1. Introduction

A major challenge of the state-of-the-art electronic-photonic integrated circuits (EPICs) is the miniaturization of optical components beyond the diffraction limit in order to bridge the dimension mismatch between the electric and optical components. An attractive solution for this challenge is to utilize surface plasmon polaritons (SPPs) excited at the metal-dielectric interfaces taking advantage of the nature of SPP that its mode can be confined in nanometer scales because of the very short penetration of electric field in metals [1, 2]. A SPP guiding structure (namely, a plasmonic waveguide), which comprises one or more metal-dielectric interfaces, is a basic platform to link various integrated functional plasmonic components to a plasmonic nanocircuit. However, due to the unavoidable resistive damping in the metals, the plasmonic waveguides which can tightly confine the mode in subwavelength dimensions exhibit much a larger propagation loss (usually in the dB/μm scale) than the conventional Si waveguides (usually in the dB/cm scale), and suffer from a fundamental tradeoff between the mode confinement level and the propagation distance [3]. Thus, the plasmonic components are not expected to replace the optical counterparts in the EPICs, but are expected to additionally implement in the EPICs to realize a wide range of functionalities that are difficult, inefficient, or impossible to be realized based on the conventional Si waveguides. Namely, the next-generation EPICs will be the integration of all electronic, photonic, and plasmonic components in a single chip [4, 5]. An ideal plasmonic waveguide thus should have (1) better tradeoff between the light confinement and the propagation distance and (2) feasibility for seamless integration in the existing EPICs using standard silicon complementary metal-oxide-semiconductor (CMOS) technology.

Many types of plasmonic waveguides as well as plasmonic waveguide components have been proposed and/or demonstrated in the past years, such as gap-SPP [6], hybrid [7], dielectric-loaded SPP waveguides [8], and many others. We regard that the recently developed horizontal metal-insulator-Si-insulator-metal nanoplasmonic waveguide [9, 10] is an attractive candidate for seamless integration into the existing Si-EPICs. First, its lateral mode confinement is solely determined by the Si core width and the surrounding insulator thickness, which can be shrunk to nanometer scales using standard CMOS technology. Second, its propagation loss around 1550-nm telecom wavelengths is relatively low when Cu is used as the metal [10]. Third, it can link with the conventional Si waveguide through a simple tapered coupler with the coupling efficiency as high as 90% [10]. Fourth, the Si core can be used as an active material for electro-optic modulation through the free-carrier dispersion effect in Si [11]. Fifth, a functional material, e.g., a dielectric with large thermo-optic, electro-optic, or nonlinear effect, can be readily inserted or replace the insulator between the Si core and the metal to introduce effective active functionalities because of the significant enhancement of the SPP field in this low-index dielectric layer. One example of such a device is an effective ultracompact SPP detector, which has been theoretically proposed utilizing a suitable ultrathin silicide layer inserted between the insulator and the Si core [12]. Finally, it is fully CMOS compatible, enabling to be seamlessly implemented into the existing Si EPICs.

The Cu-SiO₂-Si-SiO₂-Cu plasmonic waveguide as well as several waveguide components have been experimentally demonstrated on a silicon-on-insulator (SOI) platform using standard CMOS technology, including sharp 90° bends [10], power splitters [13], waveguide-ring resonators [14], and Si electro-absorption modulators [15]. In this paper, more basic building blocks, e.g. Mach-Zehnder interferometers (MZIs), are systematically investigated. The experiment results are compared with those predicted from numerical simulation. The results reported in this paper can be used to guide the design of Cu-SiO₂-Si-SiO₂-Cu waveguide-based complex integrated plasmonic nanocircuits.

2. Experimental

The devices are fabricated on SOI wafers with 340-nm-thick top-Si and 2-µm-thick buried SiO₂ using standard CMOS technology. The Cu-covered plasmonic components are inserted in the conventional Si-waveguide network, as shown in Fig. 1(a) for an example of a 1 × 4 power splitter. In terms of fabrication, the only difference between the different plasmonic devices is the pattern of Si core, which is defined along with the Si channel waveguide. For example, Fig. 1(b) shows a schematic Si pattern of the 1 × 4 power splitter. After Si pattering, a thin Si₃N₄ film and a thick SiO₂ film were sequentially deposited. A SiO₂ window, the yellow rectangle in Fig. 1(b), is then opened to expose the plasmonic area, which includes the plasmonic component and 1-µm-long tapered couplers to connect with the Si channel waveguides. After thermal oxidization of the exposed Si core, a thick Cu film was deposited, followed by copper chemical mechanical polishing (Cu-CMP) to remove the Cu outside the window. The detailed fabrication conditions have been described elsewhere [10]. Although the width of Si core (W_P) in the layout keeps 0.2 µm, its final width can be tuned by the fabrication conditions, in particular, the expose condition during the ultraviolet (UV) lithography and the photo-resist trimming process. In this work, the final Si cores have widths of 64, 80, 94, and 102 nm, respectively, surrounded by a ~28-nm-thick thermal SiO₂ layer, as shown in Fig. 1(d) for one example of W_P = 94 nm. It should be noted that the Si core as narrow as < 10 nm and the surrounding insulator as thin as ~1 nm are technically available using standard CMOS technology as that for Si nanowire field-effect transistors [16].

