Selective optical-optical switching for planar plasmonic waveguides and nodes

doi:10.1364/OE.16.008198

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Selective optical-optical switching for planar plasmonic waveguides and nodes

Michael C. Quong and Abdulhakem Y. Elezzabi »View Author Affiliations

Optics Express, Vol. 16, Issue 11, pp. 8198-8212 (2008)
http://dx.doi.org/10.1364/OE.16.008198

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▸ Article Outline
– Abstract
1. Introduction
2. Plasmonic nodes and mechanism for optical-optical switching for selective surface plasmon coupling
3. Numerical calculations
4. Conclusion
– References and links

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Abstract

Two nodes are studied as means to perform selective optical-optical switching of four planar thin surface plasmon waveguides by interfering TEM₁₀, TEM₀₁, and TEM₀₀ light beams incident upon a node. One node uses a flat-apex pyramidal reflector to reflect the incident light toward the waveguides’ ends. An alternative node is a simple square aperture, which couples surface plasmons through light diffraction at the aperture’s edges. Numerical calculations predict switching contrast, coupling efficiencies, and cross-talk between waveguides. Individually turned-off waveguides are shown to have their coupled surface plasmons attenuated by at least -10 dB and up to -21 dB.

1. Introduction

Plasmonic devices promise improved speed and greater data processing parallelism than existing electronic devices. These advantages are enabled by surface plasmons, which allow for higher signal propagation speeds and bandwidth than electrical circuits [1

J. J. Ju, S. Park, M. Kim, J. T. Kim, S. K. Park, Y. J. Park, and M.-H. Lee, “40 Gbit/s light signal transmission in long-range surface plasmon waveguides,” Appl. Phys. Lett. 91, 171117 (2007). [CrossRef]

, 2

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]

]. As such, researchers envision an all-optical data processing architecture employing nanoplasmonic devices as the basic building blocks for the next generation of circuits and computers [3–6

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005). [CrossRef] [PubMed]

]. However, there are challenges to overcome. A drawback to using surface plasmons to transport optical energy is the significant resistive losses in metallic nanostructures. Such losses are more pronounced at near-infrared to optical frequencies typical of coupled surface plasmon waves. Furthermore, radiative losses result from surface curvature, including defects and edges associated with metallic nanostructures. For a semi-infinite silver slab bounded by vacuum, surface plasmon waves have propagation distances ranging from approximately 10 µm to 100 µm depending on their frequency [2

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]

]. In order to sidestep the effect of the losses, compact devices and more efficient light-to-surface plasmon coupling schemes are desired.

Scattering of light off an end of a thin planar metallic waveguide is a simple means to couple a fraction of the incident energy to surface plasmons on the surfaces of the waveguide. In particular, using “end-fire coupling” to illuminate the waveguide end with focused p-polarized light enables field intensity coupling efficiencies of ~90%. This has been theoretically and experimentally demonstrated for a semi-infinite metal slab [7

G. I. Stegeman, R. F. Wallis, and A. A. Maradudin, “Excitation of surface polaritons by end-fire coupling,” Opt. Lett. 8, 386–388 (1983), http://www.opticsinfobase.org/abstract.cfm?URI=ol-8-7-386. [CrossRef] [PubMed]

Z. Sun and D. Zeng, “Coupling of surface plasmon waves in metal/dielectric gap waveguides and single interface waveguides,” J. Opt. Soc. Am. B 24, 2883–2887 (2007), http://www.opticsinfobase.org.login.ezproxy.library.ualberta.ca/abstract.cfm?URI=josab-24-11-2883. [CrossRef]

] and finite-width thin film waveguides [9–11

R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25, 844–846 (2000), http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-11-844. [CrossRef]

]. The power guided by straight finite-width thin metal waveguides, measured experimentally by detecting output power at the end of such waveguides using single-mode optical fibers, also demonstrates ≥90% efficiency using 1550-nm wavelength [9–11

]. However, it is difficult to discern the exact intensity distribution of the coupled surface plasmons from the far-field propagating light.

While miniaturization of nanoplasmonic devices and optical-to-surface plasmon coupling are not pressing issues, the activation of these devices at high speed is challenging due to the nanoscale spatial constraints. Optical-optical switching for selective surface plasmon coupling would ideally circumvent such limitations. Selective coupling of surface plasmons to certain waveguides, while excluding others, is analogous to switching the waveguides “on” and “off” as necessary.

