.e., from the resonant wavelength of the first nanoantenna 300B-1 to the resonant wavelength of the second nanoantenna 300B-2, and vice versa.

[0159] Panel d shows a trace of a nanodrone being translated along a figure-8 path by applying both force and torque to the nanodrone through appropriate selection of the polarization and intensity of the illuminating light.

[0160] 11a and 11b show schematic diagrams of a pitch / roll nanoantenna 1100 in accordance with an exemplary embodiment of the present invention in top and side views, respectively. The pitch / roll nanoantenna 1100 can be used in a nanodrone, such as the nanodrone 1200 of FIG. 12, to achieve control of all six degrees of freedom of movement in three dimensions.

[0161] The nanoantenna 1100 comprises two pairs of coupled resonators arranged in different planes in the substrate 202 of the nanodrone. The first pair of coupled resonators is formed by a first central resonator 1102 and a first distal resonator 1104 arranged in a first plane in the substrate 202 substantially perpendicular to the Z-axis in FIG. 11b. The resonators 1102, 1104 may be arranged at an angle to each other in a V-shaped or L-shaped configuration, in particular substantially perpendicular to each other. The resonators 1102, 1104 may be, for example, similar to the first and second resonators 302-1, 302-1 of the nanoantennas 300A, 300B in FIG. 3a, 3b. The second pair of coupled resonators is formed by a second central resonator 1106 and a second distal resonator 1108 arranged in a second plane in the substrate 202 above the first plane. The resonators 1106, 1108 may also be disposed at an angle to one another in a V-shaped or L-shaped configuration, in particular substantially perpendicular to one another. The resonators 1106, 1108 may also be similar to the first and second resonators 302-1, 302-1 of the nanoantennas 300A, 300B. In some embodiments, each of the resonators 1102 to 1108 may have substantially the same resonant wavelength.

[0162] The central resonators 1102, 1106 are arranged such that the central resonators 1102, 1106 are substantially parallel to each other. In some embodiments, the central resonators 1102, 1106 may overlap each other, for example, such that the first central resonator 1102 completely covers the second central resonator 1106 when viewed along the Z direction, or vice versa, as shown for example in FIG. 11a. In other embodiments, the central resonators 1102, 1106 may be displaced relative to each other in the XY plane and may not overlap each other. The distance between the central resonators 1102, 1106 may be, for example, 50 nm to 1 μm, preferably 50 nm to 500 nm. In some embodiments, the distance between the central resonators 1102, 1106 may be selected such that the modes of the resonators 1102, 1106 are not coupled by the evanescent field.

[0163] Light emitted by one of the central resonators 1102, 1106 may be at least partially absorbed and re-emitted by the other central resonator, and the resonant wavelengths of the resonators 1102, 1106, the common resonant wavelength of the first pair of resonators 1102, 1104, the common resonant wavelength of the second pair of resonators 1106, 1108, and / or the distance between the resonators 1102, 1106 may be selected such that light interferes constructively in a direction collinear with the Z axis and destructively in the opposite direction. This can achieve asymmetric scattering along the Z direction. In other embodiments, the resonant wavelengths of the resonators 1102, 1106 and the distance between the resonators 1102, 1106 can be selected such that scattering along the Z direction is symmetric, for example if the distal resonators 1104, 1108 exhibit asymmetric scattering patterns.

[0164] The distal resonators 1104, 1108 are disposed adjacent to opposite ends of the central resonators 1102, 1106 and extend substantially perpendicular to the central resonators 1102, 1106 in opposite directions, e.g., such that the resonators 1102 to 1108 form a stepped structure in top view as shown in Fig. 11a. The corners of the distal resonators 1104, 1108 face diagonal corners of the central resonators 1102, 1106. The orientation of the first pair of resonators 1102, 1106 is rotated 180° with respect to the orientation of the second pair of resonators 1104, 1108.

[0165] Modes that are primarily localized in the central resonators 1102, 1106 or modes that are primarily localized in the distal resonators 1104, 1108 can be excited by appropriate selection of the circular polarization of the illumination light incident along the normal direction. Modes that are primarily localized in the distal resonators 1104, 1108 can scatter light substantially symmetrically, whereas modes that are primarily localized in the central resonators 1102, 1106 can scatter light asymmetrically, e.g., such that the mean wave vector of the scattered photons has a non-zero component along the normal direction. This can generate a force on the nanoantenna 110 that enhances or at least partially compensates for the optical pressure due to illumination light incident along the normal direction. The force on the nanoantenna along the normal direction is thereby polarization dependent, which can be used to control an additional degree of freedom of motion.

