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We present a computational design for an integrated electro-optic modulator based on near-field plasmonic coupling between gold nanodisks and a thin film of vanadium dioxide on a silicon substrate. Active modulation is achieved by applying a time-varying electric field to initiate large changes in the refractive index of vanadium dioxide. Significant decrease in device footprint (200 nm x 560 nm) and increase in extinction ratio per unit length (9 dB/µm) compared to state-of-the-art photonic and plasmonic modulators are predicted.
© 2015 Optical Society of America
1. Introduction
Optical modulators are essential components of optical interconnects for integrated photonic circuits [1]. Historically, silicon optical modulators have employed carrier depletion/accumulation or diffusion effects in p-i-n junctions [2–6]. These effects are relatively weak in silicon [7], requiring either long interaction lengths or long interaction times, so that the modulators must be either extremely large on a traditional CMOS size-scale (~1 mm x 10 µm) or extremely sensitive to ambient temperature fluctuations. Thus even though all-silicon modulators exhibit modulation speeds up to 50 GHz [8], they are too large for integrated photonic circuits. Electro-optic modulators that are more compact and less temperature-sensitive than all-silicon devices can be made from III-V materials (e.g., GaAs, InGaAs) [9] or lithium niobate [10]. However, compatibility with silicon is essential for most on-chip applications. Hence, hybrid structures have been proposed that overcome the intrinsic limitations of silicon optical modulators and maintain CMOS compatibility, while adding a material with synergistic properties. For example, organic nonlinear polymers with large second-order nonlinearities [11, 12], graphene [13], and vanadium dioxide (VO2) [14–18] have been combined with silicon modulators to achieve improved performance.
VO2 is a particularly interesting material to integrate with silicon because very large changes in its dielectric function can be achieved on ultrafast time scales without requiring preparatory processing such as electric field poling. VO2 exhibits a first-order solid-solid phase transition near 68°C [19], from a semiconducting, monoclinic ground state with a bandgap of about 0.7 eV [20] to a rutile metal. Near 1550 nm, the real part of the refractive index of VO2 drops from 3.2 (semiconductor) to 1.6 (metal), and the imaginary part increases from 0.3 to 3, correspondingly. This refractive index change is three to four orders of magnitude larger than the maximum index modulation achievable in silicon photonic devices based on carrier diffusion or depletion. It is therefore possible to shrink the footprint of hybrid silicon modulators by as much as three orders of magnitude compared to silicon-only ring resonators, Mach-Zehnder interferometers (MZIs), or absorption modulators while also improving modulation speed, extinction ratio, bandwidth, power consumption, and device footprint [14, 15, 18]. For example, hybrid Si:VO2 ring-resonators with footprints of a few square micrometers support modulation speeds well in excess of 100 GHz when switched optically at an energy cost of 190 fJ per operation [14].
Plasmonics offers a complementary path to compact, low power modulators through subwavelength light confinement and a larger group index of plasmon modes compared to optical modes in silicon waveguides [21, 22]. However, as stand-alone elements, plasmonic modulators suffer from unfavorable trade-offs between footprint, losses, and extinction ratios. On the other hand, the demonstration of Si-VO2 hybrid planar optical switches utilizing surface plasmons propagating between silver and VO2 [16, 17], among other hybrid plasmonic-photonic structures [23, 24], suggests that it may be possible to overcome these tradeoffs, although the switching demonstrated in the Si-VO2 hybrid structure was slow (~25 µs) because the phase transition was initiated by heating [16, 17].
In this work, we propose and computationally model an alternative, ultra-compact device geometry for hybrid plasmonic waveguide modulators that incorporates electrical switching of VO2 beneath a plasmonic nanodisk chain to achieve ultrafast optical modulation with record values of extinction ratio per unit length. To reach higher modulation speeds, we minimize the slow thermal component of the VO2 phase transition by switching the VO2 electrically and integrating plasmonic modulators into a photonic waveguiding system that couples efficiently into other silicon photonic components. There is a precedent for integrating hybrid plasmonic components with photonic waveguides: an efficient photonic-hybrid plasmonic mode coupler has been proposed and demonstrated for converting a standard silicon waveguide (quasi-TM mode) into a hybrid Au-Al2O3-Si plasmonic mode with 75% power conversion [25]. Our design, which utilizes a photonic-hybrid plasmonic mode coupler, focuses on the active hybrid plasmonic modulator component and capitalizes on the enormous change in the VO2 refractive index across the semiconductor-to-metal transition to achieve ultrafast active switching of the hybrid plasmonic mode.
