Launching and control of graphene plasmon by nanoridge structures

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Launching and control of graphene plasmon by nanoridge structures Sanpon Vantasin, Yoshito Y Tanaka, and Tsutomu Shimura ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b01341 • Publication Date (Web): 14 Dec 2017 Downloaded from http://pubs.acs.org on December 14, 2017

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Launching and control of graphene plasmon by nanoridge structures Sanpon Vantasin,† Yoshito Tanaka,*,†,‡ Tsutomu Shimura† †

Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

‡

Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 3320012, Japan email: [email protected]

Abstract

The unique properties of graphene plasmon show great potential for plasmonic nanodevice applications such as sensors and modulators. Graphene plasmon launching, propagation control, and ultimately launching with directional control are therefore crucial for the development of such devices. However, previous studies have used foreign objects or external influencing factors to attain directional plasmon launching on graphene, which introduce defects and add complexity to the system. This study introduces a theoretical framework for a graphene-only approach to direction-controlled plasmon launching. We use graphene nanoridges, a defect-free natural structure of graphene, as a plasmon launcher. Through proper arrangement of the nanoridges, unidirectional, bidirectional, and wavelengthsorted plasmon launching with normal illumination can be achieved.

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Keywords: graphene surface plasmon, curvature, wrinkle, unidirectional, wavelength sorting

Graphene surface plasmon offers extreme tunability, long propagation lengths, and high wavelength confinement compared with conventional noble metal plasmons.1,2 These properties, together with a plasma frequency in the infrared region allows graphene plasmon to be promising for nanodevice applications such as sensors, waveguides, modulators, transformation optics devices, etc.3–6 At THz frequencies, the classic Otto or Kretschmann configurations are considered to be capable for excitation of graphene surface plasmon polariton (SPP).7,8 At mid-IR frequencies, such configurations are not viable owing to the large wavevector mismatch between free light and the graphene plasmon.9 Still, graphene plasmon in the mid-IR range has interesting properties such as uniquely short wavelengths. Therefore, tips,10,11 antenna,11,12 gratings13, and acoustic waves,14,15 have been used for graphene SPP launching. Most of these methods involve adding foreign entities on (or under) the graphene as a plasmon coupler. However, such foreign entities induce defects in the graphene.16 In addition to launching, another important aspect of graphene plasmon is control over direction and propagation. For SPP waves already propagating on graphene, methods to control their propagation, e.g. to refract,17,18 reflect,2,19 or stop20 the SPP have been developed. To realize the controllability, these methods exploit the inhomogeneous permittivity of surroundings,17,18 gate tuning,2,20 and defects.19 For nanoplasmonic device applications, it is effective to launch a SPP wave with controlled propagation in a single step, rather than uncontrolled launching at one point and then control the propagation at another point. Through the use of a magneto-optical substrate and applied magnetic field, Liu et al. demonstrated graphene SPP launching with controlled propagation in a single direction.21 Wang et al. also achieved unidirectional launching of graphene SPP


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with a semiconductor nanorod and two illuminations with precisely controlled angles.22 Angle-controlled double illumination has also been exploited by Constant et al., to directionally launch graphene SPP by ultrafast pulse lasers via a nonlinear process, without near field objects.23 However, these methods rely on external factors (e.g., a magnetic field, in-plane momentum from angled illumination, or semiconductor antennae) to achieve unidirectional SPP launching. The requirements for foreign objects or pulse lasers obviously restrict some applications. In this study, we introduce graphene-only unidirectional launching, using nanoridges within the graphene itself. Rather than external factors, the directionality originates from an internal factor, i.e., the nanoridge arrangement. We expect that this new method could provide an alternative approach for directional launching of graphene SPP and widen applications of controlled launching techniques. Graphene nanoridges, an out-of-plane curved section of a graphene sheet, are a natural structure occurring on epitaxial and CVD graphene,24–26 and can even be artificially induced (or removed) on exfoliated graphene through thermal annealing.27 Additionally, by transferring graphene onto a nanostructured substrate (nanomodulation) or a pre-strained substrate, graphene can be formed into a nanoridge-like curvature with precisely controlled size and orientation.28–30 Unlike graphene edges, where terminal carbon atoms have either dangling bonds or foreign atoms attached, which are both considered as defects,31 graphene nanoridges feature fully interconnected sp2 carbon. The absence of D band in Raman spectra confirms that graphene nanoridges have no defect.24 It has been shown that graphene nanoridges have plasmon waveguide modes along the ridge direction.32 The propagation of graphene SPP (launched by any of the aforementioned methods, such as a metallic tip) can be controlled (passed or reflected) by the graphene nanoridge structure, with the help of the substrate.33 Moreover, nanoridges (referred as wrinkles) have been shown to confine graphene plasmons launched from a metallic tip.34 We demonstrate in this study that a


