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Ultra-compact EO polymer modulators based on hybrid plasmonic microring resonators are proposed, simulated and analyzed. Comparing with Si slot microring modulator, hybrid plasmonic microring modulator shows about 6-times enhancement of the figure of merit when the bending radius is around 510 nm, due to its much larger intrinsic quality factor in sub-micron radius range. Influences of the EO polymer height and Si height on the device’s performance are analyzed and optimal design is given. When operating with a bias of 3.6V, the proposed device has optical modulation amplitude of 0.8 and insertion loss of about 1 dB. The estimated power consumption is about 5 fJ/bit at100 GHz.
© 2013 Optical Society of America
1. Introduction
Optical interconnects are envisaged as a promising way to break through the physical limits of electronic circuits in microprocessors, and enable the future continuation of Moore’s law. Significant challenges emerge in the efforts to seamlessly integrate electronic and photonic circuits on a single silicon platform, since photonic components generally have larger footprint than their electronic counterparts. Plasmonics, by localizing energy around the metal-dielectric interfaces, can enable light confinement beyond the diffraction limit and has the potential to bridge the size mismatch between optical and electrical components [1, 2]. In recent years, various kinds of plasmonic waveguides with high confinement were investigated including v-groove waveguide [3], periodic metal chain waveguide [4], metal-insulator-metal waveguide [5], but in all cases the propagation length is limited to the order of few micrometers due to inherent energy dissipation in metals. The recently proposed hybrid plasmonic waveguide is a novel option to realize light confinement in nano scale as well as relatively long propagation distance [6–9]. Functional elements to compose photonic integrated circuits have been theoretically proposed and experimentally demonstrated based on hybrid plasmonic waveguides, such as lasers [10–12], couplers [13–15], polarization beam splitters [16–18], etc. Using free-carrier dispersion effect in silicon, hybrid plasmonic metal-oxide-semiconductor (MOS) type modulators were also developed [19, 20]. However, the relatively weak free-carrier dispersion effect of silicon limits the overall modulation performance and requires demanding power consumption. On the other hand, recent endeavors show great promises of EO polymers as an alternative to Si as an active modulating material. State-of-the art polymers exhibit an electro-optic coefficient r33 approaching 500 pm/V while keeping negligible optical losses [21, 22]; highly reliable and stable EO polymer modulators with a speed larger than 100 Gb/s have been commercially available already [23, 24]. To merge the advantages of EO polymers with nano scale plasmonics, plasmonic modulators based on EO polymers have been proposed [25–28]. Unfortunately, these devices have issues of either high insertion loss [25], or large footprint [26, 27], or CMOS incompatibility [28].
As a versatile element in many applications, microring/disk resonator is a geometry of particular interest. Our previous experimental work demonstrated a Si-compatible 0.5µm-radius cavity based on hybrid plasmonic (HP) waveguides which are composed by sandwiching a thin SiO2 slot layer between Au and Si [29]. Similar to Si slot waveguide, HP waveguide localizes optical field in the thin low-index slot between Si and Au. In this paper, we propose an ultra-compact HP microring modulator by replacing the slot material with EO polymer. High-performance modulators are achievable with sub-micron HP microring because of their desirable properties including moderate quality factor (102~103), small footprint (<1 μm2), ultra-large FSR, etc.. Contrary to high-Q cavities, moderate-Q cavities are essential in high-speed modulators, since the bandwidth of a cavity-based modulator is intrinsically limited by the cavity photon lifetime [30], and a cavity with Q larger than 2000 has limited bandwidth, lower than 100 GHz. Moderate-Q cavities also relax the tolerance to resonance shifts due to temperature and fabrication variations, and eliminate the extra power needed for thermal stabilizations [31, 32]. On the other hand, small footprint of a sub-micron microring can bring down the device’s total capacitance and therefore improve the power consumption and the response speed limits due to the resistance capacitance (RC) constant [33]. Another advantage of the proposed device is that the metal cap composing HP waveguide can readily serve as one of the contacts and therefore simplify the electrical circuits as well as fabrication process.
The remainder of the paper is organized as follows. Section 2 investigates the figure of merit (FOM) of a HP microring modulator with sub-micron radius and compares its performance with a Si slot microring modulator. Section 3 analyzes the dependence of the modulator’s properties on device parameters and provides useful guidelines to reach optimal design. Section 4 discusses the device’s insertion loss, modulation speed, power consumption, fabrication process and other issues. Conclusions are made in Section 5.
