Accurate Feeding of Nanoantenna by Singular Optics for Nanoscale Translational and Rotational Displacement Sensing

Zheng Xi, Lei Wei, A. J. L. Adam, H. P. Urbach, and Luping Du

Phys. Rev. Lett. 117, 113903 – Published 9 September 2016

Abstract

Identifying subwavelength objects and displacements is of crucial importance in optical nanometrology. We show in this Letter that nanoantennas with subwavelength structures can be excited precisely by incident beams with singularity. This accurate feeding beyond the diffraction limit can lead to dynamic control of the unidirectional scattering in the far field. The combination of the field discontinuity of the incoming singular beam with the rapid phase variation near the antenna leads to remarkable sensitivity of the far-field scattering to the displacement at a scale much smaller than the wavelength. This Letter introduces a far-field deep subwavelength position detection method based on the interaction of singular optics with nanoantennas.

Received 22 March 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.113903

Physics Subject Headings (PhySH)

Polarization

Light scattering

Atomic, Molecular & Optical

Authors & Affiliations

Zheng Xi^*, Lei Wei, A. J. L. Adam, and H. P. Urbach

Optics Research Group, Delft University of Technology, Department of Imaging Physics, Lorentzweg 1, 2628CJ Delft, The Netherlands

Luping Du

Nanophotonics Research Center, Shenzhen University, Nanshan District, Shenzhen, China

^*z.xi@tudelft.nl

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Issue

Vol. 117, Iss. 11 — 9 September 2016

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Images

Figure 1
(a) Electric field amplitude $| E |$ distribution at the focal plane of a focused azimuthally polarized beam. The black arrows show the direction of polarization. (b) Line cut of $| E |$ through the singularity center. (c) $| E |$ field distribution when a resonant nanorod antenna is placed at the singularity center of the azimuthally polarized beam. (d) $| E |$ field distribution when a resonant nanorod is displaced 100 nm from the singularity center. The gold nanorod has dimensions $50 \times 50 \times 100 {nm}^{3}$ shown as the rectangular area. The wavelength is 791 nm. The permittivity of gold is fitted from Ref. [31].
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Figure 2
(a) Schematic illustration of the considered configuration, the origin of the coordinate system is chosen at the center of the two nanorods. The center of the beam is at the center of the right nanorod. The two nanorods have length $L = 100 nm$ and a square cross section with side $a = 50 nm$ . The gap between the nanorods is $g = 50 nm$ . (b) The ratio of the right ( $x > 0$ ) to left ( $x < 0$ ) scattered power. The insets show the scattering patterns in the $X Y$ plane at 758 and 840 nm, respectively. (c) Change of scattering pattern as the singular point is displaced from the origin at the wavelength of 758 nm. (d) Change of right to left scattered power ratio as the singular point is displaced from the origin at the wavelength of 758 nm.
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Figure 3
(a) Ratio of the strength and phase difference of the two induced dipoles calculated using the semianalytical method. Inset illustrates the model used to describe the unidirectional scattering behavior. Two nanorods are modeled as coupled electric dipoles. (b) Right to left ratio obtained with the semianalytical model. (c) Right to left ratio as a function of wavelength and gap between the nanorods. (d) Rotation of the far-field scattering pattern as the nanorods are rotated over the indicated angles.
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Figure 4
(a),(b) Configuration of precise alignment of the arrays with respect to the Hermite-Gaussian beam with a dark singular line (dash line) in the middle. The polarization is along the $y$ direction indicated by the black arrow. The array is shown as gold rectangles. The wavelength is 758 nm with the gap $g = 50 nm$ , and the pitch along the $y$ direction is 253 nm. For (a), the dark line is aligned to the left side of the antenna array, while for (b), it is aligned to the right. (c),(d) The far-field scattering pattern in the $X Y$ plane of the arrays corresponding to different alignment of the dark line to the left (c) and to the right (d) of the array.
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