2. Design
Figure 1(a) shows the design of the hybrid Si-VO2-Au plasmonic modulator with silicon as a bottom layer, VO2 as the active middle layer, and gold nanodisks on top. The gold nanodisk chain is chosen because of its compact footprint and regions of very high electric field confinement where the active material, VO2, can be switched by an applied field. Figure 1(b) shows the electric field distribution of the fundamental quasi-TM plasmonic mode for this structure, confirming that the mode is largely confined within the VO2 layer, thus maximizing the extinction ratio of the modulator and allowing lower-loss propagation of the hybrid plasmonic mode in the semiconducting VO2 film. When VO2 is switched into a metallic state [Fig. 1(c)], the hybrid mode no longer propagates because the loss increases significantly, resulting in signal modulation. The proposed operation of the hybrid Si-VO2-Au plasmonic modulator is as follows: (1) light is coupled from a standard silicon optical waveguide to the hybrid plasmonic modulator shown in Fig. 1(a) using the design strategy reported in Song et al. [25]; (2) a voltage is applied to the outermost gold nanodisks to switch the VO2 in the gaps between the coupled nanodisks from the semiconducting to the metallic state; (3) when VO2 is in the metallic state, the hybrid mode no longer propagates along the nanodisks and therefore does not couple back to a photonic mode. Consequently, modulating the electric field applied to the nanodisks effectively modulates the intensity of the output optical mode.
Fig. 1 (a) Schematic representation of the proposed hybrid plasmonic modulator design based on Au, VO2, and Si. Light is coupled into the modulator from a standard silicon waveguide using a photonic-hybrid plasmonic mode coupler (not shown). Electric field intensity of the hybrid mode for VO2 in the (b) semiconducting state and (c) metallic state.
In designing an active plasmonic modulator with VO2, three design goals are considered: (1) minimizing insertion loss, (2) maximizing modulation depth, and (3) minimizing active VO2 volume in order to reduce the operating power. Since the modulator is intended for use in the telecommunication band, we seek designs that maximize transmission near 1550 nm. Hybrid plasmonic waveguides – comprising a higher refractive-index dielectric, lower refractive-index dielectric, and a metal – support much longer propagation lengths than conventional plasmonic waveguides consisting of one dielectric and one metal component [26, 27] and for this reason have informed the present design.
A hybrid Si-VO2-Au waveguide without the Au nanodisks can be used as a modulator with a good extinction ratio (~15 dB/µm) and low insertion loss. Modes of this structure are shown in Figs. 1(b) and 1(c). However, it is difficult to switch the VO2 layer in this configuration using an electrical signal unless the gold layer is also used as an integrated heater [16], which would lead to the slow operational speed attendant to heating a large volume of VO2. Hence we replace the continuous metal film by a chain of plasmonic nanodisks [Fig. 1(a)] in which the outmost nanodisks serve as electrical contacts for inducing the electrical metal-insulator transition (E-MIT) in VO2 located in the gaps between nanodisks [17, 28–31]. The E-MIT in VO2 has recently been shown to occur at least as fast as 2ns and potentially much faster [30, 32]. The size and spacing of the gold nanodisks not only controls the field strength in the VO2 regions between nanodisks, but also allows control over the optical resonance wavelength.
In order to minimize the insertion loss and gain insight into the behavior of the transmission spectrum of the gold nanodisks, the disk size and VO2 film thickness were optimized in simulations using three-dimensional (3D) full field finite-difference time-domain (FDTD) simulations for a broad frequency range (1300-1700nm), fixing both the silicon thickness and width at 200 nm, dimensions for which the photonic-plasmonic coupler was optimized in [25]. VO2 was modeled using the measured real and imaginary parts of the refractive index as a function of wavelength [33]. Silicon and gold were modeled using experimental data from [34].