[0166] In some embodiments, the resonant wavelengths of the distal resonators 1104, 1108 and the distance between the distal resonators 1104, 1108 can be selected such that the scattered light interferes constructively in a direction collinear with the Z-axis and destructively in the opposite direction to obtain an asymmetric scattering pattern, in addition to or instead of asymmetric scattering by the central resonators 1102, 1106. In some examples, the resonant wavelengths and arrangements of the resonators 1102 to 1108 are selected such that the mean wave vector of the scattered photons is substantially antiparallel to the normal direction for excitation modes that are primarily localized in the distal resonators 1104, 1108 (e.g., to at least partially compensate for the optical pressure) and for excitation modes that are primarily localized in the central resonators 1102, 1106 (e.g., to at least partially enhance the optical pressure), or vice versa, i.e., the scattered light can generate opposite recoils for left and right circular polarizations.

[0167] 12 shows a schematic diagram of a nanodrone 1200 in a top view according to an exemplary embodiment of the invention. The nanodrone 1200 comprises a substrate 202 and four F-shaped nanoantennas 300B-1 to 300B-4 similar to the nanodrone 500B of FIG. 5b, allowing independent control over three degrees of freedom of movement in the XY plane, as shown in the bottom row of FIG.

[0168] Further, the nanodrone 1200 comprises a pair of roll nanoantennas 1100-1, 1100-2 and a pair of pitch nanoantennas 1100-3, 1100-4, each of which may be similar to the roll / pitch nanoantenna 1100 of Figures 11a, 11b. The roll nanoantennas 1100-1, 1100-2 are disposed along a pitch axis 1204 of the nanodrone 1200 that extends substantially perpendicular to the normal and roll axis 1202 of the nanodrone 1200. The pitch nanoantennas 1100-3, 1100-4 are disposed along the roll axis 1202, i.e., rotated 90° with respect to the roll nanoantennas 1100-1, 1100-2. The roll nanoantennas 1100-1, 1100-2 and the pitch nanoantennas 1100-3, 1100-4 are mirror symmetrical to each other, i.e., the first roll nanoantenna 1100-1 is a mirror image of the second roll nanoantenna 1100-2, and the first pitch nanoantenna 1100-3 is a mirror image of the second pitch nanoantenna 1100-4. This may result in "opposite" scattering responses of the nanoantennas of a given pair (i.e., pair of roll nanoantennas or pair of pitch nanoantennas) to the polarization of the incident light. For example, the first roll nanoantenna 1100-1 may exhibit a similar scattering response to left polarized light (right polarization) as the second roll nanoantenna 1100-2 does to right polarized light (left polarization). This may allow selective addressing of one of the roll nanoantennas and one of the pitch nanoantennas (e.g., to generate non-zero recoil by scattered light) by selecting the polarization of the incident light accordingly.

[0169] The resonant wavelengths of the roll nanoantenna 1100-1 and the pitch nanoantenna 1100-4 can be selected such that the roll nanoantennas 1100-1, 1100-2 have substantially the same resonant wavelengths, and the pitch nanoantennas 1100-3, 1100-4 have substantially the same resonant wavelengths, which may differ from the resonant wavelengths of the roll nanoantennas 1100-1, 1100-2. In this manner, the roll nanoantennas 1100-1, 1100-2 and the pitch nanoantennas 1100-3, 1100-4 can be selectively addressed by selecting the wavelength of the incident light accordingly. In combination with polarization dependent scattering, each of the nanoantennas 1100-1 to 1100-4 can be addressed by appropriate selection of polarization and wavelength. In other embodiments, different wavelength and polarization characteristics of the nanoantennas 1100-1 to 1100-4 can be selected, which also allows for selective addressing of individual nanoantennas, for example as detailed above for the nanodrone 500B of FIG. 5b.

[0170] Preferably, the resonant wavelength of the roll nano-antennas 1100-1, 1100-2 is substantially equal to one of the resonant wavelengths of the first and third nano-antennas 300B-1, 300B-3 or the resonant wavelengths of the second and fourth nano-antennas 300B-2, 300B-4, while the resonant wavelength of the pitch nano-antennas 1100-3, 1100-4 is substantially equal to the other of the resonant wavelengths of the first and third nano-antennas 300B-1, 300B-3 or the resonant wavelengths of the second and fourth nano-antennas 300B-2, 300B-4.

