We investigated surface-roughness-dependent optical loss in a plasmonic cavity consisting of a semiconductor nanodisk/silver nanopan structure. Numerical simulations show that the quality factors of plasmonic resonant modes significantly depend on the surface roughness of the dielectric-metal interface in the cavity structure. In the transverse-magnetic-like whispering-gallery plasmonic mode excited in a structure with disk diameter of 1000 nm, the total quality factor decreased from 260 to 130 with increasing root-mean-square (rms) surface roughness from 0 to 5 nm. This quantitative theoretical study shows that the smooth metal surface plays a critical role in high-performance plasmonic devices.
Plasmonic structures enable subwavelength-scale optical devices through strong confinement of surface-plasmon polaritons (SPPs) [1-11]. Further miniaturization of various nanophotonic structures such as cavities [1-4], waveguides [5-7], and nanoantennas [8-10] has been achieved by overcoming the diffraction limit of conventional optics. Plasmonic lasers are particularly promising as ultrasmall, efficient, coherent light sources in photonic/plasmonic integrated circuits [1, 2, 11]. Recent studies of plasmonic lasers/cavities show that their quality (
We consider surface roughness of a few nanometers at the dielectric-metal interface of a plasmonic structure, which could be introduced necessarily in a fabrication process involving metals. Our plasmonic structure consists of a dielectric nanodisk and a silver nanopan (Fig. 1(a)), the same structure as reported by Kwon
[FIG. 1.] (a) Schematic diagram of the semiconductor nanodisk/silver nanopan plasmonic cavity structure. The diameter and height of the InP nanodisk are 1000 and 235 nm respectively, and the refractive indices of the nanodisk and glass are 3.2 and 1.45 respectively. Random patterns were introduced on the bottom surface of the silver nanopan. (b), (c) Cross-sectional views of the nanodisk/nanopan plasmonic structure (left) and magnified images of the dielectric-metal interface at rms heights of (b) 2 nm and (c) 5 nm (right). The scale bars in the left and right panels are 200 nm and 50 nm long, respectively. (d) Top and side views of field intensity profiles of the TM-like WG plasmonic mode, TM-like radial plasmonic mode, TE-like monopole optical mode, and TE-like dipole optical mode (left to right), at an rms height of 0 nm.
To investigate the effect of surface roughness in the plasmonic cavity, first we calculate the mode profiles of two representative plasmonic and optical modes: the TM-like WG plasmonic mode (Figs. 2(a)~(c)) and the TE-like monopole optical mode (Figs. 2(d)~(f)). As shown in the calculated field intensity profile at an rms height of 0 nm, the TM-like WG plasmonic mode is well excited at the bottom surface of the silver nanopan (Fig. 2(a)). The top view of the field profile was obtained at a position 40 nm above the bottom of the silver nanopan. With increasing rms height of the surface roughness the field profiles change significantly, while the SPPs are still confined to the bottom surface of the nanopan, and the intensity antinode of the plasmonic mode is also observed. In particular, we note in Fig. 2(c) that the local excitation of SPPs at the roughened surface patterns (several bright spots at the bottom surface) leads to distortion of the field profile. Such field concentration at a metallic nanometer-sized structure can cause a qualitative deterioration of the plasmonic mode and significant optical absorption, as the rms height of the surface roughness is large . In contrast, the TE-like monopole optical mode excited inside the InP nanodisk does not show significant distortion of the field profile, despite the increased rms height of the bottom surface roughness in the nanopan. Strong field concentration at each rough feature is not observed in Figs. 2(e) and (f). These results indicate that the TM-like WG plasmonic mode confined to the bottom surface of the nanopan is more affected by metal surface roughness than is the conventional optical mode.
[FIG. 2.] Top and side views of electric-field intensity profiles of (a-c) the TM-like WG plasmonic mode and (d-f) the TE-like monopole optical mode, with varying rms height of the bottom surface from 0 to 5 nm. The rms heights are (a, d) 0 nm, (b, e) 3 nm, and (c, f) 5 nm. The correlation length is fixed at 10 nm. The top view of the field profile was obtained at a position 40 nm above the bottom surface of the nanopan, as indicated by a gray dotted line in the side view. All images are normalized to the maximum intensity at an rms height of 0 nm. In (f), the intensity was tripled after normalization.
To examine quantitatively the optical losses of the plasmonic and optical modes excited in the nanodisk/nanopan structure, we calculate each of their
[FIG. 3.] Q factors of the TM-like WG plasmonic mode (black squares), TM-like radial plasmonic mode (blue circles), TE-like monopole optical mode (red diamonds), and TE-like dipole optical mode (green stars) are calculated as a function of rms height of the metal surface roughness. Error bars denote one standard deviation from the average of five simulations.
We observe two unique features when we compare the
To further investigate the physical origin of optical losses due to surface roughness, we calculate separately the absorption loss and radiation loss of the TM-like WG plasmonic mode by accumulating electromagnetic power dissipated into the silver nanopan and scattered out of the cavity, respectively. The absorption
In summary, we have performed systematic 3D FDTD simulations to examine the surface-roughness-dependent