2. Hybrid plasmonic microring modulators with sub-micron radius
Figure 1(a) shows the schematic diagram of the proposed hybrid plasmonic microring modulator consisting of an EO polymer (EOP) ring with a radius of R and a width of W sandwiched between a silver ring and a silicon ring with the same radii and widths. The heights of EOP, Ag and Si layers are HEOP, HAg and HSi, respectively. Microwave field is applied between Ag cap and the bottom Si layer, and the refractive index of EOP can be changed through ultra-fast EO effects; correspondingly, the cavity can be switched between on- and off- resonance mode at a given frequency, resulting in the modulation of transmission power if an access waveguide is placed aside. For simplicity, the silicon thin strip used to electrically connect Si core with the other metal electrode [33–35] (not shown in Fig. 1(a)) is not considered in this study. Sufficient conductivity of Si can be achieved by Arsenic doping while introducing negligible losses [36]. Note that the losses introduced by a moderate doping level of 1017 to 1018 cm−3 are typically on an order of 1/cm [37], while the metal absorption losses are on an order of 102/cm [9,13] in hybrid plasmonic waveguides. A key merit for a ring-based modulator is the driving voltage required to shift the cavity resonance by the 3dB bandwidth distance (V3dB) [38]. The proposed EOP microring modulator has several important characteristics. The Q-factor of the cavity represents the 3dB bandwidth of the resonance and is given by Q = λ0/Δλ3dB where λ0 is 1550 nm. The tuning efficiency is denoted by , describing the resonance shift per unit change of EOP’s index. To characterize the effective modulation by switching the cavity in and out of resonance by changing the EOP index, figure of merit (FOM) can be defined as
which describes the effective resonance tuning per unit change of nEOP. One can readily see that V3dB is inversely proportional to FOM. A higher FOM enables a lower driving voltage as well as power consumption. In the following investigations, a three-dimensional (3D) finite- difference-time-domain method (FDTD) is used for numerical simulations. The mesh sizes employed in 3D-FDTD simulations are 5 nm in xyz directions. HAg is fixed at 100 nm, which is thick enough to prevent the electric field from penetrating through the metal. A moderate width of 300 nm is chosen as the waveguide width, which on one hand can ensure single-mode operation as well as low device capacitance, and on the other is wide enough so that the inner surface of the ring hardly influences on the bending-waveguide’s mode in the sub-micron-radius range [39]. By analyzing the temporal decay of the cavity’s field, the resonant frequency and the corresponding Q-factor can be deduced. Figures 1(b) and 1(c) show the Ez field distributions of a resonant mode with a wavelength of 1550 nm and an azimuthal number of 6 along the xy and xz cross-sectional plane. Here, the microring radius is 542 nm and HEOP and HSi are 30 nm and 400 nm, respectively. One can see that in such hybrid plasmonic waveguides, light is highly localized in the low-index EOP layer between the metal cap and the high-index Si, which is similar to the confinement in a Si slot waveguide [33–36, 40]. The refractive indices of Si, SiO2 and EOP are 3.455, 1.46 and 1.65 in this study, and silver is modeled by the Drude model as which is fitted by the experimental data by Johnson and Christy [41].
Fig. 1 (a) Schematic diagram of the proposed hybrid plasmonic microring modulator. Cross-sectional view along the (b) xy and (c) xz planes of the Ez field distributions of a resonant mode at 1550 nm, with an azimuthal number of 6. The bending radius is R = 542 nm.
The intrinsic quality factors of HP microrings and Si slot microrings as functions of bending radii are shown in Fig. 2. The radii are carefully chosen to enable a resonant wavelength at 1550 ± 10 nm. The Si horizontal slot waveguide which also supports a TM-polarized mode is used for a fair comparison. It has the same width as 300 nm and is composed by introducing a 30 nm EOP slot in the middle of a 400 nm high Si waveguide. As one can see from Fig. 2, the quality factor of the HP microring QHP is much higher than that of the Si slot microring QSlot when the radius is in sub-micron region, and the ratio between QHP and QSlot can be as large as 8.5 when the bending radius is around 510 nm. The enhancement of Q-factor evaluated by is attributed to the advantage of hybrid plasmonic waveguide which has a more compact mode confinement than dielectric waveguides [6–8], and the radiation loss of an ultra-sharp plasmonic bend can be much smaller as a result [29,39]. The quality factor of the hybrid plasmonic cavity asymptotically approaches the value of about 1760 when the radius increases further. The reason is that when radius is large enough, Qrad which is determined by the radiation loss of sharp bends is much larger than Qabs which originates from the absorption loss due to the energy dissipation in metals; considering that the intrinsic quality factor is governed by [42], approximately equalswhich is only dependent on the waveguide geometry as a result.