[0171] This may allow for the control of all 3D degrees of freedom of movement using two pairs of counter-propagating polarized beams, i.e., one pair at each of the two resonant wavelengths. If the intensities of the counter-propagating beams are balanced, the pitch and roll nanoantennas may generate no net force or torque, i.e., the force along the normal direction and the torque along the roll and pitch axes 1202, 1204 may be substantially zero. The nanodrone 1200 can then be moved in a plane as described above with reference to FIG. 6. By unbalancing the intensities of the pair of beams at the resonant wavelengths of the roll nanoantennas 1100-1, 1100-2, a torque substantially parallel or substantially anti-parallel to the roll axis 1202 is generated, for example to tilt the nanodrone 1200 around the roll axis 1202. The direction of the torque can be controlled by adjusting the polarization of the beams at the resonant wavelength of the roll nanoantennas 1100-1, 1100-2, for example, by illuminating the nanodrone 1200 with right-handed circularly polarized light from below and left-handed circularly polarized light from above, or vice versa. By unbalancing the intensity of a pair of beams at the resonant wavelength of the pitch nanoantennas 1100-3, 1100-4, a torque substantially parallel or substantially antiparallel to the pitch axis 1204 is generated, for example, to tilt the nanodrone about the pitch axis 1204. The direction of the torque can be controlled by adjusting the polarization of the beams at the resonant wavelength of the pitch nanoantennas 1100-3, 1100-4, for example, by illuminating the nanodrone 1200 with right-handed circularly polarized light from below and left-handed circularly polarized light from above, or vice versa. Furthermore, by using linear polarization and unbalancing the intensity of one or both pairs of beams, a force substantially parallel or substantially antiparallel to the normal direction can be generated, for example, to move the nanodrone 1200 up or down.

[0172] The embodiments of the invention disclosed herein merely constitute specific examples for illustrative purposes. The invention can be implemented in a variety of ways and with many modifications without altering the basic characteristics underlying it. The invention is therefore defined solely by the claims set forth below. [Explanation of symbols]

[0173] 100 Nano Antenna 100A First Shape Nano Antenna 100B Second Shape Nano Antenna j in Polarization of the incident light

number

Claims

1. A nanodrone (200, 500A, 500B, 1200), a substrate (202) extending perpendicular to the normal direction (Z); two or more nanoantennas disposed on and / or within the substrate (202), each of the two or more nanoantennas exhibiting an optically addressable resonance at a respective resonant wavelength; Equipped with The two or more nanoantennas comprise a first nanoantenna (100-1, 300A-1, 300B-1) and a second nanoantenna (100-2, 300A-2, 300B-2), each of which has an average wave number vector i=1 for the first nanoantenna (100-1, 300A-1, 300B-1) and i=2 for the second nanoantenna (100-2, 300A-2, 300B-2) in a plane (X, Y) perpendicular to the normal direction (Z) for left-handed circularly polarized light and right-handed circularly polarized light, respectively. [Equation 1] and configured to scatter circularly polarized light at the respective resonant wavelength incident on the nanoantenna along the normal direction (Z) so as to have j ｉ = L or R [Equation 2] is non-zero, and j ｉ In the case of =R [Equation 3] and j ｉ In the case of =L [Equation 4] is [Equation 5] is substantially zero, or [Equation 6] is substantially antiparallel to [Equation 7] At least one of [Equation 8] is substantially parallel or substantially antiparallel to one of Nanodrone (200, 500A, 500B, 1200).