In the optimization process, the transmission spectrum of a single nanodisk was first simulated by launching a hybrid plasmonic mode [Fig. 1(b)] into a continuous film Au-VO2-Si waveguide, letting it propagate through the nanodisk and couple back to the continuous film Au-VO2-Si waveguide [inset in Fig. 2(a) ], and collecting it with a frequency-domain power monitor. As shown in Fig. 2(a), the spectrum has a single broad resonance near 1600 nm; the lower wavelength side-lobe near 1400 nm is a simulation artifact due to degenerate modes reaching the power monitor through the silicon, and could be eliminated by increasing the source-to-monitor separation. Next, the VO2 and gold thicknesses were varied within experimentally achievable limits, assuming that a lift-off fabrication method is used and that VO2 is deposited as a continuous film (thickness 30-80 nm) [35]. The resulting transmission amplitude and peak resonance wavelength for the hybrid Si-VO2-Au plasmonic modulator design with a single nanodisk were then analyzed. The continuous gold film thickness was always set to the same value as the nanodisk thickness in order to maximize mode match.
Fig. 2 (a) Single gold nanodisk transmission spectrum (nanodisk diameter fixed at 180nm, Au thickness fixed at 60 nm, and VO2 thickness fixed at 40 nm). Inset shows the schematic: yellow is gold, green is semiconducting VO2, and gray is silicon. The peak position and amplitude of the resonance for varying (b) VO2 thickness (Au thickness fixed at 60 nm), (c) Au thickness (VO2 thickness fixed at 40 nm), and (d) nanodisk diameter (Au thickness fixed at 60 nm and VO2 thickness fixed at 40 nm) are shown.
Increasing the thickness of either VO2 (for gold thickness fixed at 60 nm) or gold (for VO2 thickness fixed at 40 nm) increases the resonance amplitude, as shown in Figs. 2(b) and 2(c), respectively. Increasing VO2 film thickness improves coupling to the hybrid mode, leading to increased transmission amplitude. The increased transmission amplitude with increased gold thickness is associated with improved coupling between the gold film that forms part of the hybrid plasmonic-photonic coupler, and the gold nanodisk.
Two distinct mechanisms for increasing peak transmission amplitude are apparent in the behavior of the resonant peak wavelength as a function of VO2 and gold nanodisk thickness. Increasing the VO2 thickness linearly red-shifts the peak transmission wavelength as a larger portion of the mode becomes concentrated within the semiconducting VO2 layer with its higher refractive index. Increasing the gold thickness initially blue-shifts the peak transmission wavelength as more of the mode extends into the low refractive-index gold nanodisk. However, beyond a critical thickness near 50 nm, further increases do not affect the peak wavelength because the plasmon field decays before reaching the added gold.
Next, the effect of the gold nanodisk diameter was examined with the VO2 and gold thicknesses fixed at 40 nm and 60 nm, respectively. When the diameter of the nanodisk is increased, the transmission resonance is red-shifted, as the resonance energy is reduced consistent with larger cavity size, analogous to quantum-confinement rules in quantum dots [Fig. 2(d)] [36]. The change in resonant wavelength is accompanied by an increase in transmission that is most likely caused by a smaller lateral mode mismatch between the 200 nm-wide continuous gold film and the gold nanodisk.
With the single nanodisk trends understood, we move on to investigate the effects of incorporating multiple nanodisks into the chain and varying the spacing between nanodisks. For this investigation, we select the nanodisk diameter of 160 nm, VO2 film thickness of 40 nm, and gold film thickness of 60 nm to maximize the transmission amplitude while maintaining a transmission bandwidth encompassing standard communication wavelength bands. While these parameters for a single nanodisk design produced a resonance peak near 1450 nm, when multiple nanodisks are present, the peak wavelength red-shifts [Fig. 3(a) ], which is typical for a coupled resonator system. As expected due to VO2 absorption, the maximum transmission decreases for longer nanodisk chains. Also with additional nanodisks, the resonance peak becomes sharper due to the absence of degenerate modes discussed earlier. In order to choose the most desirable number of nanodisks, one needs to consider the benefits of longer nanodisk chains in comparison to the drawbacks. The main advantage of longer chains is an enhanced extinction ratio resulting from a longer interaction length, and therefore stronger spatial light-matter interaction of the mode with the active modulator material, VO2. The primary disadvantage of longer gold nanodisk chains is increased insertion loss due to absorption in VO2 and gold. As shown in detail in the next section, the three-nanodisk chain provides the large extinction ratio that is most suitable for modulator applications and is therefore the design selected for performance benchmarking.
