Plasmonic nanopatch array for optical integrated circuit applications

Future plasmonic integrated circuits with the capability of extremely high-speed data processing at optical frequencies will be dominated by the efficient optical emission (excitation) from (of) plasmonic waveguides. Towards this goal, plasmonic nanoantennas, currently a hot topic in the field of plasmonics, have potential to bridge the mismatch between the wave vector of free-space photonics and that of the guided plasmonics. To manipulate light at will, plasmonic nanoantenna arrays will definitely be more efficient than isolated nanoantennas. In this article, the concepts of microwave antenna arrays are applied to efficiently convert plasmonic waves in the plasmonic waveguides into free-space optical waves or vice versa. The proposed plasmonic nanoantenna array, with nanopatch antennas and a coupled wedge plasmon waveguide, can also act as an efficient spectrometer to project different wavelengths into different directions, or as a spatial filter to absorb a specific wavelength at a specified incident angle.


SUPPORTING INFORMATION
Plasmonic Nanopatch Array for Optical Integrated Circuit Applications Shi-Wei Qu & Zai-Ping Nie   Electric field distributions of the operating mode are given in Figure S1a to show the mode in detail.

List of Figures
Since the PMMA has a refractive index neff = 1.49, corresponding to a relative permittivity εr = neff 2 ≈ 2.22, both the normal and the tangent components of magnetic fields are continuous according to the electromagnetic field boundary conditions, but the normal components of electric fields are related to the relative permittivity on both sides of the PMMA-air interface. Therefore, a discontinuity is observed at the PMMA-air interface. The mode size is mainly determined by the flare angle β of the V-groove, as shown in Figure S1b. When β is as small as 11 o , two magnitude peaks of the magnetic fields are very close to each other and the two wedge modes are significantly coupled with each other, so the dip at the groove center is shallow, but the mode size is significantly enlarged. When the two wedge modes are less coupled as β increases, the dip becomes deeper and deeper.  Rev. Lett. 95, 063901, 2005.), which can also provide another way to control the mode distributions of the CWPWG. (b) Normalized magnitude of magnetic fields along a referenced line, which is orthogonal to the CWPWG central axis and 50nm above the silver film.

S.2 Impact of PMMA Thickness on Array Performances
Thickness t of the PMMA layer will exert influence on the plasmonic array performance. As shown in Figure S2a, the beam direction is shifted from -13 o as t = 100nm to -7 o as t = 200nm at 1.667μm, mainly due to dependence of the beam direction on the wave number of the propagating mode in the CWPWG which is sensitive to thickness t. At the same time, the more shifted beam by a thinner PMMA layer will also cause a reduction of array effective aperture, consequently resulting in a lower peak directivity, as shown in Figure 2b. Moreover, a thinner PMMA layer will lead to more intense electric or magnetic fields under the nanopatches and higher quality factor of the cavity formed by the nanopatches and the silver film, narrowing the operating wavelength range.

S.3 Magnetic Field Distributions in Central Plane of the Plasmonic Array
Magnetic near field distributions of the proposed nanopatch array at 1.765, 1.667, 1.579, 1.5, and 1.429μm are shown in Figure S3. For clarity, only the near fields close to the last six nanopatch antennas are given albeit 10 in the proposed array.
Clearly, the optical waves emitted by the nanopatch antennas create a plane with coherent interference in front of the array which determines the emission direction of the array. Meanwhile, more optical power is reflected by the shorted termination as the operating wavelength is increased.
Without the termination, larger parasitical beams will occur, which explains its functions in improving the directivity patterns and the spectral width. The animations of near-field distributions at all wavelengths can also be found in the supplementary materials.

S.4 Array Efficiency
Array efficiency, defined by the whole emitted power into free space over the accepted power by the array, is used to measure the array ability to transform the guided plasmonic waves into free-space optical waves. As shown in Figure S4, the nanopatch array presents the highest array efficiency of 75.4% at around 1.579μm.

S.5 3D Directivity Patterns
To present more details, 3D directivity patterns at wavelengths of 1.765, 1.667, 1.579, 1.5 and 1.429μm are shown in Figure S5. It can be seen that there is only one main beam at each wavelength, the parasitical beams are relatively small, and the backward emission of the proposed array at all wavelengths is quite smaller relative to the main emission beam. All of these properties mean that most of the optical power are emitted in a solid angle around the main beam. Therefore, the 2D directional patterns in Figure 3a of the main content can present typical redirection properties of emission. The main beam is gradually shifted from -x to +x direction as the wavelength decreases from 1.765 to 1.429μm. The parasitical beams are around 0.1 times of the main beam or even smaller, i.e., 10dB lower than the main beam.

S.6 Enhancement of Peak Directivity
Directivity of the nanopatch array can be easily enhanced by adding more nanopatch antennas in each row or by placing more rows of nanopatch antennas, which is one of the advantages of the proposed nanopatch array. As complementary results to Figure 4 in the main context, Figure S6 shows the directivity patterns of the proposed array with different rows of nanopatch antennas. Clearly for the array with less rows of nanopatch antennas, the beam width is broader than the one with more rows due to smaller directivity.

S.7 CST Microwave Studio Results
To verify the resutls obtained by Ansoft High Frequency Structure Simulation (HFSS) based on the finite element method (FEM), the CST Microwave Studio based on the finite integration technique (FIT) is used to resimulate the proposed nanopatch array. Figure S7 shows the near-field distributions of the array at 1.765, 1.667, 1.579, 1.5 and 1.429μm by using the FIT. Obviously, there is no noticeable differences from the FEM results in term of emission direction and relative magnitude. The small differences in terms of directivity patterns and peak directivity are mainly caused by the different meshes of two methods, i.e., triangular meshes in the FEM but hexahedral ones in the FIT. Figure S9 gives the simulated 3D directivity patterns at 1.765, 1.667, 1.579, 1.5 and 1.429μm by using the FIT. Compared to those in Figure S5, there are only small differences in terms of the parasitic beams. The above comparisons between the FIT and the FEM results prove the correctness and validity of the results in the main context. Logarithm scale is adopted (in dB), also to clearly show the details of directivity patterns. The results obtained by the FIT also shows reasonable agreements with those by the FEM.