2. The scattering cross section A- of the first nanoantenna (100-1, 300A-1, 300B-1) at the resonance wavelength of the first nanoantenna (100-1, 300A-1, 300B-1) ｓｃ、１ and, [Equation 9] is substantially parallel or substantially anti-parallel to one of [Equation 10] and the magnitude of at least one of the two is the scattering cross section A- of the second nanoantenna (100-2, 300A-2, 300B-2) at the resonance wavelength of the second nanoantenna (100-2, 300A-2, 300B-2), ｓｃ、２ and, [0011] is substantially equal to the product of the magnitudes of [0012] for one or both of the first nanoantenna (100-1, 300A-1, 300B-1) and the second nanoantenna (100-2, 300A-2, 300B-2), [0013] are substantially antiparallel to and substantially equal in magnitude to The nanodrone (200, 500A, 500B, 1200) of claim 1. 【Request 3】 【Number 14】 For each of the first and second nanoantennas (100-1, 100-2, 300A-1, 300A-2, 300B-1, 300B-2), a connection vector connecting the center of the first nanoantenna (100-1, 300A-1, 300B-1) to the center of the second nanoantenna (100-2, 300A-2, 300B-2) [Equation 15] The nanodrone (200, 500A, 500B, 1200) of claim 1, wherein the nanodrone (200, 500A, 500B, 1200) is substantially perpendicular to the

4. The nanodrone (200, 500A, 500B, 1200) of claim 1, wherein the center of the first nanoantenna (100-1, 300A-1, 300B-1) and the center of the second nanoantenna (100-2, 300A-2, 300B-2) are arranged symmetrically with respect to the center (202) of the nanodrone (200, 500A, 500B, 1200).

5. The nanodrone (200, 500A, 500B, 1200) of claim 1, wherein the resonant wavelengths of the first and second nanoantennas (100-1, 100-2, 300A-1, 300A-2, 300B-1, 300B-2) are different.

6. When j=L or j=R, [0016] but [Equation 17] The nanodrone (200, 500A, 500B, 1200) of claim 1 , wherein the axial direction of the nanodrone is substantially antiparallel to the axial direction of the nanodrone (200, 500A, 500B, 1200). 【Request 7】 【Number 18】 However, when j=L or j=R, [Equation 19] and when j=L, [Equation 20] and when j=R, [Equation 21] The nanodrone (200, 500A) of claim 1,

8. The two or more nanoantennas further include a third nanoantenna (300B-3) and a fourth nanoantenna (300B-4), and the photons of the scattered light are arranged in a plane (X, Y) perpendicular to the normal direction (Z) for left-handed circularly polarized light and right-handed circularly polarized light, respectively, with an average wave vector i=3 for the third nanoantenna (300B-3) and an average wave vector i=4 for the fourth nanoantenna (300B-4). [Equation 22] each configured to scatter circularly polarized light at the respective resonant wavelength incident on the nanoantenna (500B) along the normal direction (Z) so as to have j ｉ = L or R [Equation 23] is non-zero, and j ｉ In the case of =R [0000] and j ｉ In the case of =L [Equation 25] is [Equation 26] is substantially zero, or [0000] is substantially antiparallel to The wave vectors for the first to fourth nanoantennas (300B-1, 300B-2, 300B-3, 300B-4) [0000] are substantially perpendicular to each other or substantially antiparallel to each other.

9. For each nanoantenna of a first pair of nanoantennas selected from the first, second, third, and fourth nanoantennas (300B-1, 300B-2, 300B-3, 300B-4), j=L or R. [0000] is non-zero, and if j=R, [Equation 30] and when j=L, [Equation 31] is [Equation 32] is essentially zero, For each nanoantenna of a second pair of nanoantennas consisting of two of the first, second, third, and fourth nanoantennas (300B-1, 300B-2, 300B-3, 300B-4) that are not included in the first pair of nanoantennas, [Equation 33] is non-zero, [Equation 34] is essentially zero, especially, the first pair of nanoantennas is composed of the first and second nanoantennas (300B-1, 300B-2), the second pair of nanoantennas is composed of the third and fourth nanoantennas (300B-3, 300B-4), [Equation 35] teeth, [Equation 36] is substantially antiparallel to [Equation 37] teeth, [Number 38] is substantially antiparallel to [Number 39] is substantially perpendicular to The nanodrone (500B, 1200) according to claim 8.

10. the resonant wavelengths of a third pair of nanoantennas selected from the first, second, third, and fourth nanoantennas (300B-1, 300B-2, 300B-3, 300B-4) are equal; The resonant wavelengths of a fourth pair of nanoantennas, which are composed of two of the first, second, third, and fourth nanoantennas (300B-1, 300B-2, 300B-3, 300B-4) that are not included in the third pair of nanoantennas, are equal; the resonant wavelengths of the third pair are different from each of the resonant wavelengths of the fourth pair; The nanodrone (500B, 1200) according to claim 8.

