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A plasmonic resonator is proposed whose electromagnetic energy density can be tuned by the polarization state of the incident light. Counter-propagating surface plasmon polaritons, which are excited by polarization-sensitive subwavelength apertures, give tunability. Stored energy density in the resonator varies from the minimum to the maximum when the orientation angle of the incoming electric field rotates by 90 degrees. After optimizing a rectangular cavity and periodic gratings, the on/off ratio is calculated as 430 and measured as 1.55. Based on our scheme, interferometric control is executed simply by rotation of a polarizer. The proposed plasmonic resonator can be utilized in all-optically controlled active plasmonic devices, coherent network elements, particle trapping systems, and polarimeters.
© 2016 Optical Society of America
1. Introduction
Surface plasmon polaritons (SPPs) are surface-bound electromagnetic waves propagating along the metal-dielectric interface [1]. Due to their ability of squeezing light far below the diffraction limit with highly resonant conditions, SPPs have been successfully applied to building nanoscale optical resonators [2]. Subwavelength plasmonic resonators, which are based on single-crystalline silver nanowires [3], few-nanometer-thick metal-insulator-metal waveguides [4], and metallic fins [5], have been demonstrated. Interactions with quantum emitters and lasing action with plasmonic resonators have been also investigated [6–8].
Along with the recent development of active plasmonic elements, tunable plasmonic resonators have been proposed. Thermo-optical and electro-optical control of resonators has been shown using metal strips [9] and graphene nanoribbons [10]. In both cases, material properties of the resonators are tuned by the external control signal. Modulation depth of such active resonators, however, is limited because of small volume of an active layer and short variation range of material properties.
All-optic control utilizing interference between coherent light sources is able to improve the controllability of nanostructured optical devices. Interaction between light and optical devices can be tuned in all-optical manner with high modulation depth by controlling interference of coherent light. For example, resonators with lossy media illuminated by coherent light sources can absorb light perfectly, which corresponds to time-reversal process of lasing [11,12]. In addition to absorption, reflection and transmission are actively tuned by controlling the phase difference of incoming coherent light [13–15]. However, an experimental apparatus to realize optical coherent control systems requires delicate alignment of optical elements and fine control of optical path length. In the visible and the near-infrared regime in particular, a few tens of nanometer change of the optical path length influences the result considerably.
Anisotropic scattering of light induced by plasmonic nanostructures is a promising tool to solve the problem of the interferometry. By utilizing the anisotropic scattering, pathway and phase of SPPs are able to be modulated by polarization of light, so that the interferometry can be replaced by integrating plasmonic elements. Recently, various types of directional coupling of SPPs, which are based on interaction between polarization of light and nanostructures, have been suggested [16–21]. Lin et al. demonstrated polarization-controlled SPP excitation using rectangular nano-apertures [22]. Phase difference between geometric phase of tilted nano-apertures and phase delay due to circularly polarized incident light made directional launching of SPPs and its switching possible. Both pathway and phase of excited SPPs can be tuned independently by changing positions and tilt angles of the nano-apertures. More advanced applications using distributed nano-apertures, multiplexed-plasmonic-lenses [23,24], vortex lenses [25,26], and arbitrary near-field synthesis [27,28] have also been proposed.
Here, we present a tunable plasmonic resonator which is controlled by compact optical instruments with high modulation depth. The proposed device consists of nano-apertures, gratings, and a cavity. The nano-apertures generate and split SPPs into two components when the nano-apertures are illuminated by linearly polarized light. Phase difference of counter-propagating SPPs, which are excited by the nano-apertures, is proportional to the orientation angle of the polarization. This polarization-dependency grants the device tunability. The periodic gratings and the rectangular cavity make a resonator. When the SPPs encounter each other at the resonator with in-phase, electromagnetic energy density in the resonator is maximized. On the other hand, for the out-of-phase case, the energy density is minimized. Utilizing the tunability, absorption and emission can be controlled when the cavity is coupled with lossy media and emitters. After introducing basic principles of interferometric control of SPPs, optimization of the resonator and simulation results will be presented. After that, experimental results will be shown using the near-field scanning optical microscopy (NSOM). In the experimental setup, only a polarizer is rotated for the interferometric control with fixed optical path length. Based on the working principle of our work, interferometric control is possible without exquisite alignment of optical path length.