 

Fig. 1 (a) Microscope picture of one fabricated device (a 1 × 4 power splitter), the Cu-covered plasmonic component is inserted in the Si-waveguide network; (b) Schematic Si pattern of the 1 × 4 power splitter, each branch of the plasmonic splitter is connected with a Si waveguide through a 1-µm-long tapered coupler, the yellow rectangle is the SiO₂ window which will be covered by Cu; (c) Schematic cross section of the Cu-SiO₂-Si-SiO₂-Cu waveguide; and (d) Cross-sectional transmission electron microcopy (XTEM) image of the fabricated plasmonic waveguide, showing a quasi-rectangular Si core (~94-nm × ~327-nm) surrounded by a ~28-nm-thick thermal SiO₂ layer and covered by a thick Cu layer.

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The diced chips are characterized using standard fiber-to-fiber measurement setup. Quasi-TE-polarized light (the electric field is parallel to the chip surface plane) from an Expo broad-band laser source, whose spectral range is ~1520–1620 nm, is coupled into the input Si waveguide through a lensed polarization-maintaining (PM) sing-mode fiber. Light transmitted from the output Si waveguide is coupled to another single-mode fiber and is measured by a power meter and an AQ6317B optical spectrum analyzer (OSA). A semi-auto micrometer piezo-stage is used to adjust the fibers to search the maximum output power.

A commercial software FullWAVE/RSOFT [17] is used for three-dimensional (3D) finite-difference time-domain (FDTD) simulation. The Si core is approximated to an ideal 340-nm-high rectangle on the SiO₂ substrate, surrounded by a uniform thermal SiO₂ layer. 1550-nm TE light is launched at the input 500-nm-wide Si channel waveguide and transports into the plasmonic waveguide through a 1-µm-long tapered coupler. The detailed settings for the 3D FDTD simulation have been described elsewhere [10]. The refractive indices of Si and SiO₂ at 1550 nm are set to 1.445 and 3.455, respectively. Cu complex permittivity data are cited from different references [18–20], and the one that match our experimental results best is adopted.

3. Straight waveguides

The straight plasmonic waveguides have length (L_P) ranging from 1 to 100 µm. The transmitted powers measured from these waveguides after subtracting that measured from the reference waveguide (i.e., the Si waveguide without the plasmonic area) are plotted in Fig. 2 as a function of L_P. Each data point is averaged from three identical waveguides and the standard deviation is indicated as the error bar. The transmitted power exhibits a good linearity with L_P. The slope of the linearly fitting lines (also shown in the figure) gives the propagation loss. They are ~0.281, ~0.286, ~0.287, and ~0.304 dB/µm for the plasmonic waveguides with W_P of ~102, ~94, ~81, and ~64 nm, respectively (the surrounding SiO₂ thickness is ~28 nm for all waveguides). The y-intercept gives the coupling loss of the 1-μm-ling tapered coupler which links the 500-nm-wide Si channel waveguide and the plasmonic waveguide. The difference in the coupling loss of these four plasmonic waveguides is smaller than the experimental error. Therefore, the coupling losses obtained from all tested waveguides are averaged, which is ~0.51 dB/facet, corresponding to coupling efficiency of ~89%. Both the propagation loss and the coupling loss are in good agreement with the previous report [10].

 

Fig. 2 Transmitted powers versus the length of straight plasmonic waveguides with different W_Ps, normalized by that measured from the reference waveguide without the plasmonic area. Each data point is averaged from three sets of waveguides. The linearly fitting lines give the propagation loss and the coupling loss of the 1-µm-long tapered coupler which links the 500-nm-wide Si channel waveguide and the plasmonic waveguide.

