Analysis of SiN_x Waveguide-Integrated Liquid Crystal Platform for Wideband Optical Phase Shifters and Modulators

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Photonic integrated circuits.

Abstract

In this study, the potential of employing SiN_x (silicon nitride) waveguide platforms to enable the use of liquid-crystal-based phase shifters for on-chip optical modulators was thoroughly investigated using 3D-FDTD (3D finite-difference time-domain) simulations. The entire structure of liquid-crystal-based Mach–Zehnder interferometer (MZI) optical modulators, consisting of multi-mode interferometer splitters, different tapering sections, and liquid-crystal-based phase shifters, was systematically and holistically investigated with a view to developing a compact, wideband, and CMOS-compatible (complementary metal-oxide semiconductor) bias voltage optical modulator with competitive modulation efficiency, good fabrication tolerance, and single-mode operation using the same SiN_x waveguide layer for the entire device. The trade-off between several important parameters is critically discussed in order to reach a conclusion on the possible optimized parameter sets. Contrary to previous demonstrations, this investigation focused on the potential of achieving such an optical device using the same SiN_x waveguide layer for the entire device, including both the passive and active regions. Significantly, we show that it is necessary to carefully select the phase shifter length of the LC-based (liquid crystal) MZI optical modulator, as the phase shifter length required to obtain a π phase shift could be as low as a few tens of microns; therefore, a phase shifter length that is too long can contradictorily worsen the optical modulation.

1. Introduction

Extensive research on liquid crystal (LC) materials has revealed their profound electro-optical properties, including birefringence behaviors [1], making them promising for various photonic applications [2,3,4]. The electro-optical properties of LC materials are involved in refractive index tuning between ordinary and extraordinary index values by external electric fields, causing the rotational motions of the LC molecules. Thanks to this capability, LC materials have been applied in photonics to achieve, for example, optical switching [5,6], tunable filters [7], and phase shifters [8,9,10,11,12]. As pointed out in [11], optical phase shifters are critical elements in various devices in which the required response times can be varied from a few microseconds to a few milliseconds. In the latter case, phase shifters prioritize device compactness and a low driving voltage over speed, and LC-based phase shifters are more favorable than thermo-optic-based and pin junction-based devices in terms of device size and/or power dissipation. However, while several previous works on LC-based waveguide phase shifters have focused on the silicon (Si) waveguide platform [7,8,11,12], SiN_x’s benefits of a relatively large transparency window, compatibility with silicon CMOS processes, and a moderate refractive index contrast with SiO₂ can be advantageous in terms of fabrication tolerance and a high optical power handling capability for wideband operation [13,14,15,16,17]. Moreover, although state-of-the-art work used a high-aspect-ratio SiN_x structure to achieve a very low propagation loss [18], relatively thick SiN_x waveguides can also lead to a low-loss propagation loss for an on-chip application [19]. Therefore, recently, the integration of LC materials into amorphous materials such as silicon nitride (SiN_x) has received great attention, although it could still be considered as being in its initial stages [9,10,20,21]. M. Caño-García et al. [10] and K. J. Sundar et al. [20] recently reported the integration of LC materials as a top cladding over a SiN_x waveguide for a phase shifter based on the electro-refraction effect. Nevertheless, to further improve performance, it was stated that the optimization of the interaction volume of the LC around the SiN_x waveguide, to improve the optical mode overlap, as well as the optimization of the LC configuration and electrode distances, would be required [20]. Moreover, the increased insertion loss due to the abrupt change in the refractive index between the waveguide and LC interface needed to be addressed [10]. M. Notaros et al. [9] subsequently reported the integration of LC materials with SiN_x, employing two different layers of SiN_x waveguides for passive optical components (waveguide and multi-mode interferometer (MMI)) and the active phase shifter region with a liquid-crystal-filled trench; therefore, an adiabatic escalator was required to vertically transfer the optical mode between the two SiN_x waveguide layers and ensure low insertion loss. In particular, Ref. [9] presented one of the first prototypes of a low-loss SiN_x waveguide-integrated MZI optical modulator. Additionally, G. Wang et al. [21] recently reported an LC-based thermo-optics effect phase shifter using joule heating with an electrical current injection; a racetrack structure was employed to achieve highly temperature-sensitive operation.

