Dynamically reconfigurable nanoscale modulators utilizing coupled hybrid plasmonics

The balance between extinction ratio (ER) and insertion loss (IL) dictates strict trade-off when designing travelling-wave electro-optic modulators. This in turn entails significant compromise in device footprint (L3dB) or energy consumption (E). In this work, we report a nanoscale modulator architecture that alleviates this trade-off while providing dynamic reconfigurability that was previously unattainable. This is achieved with the aide of three mechanisms: (1) Utilization of epsilon-near-zero (ENZ) effect, which maximizes the attainable attenuation that an ultra-thin active material can inflict on an optical mode. (2) Non-resonant coupled-plasmonic structure which supports modes with athermal long-range propagation. (3) Triode-like biasing scheme for flexible manipulation of field symmetry and subsequently waveguide attributes. By electrically inducing indium tin oxide (ITO) to be in a local ENZ state, we show that a Si/ITO/HfO2/Al/HfO2/ITO/Si coupled-plasmonic waveguide can provide amplitude modulation with ER = 4.83 dB/μm, IL = 0.03 dB/μm, L3dB = 622 nm, and E = 14.8 fJ, showing at least an order of magnitude improvement in modulator figure-of-merit and power efficiency compared to other waveguide platforms. Employing different biasing permutations, the same waveguide can then be reconfigured for phase and 4-quadrature-amplitude modulation, with actively device length of only 5.53 μm and 17.78  μm respectively.

Scientific RepoRts | 5:12313 | DOi: 10.1038/srep12313 of ITO-assisted optical modulation is the limited light-matter-interaction (LMI) achievable within the device footprint. This is because electrically-induced refractive index change only manifests within the locally-induced carrier accumulation layer, which is few nanometers in thickness and thus have negligible overlap with typical optical modal cross-section. For planar waveguide configuration, where the light wave interacts with ITO overlaid on top of the waveguide, device length of 10 s of μm is necessary 9 . This extended device footprint in turn poses limit on potential improvement in energy efficiency. On the other hand, such footprint constraint is mitigated by utilizing ITO as a dielectric layer within plasmonic waveguides [10][11][12][13][14][15][16][17][18] . Nonetheless, while a plasmonic-based approach further enhances the mode overlap and the electromagnetic field strength across the electrically modulated ITO, the improved ER of few dB/μm is accompanied by significant increase in the IL. Moreover, the aforementioned investigations have only focused on amplitude modulation and the potential for ITO-assisted phase modulation or coherent modulation have not been explored. As such, there is still a need for a compact, low-power modulator design that can better exploit the tunable properties of ITO, while averting the strict ER-IL trade-off and supporting different modulation formats.
In this work, we report a coupled-hybrid plasmonic waveguide architecture that is comprised of Si/ITO/HfO 2 /Al/HfO 2 /ITO/Si stack. The design is capable of alleviating the ER-IL trade-off and at the same time offering fJ-level power consumption as well as reconfigurable modulation modalities. In our device, the ENZ effect in electrostatically-gated ITO is utilized to manipulate the field distribution within the coupled-waveguide system. Harnessing the LMI enhancement induced by the ENZ effect, the change in permittivity within a 1 nm accumulation layer can induce strong carrier absorption as well as adversely disturb the field symmetry responsible for long-range mode propagation, rendering the otherwise low-loss waveguide highly absorptive. Utilizing different biasing configurations of the two embedded ITO layers, waveguide dispersion characteristics can then be further manipulated to enable amplitude, phase, as well as quadrature-amplitude-modulation (QAM).

