1. Introduction

Lithium niobate (LN), a rather mature bulk optical platform [1], has just found its way into the integrated photonics arena by the introduction of thin-film LN [2–6]. Due to the higher optical index of LN compared to silicon oxide (n_LN ≈ 2.2, n_SiO2 ≈ 1.44), LN-based waveguides can provide strong optical confinement when surrounded with either air or SiO₂ [7]. This enables a transition from traditional etch-less LN waveguides (e.g., titanium diffused [7] or proton exchange [8,9]) with low index contrast and large mode field diameter (MFD) to fully or partially etched subwavelength waveguides with dimensions of < 1 µm over the optical S-, C-, and L-bands (λ = 1460-1625 nm). However, the inertness of LN to etching initially led to the hybrid waveguides [9] with micromachined silicon (Si) [10–12], silicon nitride (SiN) [13,14], or tantalum pentoxide (Ta₂O₅) [15] for mode confinement. The hybrid approach eliminates the need for etching LN, but may result in low optical confinement in the LN and degrade the electro-optic performance. With proper design of the RF-optical overlap inside the LN, it is however possible to achieve good modulation performance in traveling-wave structures. In hope for a paradigm where more tightly bounded modes in LN are accessible and susceptible to electro-optic effects, partially etched waveguides in X- [4] and Y-cut [16] LN have been explored [4,17] upon advances made in micromachining of LN.

Recently, various approaches have been attempted for electro-optics in LN on insulator. These include: 1) Partially etched Z-cut LN waveguides with top and bottom electrodes [18,19]. These typically require a very large footprint and a metal electrode underneath the buried oxide layer. Because good optical confinement for the transverse magnetic (TM) mode in LN mandates a thick buried oxide (> 2 µm), these devices exhibit poor electro-optic efficiency (1.05 pm/V [18], 3 pm/V [19]). 2) Partially etched X-cut LN waveguides with side electrodes directly placed on the LN waveguide with no buffer layer in between [4,14]. The use of X-cut thin films restrains the orientation of the electrodes and imposes a fundamental limit on the electro-optic performance of microring modulators [14]. 3) Proton-exchanged X-cut LN waveguides [8] with side electrodes. Low optical confinement and the use of X-cut LN (orientation dependence) limit the capabilities of this approach. 4) Hybrid (heterogeneous) X-cut [9,13–15] or Z-cut [12] waveguides. This approach does not involve etching of LN, hence prohibiting the highest possible optical confinement in LN. Furthermore, the demonstrated fabrication process is complex and requires multiple materials such as Si, BCB, and Nickel silicide [12].

In this work, we introduce the symmetric electrode design paradigm to realize strong verticial fields in monolithic Z-cut thin-film LN electro-optic devices. Our design does not require a metal plane beneath the buried oxide or any additional material besides SiO₂ for the cladding and metals for the electrodes. Hence, it adheres to a straightforward fabrication process that does not require patterning prior to the LN film transfer. We demonstrate a fully isotropic microring modulator that exhibits up to 20 pm/V of quasi-static resonance tunability, a 20-dB extinction ratio, a very small 60-µm diameter footprint, a capacitance as low as 39 fF, and a modulation bandwidth exceeding 28 GHz. These new results add to our wide tuning range result that was recently presented [20]. Our breakthrough is paving the way for a high performance, monolithic, isotropic, thin-film LN platform.

2. Modulator design

We divide the design of the electro-optic microring modulators into two parts. Part one is the design of passive structures without the electrodes. The single-mode operation of the fully etched waveguides (for maximum optical confinement) is enforced by selecting the thickness of the LN thin-film to be about 560 nm and the waveguide width to be < 1 µm. A width of 850 nm was selected in the simulations to match the dimensions of the fabricated devices, which were measured by scanning electron microscopy (SEM) to be 800−900 nm. Grating couplers were also designed and implemented with fully etched gratings and a short taper appendix to allow vertical coupling of light, hence facilitating die-level testing of multiple devices. The details of the design can be found in our previous work [21]. The coupling efficiency is -16 dB per coupler. The bending radius threshold of waveguides for very low radiation loss (< 1 dB/cm) is calculated to be ∼25 µm; hence, a 30-µm radius is selected. This small radius results in a free spectral range (FSR) of ∼5.5 nm at λ = 1550 nm. The propagation loss of the fully etched waveguides, as well as the passive ring resonator, was measured to be ∼ 7−10 dB/cm. Using this value, the coupling between the ring and the bus waveguide can be designed (∼400-nm gap) such that the critical coupling is reached at λ = 1550 nm. The details of the design of our passive ring structures can be found in our previously published work [22] and are provided in the Appendix. Figure 1(a) shows the cross-section of the waveguide. The thickness of the buried oxide layer situated above a silicon-based substrate is set to 2.5 µm at the time of purchasing the 4-inch wafer.