2. Interferometric control of surface plasmon polaritons
Figure 1 shows a schematic illustration of the proposed device. Configuration of the nano-apertures is shown with detail in the inset at the bottom of Fig. 1. A pair of rectangular apertures, which are tilted with angles of 45° at the right side and 135° at the left side, is spaced with distance of a quarter wavelength of the SPP. Each nano-aperture can be modeled as a dipole source of the SPP on the surface with a moment along the major axis of the aperture. The nano-aperture pairs are arranged periodically with subwavelength distance along the y-direction, so that SPPs are generated with uniform wavefront [22,23]. Envelope function of the uniform SPPs to the right side aR and the left side aL at the center of the pair can be written as:
where ψ is an orientation angle of the incoming electric field. According to our coordinate system, the incoming electric field lies along the x-direction when ψ = 0, and along the y-direction when ψ = π/2. Multiplied terms of , the exponential function, and the sine function in Eqs. (1) and (2) correspond to amplitude projection factor due to tilt angles, phase retardation factor from the nano-aperture spacing, and amplitude projection factor between the incoming electric field and the nano-aperture, respectively. It is shown that the generated counter-propagating SPPs have the same amplitude with phase difference of 2ψ – π. If the spacing and tilt angles of the nano-apertures are altered, this phase-only modulation of the envelopes cannot be achieved. This result coincides with the previous work done by Lin et al. [22], considering that a polarization state of linearly polarized light equals a linear combination of a right-hand and a left-hand circular polarizations.
Fig. 1 Schematic illustration of the overall device. The resonator and the nano-apertures are illuminated by the polarized electric field with the orientation angle of ψ. Insets show detailed configuration of the resonator and the nano-apertures. t: metal thickness, wc: cavity width, dc: cavity depth, wg: grating width, dg: grating depth, pg: grating period, px: x-direction aperture distance, py: y-direction aperture period, wa: aperture width, and la: aperture length
Phase change of SPPs at a fixed distance with respect to the orientation angle is calculated with the finite element method based full-vectorial simulations (COMSOL Multiphysics®). Gold film with t = 300 nm on a glass substrate is illuminated by the wavelength of 980 nm. Dielectric constants of the gold and glass are –37.81 + 1.129j and 2.104, respectively, referring to the Weber’s textbook [29]. Geometric parameters of the nano-aperture pair are given by px = 240 nm, py = 400 nm, wa = 80 nm, and la = 320 nm. Wavelength of the SPP at the gold-air interface is 967 nm, of which px corresponds to about a one-fourth. Dashed lines in Fig. 2(a) plot ideal phase profiles according to Eqs. (1) and (2). It can be seen that dots, which represent calculated phase, follow the dashed lines. The phase difference between the two SPPs, especially, is almost the same as the analytic results, 2ψ – π.
Fig. 2 (a) Phase of SPP wavefronts generated by the nano-apertures. Blue lines and dots denote the SPPs to the right side, and red ones to the left side. Normalized electric field intensity profiles of the face-to-face nano-aperture columns illuminated by the incoming electric field with the orientation angle of (b) 0 and (c) π/2.
If the nano-aperture columns are placed with a face-to-face form, interference of counter-propagating SPPs can be controlled by the orientation angle. Figures 2(b) and 2(c) depict electric field intensity profiles when the two nano-aperture columns are illuminated by the electric field of ψ = 0 and ψ = π/2, respectively. Nodes and antinodes between the columns are reversed as the incoming electric field rotates by 90 degrees.
3. Resonator design and simulation results
The resonator is made of a rectangular cavity and periodic gratings which act as partial mirrors, so that the quality factor can be increased. As previously explained, counter-propagating SPPs encounter with in-phase at the resonator for ψ = π/2 case and with out-of-phase for ψ = 0 case. That is, averaged electromagnetic energy density inside the resonator becomes its maximum for the former case, while it becomes the minimum for the latter case. Here, we call the former case on-state and the latter case off-state. On/off ratio r is defined using of the two states as:
where S is the cavity area, and , are electric fields of the on-state and the off-state, respectively.In order to optimize the resonator, geometric parameters are investigated. At first, wc, width of the cavity, is examined. It is shown in Fig. 3(a) that the first order resonance occurs when wc is around a half of the SPP wavelength. The maximum on/off ratio is achieved as 20.1, with the width of 520 nm. Then, the grating period and the offset, which is distance between the edge of the cavity and the first grating, are inspected since they also have periodicity related with the wavelength. The on/off ratio map according to each parameter is depicted in Fig. 3(b). Other auxiliary parameters are set as dc = 200 nm, dg = 110 nm, and wg = 80 nm. The optimum condition appears when pg is about a wavelength of the SPP. The on/off ratio increases about 15 times, compared with the on/off ratio without the gratings. It indicates that the gratings play a role of amplifying the resonance. The grating period is determined as 940 nm and the offset as 180 nm. The Q-factor of the optimized resonator is 81.4.
Fig. 3 (a) The on/off ratio according to the cavity width. (b) The on/off ratio map with respect to the grating period and offset.
Figure 4 shows full-vectorial simulation results of the overall device, including the nano-apertures and the resonator. The averaged energy density inside the cavity, which is normalized by that of the off-state, rises from 1 to 430 as ψ changes from 0 to π/2. As well as the energy density of the on-state and the off-state, an arbitrary amount of the energy density can be obtained by the appropriate orientation angle that agrees with the relation of Fig. 4(a). Cross-sectional electric field intensity profiles in Figs. 4(b) and 4(c) clearly show the result. Strong electric fields appear at the cavity for the on-state, while electric fields are enhanced at the gratings rather than the cavity for the off-state.
