Subwavelength Optical Imaging through a Metallic Nanorod Array

We propose a subwavelength imaging system without a lens or a mirror but with an array of metallic nanorods. The near-field components of dipole sources were plasmonically transferred through the rod array to reproduce the source distribution in the other side. We calculated the field distribution at the different planes of imaging process using the finite-difference time-domain algorithm and found that the spatial resolution was 40 nm given by the rod size and spacing. A typical configuration is a hexagonal arrangement of silver rods of 50 nm height and 20 nm diameter. We also show that the image formation highly depends on the coherence and the polarization of the source distribution and the source-array distance.

Figure 1

Subwavelength plasmonic image transfer of a character pattern “$\lambda$” with a metallic nanorod array device. (a) The structural model of the device, which is constructed by hexagonally arranged silver nanorods of 20 nm diameter, 50 nm height, and with 40 nm pitch, respectively. (b)–(g) Field propagation process in the image transfer obtained at each longitudinal position by the FDTD simulation. The character pattern is composed of an array of $z$-polarized dipoles. Left side images show the cross-sectional intensity distributions in the $x\mathrm{\text{−}}y$ plane. The plots on the right side show the cross-sectional line profiles of dashed lines in the left images. The object plane and imaging plane are defined as $z=0$ and $z=70\mathrm{nm}$. The operation wavelength is 488 nm. The size of the scale bar is 50 nm.

Figure 2

Intensity distributions for individual polarization components obtained at the vertical ($x\mathrm{\text{−}}z$) cross section of the nanorod array including the centric rod axis and a dipole source; (a) $|E_z{|}^2$ for $z$ polarization, (b) $|E_x{|}^2$ for $x$ polarization, and (c) $|E{|}^2$ for the intensity, respectively. Line profiles of the intensity on the rod center ($a\mathrm{\text{−}}{a}^{\prime }$) and on the image plane ($b\mathrm{\text{−}}{b}^{\prime }$) are plotted at the right (log plot) and under sides (linear plot) of the $|E{|}^2$ distribution. Solid lines correspond to the intensity profiles with a nanorod array, and dashed lines correspond to that without a nanorod array. The size of the scale bar is 50 nm.

Figure 3

(a) Relationship between the peak intensity (dots) and the FWHM spot diameter (triangles) as the function of the source-array distance and exponential fitting for the dot marks (dashed curve); (b) hexagonal pitch dependence of the peak intensity at the image plane. Insets show the intensity distributions of the image obtained with the array pitch of 30 and 40 nm. Although the peak intensity decreases in proportional to the source-array distance, the nanorod array always images with a subwavelength resolution. The peak intensity becomes smaller as the pitch decreases. The image becomes broadened at a less than 40 nm pitch because of SPP coupling with surrounding rods.

Figure 4

Images of hexagonally aligned six dots in different dipole oscillation conditions. Each of the six dipoles is placed beneath each rod encircling a centric rod and they are oscillated with (a) in phase, (b) antiphase, (c) phase delayed $\pi /3$ radian steps in clockwise and (d) incoherent state, respectively. Line profiles show the horizontal cross sections of the output fields. An artifact observed in (a) is generated by the constructive interference effect of the SPP coupling between adjoining rods.

Figure 5

Field distributions for the location of the point source relative to the rod. Each point source shifts from the rod center to (a) a half of the pitch which is corresponding to the exactly middle point of two rods ($\Delta x=20\mathrm{nm}$), (b) three-quarters of a half of the pitch ($\Delta x=15\mathrm{nm}$), and (c) a quarter of the pitch which is at the edge of a rod ($\Delta x=10\mathrm{nm}$), respectively. Upper figures show the intensity distributions of the vertical ($x\mathrm{\text{−}}z$) cross section of the nanorod array including the centric rod axis and a dipole source. Lower figures show the intensity distributions at the image plane above the nanorod array. The plasmon at the most neighboring rod is excited for the dipole source except for the middle point condition. The size of the scale bar is 50 nm.