Results
Modulator Configuration. The proposed modulator architecture is shown in Fig. 1a. It consists of top and bottom hybrid plasmonic waveguides (HPWs) that are coupled through a common Al layer. Each HPW stack forms a metal-oxide-semiconductor (MOS) capacitor, where Al and ITO layers can be contacted. The application of gate voltage can capacitively induce an electron accumulation layer at the ITO-HfO 2 interface that is ~1 nm in thickness, which was calculated based on Thomas-Fermi screening theory 13 . By tuning the carrier concentration (n acc ) and thus the relative permittivity (ε r ) of the accumulation layers in the two ITO films, the fundamental ER-IL trade-off can be addressed using the following two-step design strategy:  The first step aims to maximize the modulator ER via ENZ effect. In a HPW, the optical mode is primarily confined within the nanoscale spacer region 22,23 . The mode is predominantly of a plasmonic nature with only a small fraction guided through total-internal-reflection within the high-index dielectric core. Thus, placing the actively-gated ITO within the spacer layer allows for stronger optical mode overlap and light-matter interaction, leading to compact form-factor and enhanced performance 10-12 . More importantly, in a HPW, the field intensity and power absorbed per-unit-area is proportional to Im( )/ ϵ ϵ r r of the spacer 10 . Thus, as the local ϵ r approaches zero, it is possible to draw electromagnetic energy away from the high-index Si core and the HfO 2 spacer layer, thereby concentrating the optical field across the ITO accumulation region. Due to the strong free carrier absorption and the Ohmic loss originating from the adjacent metal layer, the mode propagation length will become greatly reduced. As a result, ENZ effect can empower refractive index change within a 1 nm accumulation layer to significantly disturb a well-guided hybrid plasmonic mode [10][11][12] .
The ϵ r of ITO as a function of n acc can be described by the Drude model (See Method) 9 . To ensure that ITO can exhibit free electron behavior instead of behaving as a Mott insulator, we assume doping level of 1 × 10 19 cm −3 for bulk ITO film that is under zero external bias 9 . Moreover, we only allow n acc of up to 1.4 × 10 21 cm −3 for the 1 nm accumulation layer to prevent electric field breakdown of the HfO 2 layer 24 . From Supplementary Fig S1, it can be observed that ϵ r of ITO accumulation layer can vary rapidly from a maximum of 3.84 at n acc = 1 × 10 19 cm −3 to a minimum of 0.57 at n acc = 6.6 × 10 20 cm −3 for λ = 1550 nm. When biased to n acc = 6.6 × 10 20 cm −3 , the enhanced LMI allows full capitalization of ITO's absorptive nature, leading to significant OFF-state loss of 7.12 dB/μm (see Supplementary Fig. S2). However, similar to other plasmonic-based, ITO-assisted modulators [11][12][13][14]17,18 , this is accompanied by excessive ON-state loss of 0.91 dB/μm due to Ohmic dissipation. Defining the IL as the ON-state loss of the waveguide and the ER as the difference between ON-state and OFF-state losses, this modulator configuration provides IL = 0.91 dB/μm and ER = 6.21 dB/μm. Although 3-dB amplitude modulation only requires active waveguide length (L 3dB ) of 483 nm, the figure-of-merit (FOM), which is defined as ER/IL, for this ITO-assisted HPW is calculated to be only 6.82.
The second step aims to minimize the IL by designing athermal coupled-plasmonic structures that support long-range propagation. When the common Al layer is sufficiently thin (Fig. 1a), the mutual-perturbation of the top and bottom HPW modes will lead to the formation of transverse antisymmetric (Fig. 1b) and symmetric supermodes (Fig. 1c) 25 . The antisymmetric supermode corresponds to in-phase coupling of two HPW modes, resulting in stronger field intensity overlapping the metal and thus significant propagation loss. Conversely, the symmetric supermode is associated with destructive interference of the two HPW modes, which lowers the Ohmic loss and enables extended propagation length 26 . Therefore, utilizing the symmetric supermode as the signal carrier for modulation can significantly reduce the IL overhead. The loss characteristics of the supermodes depend sensitively on the field symmetry across the common metal layer. Specifically, IL can be minimized by manipulating the waveguide parameters such that complete field symmetry is established for the symmetric supermode when the modulator is in the ON-state. Since the mode power is distributed across the ITO and HfO 2 layers, the ϵ r of the 1 nm ITO accumulation layer will have negligible effect on this long-range hybrid plasmonic mode in the ON-state. However, when the waveguide is biased to the OFF-state, significant optical loss will then take place due to a combination of two causes: (1) the minimization of ϵ r within the accumulation region leads to propagation loss enhancement similar to the case of ITO-assisted HPW. (2) the change in ϵ r also alters the symmetry of field distribution, further increasing the mode loss. Thus, tuning the optical properties of exceedingly thin layer can render the symmetric supermode highly lossy. This approach allows us for the first time to maintain the superior ER and device footprint established with aide of ENZ effect, while minimizing the corresponding IL.