Fig. 4 (a) Averaged energy density inside the cavity normalized by that of the off-state with respect to the orientation angle. Cross-sectional normalized electric field intensity profiles of (b) the on-state and (c) the off-state.
4. Experimental results
The optimized device is fabricated on the 300-nm-thick gold film using the focused ion beam milling (Helios 650). A scanning electron microscope (SEM) image of the fabricated sample is shown in Fig. 5(a). Near-field images are measured using NSOM (MultiView 4000) with an aperture probe with 250 nm core diameter. Experimental setup is illustrated in Fig. 5(b). The sample is illuminated by the laser of 980 nm wavelength after passing a set of the waveplates and the polarizer, which renders light to linear polarization states. The orientation angle can be changed by rotating the polarizer. Near-field imaging using NSOM, which is based on raster scanning, is inadequate to measure interferometry in general because it is vulnerable to vibrational noise during the measurement. According to the experimental scheme in Fig. 5(b), however, noise in the optical path affects the same for the both path lengths, so that disturbance can be cancelled out. This makes the imaging more impervious to vibrational noise.
Fig. 5 (a) SEM image of the fabricated sample using the focused ion beam. (b) Experimental apparatus measuring the near-field images. QWP is the quarter waveplate and HWP is a half waveplate.
Near-field images of the on-state and the off-state are depicted in Figs. 6(a) and 6(b). It is shown that bright double lines appear at the cavity of the on-state. Because of low signal level of the off-state, the near-field profile is detected with more noises that result in diagonal stripes in Fig. 6(b). Figure 6(c) plots cross-sectional intensity near the center of the sample. For each case, measured NSOM data are averaged along the y-axis in order to clarity the signals. For the sake of precise comparison between the field profiles, the exact position of the cavity is obtained by analyzing surface morphology data measured by an auxiliary atomic force microscopy probe of the NSOM system. As well as shifting of nodes and antinodes, near-field intensity of the on-state is seized strongly at the edge of the cavity, whose width is lined with dash-dot in Fig. 6(c). This result seems different from the energy density profile depicted in Fig. 4(b), however, since the energy density is enhanced markedly at the center of the cavity rather than the edges. This difference can be explained by uneven coupling efficiency between each electric field component and the NSOM probe. Properties of the NSOM probe, such as aperture type, core diameter, and tilt angle can influence the coupling efficiencies among the field components [30]. Especially for the proposed resonator, amount of the in-plane electric fields (Ex-field) and the electric fields normal to the surface (Ez-field) are almost leveled inside and near the cavity. Thus, the uneven coupling efficiencies can make intensity profiles different from the exact energy density profiles.
Fig. 6 Normalized near-field images of (a) the on-state and (b) the off-state measured by NSOM. (c) Cross-sectional intensity profiles near the cavity. Dash-dotted line corresponds to the cavity.
Based on the cross-sectional intensity profiles, the on/off ratio is figured out. As previously mentioned, measured near-field intensities have some discrepancies from the exact energy density. That is, the on/off ratio cannot be computed as the same way which is applied for simulation results. Instead, the maximum intensity values inside the cavity of each state are adopted, noticing that ratios of the maximum values are similar among the field components. The final on/off ratio is found out as 1.55.
The on/off ratio derived from the experimental results, however, is not as remarkable as that from the simulation results. The major drawback is fabrication errors of the resonator. For example, due to sensitive resonant condition with high Q-factor, 20 nm difference of the cavity width from the target dimension decreases the on/off ratio down to one-tenth of the optimum value. Geometric defects of the resonator, rough surface morphology of the bottom of the cavity, tapered side walls, and fillets at the grating edges for examples, also contribute to reduce Q-factor of the resonator. With regard to the measurement system, laser source with higher output power can improve clarity of the images by increasing the signal-to-noise ratio of measured near-field intensities. Furthermore, other imaging techniques that are able to collect optical power directly proportional to energy density inside the cavity can help to improve the measurement, for instance fluorescence imaging using deposition of dye molecules and quantum dots [31–33].
5. Conclusion
A plasmonic resonator is designed and demonstrated whose electromagnetic energy density can be controlled by the orientation angle of the incident electric field. Interferometric control of SPPs, which are excited by the nano-aperture pairs, makes the resonator tunable. After optimizing the resonator, the on/off ratio reaches 430. This large tunability can be utilized in optical transceivers and particle trapping systems. Near-field images are measured using NSOM by actuating only the angle of the polarizer. Based on the working principle of our work, interferometric control is possible without exquisite alignment of optical path length. That is, experimental setup of the interferometry can be significantly simplified. We hope that our method can contribute to realizing all-optically controlled active plasmonic devices and coherent network elements, and developing more compact polarization-sensitive optical systems such as polarimeters and ellipsometers.
Funding
Ministry of Science, ICT and Future Planning (MSIP) of Korea (CAMM-2014M3A6B3063710); National Research Foundation (NRF) of Korea (21A20131612805)
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