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graphene nanoridge, by itself, is sufficient for launching graphene SPP with controlled amplitude and phase. We also studied how the proper arrangement of multiple nanoridges can allow unidirectional SPP launching with normal illumination. Even wavelength-sorted SPP launching, for which the SPP is launched unidirectionally to the left or right depending on the excitation wavelength, can be achieved.

Result and discussion Launching of SPP by graphene nanoridge(s) is studied using Finite Element Method (FEM) simulations. Figure 1 displays the setup and axis orientation. The nanoridge is modeled as a curved section of graphene with an identical material to that of flat graphene. The graphene SPP is excited by normal illumination polarized in the across-ridge direction (i.e., along the x axis). Only the transverse magnetic (TM) mode of the surface plasmon is considered in this study. Figure 2 demonstrates SPP excitation on graphene with a single nanoridge. The ridges are 30 nm high and 100–250 nm wide. This is on the basis of previous STM/AFM studies, as natural nanoridges can have various size, up to a few hundred nanometers in width,24,35 and up to several tens of nanometers in height.26 Owing to the longitudinal nature of the TM mode surface plasmon,6 the SPP waves that are launched to the left and right sides have opposite phases. The width of nanoridges and excitation wavelengths affect the SPP launching behavior. In Figure 2A two extreme cases are presented. In the first case (100 nm ridge, λexcite 3.27 µm; and 150 nm ridge, λexcite 3.72 µm), there is strong propagating SPP wave launched from nanoridge onto flat graphene and there is a relatively weak standing SPP wave on the nanoridge. (See Movie 1 for animation.) This situation will be called as a ‘launching mode’ in this manuscript. For the second case (100 nm ridge, λexcite 3.65 µm; and 150 nm ridge, λexcite 4.17 µm), the launched SPP wave onto flat graphene is very weak, but


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the standing SPP wave on the ridge is strong. (see Movie 2) This situation will be called as a ‘stationary mode’. For a certain ridge width, there can be many launching modes and stationary modes, each occurs on different excitation wavelengths (Figure S1–S4). The launched SPP wave is analyzed by sampling the y-component of the electric field (Ey) along a line above the flat graphene (outside the ridge) with a 0.1-nm distance over the graphene. The electric field values are then fitted with an exponential decaying sine function = + ∙

sin − , where A, B, C, D and E are baseline, initial amplitude, decay rate,

magnitude of wavevector, and phase, respectively. In this manuscript the initial amplitude is referred as ‘SPP amplitude’. The plasmon wavelength can also be acquired by from the fitting parameters (2π/wavevector). A plot of the launched SPP amplitude against the excitation wavelengths in Figure 2B clearly illustrates the alternating trend between the launching modes (local maxima) and stationary mode (local minima). Interestingly, the conditions for the stationary modes are almost exact to conditions for which the physical curve length of the nanoridge is a multiple of the SPP wavelength (vertical dashed lines in Figure 2B). The calculation of the ridge curve lengths is shown in Supporting Information. Figure 2B also shows that wider ridges give overall lower SPP amplitude compared with narrower ridges. This is because with fixed ridge height, increasing ridge width resulting in a larger curvature radius and the ridge become more similar to flat graphene, which cannot launch SPP wave. The effect of curvature radius of curved metal surface on SPP launching have been previously studied.36 The relationship between the wavelength of the excitation light and the wavelength of the launched SPP wave (Supporting Information Figure S8) provides an effective SPP index (/ ) of 72.5–21.9 at 3–8 µm excitation. Because the SPP wavelength (on flat graphene) is a property of the graphene-air interface, it is independent of the nanoridge size. Nevertheless, this wavelength confinement is much greater than that of a noble metal surface


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plasmon.2,6,37 The SPP wavelengths in our results (and in many previous graphene plasmon studies) are smaller than the SPP wavelength typically reported for noble metal surface plasmons, even though the excitation wavelengths are much larger.38,39 The coupling nanostructures in this study are therefore substantially larger than the SPP wavelength, rather than smaller as in the case of noble metal surface plasmons. We propose that the launched SPP results from the interference of SPP waves generated from every point on the ridge. By modeling the nanoridge as a flat plasmon generation zone of length L, and each point generates a SPP wave with the wave function , = sin2 − / − , then the wave function of interference result at the x position outside the ridge would be:

" #$/%

" #$/%

sin

2 − ' 2 − ! & = sin ! sin − !

where L, A, x, λspp, ϕ are independent of x0, denoting ridge curve length, arbitrary amplitude constant, position on the x axis, SPP wavelength, and phase of the SPP wave relative to the phase of the excitation wavelength, respectively. This model suggests that the amplitude of the launched SPP goes to zero when '/ is an integer, which fits well with the stationary mode in the numerical simulation (Figure 2B). This model also explains the 180° phase flip at the conditions of the stationary modes in Figure 2B, as when the term sin'/ produces a negative value, the overall expression could still be interpreted as consisting of a positive amplitude, but with the phase in the final term flipped by 180° instead. This model relies on the independence of A and ϕ from x0 (aside from the obviously independent L, x, and λspp). This assumption might not be perfectly accurate, but accurate enough to explain the numerical results. The numerical results and the interference model show that, the strong and near-zero amplitude of the launching and stationary modes are a direct result of interference. Therefore,


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the standing SPP wave of the stationary modes is not localized plasmon resonance, in which the electron plasma is confined. The nanoridge is also different from a plasmonic Fabry– Pérot cavity,40 although both systems can produce standing waves under the conditions where the structure length equal a multiple of the SPP wavelength. There is no reflection and no phase-flip at the end of the nanoridge, thus the nanoridge has no half-wavelength mode, such as that of a plasmonic cavity. The effects of the nanoridge height were also investigated (Figure S20). The amplitude of the launched SPP wave greatly rises as the ridge height increases. Additionally, the height contributes to the ridge curve length, therefore it slightly affects the conditions for the launching and stationary modes, further supporting the validity of the analytic model. Notably, in our numerical simulations, suspended graphene (permittivity above and below graphene of 1) was considered. This setup was chosen to understand the fundamental principles of the phenomenon, and to emphasize that the launching effect originates solely from the graphene nanoridge. This is actually not a purely hypothetical system, since ridgelike structures can be created on suspended graphene using spontaneous or thermally-induced strain.41 Nevertheless, nanoridges are clearly pronounced on epitaxial and CVD graphene, therefore the cases with a substrate (permittivity of the medium under graphene >1) are presented in Supporting Information Figure S9 and Figure S10. In this simulation, “substrate” includes both the space under flat graphene and the space under the nanoridge (i.e. there is no “air pocket” under ridge). The SPP amplitude plots in Figure S9 show that the permittivity of the substrate has only small effect on the maximum SPP amplitude. However, the conditions (excitation wavelength) of stationary and launching modes do changed. Figure S10 indicates that the changed in the conditions can be attributed to the change in plasmon wavelength. This effect in our study is very simple compared with the substrate effect in the case of localized plasmon resonance.42,43


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This result demonstrates that nanoridges can also launch SPP on graphene with substrate, and the analytical model stays intact. It is worth noting that unlike the simulation, real-life substrate can induce plasmon loss via plasmon-phonon scattering process.44,45 Therefore, substrate with phonon modes at the same frequency as the SPP wave should be avoided. Real graphene nanoridge also cause strain variation on the graphene sheet,24 which in turns affect graphene optical conductivity.46 However, the strain variation cause by graphene nanoridge is smaller than (2 × 10-3).24 Therefore, the effect on optical conductivity is less than 1%, and is insignificant to our result. In a real-life system, there are usually multiple nanoridges on a graphene sheet.24,25 Therefore, it is crucial to understand the interactions among the SPP waves generated from more than one ridge. To achieve this, graphene with two nanoridges was considered (Figure 3). The SPP launching by double-ridge systems is shown in Figure 3A and 3B. Because the structure is symmetric, the SPP released to the right and left always have equal amplitude and opposite phase (Supporting Information Figure S10). There are modes for which the SPP appears as a standing wave on each ridge, analogous to the stationary modes of the single ridge systems (Supporting Information Figure S11, S12). These modes also occur at almost the exact excitation wavelength as the corresponding stationary modes of the single nanoridge. Consequently, these modes are dependent on ridge width but not on ridge separation (Figure 3C and 3D, vertical dashed line). Figure 3A and 3B also present launching modes and a new type of stationary mode, which does not exist in the single ridge system, with a standing SPP wave between the ridges. This result indicates that the interaction between the nanoridges produces a new type of mode. The launching modes and the new type of stationary modes are dependent on ridge separation, as shown as the maxima and minima points in Figure 3C and 3D (except for the minimum indicated by a vertical dashed line).