In this paper we outline a mechanism to selectively couple surface plasmons onto four planar thin metallic waveguide arms whose ends meet at a plasmonic node. The node redirects normally-incident light toward the waveguide ends, where light-to-surface plasmon coupling occurs. By modulating the wavefront of the incident light beam via interfering Hermite-Gaussian light beams, the amount of energy redirected toward each waveguide end can be controlled. Thus, a waveguide receiving no optical energy is switched “off”. The primary advantage of optical-optical switching using this node is ease of integration with macroscopic far-field optics. The incident light originates perpendicular to the rest of the planar plasmonic waveguides and structures, enabling plasmonic system designs where selective coupling can be performed nearly anywhere in the plane of a system as required while preserving high coupling efficiency. This will allow for greater versatility and more varied plasmonic system layouts. Furthermore, the fact that these nodes are located in plane with the plasmonic system allows for conventional nanofabrication steps to be integrated into the fabrication process flows for the entire system. Notably, the fact that coupling of signals are all in phase with each other across any combination of the four waveguide arms, allowing for phase-locked clocks for timing of nanoplasmonic circuits.

2. Plasmonic nodes and mechanism for optical-optical switching for selective surface plasmon coupling

Two proposed node configurations are illustrated in Fig. 1. As shown in Figs. 1(a), 1(b), the first plasmonic node consists of a thick metal-coated flat-apexed silicon pyramidal reflector made by anisotropically etching (100) silicon and having a sidewall angle of θ=35.26°. This arrangement will henceforth be referred to as the “pyramidal reflector” (PR) node. The pyramid’s sidewalls direct incident optical energy toward the thin silver waveguides located in a plane above the base of the pyramid. These plasmonic planar waveguides are embedded in silicon dioxide layer in order to vertically position the waveguides as well as to reduce the potential effects of tarnishing. For ease of fabrication, the distance from bottom of the metallic waveguide to the top of the metal-coated substrate is much greater than the wavelength, λ, such that the embedded waveguide does not interact with the bottom metallic layer on the substrate. Fig. 1(b) depicts the cross-sectional view across the plane of the waveguides. Here, the planar layout of the four waveguide arms is shown. Two orthogonal pairs of opposing waveguides are centered about the PR. Each waveguide end is located a horizontal distance d from its corresponding pyramidal sidewall. The x- and y-axes define the locations of the four waveguides as well as the directions of the electric field polarizations of the normally-incident light beams. This fact becomes important later when optical-optical switching of the waveguides is demonstrated.

The second plasmonic node is a square aperture having a width larger than λ placed in the center of intersecting thin beveled silver waveguides as shown in Figs. 1(c), 1(d). This node will be henceforth referred to as the “square aperture” (SA) node. Similar to the PR configuration, the silver waveguides are embedded in silicon dioxide in order to prevent tarnishing. The layout of the four waveguide arms is illustrated in Fig. 1(d), showing two opposing pairs of waveguides that are centered about the SA. Similarly, the x- and y-axes define their locations as well as the electric field polarizations of the normally-incident light. Due to diffraction of an incident light beam originating from above the node at the edges of the square aperture, this node couples the incident energy primarily into the bottom face of the waveguide. Although it is expected that the SA node will not be as efficient at coupling surface plasmons as the PR node, the compact size and simplicity of fabrication makes the SA node an attractive option to study.

To selectively couple surface plasmons onto any combination of the four planar waveguide arms, one must modulate the wavefront of the light beam normally-incident on the node. Each face of the PR or each edge of the SA redirects the light wave to its corresponding waveguide, thus modifying the incident power locally on the face or edge by altering the wavefront and controlling the power coupled onto the corresponding arm. Wavefront modulation can be accomplished through the interference of multiple light wave modes, such as TEM₀₀, TEM₁₀, and TEM₀₁ Hermite-Gaussian light beams. In both the PR and the SA node configurations, each waveguide can be actively switched “off” or “on” via the interference of the Hermite-Gaussian light beams defined as:

\begin{matrix} {TEM}_{00} ∣_{x} : & {\vec{E}}_{x} = A_{0} \exp (\frac{- (x^{2} + y^{2})}{{w_{0}}^{2}}) \exp (- i (ω t + φ)) \hat{x} & (x - polarized) \end{matrix}

(1)

\begin{matrix} {TEM}_{10} ∣_{x} : & {\vec{E}}_{x} = A_{1} (\frac{\sqrt{2} x}{w_{0}}) \exp (\frac{- (x^{2} + y^{2})}{{w_{0}}^{2}}) \exp (- i ω t) \hat{x} & (x - polarized) \end{matrix}

(2)

\begin{matrix} {TEM}_{00} ∣_{y} : & {\vec{E}}_{y} = A_{0} \exp (\frac{- (x^{2} + y^{2})}{{w_{0}}^{2}}) \exp (- i (ω t + φ)) \hat{y} & (y - polarized) \end{matrix}

(3)

\begin{matrix} {TEM}_{01} ∣_{y} : & {\vec{E}}_{y} = A_{1} (\frac{\sqrt{2} y}{w_{0}}) \exp (\frac{- (x^{2} + y^{2})}{{w_{0}}^{2}}) \exp (- i ω t) \hat{y} & (y - polarized) \end{matrix}

(4)

Here, the electric fields of the light beams are defined at their respective focal planes (xy-plane), A ₀ and A ₁ are the amplitudes, w ₀ is the beam waist, ω is the angular frequency of the light, and φ is the relative phase between the TEM₀₀ and higher-order Hermite-Gaussian modes (TEM₀₁, TEM₁₀).