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The build-in Cu permittivity in RSoft [17] is ~-109 + 9.8i at 1550 nm, which is cited from Ref [18]. Numerical simulation using this Cu permittivity predicts a propagation loss much larger than the measured value [10]. We notice that there is a large discrepancy in Cu permittivity data reported in the literature, for example, the Cu permittivity is ~-122 + 6.2i at 1550 nm in Ref [19], and is ~-79.2 + 10.8i at 1550 nm in Ref [20]. This discrepancy may arise from the different Cu fabrication conditions in different references. On the other hand, it reflects that the Cu permittivity may be sensitive to the fabrication condition. In this work, we simply adopt a standard Cu process well developed for the Cu/low-k dielectrics interconnections in the CMOS technology [21], i.e., 100-nm-thick Cu sputtering as a seed layer first, followed by 1-μm-thick Cu electroplating, and then annealing at 200°C for 30 min. We do not measure the optical property of this Cu film directly. Instead, we test various reported Cu permittivity data in numerical simulation to calculate the propagation loss. We find that the permittivity of ~-122 + 6.2i at 1550 nm reported in Ref [19]. matches our experimental results best. Therefore, this Cu permittivity is adopted hereafter in this paper.

Figure 3(a) plots the propagation loss as a function of W_P. Like the conventional gap-SPP waveguides [6], the propagation loss increases with the slot between two metal interfaces decreasing (the light confinement level increases accordingly), reflecting the abovementioned fundamental tradeoff for all kinds of plasmonic waveguides. For plasmonic waveguides with a certain slot width (W_P and the surrounding SiO₂ thickness), the propagation loss is mainly determined by the Cu permittivity. In this work, the Cu fabrication condition is not intentionally modified to reduce the propagation loss. However, we regard that it may be possible to further reduce the propagation loss by optimizing the Cu fabrication condition such as the sputtering and annealing parameters.

 

Fig. 3 (a) Propagation loss, and (b) Real effective index (n_eff) at 1550 nm wavelength for the Cu-SiO₂-Si-SiO₂-Cu plasmonic waveguides with various SiO₂ thicknesses. The curves are obtained from 3D FDTD simulation with Cu permittivity of −122 + 6.2i [19]. The experimental propagation losses are read from Fig. 2 and from Ref [10]. The experimental n_eff data are extracted from the plasmonic MZIs.

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Figure 3(b) plots the real effective indices (n_eff) of the Cu-SiO₂-Si-SiO₂-Cu waveguides as a function of W_P, obtained from the 3D FDTD simulation as well as the experimental data extracted from the plasmonic MZIs. Unlike the conventional gag-SPP waveguide whose n_eff decreases monotonously with the gap width increasing [6], the n_eff-W_P relation of our plasmonic waveguides depends on the surrounding SiO₂ thickness. For waveguides with a thick SiO₂ layer (e.g., ≥ 12 nm), n_eff increases with W_P increasing from 10 to 160 nm. For waveguides with a mediate SiO₂ layer (e.g. ~6 nm), n_eff is almost independent on W_P. Whereas for waveguides with a very thin SiO₂ layer (e.g., ≤ 2 nm), n_eff decreases with W_P increasing from 10 to 160 nm. This observation can be attributed to two contradictory effects of W_P on n_eff. On one hand, the total slot width increases with W_P increasing, thus leading to n_eff decreasing as the conventional gap-SPP waveguides. On the other hand, the ratio of SPP power in the Si core increases with W_P increasing, which causes n_eff increasing. For waveguides with a very thin SiO₂ layer, the first effect dominates, making n_eff decreasing with W_P increasing. Whereas for waveguides with a thick SiO₂ layer, the second effect dominates, making n_eff increasing with W_P increasing.

4. Multiple sharp 90° bends

Our plasmonic waveguide supports sharply bending with a relatively low loss [9, 10], thus enabling to route SPP signals flexibly in plasmonic nanocircuits. Figure 4(g) illuminates the normalized magnetic field (H_y) distribution in a sharp 90° bend with 64-nm W_P and 28-nm SiO₂. The power monitored after the junction is normalized by the power monitored before the junction (where “0 dB” is indicated). The pure bending loss is calculated by subtracting the propagation loss through the same distance in the straight plasmonic waveguide (2 µm here) from the above normalized power. It is −0.77 dB, as indicated in the figure.

 

Fig. 4 (a)-(f) SEM images (the Si core patterns) of a set of bent plasmonic waveguides which contains 2, 4, 6, 8, 10, and 12 sharp 90° bends, respectively, the total plasmonci waveguide length is 13 µm; (g) Normalized magnetic field (H_y) distribution in a sharp 90° bend with 64-nm W_P and 28-nm SiO₂, obtained from the 3D FDTD simulation. The power indicated after the junction is the pure bending loss, calculated by comparing the powers monitored before and after the junction and subtracting the propagation loss through the same distance in the straight plasmonic waveguide; (h) Transmission spectra measured on a set of bent plasmonic waveguides with 64-nm W_P and a 13-µm-long plasmonic straight waveguide (represented by “0”); and (i) Transmitted powers measured on bent plasmonic waveguides with different W_Ps as a function of the number of bends, normalized by the corresponding 13-µm-long straight plsmonic waveguide. The bending loss is estimated from a linearly fitting line through zero.