 

Fig. 1. (a) Cross-section of the electro-optic waveguide phase shifter. (b) Plot of the TM optical mode in the waveguide with the DC field plotted as arrows. The DC field in the LN core exhibits near-perfect vertical direction. (c) Layout of the designed isotropic microring modulator with the layer map of our fabrication process.

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Part two is the design of the electro-optic phase shifter. As shown in Fig. 1(a), we introduce a symmetric electrode arrangement consisting of two metal strips on the sides (bottom metal layer) and one metal strip on the top (top metal layer) to ensure that a near-vertical DC or RF field is induced inside the LN waveguide when an external voltage is applied. The thicknesses of the bottom metal (M1) and top metal (M2) are chosen to be 150 nm and 300 nm, respectively. Figure 1(b) shows the electric field profile of the optical TM mode of the waveguide and the arrow plot of the DC field induced between the top and bottom electrodes. Figure 1(c) shows the finished layout of the isotropic microring modulator and the layers of our photonic process with the inclusion of metallic vias so that the inner M1 electrode can be connected to the outer M1 electrode. Therefore, ∼60 degrees of the modulator is not covered by the symmetric phase shifter. This region still has an inner bottom electrode and makes a slight contribution to the tuning efficiency. The effective filling ratio is ∼91%. Note that the electrical pads and the metal routings are designed on the M2 layer.

The inclusion of metals and their distance to the waveguide impose optical loss to the microring resonator, which affects performance. Therefore, an optimal trade-off is made in the design between the electro-optic tuning efficiency and the loss of the resonator. The electro-optic design of the modulator was conducted in COMSOL Multiphysics. The tuning efficiency of the microring was simulated by setting up an electro-static physics and coupling it to a frequency-domain optical eigenmode analysis for the fundamental TM polarization. The optical loss due to the metallic (gold) electrodes was simulated by defining the metal as a negative complex dielectric. More details are provided in the Appendix.

The design space of the modulator has been characterized so that the microring modulator can operate close to critical coupling (extinction > 20 dB) after placement of metals and provide > 5 dB of modulation depth when performing on-off keying with 4 V of peak-to-peak voltage at a speed of 10 GHz. The selected design as shown in Fig. 1(a) has 550 nm of clearance to the LN waveguide for the bottom electrodes and 700 nm of clearance for the top electrode. The simulated electro-optic effect gives a value of 8.45 pm/V for the tunability. A total excess optical loss of ∼5 dB/cm is estimated for the target design after depositing the electrodes, hence the total optical loss of the microring is estimated to be in the range of 12−15 dB/cm. The width of the electrodes is set to 5 µm so that the total capacitance of the modulator is < 50 fF. The capacitance of the symmetric phase shifter is simulated to be ∼187 pF/m and the calculated total capacitance of the microring modulator is ∼35 fF (see the Appendix).

3. Modulator implementation

The first part of the fabrication process consists of patterning the passive LN structures including the grating couplers and the microring resonator using electron beam (E-beam) lithography [22]. The Z-cut thin-film LN wafers (nominal thickness of 560 nm) on 2.5-µm thick SiO₂ on a silicon substrate were purchased from a commercial vendor (NGK Insulators, Ltd.). The thickness of the buried oxide was chosen such that the leakage of the optical mode into the substrate for both TE and TM polarizations is negligible. A ∼700 nm layer of SiO₂ is chosen as the hard mask for dry-etching LN, and was deposited using standard PECVD (∼ 113 nm/min). 300 nm of photoresist (PMMA) was spin-coated at 2000 rpm for 1 minute and electron beam lithography (EBL) was performed on the sample. A 120-nm thick chromium (Cr) layer patterned via evaporation and lift-off was chosen as the mask for etching SiO₂ (SiO₂:Cr etch rate ∼ 20:1). Next, the SiO₂ layer and then the LN layer was dry-etched using a Plasma-Therm ICP-RIE system. The SiO₂ was etched using CHF₃ (20 sccm) and O₂ (5 sccm) gases with ICP power of 800 W and RIE power of 100 W. The LN was etched using Cl₂ (5 sccm), BCl₃ (15 sccm), and Ar (18 sccm) gases under a chamber pressure of 5 mT and with ICP and RIE powers of 800 W and 280 W, respectively. The etch rates of SiO₂ and LN in the LN etching step are 140 nm/min and 200 nm/min, respectively, corresponding to the selectivity of 1.43:1. The thickness of the remaining SiO₂ after fully etching LN was measured to be ∼ 280 nm.