Fig. 1. (a). Cross-sectional view across the middle of a PR node. Here, a is the flat apex half-width along the centerline, d is the horizontal distance between the coupling end of a waveguide and its corresponding side of the pyramidal reflector, r is the distance of the coupling end of a waveguide from the center of the node, t is the metallic waveguide thickness, and pyramidal sidewall angle θ=35.26°. (b) Cross-sectional view in the plane of the metallic waveguides of the PR node, where W is the metallic waveguide width. (c) Cross-sectional view across the middle of a SA node. Here, a is the square aperture half-width along the centerline, and t is the metallic waveguide thickness. (d) Cross-sectional view in the plane of the metallic waveguides of the SA node. Here, b is the beveled corner width, and W is the waveguide width.

Initially, the default for all of the waveguides is set to the “on” state, which is accomplished by illuminating a node with in-phase TEM₁₀ and TEM₀₁ beams. Notably, this illumination arrangement results in a doughnut shaped radially-polarized light beam. As shown in Fig. 2(a), the use of the radially-polarized light beam for the default state is due to the necessity of keeping all of the waveguides in phase.

In order to selectively turn off the plasmon coupling onto a specific waveguide arm, one must consider how to laterally shift the intensity distribution of the incident beams. The fact that energy in the lobes of the TEM₁₀ and TEM₀₁ modes is coupled to surface plasmons ensures that by destructively interfering either mode with a TEM₀₀ mode will minimize coupling to one arm. As can be seen in Fig. 3, a TEM₀₀ beam having φ=0 or π can nearly totally destructively interfere with one of the lobes of a TEM₁₀ or TEM₀₁ mode having the same polarization, thus allowing a waveguide to be switched off. It should be noted that when this interference occurs, the intensity in the center of the beam is non-zero. However, this light does not couple to any of the arms as it will be reflected away by the wide flat apex of the PR node or pass through the aperture of the SA node. All possible combinations consisting of one or two of the considered Hermite-Gaussian beams are illustrated in Fig. 4. It is evident that the wavefronts are strongly modulated. For illustrative purpose the resultant coupling to the waveguide arms are shown. Similarly, the modulated wavefronts and waveguide states resulting from the interference of three or more of the considered beams are shown in Fig. 5.

Fig. 2. (a). Cross-sectional view of a pair of opposing waveguides illuminated with a (doughnut shaped) radially-polarized light beam. The black arrows indicate the electric field polarizations of peaks in the field. (b) Three-dimensional representation of the PR node illuminated with doughnut-shaped radially-polarized light showing coupling surface plasmons onto the metallic waveguides. The dark blue lines indicate the radial electric field polarization. (c) Three-dimensional representation of the SA node illuminated with the same radially-polarized light showing coupling surface plasmons onto the bottom surface of the metallic waveguides. The dark blue lines indicate the radial electric field polarization.

Fig. 3. Relative intensity cross-section along the x-axis for a TEM₁₀ beam (black dashes), TEM₀₀| _x beam (red dots), and the sum of the TEM₁₀ and TEM₀₀| _x beams (blue line). Here, w ₀=450 nm and A ₀/A ₁=1.2. Note the center region at x=0 where the TEM₁₀ beam has nearly zero intensity while the beam resulting from the aforementioned interference has a non-zero intensity at the center.

Fig. 4. Possible incident beam profiles consisting of one or two Hermite-Gaussian beams. (a) TEM₁₀ mode. (b) TEM₀₁ mode. (c) TEM₁₀+TEM₀₁, yielding radial polarization. (d) TEM₁₀-EM₀₀| _x . (e) TEM₁₀+TEM₀₀| _x . (f) TEM₀₁ - TEM₀₀| _y . (g) TEM₀₁+TEM₀₀| _y . The red arrows illustrate the direction of electric field polarization at an arbitrary point in time. The green bars indicate waveguides that couple surface plasmons. The grey bars indicate waveguides that have attenuated surface plasmon coupling.

Fig. 5. Possible incident beam profiles resulting from the interference of three or more Hermite-Gaussian beams. (a) TEM₁₀+TEM₀₁+TEM₀₀| _x . (b) TEM₁₀+TEM₀₁ - TEM₀₀| _x . (c) TEM₁₀+TEM₀₁+TEM₀₀| _y . (d) TEM₁₀+TEM₀₁ - TEM₀₀| _y . (e) TEM₁₀+TEM₀₁+TEM₀₀| _x +TEM₀₀| _y . (f) TEM₁₀+TEM₀₁ - TEM₀₀| _x +TEM₀₀| _y . (g) TEM₁₀+TEM₀₁ - TEM₀₀| _x - TEM₀₀| _y . (h) TEM₁₀+TEM₀₁+TEM₀₀| _x - TEM₀₀| _y . The red arrows illustrate the direction of electric field polarization at an arbitrary point in time. The green bars indicate waveguides that couple surface plasmons. The grey bars indicate waveguides that have attenuated surface plasmon coupling.