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The existence of ridge separation-independent and separation-dependent modes suggests that the phenomenon arises from interference. The SPP launching behavior of a single ridge is described above; hence, the interference result can be simply predicted by superimposing the SPP waves launched by each ridge through the equation for sine wave addition: )*+,- =

./ % + % % + 2/ % cosΔ, where is the amplitude and Δ is the phase difference.

However, the phase difference is not simply the ridge separation divided by the SPP wavelength, because the SPP wave generated from a ridge must ‘climb over’ another ridge before interfering with the SPP wave from that ridge. This effect is demonstrated in Figure 4, where Figure 4A illustrates the case of no illumination and no SPP coupling, but with a SPP wave simulated to propagate from a distant source on the left side. From the figure, it is clear that when a SPP wave propagates over a nanoridge, it has to follow the curve, resulting in a phase delay from the extra distance compared with that of a SPP wave traveling on flat graphene. At a first glance, it is surprising that the narrower ridge (100 nm) causes a greater phase delay to the SPP wave than the wider ridge (150 nm). However, considering that the ridges provide a path difference relative to the straight line under it, the narrower ridge, which is more curved compared with the wider ridge, provides a greater path difference, and hence a greater phase delay (Supporting Information Figure S7). Note that the nanoridges could potentially reflect some parts of the SPP wave,33 but the reflection in this case is negligible because the permittivity of the medium on the top and bottom of graphene is the same.33 (In the case of different permittivity on the top and bottom of graphene, ﬁrst-order Born approximation (FOBA) can be applied to determine SPP reflection.)33 Assuming that the phase delay arises almost entirely from the additional distance caused by the ridge curve, the phase delays from the 100 and 150 nm ridges can be analytically calculated (Figure 4B). The close similarity between the analytic results and the numerical simulations indicate that this assumption is accurate.


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Figure 5 shows results of the symmetric double ridge system based on the analytic model. With known phase delays (Figure 4B) and known SPP wavelengths (Supporting Information Figure S8), the phase difference of the two SPP waves generated from each ridge in the double ridges system can be calculated trivially from Δ = / + 3*,45 , where is the

ridge separation and 3*,45 is the phase delay. Figure 5A and 5C illustrate the phase difference in the case of double 100-nm and double 150-nm ridges, respectively. Then, using the phase difference values in Figure 5A and 5C, together with the amplitudes of the SPP wave launched from a single nanoridge (Figure 2B), the amplitude of the resulting SPP wave in the double ridge system can be analytically calculated for any ridge separation distance. The analytically calculated amplitude values for the 150–900 nm ridge separation are shown as two-dimensional maps in Figure 5B and 5D. The amplitude maps clearly illustrate the separation-independent (vertical white stripe) and separation-dependent stationary modes (curved white stripe), while the launching modes are high-amplitude regions between the stationary modes. Figure 5E and 5F demonstrate that the amplitude values from the numerical simulation and from the analytic model show a similar trend. The similarity between the analytic and simulation results is crucial because it demonstrates that we can precisely understand, predict, and optimize the coupling phenomena through the analytic model. Thus, we can use the model to design more complex structures, which can control surface plasmon interestingly. One example is the use of an asymmetric doublenanoridge structure for unidirectional SPP launching and wavelength sorting, as demonstrated in Figure 6. Using the analytic model discussed above, the launched SPP amplitude from the asymmetric double nanoridge system with 100 and 150 nm ridges, can be predicted (Supporting Information Figure S14). For this system, the launched SPP waves to the left and right sides have different amplitudes. The main feature that enables asymmetric SPP