Fig. 2 Quality factors of Si slot microrings and HP microrings as functions of bending radius. QSlot and QHP are shown by the left Y axis and the ratio between QHP and QSlot is shown by the right Y axis.
Next, resonance shifts ΔλRes of the HP microring and Si slot microring with the change of EOP’s index ΔnEOP are studied. For HP cavity with radius of 542 nm and Si slot cavity with radius of 583 nm, ΔλRes as functions of ΔnEOP are shown in Fig. 3(a). By calculating the slopes of the linear curves, tuning efficiencies of two cavities can be determined as and, respectively. Note that the radii are chosen so that the cavity resonances are at 1550 nm when ΔnEOP = 0 for fair comparison. It’s worth mentioning that tuning efficiencies of both cavities are almost independent on the radius variations; more simulation results indicate that Γ changes less than 4% in the studied radius range. This can be explained by looking into the definition of tuning efficiency as , where neff is the effective index of the bending-waveguide, and describes the effective index change per unit change of EOP index which is linearly proportional to the overlap integral of optical field with the EOP slot expressed as [33]
where Z0 is the impedance of free space. When decreasing the bending radius, since peak of the field density of the fundamental mode would shift more towards the outer perimeter of the ring, unit change of EOP index would result in smaller change of effective index based on Eq. (2); on the other hand, neff would also decrease due to larger amount of radiation field [39]. Hence, influences of radius variations on Ov and neff counteract and Γ as the ratio between these two factors is insensitive to radius variations. Using Eq. (1), FOM of HP microring and Si slot microring can be calculated, and the enhancement of FOM by HP microring is shown in Fig. 3(b). One can see that FOM can be significantly enhanced by HP microring due to its much larger quality factor. The maximum FOM enhancement is about 6 when R is around 510 nm.Fig. 3 (a) Tuning efficiencies of Si Slot microring and HP microring. (b) Enhancement of FOM by HP microring as a function of bending radius.
3. Optimal design of a hybrid plasmonic microring modulator
In this section, the influences of parameters including EOP slot height HEOP and silicon height HSi on the performance of the HP microring modulator will be investigated. In the first study, HEOP varies from 20 nm to 100 nm at a step of 10 nm, and HSi is fixed at either 400 nm or 300 nm. Note that such value is close to the optimal HSi which can neither be too large for single mode operation and decent tuning efficiency nor too small for proper waveguide performance, as will be discussed later in this section. The bending radii of the cavities are chosen around 550 nm. In this sub-micron radius range, the enhancement of FOM by hybrid plasmonic microring is maximal as discussed in Section 2. The selected radii can enable a resonance at 1550 nm and the azimuthal order M is 6 for all the cases. Figure 4(a) shows the quality factors and tuning efficiencies of the HP microring as functions of EOP slot height. One can see that when the EOP height increases from 20 nm to 100 nm, Q of microring with HSi = 300 nm increases at first, then drops and approaches a lower limit; while Q for HSi = 400 nm increases continuously to an upper limit. The above-mentioned limits in fact equal to the quality factors of HP microrings with infinite EOP height which can be regarded as pure-dielectric microrings. Different tendencies of the curves result from combined effects of radiation loss and absorption loss. Looking into the tuning efficiencies as shown in Fig. 4(a), however, one can see that Γ decreases significantly when increasing the EOP slot height for both cases. This is because when the slot height increases, although the slot area is larger, the enhancement of electrical field in the slot region decreases dramatically. The overall integral of electrical field with the slot area decreases, which can be calculated by Eq. (2), and the tuning efficiencies drop correspondingly. Figure of merits as defined in Eq. (1) are also evaluated, as shown in Fig. 4(b). One can see that there is an optimal EOP slot height for both Si heights when the FOM can be maximized. The optimal EOP height is a tradeoff between large quality factor and high tuning efficiency. For both silicon heights of 400 nm and 300 nm, the optimal EOP slot heights are around 30 nm. The results also show the degree of FOM’s deterioration due to the variation of EOP slot thickness. One can see from Fig. 4(b) that for both cases, when HEOP doubles from 30 nm to 60 nm, FOM drops by less than 20%.