3. Numerical calculations

Numerical calculations are performed using three-dimensional finite-difference time-domain (FDTD) algorithms, with the calculation space is bounded by perfectly-matched layers [12

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Ma, 1995).

,13

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]

]. The metal and the dielectric used are silver and silicon dioxide having relative permittivities of ε_m =-15.7+i0.6 [14

L. A. Sweatlock, S. A. Meier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly-coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005). [CrossRef]

] and ε_d =2.04, respectively. In order to incorporate the silver’s complex permittivity in the FDTD algorithm, the auxiliary differential equation method implementing the Drude model is chosen [15

A. Dechant and A. Y. Elezzabi, “Femtosecond optical pulse propagation in subwavelength metallic slits,” Appl. Phys. Lett. 84, 4678–4680 (2004). [CrossRef]

]. The free-space wavelength is λ ₀=590 nm. The time-averaged Poynting vector, < S >=< E × H >, where E is the electric field and H is the magnetic field, is used to calculate the intensity distribution. Intensity distributions are calculated on perpendicular planes cutting across the waveguides. As such, determining the intensity distributions for the waveguide arms on the x-axis require the calculation of <S_x > while the arms on the y-axis require the calculation of <S_y >. The total power coupled to each waveguide is found by integrating under its corresponding intensity distribution.

Since there will be far-field light propagating near the surface of the waveguides in the same direction as the surface plasmons, one must isolate this contribution to the calculated time-averaged power flow made by the surface plasmons. This is performed by assuming that the calculated time-averaged intensity on external surface of the waveguides, I_surface,ext , is due entirely to the coupled surface plasmons. This is a reasonable assumption given the near-perfect coupling of the incident electric fields onto the metal surface typical of end-fire coupling [7

]. Furthermore, the surface plasmon intensity distribution in the dielectric layer is taken to be [16

J. R. Sambles, G. W. Bradberry, and F. Yang, “Optical excitation of surface plasmons: an introduction,” Contemporary Phys. 32, 173–183 (1991). [CrossRef]

I_{SP, d} = I_{surface, ext} \exp (- {2 k}_{d, norm} ∣ z - z_{surface} ∣)

(5)

where

k_{d, norm} = \sqrt{{k_{SP}}^{2} - ε_{d} {k_{0}}^{2}}

and

k_{SP} = k_{0} \sqrt{\frac{ε_{m} ε_{d}}{ε_{m} + ε_{d}}}

. Here, z is the direction perpendicular to the planar waveguides, z_surface is the location of the metal-dielectric interface, k_SP =2π/λ_SP is the surface plasmon wavenumber, λ_SP is the surface plasmon wavelength, and k ₀=ω/c is the free-space wavenumber, where c is the speed of light in free space. Similarly, by knowing the time-averaged intensity on the internal surface of the waveguides, I_surface,int , the evanescent surface plasmon intensity distribution inside the metal can be calculated from [16

J. R. Sambles, G. W. Bradberry, and F. Yang, “Optical excitation of surface plasmons: an introduction,” Contemporary Phys. 32, 173–183 (1991). [CrossRef]

I_{SP, m} = I_{surface, int} \exp (- {2 k}_{m, norm} ∣ z - z_{surface} ∣)

(6)

where

k_{m, norm} = \sqrt{{k_{SP}}^{2} - ε_{m} {k_{0}}^{2}}

The time-averaged power of the coupled surface plasmons is then calculated by integrating the intensity distribution curves. Note that in these calculations, the highly-confined on-edge modes [17

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000). [CrossRef]

,18

J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76, 035434 (2007). [CrossRef]

] are not included, so the calculated total coupled power values will be slight underestimates. Moreover, since the far-field light is not included in the calculations, it is expected that the estimated coupled power here will be less than values obtained from calculations and measurements that encompass the Gaussian-like mode-field intensity distribution typical of finite-width thin metal waveguide [9–11

Prior to determining the off/on switching contrast, it is essential to optimize the waveguide parameters and know the exact coupling efficiency. Referring back to Fig. 1(b), the chosen parameters for a PR node having wide waveguides are a=180 nm, d=550 nm, r=730 nm, and W=860 nm. The focal beam waist for the Hermite-Gaussian beams used for the PR node is w ₀=450 nm, and the ratio of mode amplitudes from Eqs. (1–4) is A ₀/A ₁=1.2. In coupling the beam, the focus is located 20 nm above the pyramidal reflector’s flat apex and the pyramidal reflector is modeled as solid silver reflector. Interestingly, due to the angle of the pyramidal reflector’s sidewalls and the divergence of the light beams incident on the PR node, the direction of propagation of the reflected light is not in-line with the corresponding waveguides. As shown in Fig. 6, the majority of the power coupled to surface plasmon waves is localized to the top surface of the waveguides. Consequently, nanostructures intended to interact with coupled surface plasmons should be placed on the same side as the top surface of the waveguides. As such, the mode on the top surface of each waveguide excluding the edges should be considered to be the “mode of interest” (MOI).