The second part of the fabrication process consists of adding the bottom and top electrodes to the microring resonator. Gold electrodes are deposited using evaporation and lift-off. To facilitate lift-off of the bottom electrodes, the thickness was set to 150 nm. Thinner bottom electrodes also help to create a better vertical DC field inside the LN waveguide by pulling the DC field down near the vertical edges of the LN waveguide. After deposition of the bottom electrodes, the oxide cladding (PECVD SiO₂) was uniformly deposited to achieve ∼700 nm of oxide on top of the LN waveguide. Because the growth rate of the oxide on the LN regions was observed to be slower than in other places, the deposited oxide ends up with a larger thickness on top of the bottom electrodes (∼900 nm). This works to our advantage because it helps to partially planarize the oxide cladding. Next, vias are patterned and etched before the top electrodes are finally deposited. Test structures were also fabricated to ensure that vias would work properly. Figure 2(a) shows the top-view SEM image of the fabricated device. Top and bottom metals, as well as vias, are clearly seen in this picture. Figure 2(b)-(e) show the focused ion beam (FIB) cut images taken of one of the dummy samples in the fabrication process to ensure that the thickness of the oxide cladding is consistent at different places. As expected, the contour of oxide cladding in Fig. 2(b) is adequately smooth. However, we observed about 50−200 nm of misalignment for the left and right electrodes in different samples, which causes the optical loss of the bottom electrodes to increase from its designed value of 2.5 dB/cm in simulations to a value of ∼6−8 dB/cm. Other parts of the device, including vias and their sidewall coverage shown in Fig. 2(c), straight sidewall definition of LN waveguides shown in Fig. 2(d), and cladding over the microring and waveguides shown in Fig. 2(e), were fabricated as designed.

 

Fig. 2. (a) Microscope image of the fabricated microring with the top and bottom electrodes and vias. FIB images showing cross-section views of (b) the microring before depositing the top metal, (c) a deposited via and its sidewall coverage, (d) the microring and its bus waveguide, and (e) the bus waveguide with top SiO₂ cladding.

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4. Measurements and results

Figure 3(a) shows the layout of the passive device (no electrodes) with its ports numbered from left to right. A four-fiber linear array with a pitch of 250 µm is used for coupling light from fibers into the grating couplers. The vertical alignment is assisted with the side mirrors, and the in-plane alignment is assisted with the alignment markers that are placed on the LN die. A continuous-wave (CW) tunable laser (Santec 710 TSL) accompanied by a polarization controller (PC) is used to control the wavelength, power, and polarization of the light inside the incoming fiber. The light was injected in port 1 and detected at port 4. The output light from the through path goes to the photodiode (Thorlabs DET08CFC). The generated photocurrents are amplified by a log-amplifier circuit (ADL5310 from Analog Devices) and voltages are read out by a National Instrument data acquisition device (NI DAQ model USB-6009) and imported into LabVIEW software. This configuration is limited to low-frequency measurements (< 10 kHz).

 

Fig. 3. (a) Schematic of the fabricated microring without metal electrodes. The long waveguide (∼1.5 mm) connecting each grating coupler and the microring is necessary to create enough space for the placement of a fiber array and a GSG electrical probe. (b) Measured spectrum of the passive microring. (c) Measured spectrum of the microring after depositing bottom metal (M1). The extinction of resonance has declined to 10 dB. (d) Measured spectrum of microring after deposition of oxide cladding. The extinction has been restored to >20 dB. (e) Measured spectrum of microring after deposition of top metal (M2), showing a consistent extinction ratio of 20 dB.

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Figure 3(b) shows the measured optical spectrum of the passive device without any metal electrodes. The maximum extinction is 25 dB which meets the design target of > 20 dB. Figure 3(c) shows the measured optical spectrum after deposition of the bottom electrodes and before deposition of oxide cladding. We see that the extinction of resonances has reduced to 10 dB, which is a significant reduction. This is mainly caused by increased metal loss due to the slight misalignment of the bottom electrodes. Our simulations show that an extra 6.5 dB/cm loss (added to 7 dB/cm of the passive ring) reduces the extinction of resonance from 25 dB to 10 dB, which is consistent with the measured results. Figure 3(d) shows the measured optical spectrum after the deposition of the top oxide cladding. The deposition of the oxide cladding reduces the confinement of the optical mode inside the LN waveguide and hence increases the coupling strength between the microring and the bus waveguide. This helps reduce the imbalance between the loss and coupling of the resonator and restores the extinction ratio and even increases it to 30 dB. The top oxide cladding also significantly boosted the grating coupler efficiency at longer wavelengths, which resulted in the peak redshifting to ∼1620 nm. Finally, Fig. 3(e) shows the optical spectrum of the finished device after the deposition of the top electrode. Because the estimated loss of the top metal is ∼2 dB/cm, the extinction of resonances is expected to experience only a small reduction. This is clearly observed in the measurement where a consistent 20 dB of extinction is observed. Note that the noise floor of our optical measurement is -62 dBm; hence, the observed extinction of the resonances at the shorter wavelengths is limited by the noise floor.