11. the resonant wavelengths of a third pair of nanoantennas selected from the first, second, third, and fourth nanoantennas (300B-1, 300B-2, 300B-3, 300B-4) are equal; The resonant wavelengths of a fourth pair of nanoantennas, which are composed of two nanoantennas among the first, second, third, and fourth nanoantennas (300B-1, 300B-2, 300B-3, 300B-4) that are not included in the third pair of nanoantennas, are equal; the resonant wavelengths of the third pair are different from each of the resonant wavelengths of the fourth pair; The nanodrone (500B, 1200) of claim 9, wherein the third pair of nanoantennas is composed of a nanoantenna selected from the first pair of nanoantennas and a nanoantenna selected from the second pair of nanoantennas.

12. 10. The nanodrone (200, 500A, 500B, 1200) of claim 1, wherein the optically addressable resonance of each of the two or more nanoantennas is a plasmonic resonance, a phononic resonance, or a Mie resonance.

13. The nanodrone (200, 500A, 500B, 1200) of claim 1, wherein some or all of the two or more nanoantennas each comprise a pair of coupled resonators (302-1, 302-2), and the resonator axes (304-1, 304-2) of the pair of resonators (302-1, 302-2) are inclined to each other, and in particular, the resonator axes (304-1, 304-2) are substantially perpendicular to each other.

14. The nanodrone (200, 500A, 500B, 1200) of claim 13, wherein some or all of the two or more nanoantennas each further comprise a third resonator (302-3), the third resonator (302-3) being substantially parallel to the first resonator (302-1) of the pair of coupled resonators (302-1, 302-2) of each of the nanoantennas.

15. For some or all of the nanoantennas comprising a third resonator (302-3), the first resonator (302-1) of the pair of coupled resonators (302-1, 302-2) is disposed adjacent to a first end of the second resonator (302-2) of the pair of coupled resonators (302-1, 302-2); The nanodrone (200, 500A, 500B, 1200) of claim 14, wherein the third resonator (302-3) is disposed adjacent to a second end of the second resonator (302-2) opposite the first end, or the first resonator (302-1) is disposed between the second end of the second resonator (302-2) and the third resonator (302-3).

16. 2. The nanodrone (200, 500A, 500B, 1200) of claim 1, wherein the arrangement of the two or more nanoantennas or a subset thereof exhibits discrete rotational symmetry about the center (204) of the nanodrone (200, 500A, 500B, 1200) and / or mirror symmetry with respect to one or more planes of symmetry extending through the center (204) of the nanodrone (200, 500A, 500B, 1200), wherein the one or more planes of symmetry span a normal vector parallel to the normal direction (Z) and a respective in-plane vector perpendicular to the normal direction (Z).

17. 10. The nanodrone (1200) of claim 1, wherein the two or more nanoantennas further comprise one or more roll nanoantennas (1100-1, 1100-2) and / or one or more pitch nanoantennas (1100-3, 1100-4), wherein the one or more roll nanoantennas (1100-1, 1100-2) are arranged along a pitch axis (1204) of the nanodrone (1200) that is substantially perpendicular to the normal direction (Z), and the one or more pitch nanoantennas (1100-3, 1100-4) are arranged along a roll axis (1202) of the nanodrone (1200) that is substantially perpendicular to each of the normal direction (Z) and the pitch axis (1204).

18. A part or all of the roll nanoantenna and the pitch nanoantenna (1100-1, 1100-2, 1100-3, 1100-4) are a first pair of coupled resonators (1102, 1104) in which the resonator axes of the resonators (1102, 1104) are tilted with respect to each other; a second pair of coupled resonators (1106, 1108) in which the resonator axes of the resonators (1106, 1108) are tilted relative to each other; The nanodrone (1200) of claim 17, wherein one or both resonators of the first pair of coupled resonators (1102, 1104) are substantially parallel to the respective resonators of the second pair of coupled resonators (1106, 1108).

19. 19. The nanodrone (1200) of claim 18, wherein each of the first and second pairs of resonators (1102-1108) comprises a central resonator (1102, 1106) and a distal resonator (1104, 1108), the distal resonators (1104, 1108) of the first and second pairs of resonators (1102-1108) being positioned adjacent to opposite ends of the central resonator (1102, 1106), and in particular, the distal resonators (1104, 1108) extending in opposite directions from respective ends of the central resonators (1102, 1106).