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In our experiment, the measurement error of identical waveguides in the same chip is ~ ± 1 dB due to the small variation in fabrication (especially at the tip area) from one waveguide to the next [22], which is larger than the expected pure bending loss. To measure the pure bending loss accurately, bent plasmonic waveguides with multiple sharp 90° bends are fabricated, as shown in Figs. 4(a)-4(f), which contains 2, 4, 6, 8, 10, and 12 sharp 90° bends, respectively. Because the final Cu-covered plasmonic devices are not observable by scanning electron microscopy (SEM), the Si core patterns are shown here to represent the individual devices (and hereafter in this paper). The total length of these bent plasmonic waveguides keeps the same 13 µm. Figure 4(h) depicts the transmission spectra measured on a set of bent plasmonic waveguides with 64-nm W_P as well as a 13-µm-long straight plasmonic waveguide (i.e., 0 bend) for reference. The spectra of the straight and 2-bend plasmonic waveguides are almost wavelength independent, at least in the spectral range of 1520–1620 nm, in agreement with the previous reports [9, 10]. The spectra are wavelength dependent for the bent waveguides with multiple bends, most probably due to the refection of SPP from the bent junction [23]. Since the reflection is expected to be very small, the reflection induced Fabry-Perot (F-P) resonances are only observable on the bent waveguides with multiple bends. Figure 4(i) depicts the transmitted powers as a function of bend number for the bent plasmonic waveguides with W_P of 102, 94, 81, and 64 nm, respectively, normalized by the corresponding 13-µm-long straight plasmonic waveguide. For the waveguides with 64-nm W_P, three sets of bent plasmonic waveguides are measured and the standard deviation is indicated as the error bar. The deviation is relatively large due to the abovementioned reflection-induced F-P resonations, and is in the same magnitude as the W_P-induced difference in the bending loss. Therefore, it is impossible to experimentally extract the possible dependence of pure bending loss on W_P. Nevertheless, it is expected that the possible W_P dependence should be small because the test waveguides have the same SiO₂ layer and the SiO₂ layer is relatively thick so that the SPP mode is mostly confined in it, in agreement with that predicted from numerical simulation. Also due to the abovementioned reflection-induced F-P resonations, the linearity of the normalized power versus the bend number is very poor, making it difficult to extract the bending loss accurately. Nevertheless, a linearly fitting through the origin point for all data points is still performed, as shown in Fig. 4(i), which gives an approximate bending loss of ~0.73 ± 0.06 dB/turn, close to the value predicted from the 3D FDTD simulation.

The bending property of our plasmonic waveguide is more like the gap-SPP waveguide [6], rather than the hybrid [7] and DLSPP [8] waveguides. The latter two types of plasmonic waveguides do not support the sharp 90° bending because of their relatively weaker light confinement compared with our and gap-SPP waveguides.

5. Symmetric and asymmetric power splitters

The Cu-SiO₂-Si-SiO₂-Cu plasmonic waveguides support large-angle power splitting with relatively low excess loss [13]. Figures 5(a) and 5(d) show SEM images of symmetric 1 × 2 and 1 × 4 splitters with a 90° open angle, respectively. The total length of each plasmonic route is 3 µm. Figures 5(b) and 5(e) illuminate the normalized H_y distributions in the splitters with 64-nm W_P and 28-nm SiO₂, obtained from 3D FDTD simulation. The power indicated in each output branch is the power normalized by the input power and subtracted the propagation loss of the same distance in the straight plasmonic waveguide. They are −3.63 dB for the 1 × 2 splitter and −6.95 dB for the 1 × 4 splitter. Because the 1 × 2 splitter contains an additional 45° sharp bend, the theoretical excess loss for one Y-splitter is estimated to be ~0.46 dB. Figures 4(c) and 4(f) depict the spectra measured from each output port of the 1 × 2 and 1 × 4 splitters with 64-nm W_P, respectively. We can see that the spectra are almost wavelength independent and the difference among different output ports in the splitters is within the measurement error, confirming the symmetric nature of our splitters. To reduce the experimental uncertainty, three identical splitters are measured. The averaged output power after subtracting that measured on the 3-µm-long straight plasmonic waveguide is −3.8 ± 0.4 dB for the 1 × 2 splitter and −7.5 ± 0.2 dB for the 1 × 4 splitter. Both are in good agreement with the simulation results. The experimental excess loss for one Y-splitter is estimated to be ~0.74 dB. The splitters with larger W_Ps are also examined. They exhibit similar splitting behaviors (not shown here). The apparent insensitivity of the excess loss on W_P may also be attributed to the relatively thick SiO₂ layer, as the above-observed apparent insensitivity of the pure bending loss on W_P.