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launching in this system is the phase delay. On the right side, the SPP wave launched by the 100-nm ridge experiences phase delay when propagating over the 150-nm ridge. On the left side, the SPP wave launched by 150-nm ridge also experiences phase delay; however, this delay is greater because the wave propagates over the 100-nm ridge (see Figure 4B). This inequality produces different interference results on each side, and hence different launched amplitudes on the left and ridge sides. The ratios between the amplitude of SPP waves launched to right and left side are presented in Figure 6A, and one can find the conditions that provide strong unidirectional SPP launching (blue and red regions), and also the conditions for bidirectional launching (white regions). Because the conditions for directional SPP launching (red and blue areas) are broad, there is some tolerance in both ridge separation (vertical axis) and excitation wavelength (horizontal axis). High precision is not necessary to get directional SPP launching. The fine-tuned precision is, however, effective to maximize the directivity (right/left ratio). These results demonstrate that a graphene-only system, without foreign objects, can provide direction-controlled SPP launching under normal illumination. Unlike previous studies, where the directionality originates from external factors (i.e., a magnetic field or illumination angle),21,23 the directions of the launched SPP waves in this study are governed by the arrangement of nanoridges, which are an intrinsic part of the graphene. The directionality of this system is passively-controlled and thus permanent. This principle could be applied in a device to provide unidirectional launching without the need for precise actively-controlled external factors. Furthermore, some ridge separation values (for example, 275 nm in Figure 6B and 6C), provide right-side unidirectional launching for some excitation wavelengths, and left-side unidirectional launching for other wavelengths. This allows wavelength sorting application, where the multi-wavelength illumination can be ‘separated’ into the right/left SPP waves, depending on the wavelengths. For the first time, wavelength-


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sorted launching of graphene surface plasmon is demonstrated. The comparison between the analytic and numerical simulation in Figure 6D confirms that the analytic model can predict the simulation results with good accuracy.Although passive control of unidirectional launching is the strength of this system, it does not forbid the use of active control for even wider applications. A good example is the adjustment of the Fermi energy as shown in Supporting Information Figure S17. The asymmetric double ridge structure with 275-nm separation and 0.5 eV Fermi energy, which launches a SPP wave to the right when illuminated with 3.58 µm light, would instead launch a SPP wave to the left at 0.56 eV Fermi energy. This result indicates that active control of directional SPP launching might be possible by using gate tuning. More details about the effects of the Fermi energy are presented in Supporting Information. Another possible active control is to dynamically adjusting the ridge height47,48 to dynamically control the launched SPP wave. The applications are certainly not limited to wavelength-sorted SPP launching, which is presented as an example to illustrate that the ridge structures can be used to control graphene surface plasmon. Designing a more complex system of nanoridges is feasible because of the accuracy of analytic model. The shape of ridge structures can certainly be modified for other applications, such as controlling the wavefront of the launched SPP wave (Figure S19). Launching efficiency is also an important aspect for the application of graphene SPP. Therefore, we compare the launching efficiency between nanoridge and gold nanoparticle as a SPP launcher onto flat graphene (see Figure S21). For normal illumination, size of gold nanoparticle comparable to the 100-nm nanoridge, and excitation wavelength providing launching mode, nanoridge can launch SPP waves more efficiently than a gold nanoparticle located 2 nm above flat graphene. A simple method to amplify the SPP amplitude is to use arrays of nanoridge, which is covered in the Supporting Information (Figure S22).


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Conclusion We demonstrated graphene plasmon excitation using nanoridge structures. A single graphene nanoridge, without any foreign objects, can launch or produce standing SPP waves depending on the relationship of the SPP wavelength and the ridge curve length. For the double nanoridge system, the properties of the launched SPP wave can be modeled as an interference result between the SPP wave launched by each ridge. Since the SPP wave must follow the curvature of graphene, it experiences a phase delay when propagating over the nanoridge, depending on the size of the ridge. The unequal phase delay of the asymmetric double nanoridge system produces different interference results in each direction, allowing the SPP wave to be launched with uneven left-right side amplitudes. With suitable arrangements of nanoridges, unidirectional or bidirectional SPP launching can be attained. Using the phenomenon, wavelength-sorted launching of graphene SPP is demonstrated for the first time. Because the system uses only normal illumination with linear polarization and no other external factors, it achieved directional graphene SPP launching with solely graphene.

Method FEM simulation was performed by frequency domain study of COMSOL Multiphysics. Graphene was modeled as a thin slab with a thickness of 0.5 nm, with nanoridge(s) in the middle. The illumination was a Gaussian beam (with much larger beam radius than the nanoridges) in the normal direction to graphene, with polarization across the ridge. The nanoridges were modeled by a circular curve and connected smoothly to the flat graphene with inverse circular curves on both sides. There were no sharp corners in the structure. The circular curve was chosen because it is the shape of nanoridge curvature from experimental results,25 and the curve length of a circular curve can be calculated analytically, whereas


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Gaussian and sine curves cannot. The nanoridge height and width reported in the results and discussion are for the main ridge body. The corners are defined to have a curvature radius of 1/10 of the main ridge body; however, this ratio does not significantly affect the results (Supporting Information Figure S18). The permittivity of graphene was calculated from the relationship 6 = 1 + 89/6 :; , where 9 and t are graphene conductivity and graphene thickness, respectively. The conductivity itself was calculated by the random phase approximation,49,50 using typical parameters of 0.5 eV Fermi energy, 300 K temperature, and 0.1 meV relaxation energy.