Fig. 4 (a) Quality factors and tuning efficiencies of HP microrings as functions of EOP slot height; the silicon height is either 400 nm or 300 nm. (b) Figure of merits of HP microrings as functions of EOP slot height.
Next, the influence of Si height HSi on the performance of the HP microring modulator is analyzed. In the following study, HSi varies from 200 nm to 500 nm at a step of 50 nm, and HEOP is set to be 30 nm. The enhancement of FOM is evaluated by normalizing the FOM with the FOM when HSi = 200 nm, and it can be written as
where and are the enhancement of quality factor and tuning efficiency, respectively. Figure 5(a) shows the quality factor of the HP microring as functions of radii and HSi; the azimuthal orders in the studied radius range contain M = 3, 4…, and 7. Note that the proper radii to render a resonance around 1550 nm depend simultaneously on the silicon height and azimuthal number. Figure 5(b) shows the enhancement of quality factor and tuning efficiency when changing HSi for different azimuthal numbers. One can see that by increasing HSi, the cavity’ Q can be enhanced, and the enhancement is dependent on the azimuthal number. This can be understood by considering that for the hybrid plasmonic mode, the quality factor is related to Qabs and Qrad at the same time, and larger silicon height implies smaller absorption loss by metal as well as weaker mode confinement since more portion of the hybrid mode is confined in dielectrics; at lower azimuthal order, radiation loss plays a more important role to determine the overall quality factor, therefore the enhancement of Q at lower M is not as obvious as that at higher M. One can also see from Fig. 5(b) that although Q increases with silicon height, the tuning efficiency is inversely proportional to HSi and it is only dependent on the silicon height. This is because when the height of high-index layer is larger, smaller amount of light will be confined at the vicinity of metal and in the low-index slot [8]; the reduction of the overlap integral of optical field with the EOP slot results in the decrease of the tuning efficiency based on Eq. (2) as a result. The dependence of FOM as a product of quality factor and tuning efficiency on silicon height is shown in Fig. 5(c). One can see that for each azimuthal order, there’s an optimal Si height when the enhancement of FOM can be maximized. The optimal HSi as a function of M is shown in Fig. 5(d). Results for azimuthal order larger than 8 is not considered in this section, since when radius is large, Si slot microring would give better performance than HP microring, as shown in Fig. 3(b).Fig. 5 (a) Quality factors of HP microrings as functions of radius and silicon height. (b) Enhancement of quality factor and tuning efficiency for different azimuthal numbers. (c) Enhancement of figure of merit. (d) Optimal Si height as a function of azimuthal number.
4. Discussion
In previous sections, the properties of the proposed HP microring modulator are evaluated based on a stand-alone cavity. For optical interconnects, a dielectric waveguide-loaded HP microring can be introduced by utilizing the evanescent coupling between the HP cavity with a Si dielectric straight waveguide, as proposed in our previous work [39], and the transmission power can be modulated by tuning the EOP index. For such loaded microring, the transmission spectrum can be analytically modeled by time-domain coupled mode theory as [43]
where Qi is the intrinsic quality factor of the HP cavity, Qw is the waveguide-coupling quality factor, is the resonant frequency, and is the frequency detuning. To maximize the extinction ratio, i.e., ratio between On-state and Off-state transmission powers, operation in critical coupling condition is assumed, i.e. Qi = Qw. Since Q-factor of a loaded microring is governed by 1/Qload = 1/Qi + 1/Qw, one can see that Qload = Qi/2 and FOM of a loaded microring is also half of the FOM of a stand-alone microring. Hence, optimizations and conclusions on the device design drew based on stand-alone microrings in previous sections still hold. For a HP microring with parameters as discussed in section 2, based on Eq. (4) and the FDTD simulation results from previous sections, the cavity’s transmission spectra when the EOP index changes by 0 and 0.025 can be calculated as shown in Fig. 6. One can see from Fig. 6 that 0.025 change of the EOP index would shift the cavity’s resonance by 3.4 nm which is larger than its 3dB bandwidth given by Δλ3dB = λ0/Qload = 2.9 nm. When the CW input has a wavelength of λ0 = 1549 nm, the cavity can efficiently switch from in-resonance to out-resonance mode, and the transmission power at the through port changes from 0 to 0.85, correspondingly. In this specific operation point, optical modulation amplitude (OMA) is 0.85, and the