Figure 4(a) shows the positions of the fiber array and the GSG probe on the LN die. Electro-optic tuning was performed for both positive and negative voltages up to 30 V. The positive voltage refers to applying a positive voltage to the top electrode and grounding the bottom electrodes. Figure 4(b) shows the measured spectra of one of the resonances for negative and positive voltages, respectively. The observed blue-shift (red-shift) is expected because the induced DC field is upward (downward) inside the LN waveguide and the positive direction of the extraordinary axis is upward. Hence, the induced index change is negative (positive) which results in a blue-shift (red-shift) of the resonance. Figure 4(c) shows the plot of resonance wavelength versus applied DC voltage. This plot shows a tuning efficiency of 6.7 pm/V at zero voltage, which is somewhat smaller than predicted by our simulation. However, the tuning efficiency is significantly enhanced for negative voltages. We observe a global tuning efficiency of 13.7 pm/V for 0 V to -30 V and a local tuning efficiency of 20.3 pm/V for -25 V to -30 V. To confirm this better-than-expected behavior, electro-optic measurements were also conducted on another device and similar results were observed (see the Appendix). In comparison to other works on tunable microring modulators in X-cut [4,13–15,23–25], Y-cut [16,26], or Z-cut LN [12,18,27–29] as shown in Fig. 4(d), our modulator well surpasses the state-of-the-art (SoA) in the trade-off between extinction and tunability of the resonance.

 

Fig. 4. (a) Device testing setup with the mounted fiber array and the electro-optic measurement using a GSG probe. (b) Measured resonant spectra under applied negative (top) and positive (bottom) voltages. The extinction of resonance remains unaffected by the applied voltages. (c) Resonance wavelengths for a wide range of applied voltages. A tuning efficiency of 20 pm/V is observed for negative voltages. (d) Comparison of the modulator performance in this work with the state-of-the-art LN microring modulators.

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The misalignment of the bottom electrodes may have compromised the symmetry of the phase shifter and created non-negligible horizontal components of the electro-static E-field inside the LN waveguide. However, the presence of such a horizontal field component and its contribution to the electro-optic tunability do not explain the asymmetry of the tunability considering only the linear electro-optic effect. We also believe that this asymmetry of tunability is not caused by the χ⁽³⁾ nonlinearity because no resonance shift was observable when the laser power was varied at a fixed applied voltage. Our simulations of the strength of the static E-field inside the LN waveguide also revealed that the E-field remains well below the coercive threshold of LN (184 V in our structure to produce >21 MV/m); hence, no ferroelectric domain reversal should have happened up to 30 V. Therefore, we believe that the asymmetry in the static electro-optic tunability of the fabricated microring modulators is due to a slow charging process (Maxwell-Wagner effect [30–32]) that takes place at the interface of LN waveguide and its surrounding SiO₂. To confirm this and measure the effective AC electro-optic tunability, an alternating polarity square-wave with a frequency of 1 kHz as shown in Fig. 5(a) was applied to the modulator and the output optical spectrum was measured for different pulse amplitudes as shown in Fig. 5(b). Because the frequency of the electrical signal is much faster than the speed of the wavelength sweep (1 nm/sec), two stable resonances are observed, each corresponding to the negative and positive portions of the applied voltage. An extremely wide total tuning range of 1.8 nm, i.e., 207 GHz is achieved. Figure 5(c) shows the measured effective resonance shift as a function of the amplitude of the pulse. It clearly demonstrates a symmetric and linear trend of 9 pm/V up to 60 V for both the positive and negative voltages. At voltages beyond ±60 V, a nonlinear behavior emerges which can still be attributed to the charging effects. Our observations showed that the nonlinearity gets stronger at lower pulse frequencies.

 

Fig. 5. (a) Experimental setup for measuring the effective electro-optic modulation efficiency of the fabricated modulator. (b) Captured spectra over a period of time under square-wave biasing. (c) Resonance shifts as a function of square-wave amplitude, displaying a slope of 9 pm/V.