To demonstrate the effect of field symmetry engineering, the thickness of the top Si layer (h) is varied and the dispersion and loss properties of the supermodes supported by the example structure shown in Fig. 1a are plotted in Fig. 2. For simplicity, the thickness of other material layers are kept constant and the two ITO films are injected with the same n acc . The modal properties of the top and bottom HPWs are also displayed for comparison. For n acc = 1 × 10 19 cm −3 , n eff of the top HPW increases with h and approaches that of the bottom HPW, eventually intersecting at h = 240 nm (Fig. 2a). Concurrently, the propagation loss of the symmetric supermode decreases with increasing h, with a minimum propagation loss of 0.03 dB/μm at the crossing point (Fig. 2b). Figure 2c reveals that this crossing point corresponds to the complete symmetric field distribution that is required for a transparent ON-state. On the other hand, for n den = 6.6 × 10 20 cm −3 , the loss of the symmetric supermode is no longer minimized at the crossing point (Fig. 2e) and the modal energy distribution with respect to the metal becomes slightly asymmetric (Fig. 2f). Due to the ENZ effect and the asymmetric field distribution, the waveguide is transformed into OFF-state with propagation loss of 4.86 dB/μm at h = 240 nm (Fig. 2e). Thus, field symmetry engineering, which leads to long-range mode propagation within the waveguide, can offer ER = 4.83 dB/μm, IL = 0.03 dB/μm, and FOM = 161.
When compared with that of a single ITO-assisted HPW modulator, the coupled-HPW structure designed using this methodology provides a 97% reduction in the IL and a 24-fold improvement in the FOM, at the cost of only 22% reduction in the ER. This alleviates the ER-IL trade-off while maintaining a nanoscale footprint of L 3dB = 622 nm. Moreover, the propagation loss of the symmetric supermode at n acc = 1 × 10 19 cm −3 only increases by 0.01 dB/μm when h deviates from the optimal value by ± 25 nm, which is ~ ± 10% of the intended dimension (Fig. 2b). This highlights how the design is non-resonant and athermal, with strong fabrication tolerance. In general, the antisymmetric supermode has n eff and loss that are at least 0.8 and 7 dB/μm higher than that of the symmetric supermode respectively. Thus, single-mode operation and negligible cross-coupling can be expected for this architecture. Table I provides a comparison of the performance of our design against previous reports of ITO-assisted modulators, which utilized various thicknesses for the voltage-induced accumulation layer, ranging from 1 nm to 10 nm 9,11,12,14,17 . Our device, with 1 nm accumulation layer, exhibits ER and IL comparable to  plasmonic-based and dielectric-based designs respectively, thus showing significant improvement in the overall modulator FOM. Note that the FOM of our design can be further enhanced by allowing the thickness of the accumulation region to increase, reaching 641 when the entire 10 nm ITO layer undergoes change in refractive index (see Supplementary Fig. S3). It should be pointed out that the work in Ref. 18 applied a similar approach where the n acc of gallium-doped zinc-oxide is tuned to perturb the symmetric supermode of a long range plasmonic structure. However, the accumulation layer thickness was taken to be 10 nm and since field symmetry effect was not exploited, their modulator IL could not be reduced to a level comparable to its dielectric counterparts.

Bias Configuration and Modes of Operation.