 

Fig. 5 (a) SEM image (the Si core pattern) of a symmetric 1 × 2 splitter with 90° opening angle; (b) Normalized H_y distribution in the 1 × 2 splitter with 64-nm W_P and 28-nm SiO₂, obtained from the 3D FDTD simulation, the indicated values after the junction are normalized by the input power and subtracted the propagation loss through the same distance in the straight waveguide; (c) The spectra measured from output ports of a 1 × 2 splitter with 64-nm W_P, normalized by that measured on a corresponding 3-µm-long straight plasmonic waveguide. The indicated values are averaged from three identical splitters; (d)-(f) are the corresponding figures for a symmetric 1 × 4 splitter.

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Asymmetric splitters which deliver unequal power to each output port can be flexibly designed based on our plasmonic waveguide. Figure 6 shows 1 × 2 asymmetric plasmonic splitters fabricated in this work, where the one output branch (out-1) is straight up from the input arm while the other output branch (out-2) is obliquely connected to the input arm with a certain angle. The angle is 30° in Fig. 6(a), 60° in Fig. 6(d), and 90° (i.e., ⊥-splitter) in Fig. 6(g), respectively. Figure 9(j) is a symmetric T-splitter for comparison. The total length of each plasmonic route is 3 µm. The simulation results of these splitters with 64-nm W_P and 28-nm SiO₂ are illuminated in Figs. 6(b), 6(e), 6(h), and 6(k), respectively, and the measurement results are plotted in Figs. 6(c), 6(f), 6(i), and 6(l), respectively.

 

Fig. 6 (a) SEM image (the Si core pattern) of an asymmetric 1 × 2 splitter with 30° opening angle; (b) Normalized H_y distribution in the splitter with 64-nm W_P and 28-nm SiO₂, obtained from the 3D FDTD simulation. The indicated values after the junction are normalized by the input power and subtracted the propagation loss through the same distance in the straight waveguide; (c) The spectra measured from each output port of a splitter with 64-nm W_P, normalized by that measured from the 3-µm-long straight plasmonic waveguide. The indicated values are averaged from three identical splitters; (d)-(f) are the corresponding figures for an asymmetric 1 × 2 splitter with 60° opening angle; (g)-(i) are the corresponding figures for an asymmetric 1 × 2 splitter with 90° opening angle (the ⊥-splitter); (j)-(l) are the corresponding figures for a symmetric 1 × 2 T-splitter for comparison.

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Fig. 9 (a) Schematic top view of plasmonic MZIs designed in this work, ΔL varies from 0 to 0.8 µm with a step of 0.1 µm; (b) SEM image (Si core pattern) of MZI with ΔL = 0; (c) Normalized H_y distribution in the MZI with 64-nm W_P and 28-nm SiO₂, obtained from the 3D FDTD simulation. The indicated value at the output plasmonic waveguide is normalized by the input power and subtracted the propagation loss of 5-µm-long straight plasmonic waveguide; (d)-(e) are the corresponding figures for the MZI with ΔL = 0.4 µm; and (f)-(g) are the corresponding figures for the MZI with ΔL = 0.8 µm.

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From simulation, we can see that the power delivered to the out-2 branch decreases significantly from 43.1% to 36.1%, while the power delivered to the out-1 branch increases slightly from 48.5% to 51.6%, with the angle increasing from 30° to 90°. It indicates that only a small fraction of the decreased power in the out-2 branch due to the angle increasing is rerouted to the out-1 branch, making the overall excess loss increasing from 0.38 dB to 0.57 dB with the angle increasing from 30° to 90°. In particular, the ⊥-splitter delivers 51.6% power to the out-1 branch and 36.1% power to the out-2 branch, for comparison, the T-splitter delivers 36.8% power to each branch and the remaining 26.4% power is lost mainly due to reflection at the junction. Moreover, we find that the ratio of powers delivered to two branches of the above 1 × 2 asymmetric splitters increases, as well as the excess loss of T-splitter increases, with the slot width (both W_P and the surrounding SiO₂ thickness) of the plasmonic waveguide increasing (not shown here), in agreement with the report that the reflection from the junction increases with the slot width increasing [23].