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High-speed measurements are done using a network analyzer (Agilent N5230A) from 100 MHz up to 28 GHz as shown in Fig. 6(a) by placing a GSG probe on the electrical pads after aligning the fiber array with the gratings. Port 1 is used as the RF source that generates the modulation signal applied on the electro-optic modulator with RF power of 1 dBm. Port 2 measures the RF signal from the photo-receiver (Thorlabs RXM40AF). In order to reduce the effects of the measurement setup, especially the frequency-dependent RF attenuation, the measurement reference planes are moved to the RF probe and the output port of the photo-receiver by performing calibration with the SLOT mechanical calibration kit (Keysight 3.5 mm 85052D).

 

Fig. 6. (a) Experimental setup for measuring the electro-optical modulation frequency response of the modulator. (b) Measured EO amplitude |S₂₁| of the modulator at different resonance detunings up to 22.9 GHz, showing good agreement with the analytic predictions. (c) Measured bandwidth versus optical detuning of the laser, exhibiting > 10 GHz of modulation bandwidth at zero detuning and > 28 GHz of modulation bandwidth at > 10 GHz of detuning.

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The high-frequency electrical S-parameter measurement of the microring modulator (RF S₁₁) resulted in a measured total capacitance of 69.4 fF for the device of which 29.8 fF is measured to be the parasitic capacitance from the electrical pads and metal traces on the chip; hence, the capacitance of the modulator is ∼39.6 fF (see the Appendix). This is slightly higher than our design target (∼35.1 fF) for the perfectly symmetric electrode arrangement. The difference can be attributed to the variation in the thickness of the oxide cladding and the misalignment of the bottom electrodes.

The electro-optical modulation frequency response (EO S₂₁) of the microring modulator was measured using the 40 GHz photo-receiver according to the setup in Fig. 6(a). The RF path was characterized beforehand for later de-embedding. The frequency response of the photo-receiver, which was measured by Thorlabs, was de-embedded to unmask the frequency response of the electro-optic modulator. The measured frequency response is limited to 28 GHz because the observed noise floor of the network analyzer increases significantly for higher frequencies. Figure 6(b) shows the S₂₁ after de-embedding the frequency response of the photodiode and the RF path. Each curve corresponds to a particular detuning between the input laser and the microring resonance (measured value of 1621.88 nm). The optical detuning was performed in steps of 40 pm (4.57 GHz). Based on a rigorous RF harmonic analysis [33] the S₂₁ was also analytically estimated and plotted in Fig. 6(b) which shows a good agreement with the measurements. Both the simulations and the measurements indicate frequency peaking for larger resonance detunings. This peaking can be explained using a system-level perspective in which the small-signal EO response behaves like an under-damped second order linear system [33–36]. Figure 6(c) shows the detuning range of the resonance and the plot of the modulation bandwidth as a function of the optical detuning (both before and after de-embedding), which clearly demonstrates an increase in the electro-optical modulation bandwidth with the detuning. The results of our analytical modeling also agree well with this observation and predict modulation bandwidth in excess of 30 GHz for detunings greater than 10 GHz.

5. Conclusions

The symmetric electrode design with optimized spacing between the electrodes and the microring core resulted in strong vertical electrical field strength in Z-cut LN without significant optical loss for the TM mode. By conducting detailed static and dynamic electrical and optical multiphysics modeling studies and by developing well-controlled fabrication techniques that were aided by FIB, SEM, and microscope inspection and device characterization after critical processing steps, high performance modulators were demonstrated that matched predictions in almost every regard. The unexpected and extraordinary enhancement in the quasi-static tuning efficiency at negative voltages was attributed to the Maxwell-Wagner effect; future research may seek to engineer devices that more advantageously utilize this effect to achieve even higher tuning efficiency and overall tuning range of the resonances.

Appendix: electro-optical design of microring modulator

The electro-optic design of the modulator was performed in the COMSOL Multiphysics software (version 5.1) [37] by defining an electro-static physics (solving Laplace’s equation) and coupling its results to an optical eigenmode solver.

Effective index, group index, and field profile of TM₀₀ mode

The maximum width for single-mode operation of the waveguide is determined by sweeping the width and solving an optical eigenmode problem in the frequency domain. Figure 7(a) shows the calculated modes for a waveguide (including the effect of metals but no DC field) with a thickness of 560 nm. The thickness was chosen in the range of 400 nm − 600 nm such that the coupling efficiency of the fully etched grating couplers was the best. Note that because COMSOL solves the 2D simulation in the x-y cross-section whereas for the z-cut LN crystal the cross-section is assumed to be x-z, we use the notation of 1, 2, 3 instead of x, y, z to refer to the components of the electric fields in the principal axes of the crystal. Therefore, E₁ is the in-plane horizontal component (ordinary direction), E₂ is the out-of-plane component (ordinary direction), and E₃ is the in-plane vertical component (extraordinary). We observe a constant effective index for the TM₁₀ equal to that of the oxide cladding below a width of 900 nm. Thus, the fully etched waveguide is single-mode up to this width. In order to achieve the highest optical confinement and highest overlap with the DC field, a nominal width of 900 nm was chosen for the waveguides. After the etching of LN in the fabrication, we observed a reduction of the width of the waveguide from 900 nm to ∼850 nm due to the slight undercutting of the etch mask. Figure 7(b) shows the electric field profile of the optical TM₀₀ mode. As expected, the vertical component in the extraordinary direction (E₃) is the strongest and is the main component that interacts with the DC field inside the LN waveguide. Next, we sweep the wavelength and find the effective index and group index of an 850 nm × 560 nm waveguide, which are subsequently used in the design of the microring modulator.