For a single modulator to support different modulation formats, a triode-like biasing configuration that allows the ITO and Al films to be independently biased is required (Fig. 3). The proposed experimental waveguide configuration is illustrated in Fig. 3a, while the supported modulation formats and the corresponding gating conditions are shown in Fig. 3b-d. The fabrication of our multilayer structure requires electron-beam-lithography patterning in combination with lift-off process 11,14 . The HfO 2 and ITO layers can deposited through RF magnetron sputtering, where the carrier concentration of as-deposited ITO can be controlled by tuning the oxygen concentration during deposition 14 . Moreover, hydrogenated amorphous polysilicon can be deposited via low temperature-PECVD and serves as the top high-index dielectric layer 27 . To minimize the disturbance to the optical mode, electrical contacts will be made through Au pads 11,14 that are evaporated onto narrow strips of Al and ITO films, which have been extended several hundred nanometers away from the waveguide. Figure 4a shows the modulator characteristics for the simplest biasing configuration where the Al contact is grounded (V b = 0 V) while V a = V c = V g . The ITO films are assumed to be chemically doped to n acc = 1 × 10 19 cm −3 at V g = 0 V. As expected from previous analysis, waveguide loss reaches maximum of 4.86 dB/μm at V g = 2.32 V (n acc = 6.6 × 10 20 cm −3 ) due to field asymmetry and minimization of ϵ r . Thus, amplitude modulation with L 3dB = 622 nm can be obtained for Δ V = 2.32 V (biasing conditions 1 and 2 on Fig. 4a). The modulator energy-per-bit (E), defined by |E OFF − E ON |, is calculated to be 14.8 fJ. For direct comparison against previously proposed designs, the energy consumed along the extended contact regions is not incorporated into the calculation. Moreover, the experimental power budget will likely be higher, since the exact doping level of as-deposited ITO may be difficult to control and a DC bias will be required to offset the deviation. Nonetheless, the coupled-waveguide architecture, which comprised of two ITO films that each require biasing, shows a 47% reduction in E compared against that of a single HPW 11 (Table I). Note that although complete field symmetry is designed for V g = 0 V, the waveguide loss decays exponentially as V g deviates away from 2.32 V in both directions. This is because once ϵ r has shifted away from its minimum, the optical power overlapping the ITO accumulation layers becomes minimized and is redistributed into the undoped ITO, HfO 2 , and Si layers. Thus, with limited LMI, field symmetry created by manipulating the thickness of other material layers can still be preserved, despite the difference in ITO's ϵ r at higher and lower V g . Naturally, propagation loss decreases at a faster rate for lower V g since free carrier absorption is weaker in the low n acc regime (see Supplementary Fig.  S1).
Typically, the bandwidth (f 3dB ) of ITO-assisted modulators is dictated by the RC constant of the device instead of the formation time of the accumulation layer inside ITO 11,14,16,17 . Here we assume contact and wiring resistance of 500 Ω 11 and define f 3dB as 1/RC 11,14 . This leads to calculated f 3dB of 363 GHz, comparing favorably against the ~70 GHz reported in previous ITO-modulator that also utilized 5 nm HfO 2 as gate dielectric 17 . It can be anticipated that the experimental f 3dB and power consumption will also be limited by disorder in the deposited films, additional parasitics from the extended waveguide regions, wiring, and driver electronics. However, utilizing gate dielectric with smaller ϵ r may allow further improvement in our modulator f 3dB 11,15 . On the other hand, the wavelength dependence of the modulator is displayed in Fig. 4b. In the ON-state, loss can be maintained below 0.05 dB/μm from λ = 1300 nm to 1700 nm, further elucidating the robustness and athermal behavior of a coupled-waveguide structure that has engineered field symmetry. On the other hand, in the OFF-state, the waveguide loss is dictated by the ENZ effect and thus is wavelength-sensitive with maximum loss at λ = 1535 nm and 3-dB bandwidth of ~270 nm.
Another unique advantage of designing modulators via the two-step methodology is that phase modulation can take place without incurring additional loss. Due to plasma dispersion effect, electrical tuning of carrier concentration in ITO will inevitably leads to change in both material absorption and refractive index. However, in a coupled waveguide structure where long-range propagation is sustained except under the disturbance of the ENZ effect, waveguide loss decays exponentially and nearly symmetrically away from the ENZ point while the change in n eff is antisymmetric (Fig. 4a). This allows two biasing points on either side of the ENZ peak to have large contrast in n eff but correspond to identical loss (biasing conditions 3 and 4 on Fig. 4a), which is the necessary condition for phase modulation. Specifically, δn of 0.14 and IL = 2 dB/μm can be obtained when the waveguide is biased between V g = 2 V and 2.75 V. The corresponding interaction length for full-phase modulation is only 5.53 μm, with V π L π of 4.15 Vμm, E of 13.8 fJ, and theoretical operating f 3dB of 40.9 GHz.