Fig. 6. Time-averaged surface plasmon intensity distribution measured at a cross-sectional cut of a PR node waveguide located at: (a) 570 nm and (b) 1710 nm from the waveguide’s coupling end. Other parameters for the PR node are a=180 nm, d=550 nm, r=730 nm, θ=35.26°, W=860 nm, and t=50 nm.

In order to determine the light-to-surface plasmon coupling efficiency, the power of surface plasmon waves coupled onto each waveguide is measured at multiple distances from the waveguides’ ends, D. From this data, one can determine the surface plasmon 1/e propagation length, L_SP , and back calculate the coupled power. The coupling efficiency of radially-polarized light to surface plasmon waves on all four waveguides as a function of waveguide thickness, t, is shown in Fig. 7. Relative to the power incident upon the node, the maximum total power coupled is α=37.6%, or 9.40% per waveguide, as shown in Fig. 7(a) for t=50 nm. It should be noted in using four arms, only 69.8% of the power incident upon the node can interact with the waveguide ends as the rest of the light propagates away into free space. Thus, in considering the relative power that interacts with the four waveguide ends, one obtains a coupling efficiency of β=53.9%. As shown in Fig. 7(b), taking into account only the MOI, the maximum calculated values of coupled power are α=24.6% and β=35.3%, or 6.15% and 8.83% per waveguide, respectively. Clearly, the coupling efficiency increases as the waveguide thickness decreases. For this range of t (50–80 nm), the change in coupling efficiency as a function of t is approximately linear. This can be interpreted as the end facet area of the waveguide increasing linearly with t while W is held constant.

Fig. 7. (a). Total coupled power of all modes with respect to the radially-polarized light beam incident on the node, α, and with respect to the power incident on the waveguide ends, β. (b) Total coupled power of the MOI with respect to the radially-polarized light beam incident on the node, α, and with respect to the power incident on the waveguide ends, β. Both plots are for a PR node having parameters a=180 nm, d=550 nm, r=730 nm, W=860 nm, θ=35.26°, and waveguide thickness t. The TEM₁₀ and TEM₀₁ modes comprising the radially-polarized light beam have a beam waist of w ₀=450 nm. In each plot, the red dotted line indicates the power incident on the waveguide ends. Values are taken for D=190 nm (red circles), 280 nm (orange squares), 380 nm (green triangles), 480 nm (magenta stars), and 570 nm (blue diamonds), where D is the distance from the waveguide coupling ends.

Using the data, L_SP of the coupled surface plasmon power as a function of t can also be calculated. For D≥1.5λ_SP (=570 nm), L_SP is calculated assuming an exponential decay of the coupled surface plasmon power as the plasmon waves propagate, illustrated in Fig. 8(a). A maximum value of L_SP =(1.05±0.10) µm is obtained. It should be noted that in addition to resistive losses, radiative losses at the edges of the waveguides are included in the calculated values of L_SP . Additionally, as shown in Fig. 8(b), the effect of the thin film limit manifests itself as a decrease in propagation length as a function of increasing waveguide thickness, t. When t is reduced, the evanescent fields in the metal are not fully confined within the metal layer, which results in a reduction of losses. Interestingly, the expected exponential decay of the surface plasmon fields is not observed for D<1.5λ_SP (=570 nm) due to the close proximity of the measurements to the waveguides’ coupling ends.

Fig. 8. (a). Surface plasmon MOI coupled power as a function of the distance from the waveguide end, D, for waveguide thickness t=50 nm (black squares), 60 nm (red circles), 70 nm (blue triangles), 80 nm (green diamonds), and 190 nm (purple stars). Fitted exponential decay curves are shown as solid lines. (b). Surface plasmon MOI coupled power 1/e propagation length, L_SP , as a function of waveguide thickness, t, for a PR node having parameters a=180 nm, d=550 nm, r=730 nm, W=860 nm, and θ=35.26°. The fitted decay length is t ₀=11 nm. The other fitted parameters are L_inf =0.78 µm and C=24.7 µm.

It should also be noted that the decay of the total power of all coupled modes is more rapid than for the mode of interest since the mode of interest is most intense in the middle of each waveguide, away from the edges. Furthermore, since edge-coupled modes evolve differently, the propagation length varies with distance from the waveguide ends, particularly when considering the total coupled power.

The effectiveness of selective coupling to surface plasmons on waveguides of thickness t=50 nm using the PR node and the interference of Hermite-Gaussian beams is tabulated in Table 1. The baseline value refers to the MOI, where 24.6% of the power of the radially-polarized light incident on the node is coupled to all four waveguides, or 6.15% per waveguide. Moreover, charge distributions on the waveguides’ surfaces for various conditions are illustrated in Fig. 9. This charge distribution illustrates the off/on switches state.