insertion loss (IL) is 0.7dB. Note that the average loss of an intensity modulator contains intrinsic 3dB loss due to On-off keying. Given that the EO polymer has a bulk electro-optic coefficient of 500 pm/V and in-slot r33 degrades to about 10% - 30% of the r33 provided by the EO polymer [44], a moderate r33 of 80 pm/V is assumed in the hybrid plasmonic modulator, as in [26]. Note that in practical demonstration, effective approaches can further enhance the poling efficiency hence the in-slot r33 by decreasing the leakage current [22, 45]. Based on , the modulation voltage for an index modulation of 0.25 is calculated to be 4.25 V, well below the achievable breakdown voltage [33–36]. In fact, an index change of 0.021 is enough to shift the resonance by 3dB bandwidth distance, and the required driving voltage is V3dB = 3.6 V. Further calculations indicate that in such operation point, one would obtain optical modulation amplitude (OMA) of 0.8 and an IL of 0.97 dB. Due to the small footprint of the device, the capacitance is as small as 0.82 fF, estimated by , where ε0 is the permittivity of vacuum, and is the approximate area of the metal plates. The modulation bandwidth limited by the RC time constant is above 100 GHz, given a resistance below 1500 Ω achievable by proper electronics [35]. Bandwidth limited by cavity photon lifetime is above 300 GHz in this design, estimated by the 3dB bandwidth of the cavity resonance. When operating with a bias of V3dB = 3.6 V and a bandwidth of 100 GHz, the device has a power consumption about 0.5 mW estimated by , corresponding to an average power consumption of 5 fJ/bit.Fig. 6 Transmission spectra of the waveguide-loaded HP microring modulator when EOP index changes by 0 and 0.025. CW light has a wavelength at 1549 nm.
The proposed hybrid plasmonic modulators can be realized following a similar process as in Ref [9]. with several modifications and additional steps [34, 35, 38]. Firstly, microring and waveguide geometries are patterned on a SOI wafer by lithography and etching. Then, shallow-etched grating couplers for in and out coupling are patterned similarly. Subsequently, the sample is doped by ion implantation, followed by the definition of bottom contact through a metal evaporation and liftoff process. After that, the EO polymers are spin-coated as the slot layer of hybrid plasmonic waveguide. Note that the thickness of the slot layer can be controlled by using different spin-coating recipes [9], aided by etching-back processes. After that, another liftoff process is done to deposit the noble metal which serves as part of the hybrid plasmonic waveguide as well as top contact. A thin layer of insulator with low-conductivity may be deposited before coating the noble metal to decrease the leakage current [22]. Note that before device operation, the polymer should be effectively poled by applying high electric field through the defined contacts.
The deterioration of the device’s performance due to the fabrication errors can also be evaluated from the study in Section 3. As one can see from Fig. 4(b), when EOP thickness increases from the optimal 30 nm to 100 nm, FOM drops to about 57% of the maximal value. In practical fabrications, such larger slots can be employed to pursue a higher poling efficiency as well as in-slot r33. On the other hand, when Silicon height of the HP waveguide varies 100 nm from the optimal design, FOM decreases by about 15% only, as shown in Fig. 5(c). Other characteristics as insertion loss and extinction ratio of the proposed device would not deteriorate much given that the microring operates still around critical coupling condition.
5. Conclusions
Ultra-compact hybrid plasmonic microring modulators based on E-O polymers are proposed and analyzed. Comparisons have been made with traditional Si slot microring modulator when the bending radius is at sub-micron scale. Enhancement of figure of merit by hybrid plasmonic microring can be as large as 6 when radius is around 510 nm, due to the increased intrinsic quality factor. Optimal EO polymer height and Si height are investigated, and the design guidelines are given. A modulation voltage of 3.6 V can shift the cavity resonance by 3dB bandwidth. The corresponding optical modulation amplitude and insertion loss are 0.8 and 0.97 dB, respectively. The power consumption is about 5 fJ/bit at a modulation frequency of 100 GHz. The proposed device can find potential use in high-speed, small footprint, low-power-consumption modulation applications.
Acknowledgment
The work described in this paper was partly supported by the Swedish Research Council (VR) through its Linnæus Center of Excellence ADOPT and proj. VR-621-2010-4379. Constructive discussion with Dr. Petter Holmström is also acknowledged.
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