Fig. 3 (a) Transmission spectra of the devices with varying number of nanodisks (160 nm nanodisk size, 40 nm VO2, 60 nm gold). (b) Coupling strength dependence on the gap size between nanodisks (160 nm nanodisk size, 40 nm VO2, 60 nm gold). Electric field distribution at resonant wavelength for three nanodisk chain shown in the (c) top view and (d) side view (160 nm nanodisk size, 40 nm VO2, 60 nm gold, 20 nm gap). The field is strongest in the gaps between nanodisks and extends into the VO2 region below the nanodisks.
The spacing between nanodisks plays an important role in both the efficiency of light propagation through the hybrid modulator and the strength of light-matter interaction between the hybrid mode and VO2. As predicted by a simple plasmonic model of two circular particles, the coupling strength between two nanodisks increases when they are brought closer together. Figure 3(b) illustrates the relationship between coupling strength (determined by the maximum transmission amplitude) and inter-nanodisk spacing for the hybrid modulator design, and exemplifies this trend. Although better near-field coupling is achieved for a gap of 10 nm, a 20 nm gap relaxes the fabrication tolerance and would be achievable with standard electron-beam lithography [37]. The electric field of the propagating mode is shown in Figs. 3(c) and 3(d) for a three-nanodisk chain on resonance. The intensity of the field is highest in the space between the nanodisks, but a fraction of the field does extend into the underlying VO2 layer. The bending tails of the mode between nanodisks arise from longitudinal propagation of the resonating mode. Ideally, VO2 would be deposited in the gaps between nanodisks to achieve best device performance, as the fabrication would be realizable but challenging.
Following the design studies, a three-nanodisk chain having a gold nanodisk diameter of 160 nm, a gold film and nanodisk thickness of 60 nm, and a VO2 film thickness of 40 nm was selected to benchmark the modulator performance. This design minimizes overall footprint, minimizes active VO2 volume, which in turn will minimize operating power, and minimizes insertion losses while providing a relatively large operating bandwidth. The extinction ratio of this modulator design is examined in the next section.
3. Performance
With the hybrid Si-VO2-Au modulator geometry selected, the performance metrics can be assessed. A major advantage of this modulator configuration is that the applied DC electric-field maxima coincide perfectly with the maxima of the propagating plasmon mode, indicating that the optical properties of VO2 as it undergoes the phase transition will have maximal impact on the propagating optical mode. The hybrid plasmonic mode for the configuration shown in Figs. 3(c) and 3 (d) is concentrated in an 80 nm x 80 nm area between three nanodisks, making the active VO2 volume extremely small. A linear extrapolation from experimental data for larger patches of VO2 shows that the switching voltage in this configuration would be only 400 mV [38].
In order to confirm the required switching voltage, we carried out a finite-element analysis using the COMSOL heat transfer package. The simulation also includes the photonic-plasmonic couplers from [25] that serve as electrical contacts to the nanodisk chain. A voltage of 1 V was applied to the contacts, resulting in fields on the order of 107 V/m, above the measured threshold switching value for VO2 (~5 x 106 V/m) [28–30, 38, 39]. The switching power in this configuration is calculated to be 4.8 mW (400 mV), almost an order of magnitude lower than the power consumed by a hybrid plasmonic-VO2 device utilizing Joule heating (32.8 mW) [16]. The global temperature increase was calculated to be only 3°C above room temperature, suggesting that the electric field possibly augmented by local nanoscale heating are the primary switching mechanisms [Fig. 4(c) ]. It is known that the electrical metal-insulator transition in VO2 is triggered by two primary mechanisms, namely electrical tunneling and Joule heating. If Joule heating is minimized by limiting the current through the device, the primary mechanism will be electron tunneling. The size of the tunneling current path is largely unknown. Therefore, in order to estimate the extinction ratio, different sizes of metallic VO2 filaments within a semiconducting matrix were simulated using 3D FDTD calculations.