In this paper, contrary to [9], to investigate the potential of employing a SiN_x waveguide platform with a potentially simpler fabrication process for low-loss LC-based phase shifters and MZI optical modulators, we focus on achieving such an optical device using the same SiN_x waveguide layer for the entire device, including both the passive and active regions. Several important parameters of the SiN_x waveguide-integrated LC-based optical modulators in the widely used C-band region are systematically taken into consideration. The trade-offs between some related parameters in relation to phase-shifting performance are discussed in order to reach a conclusion on the possible optimized parameter sets and design rules for LC-based phase shifters/optical modulators over a given spectral region. Moreover, a compromising design of a suitable MMI splitter and a linear taper, needed to transfer the optical mode between the passive SiN_x waveguide and the LC-based phase shifter, is also presented, taking into account the previously optimized data sets and design rules to finally achieve a competitive Mach–Zehnder interferometer (MZI) optical modulator with good modulation efficiency.

2. Setup and Methods

To evaluate the potential of Mach–Zehnder interferometer (MZI) optical modulators based on a liquid-crystal-based phase shifter on a SiN_x waveguide platform, half of the entire structure shown in Figure 1, consisting of a liquid-crystal-based phase shifter integrated into a SiN_x waveguide structure, a multi-mode interferometer (MMI) splitter, and linear tapers of the liquid crystal (LC) section to accommodate optical integration between the two sections, is holistically and systematically investigated. The interplay between each parameter is subsequently discussed. Electric fields applied across the LC-filled region are also observed to determine the contact configuration that is compatible with the CMOS drivable voltage. The LC phase shifter is based on a 4-n-pentyl-4′-cyanobiphenyl (5CB) liquid crystal material due to its well-known optical and electrical nematic-phase properties during room-temperature operation [22]. Finally, to reliably evaluate the extinction ratio (ER) and overall insertion loss (IL) of the LC-based MZI optical modulator, we perform a 3D-FDTD simulation of the entire structure from the SiN_x input to the SiN_x output waveguide, including two MMIs, the linear tapering of the LC section, and the two arms of the LC-based phase shifter integrated with the SiN_x waveguide. For a numerical calculation with high accuracy, the finite-difference time-domain (FDTD) method (Ansys-Lumerical FDTD 2023 R1) is employed [23,24]. The smallest grid size is ~2 nm, and transparent boundary conditions are implemented using perfectly matched layers (PMLs) to suppress reflections from the simulation region boundaries. A 3D-FDTD simulation of the entire structure is also performed to reliably evaluate the extinction ratio (ER) and overall insertion loss (IL) of the LC-based MZI optical modulator. The ER is the ratio between the optical power of the quasi-transverse-electric (TE) fundamental mode at the output SiN_x waveguide in the ON and OFF statuses, 10log₁₀($I_{OUT,ON}$/$I_{OUT,OFF}$). The IL is the ratio between the optical power of the quasi-TE fundamental mode at the input SiN_x waveguide and of the quasi-TE fundamental mode at the output SiN_x waveguide in the ON status, 10log₁₀($I_{IN}$/$I_{OUT,ON}$).

3. Results and Discussion

3.1. Liquid-Crystal-Based Phase Shifter Integrated on a SiN_x Waveguide Structure

Firstly, in order to gain an understanding of the potential and limitations of an LC-based phase shifter integrated on a SiN_x waveguide, as shown in Figure 2a, the effects of seven important parameters, namely, the SiN_x waveguide width ($W_{SiNx}$), SiN_x waveguide thickness ($H_{SiNx}$), liquid-crystal-filled trench width ($W_{LC}$), liquid-crystal-filled trench height ($H_{LC}$), SiO₂ vertical gap between the liquid-crystal-filled trench and SiN_x ($D$), SiN_x refractive index ($n$), and optical wavelength in the C-band region (λ), are holistically investigated. As shown in Figure 2b,c, the change in the alignment of LC molecules from parallel (0°) to perpendicular (90°) with respect to the SiN_x waveguide propagation direction results in variations in the optical mode effective index values. This will introduce the phase-shifting effect as discussed above; hence, knowledge on the obtainable phase shift dependence on each parameter between 0° and other LC orientations from 15° to 90° is valuable.