 

Fig. 7. (a) Calculated effective index of the optical modes to determine the single-mode operation region of the waveguide. (b) Electrical field profile of the optical TM₀₀ mode. The extraordinary direction of the crystal is marked by 3.

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Electro-static simulation

In order to find the DC E-field, the electrostatic physics was setup in COMSOL. The permittivities of the materials are set to their corresponding values at DC (or low frequency). Note that there is a large difference between the permittivity of LN at DC and at optical frequencies. The permittivity of LN material is set up according to a diagonal tensor:

(1)$${{\epsilon}_{LN}} = \left( {\begin{array}{{ccc}} {{{\epsilon}_o}^{DC}}&0&0\\ 0&{{{\epsilon}_e}^{DC}}&0\\ 0&0&{{{\epsilon}_o}^{DC}} \end{array}} \right), $$

where ϵ_o and ϵ_e are the ordinary and extraordinary permittivities, respectively. The bottom electrodes are set to ground (zero voltage) and a constant voltage (V_dc) is applied to the top electrode. The boundary conditions of the simulation region are set to “zero charge” (i.e., $\hat{n} \cdot \vec{D} = 0$) to mimic an infinitely long region by enforcing no charge accumulation on the boundary. Figure 8(a) and Fig. 8(b) show the optical TM mode for the symmetric and single-pair electrode structures, respectively. Figure 8(c) and Fig. 8(d) show the simulated profile of the electrostatic potential upon applying 1 V to the top electrode of the symmetric design and the single-pair electrode design, respectively. The simulations include the effect of SiO₂ cladding contour. Figure 8(e) and Fig. 8(f) show the direction and relative magnitude (size of the arrows) of the electrostatic field at each point inside the waveguide. As expected, the structural symmetry enforces a near-perfect vertical field inside the LN waveguide.

 

Fig. 8. (a) Symmetric electrode design. (b) Single-pair electrode design. (c)-(f) Distribution of the electrostatic potential upon applying 1 V to the top electrode.

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After solving the electro-static simulation for V_dc = 1 V, we can also calculate the static capacitance per unit length by integrating the surface charge (${\rho _s} = \hat{n} \cdot \vec{D}$) density over the top electrode:

(2)$$Q = \int\!\!\!\int {{\rho _s}dS \to {C_l} = \frac{Q}{{{V_{dc}}}}}$$

The result is C_l = 186.22 pF/m. The total electrode capacitance of the microring modulator is ${C_{tot}} \approx {C_l} \times 2\pi R$ which gives a value of C_tot= 35.1 fF. The capacitance of the modulator was extracted by measuring the Y₁₁ parameter from the GSG pads up to 8.5 GHz as shown in Fig. 9. The structure (including pads and metal traces) has a total capacitance of 69.38 fF of which 29.77 fF is from the pads and metal traces. Therefore, the capacitance of the modulator itself is ∼39.6 fF, which has a good agreement with the simulation.

 

Fig. 9. Measurement of the Y parameter using a GSG probe. Admittance (20 log₁₀|Y₁₁|) for the red curve refers to a GSG probe that measures the Y₁₁ parameter of the structure and the blue curve refers to the GSG probe measuring the Y parameter of a structure with only the pads and metal traces leading to the modulator. The difference is the capacitance of the modulator.

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The 3-dB electrical RC bandwidth of the modulator is

(3)$${f_{\textrm{3dB}}}[\textrm{electrical}] \approx \frac{1}{{2\pi {R_\Omega }{C_{tot}}}}, $$

where R_Ω ≈ 50 Ω is considered the source impedance. Based on the total capacitance of 35.1 fF, the electrical bandwidth is estimated to be ∼90 GHz. Therefore, the speed of our microring modulator is not limited by the electrical effects but rather by the photon lifetime of the resonator.