Fig. 4 (a) Schematic illustrating regions of VO2 metallization when a voltage is applied across the gold nanodisk chain. (b) Extinction ratio of the hybrid Si-VO2-Au optical modulator as a function of the metallic VO2 region width. (c) Joule heating simulation of the hybrid modulator.
A schematic of the simulation geometry is shown in Fig. 4(a) and results are shown in Fig. 4(b). The greatest improvement in extinction ratio is observed for the smallest width of metallic VO2, while saturation in the extinction approaching 8 dB is observed for widths greater than approximately 100 nm. Gains in extinction ratio diminish when the metallic region of VO2 extends beyond the width of the plasmonic field (~80 nm) between nanodisks. If the tunneling path width is assumed to be 40-60 nm, the typical size of a single grain of multi-crystalline VO2, the extinction ratio is of order 4-6 dB. This is an astonishingly large value considering that the hybrid modulator is only 560 nm long. Since this extinction ratio is sufficient for most modulator applications, there is no need to add additional nanodisks to the chain, which would further increase extinction ratio at the cost of increased insertion loss.
We compare our device with other proposed and demonstrated silicon and silicon hybrid modulators in Table 1 . The performance metrics highlighted in the table exhibit the advantages of the proposed design. The most significant improvements to the state-of-the-art are made in device footprint (560 nm x 200 nm), extinction ratio per unit length (~9 dB/µm) and switching power (4.8 mW).
Table1. Comparison of plasmonic nanodisk chain hybrid Si-Au-VO2 modulator with other plasmonic and photonic electro-optic modulators.
A critical performance-limiting factor is the anticipated VO2 switching time for the electrically actuated phase transition, which currently appears to limit the modulation speed to approximately 1 GHz according to published work related to electrical switching of VO2 [30]. The phase transition into the rutile metallic state occurs in less than 100 fs using ultrafast optical excitation, with the reversion to the semiconducting state on the order of a few picoseconds for optical fluences below a critical fluence near 5 mJ/cm2 [40, 41]. Whether terahertz electrical modulation of an optical signal is achievable in the hybrid Si-VO2-Au geometry depends on the ultimate achievable speed of the VO2 transition from the metallic to the semiconducting state. In this work, we estimate the modulation speed of our device based on the currently reported state-of-the-art electrical switching time for VO2 (1 GHz).
However, there are grounds for optimism. The electronic transition of VO2 has been found to occur prior to completion of the monoclinic-to-rutile transition for epitaxial films [42, 43]. Moreover, a metallic monoclinic state has been found to be accessible by both optical [44, 45] and thermal [46] excitation. It is therefore likely that more careful study will yield similar results for electrical excitation. In particular, evidence for possible increased speed of transition for smaller VO2 patch size [47] is consistent with a conjectured two-stage quasi-electric-field excitation [48]. If it is possible to metallize the VO2 without transforming the crystal structure, then electrical switching speeds substantially faster than 1 ns should be possible.
4. Conclusion
We have developed a design methodology and simulated the performance of a hybrid Si-VO2-Au modulator based on near-field plasmonic coupling between gold nanodisks. The hybrid modulator exhibited excellent performance in several important categories, including ultra-small footprint (560 nm x 200 nm), large extinction ratio per unit length (~9 dB/µm), and low operating power (4.8 mW). With the potential for direct integration into silicon waveguides, this new design is expected to dramatically improve the performance of silicon optical modulators without requiring a disruptive fabrication process.
Acknowledgments
PM and SMW acknowledge support from the Air Force Office of Scientific Research (FA9550-10-1-0366). KA was supported by the U. S. Department of Energy, Office of Science (DE-FG01-02ER45916) and contributed expertise on plasmonics and plasmonic coupling with vanadium dioxide.
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