20. A method (800) of operating a nanodrone (200, 500A, 500B, 1200) according to any one of claims 1 to 19, comprising: irradiating the nanodrones (200, 500A, 500B, 1200) substantially along the normal direction (Z) with polarized light at the resonant wavelength of the first nanoantenna (100-1, 300A-1, 300B-1) and polarized light at the resonant wavelength of the second nanoantenna (100-2, 300A-2, 300B-2), wherein the polarized light at the resonant wavelength of the first nanoantenna (100-1, 300A-1, 300B-1) and the polarized light at the resonant wavelength of the second nanoantenna (100-2, 300A-2, 300B-2) are The method (800) is characterized in that the linear momentum transferred to the nanodrone (200, 500A, 500B, 1200) by the light scattered by the first and second nanoantennas (100-1, 100-2, 300A-1, 300A-2, 300B-1, 300B-2) is selected to generate a force (F) acting on the nanodrone (200, 500A, 500B, 1200) that is substantially perpendicular to the normal direction (Z) and / or a torque (M) acting on the nanodrone (200, 500A, 500B, 1200) that is substantially collinear with the normal direction (Z).

21. 21. The method (800) of claim 20, wherein the resonant wavelengths of the first and second nanoantennas (100-1, 100-2, 300A-1, 300A-2, 300B-1, 300B-2) are different, and the intensity of the light at the resonant wavelengths of the first and second nanoantennas (100-1, 100-2, 300A-1, 300A-2, 300B-1, 300B-2) is selected to generate a force (F) but no net torque (M), or to generate a torque (M) but no net force (F).

22. adjusting the polarization, intensity, and / or wavelength of the light; changing the direction of said force (F) and / or said torque (M); Producing a force (F) instead of a torque (M), or vice versa; Varying the magnitude of the force (F) and / or the torque (M); 21. The method (800) of claim 20, wherein in particular only the polarization and / or the intensity of the light is adjusted.

23. Determining the orientation of the nanodrone (200, 500A, 500B, 1200) in a plane (X, Y) substantially perpendicular to the normal direction (Z); and adjusting the polarization, intensity, and / or wavelength of the light based on the determined orientation of the nanodrone (200, 500A, 500B, 1200).

21. The method (800) of claim 20.

24. Providing a bottom surface (720A) on which the nanodrone (200, 500A, 500B, 1200) operates, the bottom surface (720A) extending perpendicular to the normal direction (Z); and generating a repulsive force between the bottom surface (720A) and the nanodrone (200, 500A, 500B, 1200) to counteract the optical pressure generated by the irradiated light.

21. The method (800) of claim 20.

25. 25. The method (800) of claim 24, wherein the repulsive force is an electrostatic force generated by charging the bottom surface (720A) and the nanodrone (200, 500A, 500B, 1200) with the same polarity.

26. A system (700) for operating a nanodrone (200, 500A, 500B, 1200) according to any one of claims 1 to 19, comprising: an illumination system (702) configured to generate polarized light at the resonant wavelength of the first nanoantenna (100-1, 300A-1, 300B-1) and the resonant wavelength of the second nanoantenna (100-2, 300A-2, 300B-2), wherein the illumination system (702) is configured to adjust the polarization and intensity of the light at the resonant wavelengths of the first and second nanoantennas (100-1, 100-1, 300A-1, 300A-2, 300B-1, 300B-2); an imaging system (714, 716) for imaging the nanodrone (200, 500A, 500B, 1200); a controller (718) for controlling the illumination system (702), The controller (718) Obtaining a movement command specifying a movement to be performed by the nanodrone (200, 500A, 500B, 1200); determining the orientation of the nanodrone (200, 500A, 500B, 1200) from images obtained from the imaging system (714, 716); determining a polarization and intensity of the light generated by the illumination system (702) at the resonant wavelength of the first and second nanoantennas (100-1, 100-2, 300A-1, 300A-2, 300B-1, 300B-2) based on the movement command and the determined orientation; and a controller (718) configured to use the illumination system (702) to illuminate the nanodrone (200, 500A, 500B, 1200) with light at the resonant wavelength of the first and second nanoantennas (100-1, 100-2, 300A-1, 300A-2, 300B-1, 300B-2) with the determined polarization and intensity to perform the movement specified by the movement command.

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