As shown in Table 1, relative to the default state, the shut-off waveguides received anywhere from -9.9 dB to -20.9 dB of the power coupled to the waveguides when the PR node is illuminated with radially-polarized light. This indicates a significant shutting off of the targeted waveguides, although the cross-talk is still appreciable, as can be seen in Fig. 9. Shutting off a waveguide by adding a TEM₀₀ beam increases the power coupled to the opposing waveguide by up to +5.3 dB.

Table 1. Surface Plasmon Coupling with Respect to Incident Light Beam for On-Off States (PR Node)

Fig. 9. Charge distributions across a plane including the W=860 nm waveguides’ surfaces for a PR node illuminated by: (a) TEM₁₀ and TEM₀₁ beams; (b) TEM₁₀, TEM₀₁, and TEM₀₀| _x beams; (c) TEM₁₀, TEM₀₁, TEM₀₀| _x , and TEM₀₀| _y beams; (d) a TEM₁₀ beam; and (e) TEM₁₀ and TEM₀₀| _x beams.

Referring back to Fig. 1(d), the chosen parameters for the SA node are a=430 nm and W=860 nm. The focal beam waist for the Hermite-Gaussian beams used for the SA node is w ₀=600 nm, and the ratio of mode amplitudes from Eqs. (1–4) is A ₀/A ₁=0.80. The focus is located 20 nm above the square aperture. Unlike the PR node, the SA node couples the majority of its power, and hence the MOI, onto the bottom side of a waveguide as shown in Fig. 10.

Fig. 10. Time-averaged surface plasmon intensity distribution measured at a cross-sectional cut of a SA node waveguide located at: (a) D=570 nm and (b) D=1710 nm. Other parameters for the SA node are b=200 nm, W=860 nm, and t=50 nm.

Using t=50 nm, the effect of the width, b, of the beveling of corners shown in Fig. 1(d) on the total coupled power using radially-polarized light is illustrated in Fig. 11. For small or zero b that is less than the skin depth, the energy scattered at the square aperture’s corners escapes into the surrounding dielectric, whereas having b>50 nm increases the coupling efficiency. This is due to the fact that the bevels provide avenues for the small amount of energy coupled by the corners of the aperture to be guided into the waveguides. This is further confirmed by the diminishing increases in coupling efficiency with increasing b. Once a sufficient pathway is provided for the guiding of waves into the waveguides, any further increases above b>150 nm in the size of the pathway become inconsequential.

Fig. 11. Total coupled power, α, of the MOI with respect to radially-polarized light incident on a SA node measured 570 nm from the waveguides’ coupling ends. The parameters used are a=430 nm, t=50 nm, W=860 nm, and corner bevel width b. The TEM₁₀ and TEM₀₁ modes comprising the radially-polarized light beam both have a beam waist of w ₀=600 nm.

Setting b=200 nm, the effect of the waveguide thickness t on the coupling efficiency of radially-polarized light to surface plasmon waves is characterized for the SA node. As shown in Fig. 12, the coupling efficiency increases with decreasing t, similar to the PR node.

Fig. 12. Total coupled power of the MOI with respect to radially-polarized light incident on a SA node, α. Other parameters are a=430 nm, b=200 nm, W=860 nm, and waveguide thickness t. Calculated values are taken for D=380 nm (red circles), 480 nm (orange squares), 570 nm (green triangles), and 660 nm (magenta stars). The black squares indicate the estimated coupling efficiencies into the waveguide. The TEM₁₀ and TEM₀₁ modes comprising the radially-polarized light beam have a beam waist of w ₀=600 nm.

Comparing the MOIs, the coupling efficiency of radially-polarized light using the SA node is less than that when using the PR node (11.5% versus 24.6%). This is due to the fact that coupling onto the surface of the waveguides on the far side of the aperture relies on diffraction by the aperture’s edges. This diffraction is not as strong as if one were to use a subwavelength aperture. A subwavelength aperture, however, will strongly diffract any incident beam, always coupling surface plasmons onto both opposing arms regardless of the modes comprising the beam. This necessitates a larger aperture in order to accommodate the selective surface plasmon coupling.

The effectiveness of selective coupling to surface plasmons on waveguides of thickness t=50 nm and b=200 nm using the SA node and the interference of Hermite-Gaussian beams is tabulated in Table 2 and typical charge distributions on the waveguides’ surfaces for various conditions are illustrated in Fig. 13.