From experiment, we can see that the transmission spectra measured from each output port of 1 × 2 asymmetric splitters are also almost wavelength independent in the spectral range of 1520−1620 nm. The power delivered to the out-1 branch increases and the power delivered to the out-2 branch decreases, with the angle increasing, in agreement with the simulation results. However, except the 30° splitter, the power delivered to the out-1 branch is larger, and that delivered to the out-2 branch is smaller, than that predicted from simulation. This discrepancy may partially be attributed to the enlarged junction in the fabricated splitters due to the fabrication limitation, as observed in Figs. 6(d) and 6(g). Consistently, the larger excess loss of the T-splitter than that predicted from simulation may also partially arise from the enlarged junction [13], as observed in Fig. 6(j). The enlarged junction makes the splitter behaving as a splitter with a larger slot width, thus leading to a large reflection of SPP wave at the junction. For the 30° splitter shown in Fig. 6(a), on the other hand, the two output branches near the junction are not physically separated due to the limitation of our UV lithography. The two output branches are apparently almost symmetric near the junction, thus resulting in almost equally power splitting with low excess loss of ~0.5 dB.

To verify the above hypothesis, the ⊥- and T-splitters with an enlarged junction are simulated. For simplification, the Si core of the enlarge junction is approximated to an equilateral triangle with the side length of 0.3 μm. The simulation results are given in Fig. 7 . Compared with the corresponding values indicated in Fig. 6(h) and 6(k), the power delivered to the out-1 branch becomes larger and that delivered to the out-2 branch becomes smaller for the ⊥-splitter, and the power delivered to the each branch becomes smaller for the T-splitter. The trend agrees qualitatively with the above hypothesis although the predicted values still deviate relatively largely from the experimental data. We expect that this deviation may be reduced if a more accurate morphology of the Si core as well as the surrounding SiO₂ is taken into account in the numerical simulation.

 

Fig. 7 3D FDTD simulation results of (a) ⊥-splitter and (b) T-splitter, which have the same parameters as those shown in Figs. 6 (h) and (k), respectively, but with an enlarged junction which is approximated to an equilateral triangle with the side length of 0.3 μm for simplification.

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According to the above result that a substantial fraction of power can be delivered to the orthogonal branch, more complex splitters can be designed, as shown in Fig. 8 just for some examples. Figure 8(a) is a 1×3 cross splitter with one junction. Figure 8(d) is a 1×3 splitter with two junctions, which actually consists of two sequent ⊥-splitters. Figure 8(g) is a 1×5 splitter with 4 junctions, which actually consists of four sequent ⊥-splitters. Their simulation results are illuminated in Figs. 8(b), 8(e), and 8(h), respectively. The value indicated at each output branch is the power normalized by the input power and subtracted the propagation loss through the same distance in the straight waveguide (be noted that each plasmonic route in these splitters has a different length). We can see that the SPP power can be delivered to the orthogonal branches accordingly, in consistence with the result of ⊥-splitter shown in Fig. 6(g). Figures 8(c), 8(f), and 8(i) show the measurement results of these three splitters, respectively. The transmission spectra measured from each output ports are almost wavelength independent. The indicated values are averaged from three identical splitters, normalized by the straight plasmonic waveguide with the same length. In agreement with that predicted from simulation, the SPP power is delivered to each branch accordingly. Like the asymmetric splitters shown in Fig. 6, the power delivered to the straight branch is larger, whereas the power delivered to the orthogonal braches is smaller, than that predicted from simulation partially due to the enlarged junctions. The splitters with large W_Ps are also measured (not shown here). They deliver even larger fraction of power to the straight branch and even smaller fraction of power to the orthogonal branches than those indicated in Fig. 8, in agreement with the abovementioned effect that the large slot width of the plasmonic waveguide results in a large reflection of SPP power at the junction.

 

Fig. 8 (a) SEM image (the Si core pattern) of a 1 × 3 cross splitter with one junction; (b) Normalized H_y distribution in the splitter with 64-nm W_P and 28-nm SiO₂, obtained from the 3D FDTD simulation. The indicated values after the junction are normalized by the input power and subtracted the propagation loss through the same distance in the straight plasmonic waveguide; (c) The spectra measured from each output port of the splitter, subtracted by the straight waveguide with the same plasmonic route length. The indicated values are averaged from three identical splitters; (d)-(f) are the corresponding figures for a 1 × 3 splitter with two junctions; (g)-(i) are the corresponding figures for a 1 × 5 splitter with four junctions.

