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3D-steering and superfocusing of second-harmonic radiation through plasmonic nano antenna arrays
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Image of FIG. 1.

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FIG. 1.

Fundamental field distributions of a spherical nanoparticle (a), a nanorod (b), and a nanocone (c) calculated with the MMP method (Refs. 15 and 16). The particles are illuminated by a plane wave () incident from the left ( = 800 nm), and they are embedded in a medium with n = 1.5. The second-harmonic dipole moments are marked by white arrows.

Image of FIG. 2.

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FIG. 2.

SHG radiation pattern of a nanocone with a height of 40 nm in a medium with n = 1.5. A dipole which radiates at 400 nm and which is oriented parallel to the cone axis is located within the cone tip. The plotted angle-dependent far field radiation intensity of the nanoparticle a dipolar radiation pattern.

Image of FIG. 3.

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FIG. 3.

A circle of nanorod emitters (a) or nanocone emitters (b) is excited by a z-polarized focus. The focused beam aims on the center of the 400-nm-big circle, with the angle of incidence between the beam propagation direction given by and the z axis. The SHG dipole moments at the nanorod apexes are taken as radiating emitters (a), while each nanocone yields a single emitter (b). Assuming the dipole moments as Hertzian emitters, we can calculate their electromagnetic field at each point P in the coordinate system.

Image of FIG. 4.

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FIG. 4.

(a) Field distribution of and . Coordinates and field lines of rotated exciting Bessel beam.

Image of FIG. 5.

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FIG. 5.

SHG field intensity within the emitter circle for different incident angles  = 0°, 15°, and 30° with respect to the z axis. Plotted are top-views on the xy field distribution at z = 0 nm (top row) and z = 100 nm (bottom row), while the middle row displays the xz sideview if the SHG focuses. The dashed lines mark the intersecting lines of the plotted planes. The spatial displacement of the field maximum caused by the tilt of the exciting beam is shown by blue arrows.

Image of FIG. 6.

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FIG. 6.

SHG field intensities for a nanorod circle in the z = 150 nm plane parallel to the xy plane, and in the xz plane for different angles of incidence. The green vector symbols show the emitting dipoles. The solid green lines mark the -dependent shift of the SHG field maxima.

Image of FIG. 7.

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FIG. 7.

Plot of the SHG field intensities generated by the cone emitters along the x axis for different . The FWHM lies around 100 nm.

Image of FIG. 8.

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FIG. 8.

A possible application of the SHG field maximum: SHG emitters are placed in a transparent polymer matrix (brown), whose surface lies 100 nm above the emitters. The SHG field maximum A from the emitters can yield photochemical reactions in a photoreactive layer (green) deposited on that surface.

Image of FIG. 9.

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FIG. 9.

A hexagonal arrangement of single dipolar emitters (marked by yellow lines) can be arrayed over the whole substrate surface, each hexagon still suitable for a SHG focusing. The hexagon radius equals the FWHM of the fields of the focus, but there is still a weak excitation of the emitters outside the hexagon on that the exciting beam is focused. Some emitters are not excited at  = 0 because they lie on the first node line of the Bessel function which describes . Shown are the data for single dipole emitters (cones), but the principle does not change when we consider nanorod emitters instead.


Generic image for table

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Size, volume, field enhancement , and the SHG dipole polarizations of differently shaped nanoantennas. The polarizations are normalized in a way that the contribution from for the sphere is equal to i. The last column shows sketches of the particle excitation and the resulting second-harmonic dipole moments. For equal susceptibilities, the bulk contributions are, in all cases, about an order of magnitude larger than the contributions, which are the smallest ones. For each contribution, the dipole moment on the nanorod apex is about 2 orders of magnitude larger than the dipole moment of the sphere. The cone dipole moment is about 1 order of magnitude larger than the sphere dipole moment. The last line of the table shows that the major part of the total second-harmonic dipole moment is localized within the upper 10 nm of the (40 nm high) cone. Hence, the dipole moment is localized in the cone tip region.


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Second-harmonic generation (SHG) of light at nanoparticles provides the possibility to generate light (of a desired frequency) in-situ instead of introducing it by focusing an external light beam. Our theoretical study provides steering SHG light through the superposition of the radiation from a number of nanoparticles which are arranged in a circle. The authors assume cone-shaped or rod-shaped nanoparticles. Their radiation can be modeled as radiating dipoles. The superposition of their fields yields a “hot spot” with a full width at half-maximum of around 100 nm. Even more important, the position of the hot spot within the circular arrangement of nanoantennas can be adjusted in the xy plane simply by changing the incident angle of the exciting beam.


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Scitation: 3D-steering and superfocusing of second-harmonic radiation through plasmonic nano antenna arrays