Perturbation of the optical mode

In order to find the electro-optic response, the results of the electro-static simulation are coupled to the optical eigenmode calculation using the electro-optical coefficients of the lithium niobate. We first solve the electro-static simulation in COMSOL and then define the optical permittivity of LN as ϵ_LN = ϵ_LN,0 +Δϵ where Δϵ is calculated using the DC field (see [38] for more details). Figure 10(a) shows the result of perturbation of the optical effective index due to an applied DC voltage for the symmetric electrode design. The linear behavior has a slope of Δn_eff (per volt) ≈ 1.3×10⁻⁵. The single-pair electrode design exhibits an electro-optical efficiency of Δn_eff (per volt) ≈ 8.3×10⁻⁶.

 

Fig. 10. (a) Calculated perturbation of the optical effective index due to the applied DC voltage to the symmetric electrode design. (b) Calculated electro-optic tuning efficiency of the microring modulator.

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Tuning efficiency of microring resonator

The condition for the resonance of the ring resonator is that the round-trip phase is an integer multiple of 2π ($\phi (\lambda ) = 2m\pi $). Therefore:

(4)$$\delta \phi = 0 \to \frac{{d\phi }}{{d\lambda }} \times \delta {\lambda _{res}} + \Delta {\phi _{EO}} = 0$$

Here, Δϕ_EO is the phase shift perturbation due to the electro-optic effect:

(5)$$\phi (\lambda ) = \frac{{2\pi }}{\lambda }{n_{eff}}(\lambda )L \to \frac{{d\phi }}{{d\lambda }} = \frac{{2\pi L}}{{{\lambda ^2}}}( - {n_g})$$

If ff (fill factor) is the fraction of the ring that is impacted by the electro-optic effect, then

(6)$$\frac{{\delta {\lambda _{res}}}}{{\delta {V_{DC}}}} = ff \times \frac{{{\lambda _{res}}}}{{{n_g}}} \times \Delta {n_{\textrm{eff}}}(\textrm{per}\;\textrm{volt})$$

The group index of the fully etched waveguide has a simulated value of n_g = 2.29 at δ = 1600 nm. Hence, the free spectral range is estimated to be 6.06 nm for a ring with a radius of 30 µm. This leads to a maximum tuning efficiency (ff = 1) of 9.26 pm/V for our microring resonator.

Due to the presence of vias for the connection of the top metal to the inner bottom electrode and the coupling of the bus waveguide to the ring (see Fig. 1(c)), the symmetric electrode arrangement cannot cover the entire resonator. We designed the electrodes such that the symmetric electrodes cover 300° of the ring, hence the filling factor is ∼ 83% for the symmetric part. The single-pair top-bottom electrode also covers ∼40° of the rest of the modulator. Therefore, the symmetric electrode tuning efficiency is effectively applied to ∼91% of the structure. Using this, we expect our modulator to exhibit an electro-optic tunability of ∼8.45 pm/V as shown in Fig. 10(b). This agrees with the 9 pm/V observed for low frequency (1 kHz) square wave modulation in Fig. 5.

Calculating excess metal loss

The proximity (clearance) of the top and bottom metal electrodes to the waveguide can induce excess optical loss. The optical loss due to the metallic (gold) electrodes was simulated by defining the metal as a negative complex dielectric (ɛ_metal = -115.13-11.26j) from Johnson et al. [39]. In order to estimate the loss (in dB/cm) of the optical mode, we calculate the attenuation coefficient (damping factor) of the electric field (α_E in units of m^-1) in COMSOL and convert it to optical power attenuation (dB/cm) using the following equation:

(7)$$\alpha \left[ {\frac{{\textrm{dB}}}{{\textrm{cm}}}} \right] = {\alpha _E}[{\textrm{m}^{\textrm{ - 1}}}] \times 2 \times 0.0434$$

Figure 11(a) shows the calculated loss due to the top metal and Fig. 11(b) shows the calculated loss for each of the bottom electrodes. The desired operating points are indicated in the figure.

 

Fig. 11. (a) Optical loss due to the top electrode as a function of its vertical distance from the upper edge of the waveguide. (b) Optical loss due to each of the bottom electrodes as a function of its lateral distance from the waveguide sidewall.

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Effect of M1 metal misalignment

Misalignments can happen during the E-beam lithography for the patterning of the bottom or top electrodes. Because the width of the top electrode is 5 µm, the electro-optic performance does not experience a change for large misalignments of the top electrode (even for 1-µm misalignment). The fabricated devices display ∼50−200 nm of misalignment (decrease in the clearance for one of the bottom electrodes). The misalignment of the bottom electrodes to the LN waveguide is the combined result of the angular and linear misalignments, which are expected to vary slightly around the ring. Nonetheless, such bottom electrode misalignment can affect both the optical loss and the electro-optic tunability because it places the metal closer to the optical mode and compromises the symmetry of the induced DC field.