Table 2. Surface Plasmon Coupling with Respect to Incident Light Beam for On-Off States (SA Node)

As shown in Table 2, the shut-off waveguides received anywhere from -11.3 dB to -15.5 dB of the power coupled to the waveguides when the SA node is illuminated with radially-polarized light. As with the PR node, this indicates a significant shutting off of waveguides as desired using the SA node. Again, the cross-talk is notable as Fig. 13 illustrates. Shutting off a waveguide by adding a TEM₀₀ beam increases the power coupled to the opposing waveguide by up to +5.3 dB, similar to the PR node.

Fig. 13. Charge distributions across a plane including the waveguides’ surfaces for a SA node illuminated by: (a) TEM₁₀ and TEM₀₁ beams; (b) TEM₁₀, TEM₀₁, and TEM₀₀| _x beams; (c) TEM₁₀, TEM₀₁, TEM₀₀| _x , and TEM₀₀| _y beams; (d) a TEM₁₀ beam; and (e) TEM₁₀ and TEM₀₀| _x beams.

Of particular interest is L_SP , which can be determined by examining coupled surface plasmon MOI power as functions of D≥λ_SP (=380 nm) for various values of t as shown in Fig. 14(a). Unlike for the PR node, the decrease in power with propagation cannot be fitted to an exponential decay curve. In particular, the attenuation increases for D≥1.1 µm for all values of t. This can be explained by the divergence of the coupled surface plasmon waves for greater values of D, as shown in Fig. 14(b). Notably, at D=380 nm, the coupled power for t=50 nm is less than that for t=60 and 70 nm, contrary to all other values of D. The light beam incident on the top side of the waveguides interfering detrimentally with the fields coupled to the bottom side. This is illustrated in Fig. 15(a) for t=50 nm, where interfering electric fields inside the metal waveguides are observable, particularly at smaller values of D corresponding to the more intense incident beam. The effect of the interference is minimized when the SA node’s waveguide thickness is increased to t=70 nm and beyond. As shown in Fig. 15(b) for t=80 nm, the electric fields on both surfaces of the waveguides do not interact in any significant way inside the metal waveguide.

Fig. 14. (a). Total coupled power, α, of the surface plasmon MOI for a SA node having parameters a=430 nm, b=200 nm, and W=860 nm as a function of distance from the waveguides’ ends, D, for t=50 nm (black squares), 60 nm (red circles), 70 nm (blue triangles), and 80 nm (green diamonds). (b) Surface charge distribution plot illustrating the divergence of surface plasmon waves for D≥1.1 µm. The dashed lines indicate the widths of the surface plasmon waves along the waveguides.

Fig. 15. Cross-sectional electric field magnitude distributions for SA nodes having waveguide thicknesses of: (a) t=50 nm, and (b) t=80 nm. Other geometric parameters are a=430 nm, b=200 nm, and W=860 nm. The nodes are being illuminated by radially-polarized light having a beam waist of w ₀=600 nm.

4. Conclusion

Two compact node designs that enable the selective optical-optical switching of four planar surface plasmon waveguides have been presented. Both nodes redirect normally-incident light energy to four directions, where each direction corresponds to a thin metal waveguide. The first design is a node employing a flat-apexed pyramidal reflector while the second design is a simple square aperture whose edges diffract incident light. Any redirected p-polarized light is coupled onto the surfaces of the waveguides. By modulating the incident wavefront through the interference of light beams, the optical energy incident on each of the pyramidal reflector’s sidewalls or each of the square aperture’s edges can be controlled. Individual waveguide arms can be selected to be turned “on” or “off” for light-to-surface plasmon coupling by interfering TEM₁₀, TEM₀₁, and TEM₀₀ Hermite-Gaussian beams. In doing so, the power of surface plasmons on any waveguide’s surface can be attenuated by -9.9 dB to -20.9 dB depending on the geometry and parameters used. The switching performances of both nodes are similar; however, the pyramidal reflector node demonstrated greater coupling efficiency and surface plasmon propagation lengths than the square aperture node.

Overall, it can be concluded that the pyramidal node reflector is the best-performing node, although the simplicity of fabrication of the square aperture node makes it an attractive option. We envision that these nodes that function on normally-incident light will enable more versatile plasmonic systems with more varied layouts.

Acknowledgments

The authors would like to acknowledge funding from the Natural Sciences and Engineering Research Council (NSERC) of Canada. The authors would also like to thank Dr. Vien Van of the Department of Electrical and Computer Engineering, University of Alberta, for insightful discussions. Finally, the authors would like to thank the reviewers of this paper for their helpful suggestions.