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6. Plasmonic Mach-Zehnder interferometers

MZI is a basic building block for many optical devices. Figure 9(a) shows schematically a typical design of an ultracompact plasmonic MZI, where the opening angle of the splitter and the combiner is 120°, the upper oblique arm is 1-µm long, and the bottom oblique arm is (1 + ΔL)-µm long. ΔL varies from 0 to 0.8 µm with a step of 0.1 µm. The input plasmonic waveguide before splitting and the output plasmonic waveguide after combing are both 1-µm long. Therefore, the total plasmonic route through the upper arm is 6 µm, and that through the bottom arm is (6 + ΔL) µm. Figures 9(b), 9(d), and 9(f) show SEM images of the MZIs with ΔL = 0, 0.4, and 0.8 µm, respectively. Figures 9(c), 9(e), and 9(g) illuminate the simulation results for these three MZIs, respectively. We can see that two plasmonic waves propagating along the upper and bottom arms are constructively recombined at the combiner in the cases of ΔL = 0 and 0.8 µm, whereas they are destructively recombined at the combiner in the case of ΔL = 0.4 µm. The transmitted powers normalized by the input power and subtracted the propagation loss of the 6-µm-long straight plasmonic waveguide are −2.58, −22.7, and −2.93 dB for MZIs with ΔL = 0, 0.4, and 0.8 µm, respectively. It indicates that the plasmonic MZI has the same working mechanism as the conventional dielectric waveguide based MZIs. Therefore, the normalized transmission, T(λ), can be expressed as follows [24]:

Figure 10(a) depicts the measured transmission spectra of a set of MZIs with 64-nm W_P whose ΔL is 0, 0.1, 0.2, …, and 0.8 µm, respectively, normalized by the 6-µm-long straight plasmonic waveguide. As expected from Eq. (1), the transmission spectrum of the balanced MZI (i.e., ΔL = 0) is wavelength independent, whereas the spectra of the unbalanced MZIs (i.e., ΔL ≠ 0) become wavelength dependent, especially in the case of ΔL = 0.4 µm. But, no clear peak can be observed in the spectra due to the large free spectral range (FSR, = ${\lambda }_r{}^2/(n_{eff}\Delta L)$) and the narrow spectral range (~1.52-1.62 µm) of our measurement setup. FSR decreases with ΔL increasing. For our MZI with the largest ΔL of 0.8 µm, FSR is estimated to be ~1.5 µm around 1550-nm wavelengths, which is much larger than the spectral range of 0.1 µm. Figure 10(b) plots the measured transmitted powers as a function of ΔL, normalized by the 6-µm-long straight plasmonic waveguide. Each data point is averaged from three identical MZIs and the standard deviation is indicated as the error bar. The transmitted powers obtained from the 3D FDTD simulation are also shown for comparison. They agree well with the measurement values. The measurement data are fitted using Eq. (1) by setting α₂ = 10^{-0.0304 × ΔL} (because the corresponding straight plasmonic waveguide has propagation loss of ~0.304 dB/µm, as indicated in Fig. 2) and setting n_eff and α₁ as the fitting parameters. The best fit parameters are found to be α₁ = 0.69 and n_eff = 1.85. The MZIs with large W_Ps are also examined. They exhibit similar property as that shown in Fig. 10 (not shown here). From best fitting using Eq. (1), the real effective indices are extracted to be ~1.85, ~1.95, ~2.00, and ~2.05 for plasmonic waveguides with W_P of 64, 81, 94, and 102 nm, respectively. These n_eff values are plotted in Fig. 3(b) as a function of W_P. We can see that they agree well with those extracted from the 3D FDTD simulation of the straight plasmonic waveguides.

 

Fig. 10 (a) The normalized transmission spectra measured on MZIs with ΔL of 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, and 0.8 µm, respectively; (b) The transmitted powers obtained from measurement and simulation as a function of ΔL, as well as the fitting curve based on Eq. (1) with the best fitting parameters of α₁ = 0.69 and n_eff = 1.85.

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From Fig. 10(b), we can see that the fabricated MZIs have normalized insertion loss (IL) of ~1.7 dB and extinction ratio (ER) of ~18 dB. The ER is mainly limited by the power difference between the upper and bottom arms. Theoretically, it can be as large as ~35 dB (in the case of ΔL = 0.43 around 1550-nm wavelengths). The normalized IL is due to splitter, combining, and bending. The value of 1.7 dB insertion loss quantitatively agrees well with the experimental results of the symmetric 1 × 2 splitter shown in Fig. 5 and the sharp bend shown in Fig. 4.