The change in the optical loss can be extracted from Fig. 11(b). The impact of the misalignment of one of the bottom electrodes on the optical effective index is shown in Fig. 12(a) and is converted to the resonance tunability in Fig. 12(b). A negative misalignment means that the bottom electrode is closer to the LN waveguide. We see that the impact is not significant on tunability.

 

Fig. 12. (a) Impact of the misalignment of one of the bottom electrodes on the optical mode. (b) Impact of the bottom electrode misalignment on the resonance tunability.

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Lorentzian fitting of the measured optical spectrum

The optical parameters of the microring modulator after deposition of all the metal layers is fitted to the Lorentzian model to extract the optical parameters at a particular resonance of interest (near 1621.8 nm) as shown in Fig. 13. The extracted parameters are: extinction of resonance (ER) = 22.5 dB, loaded quality factor (Q) = 5432, free spectral range (FSR) = 6.05 nm, E-field coupling coefficient (κ) = 0.365, round-trip loss (α) = 22 dB/cm. These agree with the predicted value of FSR = 6.07 nm and α = 15−19 dB/cm. Due to the dependence of the group index of the LN waveguide on wavelength, the FSR slightly decreases at shorter wavelengths. In Fig. 3(e), we also see that the measured FSR is 5.46 nm near 1550 nm, which is close to the expected value of ∼5.5 nm.

 

Fig. 13. Lorentzian fitting to the measured resonance. The fitted curve (red curve) matches very well to the measured resonance (blue curve). The extinction of the resonance is > 20 dB and the Q-factor of the microring is ∼ 5400.

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Low extinction ratio microring modulator

We also designed a low-ER undercoupled microring modulator by setting the coupling gap between the ring and bus waveguide to ∼500 nm. Figure 14(a) shows the measured spectra under positive and negative applied voltages and Fig. 14(b) shows the measured values of the resonance wavelength and the tuning efficiency. The outer bottom electrode in this device showed -200 nm misalignment which according to Fig. 12(b) should result in a tuning efficiency of ∼8.9 pm/V. This is in agreement with the measurement at 0 V.

 

Fig. 14. (a) Measured spectra of the low-ER modulator under the positive and negative applied voltages. (b) Resonance wavelengths for a wide range of applied voltages. A tuning efficiency over 20 pm/V is observed for negative voltages.

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Electro-optic frequency response of the ring modulator

Considering a phase shifter embedded in a microring resonator, we can generally assume a linear phase relation between applied RF voltage and the electro-optical phase shift in case of a small signal excitation [40]. If the input light has no RF harmonics, the output light of the modulator is accompanied by all of the RF harmonics (i.e., modulation sidebands). The theory of RF-optical harmonic coupling can be found in our recent publication [33] and was used to analytically model the electro-optic frequency response of the fabricated microring modulator.

The electro-optical frequency response for the first two RF harmonics (normalized to the first harmonic) is calculated and plotted in Fig. 15(a) at 1 GHz of resonance detuning. The electrical power of the first harmonic of the output light drops to half at ∼12 GHz, indicating a 3-dB electrical-to-optical-to-electrical bandwidth of > 10 GHz. Note that the definition of linear (small-signal) bandwidth loses its meaning exactly at the resonance because the optical transfer function of the modulator is quadratic and has zero linear term. Hence, it does not output any 1^st-order harmonic. Simulations of the first harmonic at several different resonance detunings up to 22.9 GHz were also performed and presented in Fig. 6(b) of the main text.

 

Fig. 15. (a) Simulated electro-optical frequency response (first harmonic) and nonlinearity (second harmonic) of the fabricated LN modulator at 1 GHz of optical detuning from the resonance. A 3-dB bandwidth of > 10 GHz is observed for the first harmonic. (b) Impact of the RC bandwidth limitation on the electro-optical frequency response (first RF harmonic) of the fabricated LN modulator.

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Figure 15(b) shows that the bandwidth of our modulator (first RF harmonic) does not experience any change for an RC bandwidth of 90 GHz (C_mod ≈ 35.1 fF and resistance = 50 Ω). Even if we include the extra 29 fF from the contact pads and metal traces (RC bandwidth of 50 GHz), the 3-dB electro-optical bandwidth remains nearly unchanged indicating the dominance of the photon lifetime.

Funding

National Aeronautics and Space Administration the early career faculty (ECF) award (80NSSC17K052).

Acknowledgments

Authors would like to thank Edmond Chow from Micro and Nanotechnology Laboratory at the University of Illinois Urbana-Champaign for his help with the electron-beam lithography.

Disclosures

M. Bahadori, L. L. Goddard, and S. Gong claim a U.S. patent on the presented design in this work through the University of Illinois at Urbana-Champaign.

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