Supporting Information Other launching and stationary modes of single/double nanoridge structure; ridge curve length calculation; relationship of SPP wavelength and excitation wavelength; effect of nanoridge height, substrates, Fermi energy, and curvature of ridge-flat junction; launching of SPP with circular wavefront using a nanobump structure; launching efficiency comparison with gold nanoparticle; amplifying amplitude by multiple nanoridges.

Acknowledgement This work was supported by JST PRESTO Grant JPMJPR15PA, Japan, JSPS KAKENHI Grant JP17H05462, in Scientific Research on Innovative Areas “Nano-Material OpticalManipulation”. Sanpon Vantasin received financial support from the Japan Society for the Promotion of Science (JSPS) as a JSPS International Research Fellows.

References


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Figure 1. Schematic illustration of the numerical simulation. Excitation light is normally illuminated on a graphene sheet with a nanoridge. The flat graphene and the nanoridge consist of the same material and are smoothly connected. Note that the simulation was performed in two dimensions (X and Y), the Z axis in this figure is only for presentation.


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Figure 2. Numerical simulation of SPP excitation using a single nanoridge. (A) Snapshots of Ey at phase = 0 of excitation light, representing the SPP wave. Of the many possible launching and stationary modes (Figure S1–S4), only examples for launching and stationary modes of 100 and 150 nm ridges, are shown. (B) Amplitudes and phases of the SPP wave launched onto flat graphene. Vertical dashed lines show conditions for which the SPP wavelengths are an integer fraction of the ridge curve length.


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Figure 3. Numerical simulation of SPP excitation using symmetric double nanoridge. (A),(B) Snapshots of double 100- and 150-nm ridges, respectively, of Ey at phase = 0 of excitation light, showing separation-independent stationary mode, launching mode, and separationdependent stationary mode. (C),(D) Amplitude of SPP launched onto flat graphene in the cases of double 100- and 150-nm ridges, respectively.


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Figure 4. Phase delay of SPP wave when propagating over a nanoridge. In this figure, there is no illumination, as the SPP wave is considered to come from a distance source from the left. (A) Snapshot of Ey at phase = 0 of incoming wave, illustrating SPP wave propagate over flat graphene, 100- and 150-nm ridges. Green arrows mark the corresponding crests in each case (through crest-counting). (B) Phase delay from numerical simulation and analytic model plotted against excitation wavelength for the 100- and 150-nm ridges.


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Figure 5. Results from analytic model of symmetric nanoridges. Phase difference of SPP wave launch from each ridge and resulting launched amplitude, respectively, for (A),(B) double 100-nm nanoridge and (C),(D) 150-nm nanoridge. (E),(F) Launched amplitude from numerical simulation and analytic model in the case of double 100- and 150-nm nanoridges, respectively, at a ridge separation of 275 nm (conditions indicated by dashed red line in (B), and (D)).


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Figure 6. Unidirectional SPP launching by asymmetric double nanoridge. (A) Ratio of launched amplitude on right/left direction from analytic model. (B) Numerical simulation result showing snapshots of Ey at phase = 0 of excitation light, presenting plasmon launching of asymmetric double nanoridge with 275-nm ridge separation. Wavelength sorting is demonstrated as the same structure launches plasmon to the right or left depending on the excitation wavelength. (C) Same as (B) but instead presenting the averaged SPP intensity (|Ey|2) for all phases of excitation light. (D) Right/left launched amplitude ratio of the conditions with a ridge separation of 275 nm, from numerical simulations and analytic model, plotted against excitation wavelength.


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Movie 1. Numerical simulation of SPP excitation using a 100-nm width nanoridge and 3.27 µm excitation wavelength, presenting a launching mode. The color represents Ey. Movie 2. Numerical simulation of SPP excitation using a 100-nm width nanoridge and 3.65µm excitation wavelength, presenting a stationary mode. The color represents Ey.


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Graphical Table of Contents


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Launching and control of graphene plasmon by nanoridge structures

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