Our plasmonic waveguide allow us to design more compact MZIs. One example is shown in Fig. 11(a) schematically, where two arms are the upper and bottom arcs of a ring with radius R. The output plasmonic waveguide deviates from the parallel line of the input plasmonic waveguide by ΔL. In this work, R is set to 0.9 µm and ΔL is set to 0, 0.1, 0.15, 0.2, 0.25, and 0.3 µm, respectively. The input plasmonic waveguide before splitting and the output plasmonic waveguide after combing are both 1-µm long. Therefore, the total length of plasmonic route through the upper arm is ~(4.8 - ΔL) µm, and that through the bottom arm is ~(4.8 + ΔL) µm. Figures 11(a) and 11(d) shows SEM images of the fabricated MZIs with ΔL = 0 and 0.2 µm, respectively. Their corresponding simulation results are illuminated in Figs. 11(c) and 11(e), respectively. Similar to the MZIs shown in Fig. 9, the two SPP waves propagating along two arms are constructively recombined at the combiner in the case of ΔL = 0, and are destructively recombined in the case of ΔL = 0.2 µm. The normalized output power is −3.21 and −19.0 dB, respectively.

 

Fig. 11 (a) Schematic top view of ultracompact plasmonic MZIs with R of 0.9 µm and ΔL varying from 0 to 0.3 µm; (b) SEM image (Si core patterns) of MZI with ΔL = 0; (c) Normalized H_y distribution in the MZI with 64-nm W_P and 28-nm SiO₂, obtained from the 3D FDTD simulation, The indicated value at the output plasmonic waveguide is normalized by the input power and subtracted the propagation loss of 3.8-µm-long straight plasmonic waveguide; and (d)-(e) are the corresponding figures for MZI with ΔL = 0.2 µm.

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Figure 12(a) plots the spectra measured on a set of MZIs with ΔL = 0, 0.1, …, and 0.3 µm, respectively, normalized by the 4.8-µm-long straight plasmonic waveguide. Similar to Fig. 10(a), the spectrum of the balanced MZI is almost wavelength independent, whereas the spectra of the unbalanced MZIs are wavelength dependent. Again, due to the very large FSR and the narrow spectral range, no clear peak can be observed in the spectra. Figure 12(b) plots the normalized output powers as a function of ΔL, as well as those obtained from 3D FDTD simulation. The fitting curve using Eq. (1) (be noted that ΔL in Eq. (1) should be replaced by $2\cdot R\cdot arcsin\left(\Delta L/R\right)$ here) is also shown. The best fitting parameters are α₁ = 0.45 and n_eff = 1.75. The large normalized IL of this type of MZIs is due to the large excess loss of the T-splitter and combiner, as shown in Fig. 6(j). The footprint of this type of MZIs can be reduced simply by reducing the radius of the ring.

 

Fig. 12 (a) The transmission spectra measured on MZIs with ΔL = 0, 0.1, 0.15, 0.2, 0.25, and 0.3, respectively, normalized by the 4.8-µm-long straight plasmonic waveguide; (b) The transmitted powers obtained from measurement and simulation as a function of ΔL, as well as the fitting curve based on Eq. (1) with the best fitting parameters of α₁ = 0.45 and n_eff = 1.75.

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7. Conclusions

Various horizontal Cu-SiO₂-Si-SiO₂-Cu plasmonic waveguide components are systematically investigated. The propagation losses measured from the fabricated straight plasmonic waveguides agree with those predicted from 3D FDTD simulation using the Cu permittivity reported in Ref [19]. The plasmonic waveguide supports sharp 90° bend with a relatively low bending loss of ~0.73 dB/turn. However, the bending loss extracted from the bent plasmonic waveguides with multiple sharp 90° bends suffers from large uncertainty due to the weak F-P resonances induced by weak reflection of SPP power at the junction. Therefore, a new testing structure should be designed to extract the bending loss accurately.

Owing to the low bending loss, various ultracompact power splitters and MZIs can be flexibly designed for plasmonic nanocircuits. The fabricated 1 × 2 Y-splitter has excess loss of ~0.74 dB and MZIs has normalized insertion loss of ~1.7 dB and extinction ratio of ~18 dB, in good agreement with those predicted from the 3D FDTD simulation. For asymmetric, T-, ⊥-, and cross- splitters, the ratio of powers delivered to output ports depends on the slot width of the plasmonic waveguide, and the power delivered to each output port differs quantitatively from that predicted from simulation partially due to the enlarged junction caused by the fabrication limitation. The plasmonic waveguide with narrower slot width has better performance for rerouting, but has a larger propagation loss. It indicates that a main challenge for plasmonic nanocircuits is to reduce the propagation loss without sacrificing the confinement level.