In addition to amplitude and phase modulation, independent biasing of the ITO layers can reconfigure the waveguide to support complex, coherent modulation schemes. With V a ≠ V c , it is now possible to determine multiple pairs of V c 's, one for each value of V a , that lead to similar waveguide loss. Concurrently, the difference in V a will alter the field distribution within the waveguide and therefore the different pairs of gating conditions will be associated with different n eff values. This offers a path for generating the constellation points required for QAM. For example, four pairs of gating conditions are identified and labeled in Fig. 4c,d, corresponding to identical waveguide loss of ~0.32 dB/μm. At the same time, the associated n eff values differ significantly and are separated by an uniform Δ n of 0.0218. As a result, the four constellation points required for 4-QAM can be generated after light has propagated though a 17.78 μm long waveguide. This is a simple example of how this architecture can extend the amplitude and phase modulation into coherent modulation formats. As shown in Fig. 4e,f, numerous other combinations of gating conditions are available and could also be utilized to compensate for the difference in coupling loss for each constellation point. By utilizing additional permutations of biasing conditions, an array of higher-order modulation formats could be addressed in the same fashion, confirming the degree of versatility of this architecture.

Discussion
In summary, we reported an architecture for implementing optical modulators that can fully and effectively utilize the tunable properties of ITO. Utilizing an interplay of ENZ effect and field symmetry engineering, hybrid plasmonic waveguide platform with enhanced LMI but minimal loss was realized. This in turn led to integrated modulators with previously unattainable ER-IL ratio, nanoscale footprint, and fJ-level power consumption. Moreover, with a triode-based biasing strategy, it is possible to dynamically induce changes to either the propagation loss or n eff of a waveguide, thus allowing amplitude, phase, or coherent modulation to be achieved within a single device. As the proof-of-concept, we have only examined how the thickness of the top Si layer and the optical properties of ITO can influence modulation characteristics. These results demonstrated athermal and fabrication tolerant performance. However, further optimization of the properties of other waveguide layers may lead to additional performance enhancement.
It is essential to highlight that field symmetry engineering does not require the two waveguides within the coupled system to be identical. For example, Supplementary Fig. S4 demonstrates that, in a highly asymmetric waveguide structure consisting of Si/ITO/HfO 2 /Al/SiO 2 /Ge stack where only one layer of active material is utilized, IL and modulator FOM can still be minimized and maximized respectively. Thus, high-performance modulators can be designed with great flexibility to suit a wide range of platforms and fabrication processes.
More importantly, the architecture may be utilized for optical modulators that are integrated with other TCOs 10,18 , polymers [28][29][30] , metamaterial 31 , gallium nitride 32,33 , or graphene [34][35][36][37][38][39][40][41][42][43][44][45][46][47] . These active material platforms are often integrated with plasmonic structure for LMI enhancement and thus could benefit from IL mitigation. In particular, the tunability and ENZ effect within a monolayer graphene, which has thickness comparable to that of the accumulation layer in ITO, has been extensively studied Scientific RepoRts | 5:12313 | DOi: 10.1038/srep12313 and could utilize our design approach. However, it should be pointed out that the possibility of ENZ effect has recently been a subject of debate due to the anisotropy nature of graphene 48 . If the optical modal field could be engineered to align with the in-plane tunable optical conductivity of graphene, a coupled-plasmonic waveguide modulator may offer ER = 22.5 dB/μm, IL = 0.05 dB/μm, FOM = 450, E = 0.04 fJ, and bandwidth of 11.7 THz (see Supplementary Fig. S5). Overall, our modulator architecture could serve as a platform for implementing thin-film-integrated, travelling-wave modulators, with ER comparable to plasmonic-based designs, IL attainable only in dielectric-based designs, and dynamic reconfigurable modulation formats.

Methods
Optical properties of carrier-injected ITO. The permittivity of ITO can be described by the Drude model as 9 : where ∞ ϵ = 3.9 is the high-frequency dielectric constant, γ = 1.8 × 10 14 is the electron scattering rate, ω p is the plasma frequency, and ω is the frequency of light. The plasma frequency term depends on electron concentration (n) and is given by: where κ Hf O 2 = 25 and t Hf O 2 = 5 nm are the DC permittivity and thickness of the HfO 2 gate dielectric, t acc is the accumulation layer thickness, and e and ϵ 0 are the fundamental charge and the permittivity of free space respectively. We have assumed t acc of 1 nm in this report.