References and links

1.	J. J. Ju, S. Park, M. Kim, J. T. Kim, S. K. Park, Y. J. Park, and M.-H. Lee, “40 Gbit/s light signal transmission in long-range surface plasmon waveguides,” Appl. Phys. Lett. 91, 171117 (2007). [CrossRef]
2.	W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]
3.	N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005). [CrossRef] [PubMed]
4.	J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407 (2006). [CrossRef]
5.	K. J. Chau, M. Johnson, and A. Y. Elezzabi, “Electron-spin-dependent terahertz light transport in spintronic-plasmonic media,” Phys. Rev. Lett. 98, 133901 (2007). [CrossRef] [PubMed]
6.	E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006). [CrossRef] [PubMed]
7.	G. I. Stegeman, R. F. Wallis, and A. A. Maradudin, “Excitation of surface polaritons by end-fire coupling,” Opt. Lett. 8, 386–388 (1983), http://www.opticsinfobase.org/abstract.cfm?URI=ol-8-7-386. [CrossRef] [PubMed]
8.	Z. Sun and D. Zeng, “Coupling of surface plasmon waves in metal/dielectric gap waveguides and single interface waveguides,” J. Opt. Soc. Am. B 24, 2883–2887 (2007), http://www.opticsinfobase.org.login.ezproxy.library.ualberta.ca/abstract.cfm?URI=josab-24-11-2883. [CrossRef]
9.	R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, “Experimental observation of plasmon polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25, 844–846 (2000), http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-11-844. [CrossRef]
10.	R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 477–494 (2006). [CrossRef]
11.	K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, “Long-range surface plasmon polariton nanowire waveguides for device applications,” Opt. Express 14, 314–319 (2006). [CrossRef] [PubMed]
12.	A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Ma, 1995).
13.	J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
14.	L. A. Sweatlock, S. A. Meier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly-coupled Ag nanoparticles,” Phys. Rev. B 71, 235408 (2005). [CrossRef]
15.	A. Dechant and A. Y. Elezzabi, “Femtosecond optical pulse propagation in subwavelength metallic slits,” Appl. Phys. Lett. 84, 4678–4680 (2004). [CrossRef]
16.	J. R. Sambles, G. W. Bradberry, and F. Yang, “Optical excitation of surface plasmons: an introduction,” Contemporary Phys. 32, 173–183 (1991). [CrossRef]
17.	P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000). [CrossRef]
18.	J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76, 035434 (2007). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(310.2790) Thin films : Guided waves

ToC Category:
Optics at Surfaces

History
Original Manuscript: February 26, 2008
Revised Manuscript: March 27, 2008
Manuscript Accepted: April 13, 2008
Published: May 21, 2008

Citation
Michael C. Quong and Abdulhakem Y. Elezzabi, "Selective optical-optical switching for planar plasmonic waveguides and nodes," Opt. Express 16, 8198-8212 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-8198

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References

J. J. Ju, S. Park, M. Kim, J. T. Kim, S. K. Park, Y. J. Park, and M.-H. Lee, "40 Gbit/s light signal transmission in long-range surface plasmon waveguides," Appl. Phys. Lett. 91, 171117 (2007). [CrossRef]
W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003). [CrossRef] [PubMed]
N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005). [CrossRef] [PubMed]
J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006). [CrossRef]
K. J. Chau, M. Johnson, and A. Y. Elezzabi, "Electron-spin-dependent terahertz light transport in spintronic-plasmonic media," Phys. Rev. Lett. 98, 133901 (2007). [CrossRef] [PubMed]
E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006). [CrossRef] [PubMed]
G. I. Stegeman, R. F. Wallis, and A. A. Maradudin, "Excitation of surface polaritons by end-fire coupling," Opt. Lett. 8, 386-388 (1983), http://www.opticsinfobase.org/abstract.cfm?URI=ol-8-7-386. [CrossRef] [PubMed]
Z. Sun and D. Zeng, "Coupling of surface plasmon waves in metal/dielectric gap waveguides and single interface waveguides," J. Opt. Soc. Am. B 24, 2883-2887 (2007), http://www.opticsinfobase.org.login.ezproxy.library.ualberta.ca/abstract.cfm?URI=josab-24-11-2883. [CrossRef]
R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, "Experimental observation of plasmon polariton waves supported by a thin metal film of finite width," Opt. Lett. 25, 844-846 (2000), http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-11-844. [CrossRef]
R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, "Passive integrated optics elements based on long-range surface plasmon polaritons," J. Lightwave Technol. 24, 477-494 (2006). [CrossRef]
K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, "Long-range surface plasmon polariton nanowire waveguides for device applications," Opt. Express 14, 314-319 (2006). [CrossRef] [PubMed]
A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Ma, 1995).
J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994). [CrossRef]
L. A. Sweatlock, S. A. Meier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly-coupled Ag nanoparticles," Phys. Rev. B 71, 235408 (2005). [CrossRef]
A. Dechant and A. Y. Elezzabi, "Femtosecond optical pulse propagation in subwavelength metallic slits," Appl. Phys. Lett. 84, 4678-4680 (2004). [CrossRef]
J. R. Sambles, G. W. Bradberry, and F. Yang, "Optical excitation of surface plasmons: an introduction," Contemporary Phys. 32, 173-183 (1991). [CrossRef]
P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B 61, 10484-10503 (2000). [CrossRef]
J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, "Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding," Phys. Rev. B 76, 035434 (2007). [CrossRef]

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