Figure 3a–g systematically shows the variation in phase-shifting performance with respect to each of the aforementioned parameters at a chosen shifter length of 50 µm and different LC molecule alignment values; the latter can be controlled via external electric fields and is later discussed. For consistency in every case reported in Figure 3, when the parameters are not varied, the values are as follows: $W_{SiNx}$~500 nm, $H_{SiNx}$~200 nm, $W_{LC}$~1500 nm, $H_{LC}$~600 nm, $D$~25 nm, $n$~2, and λ~1.55 µm. The data points include only the cases in which the structures support single-mode propagation. As shown in Figure 3a, larger values of $W_{SiNx}$ tend to decrease the obtainable phase shift values, as the optical mode is increasingly confined in the SiN_x waveguide. Interestingly, a too-narrow value of ~400 nm for $W_{SiNx}$ also leads to a reduction in the obtainable phase shift; this is because the optical mode becomes too loosely confined in the SiN_x waveguide, and a significant part of the mode interacts with the LC sidewall, as shown in the top inset of Figure 3a [9]. In Figure 3b, as expected, larger values of $H_{SiNx}$ significantly decrease the obtainable phase shift values because the optical mode is increasingly confined in the SiN_x waveguide, as shown in the right insets. Nevertheless, $H_{SiNx}$ values lower than 200 nm are not possible when attempting to achieve a well-supported optical mode in the SiN_x waveguide. In Figure 3c,d, a larger LC-filled trench width ($W_{LC}$) and height ($H_{LC}$) both positively increase the obtainable values of the phase shift. Nevertheless, as shown in the inset of Figure 3c, too-wide values of ~2500 nm for $W_{LC}$ lead the structure to support a higher-order optical mode. Additionally, as shown in the inset of Figure 3d, too-thick values of ~700 nm for $H_{LC}$ push the optical mode to be largely confined in the upper LC region; this could potentially make it highly difficult to integrate the optical structure with a lower input SiN_x waveguide, which is later discussed. In Figure 3e, expectedly, a smaller gap between the liquid-crystal-filled trench and the SiN_x waveguide ($D$) helps to increase the obtainable phase shift values, as a higher portion of the optical mode is in the LC region instead of the SiO₂ gap. Taking into account the fabrication uniformity of the modern CMOS process for photonics of ~10 nm [25,26,27], a $D$ value of 25 nm is preferable, as it can render a more relaxed fabrication tolerance together with phase-shifting performance comparable to that when using a $D$ of 10 nm. The phase-shifting performance presented in Figure 3a–e is based on a refractive index ($n$) of SiN_x~2 (stoichiometric Si₃N₄); however, the $n$ values of SiN_x can be conveniently increased if the SiH₄ and N₂ gas ratio becomes larger during the deposition process [13]. As shown in Figure 3f, using SiN_x with higher $n$ values lead to a significant decrease in the obtainable phase shift, as the optical confinement becomes stronger in the SiN_x waveguide, leading to a smaller optical overlap with the LC region, as shown in the right inset. Last but not least, Figure 3g shows that the phase-shifting performance over the entire C-band wavelength region of the LC-based phase shifter integrated on the SiN_x waveguide structure is better in the lower wavelength values according to the LC molecular properties [22]. To summarize, the values of $W_{SiNx}$_, $H_{SiNx}$_, $W_{LC}$_, $H_{LC}$_, $D$, and $n$ need to be carefully considered with a view to obtaining competitive phase-shifting performance while maintaining single-mode propagation in the LC-based phase shifter section ($W_{SiNx}$_, $H_{SiNx}$_, $W_{LC}$, and $n$), the ability to be later integrated with input SiN_x waveguides ($H_{LC}$), and relaxed fabrication tolerance ($D$).

3.2. Multi-Mode Interferometer (MMI) Splitter for Compact LC-Based Optical Modulator

As shown in Figure 1, a multi-mode interferometer (MMI) splitter is needed to transfer light from one SiN_x waveguide into two separate LC-based phase shifters integrated on the same SiN_x layer. As the SiN_x waveguide thickness ($H_{SiNx}$) value should be consistent over the entire structure to allow for low fabrication complexity, and as larger $H_{SiNx}$ values significantly decrease the obtainable phase shift (Figure 3b), we focus on an $H_{SiNx}$ of 200 nm. The inset of Figure 4a shows the intensity profile of the optical propagation inside the 200 nm thick SiN_x MMI at an optical wavelength of 1.55 µm. After optimization, we arrive at $W_{MMI}$ = 11 µm, $L_{MMI}$= 66 µm, $G$ = 2.6 µm, and $W_{SiNx, MMI}$ = 3 µm. It should be noted that the tolerance of an MMI device to wavelength variation depends essentially on the width of the access waveguide, $W_{SiNx,MMI}$; a wider value of $W_{SiNx,MMI}$ will relax the optical wavelength and dimension variation constraints [16]. Indeed, SiN_x MMIs have been previously studied because of their benefits of a lower refractive difference with SiO₂ compared to Si and reduced sensitivity to temperature changes [28,29,30]. Our designs are based on our previous investigation indicating that a relatively large access waveguide width reduces the refraction caused by a narrower entrance section and allow them to properly cover the entire wavelength of interest [16]. Therefore, with a relatively large value of $W_{SiNx, MMI}$ = 3 µm, the 200 nm thick SiN_x MMI can maintain a high optical power transmission of around 98% (~0.09 dB optical loss) over the entire C-band wavelength range, as shown in Figure 4a. On the contrary, as previously discussed (Figure 3a), a larger value of the SiN_x waveguide width ($W_{SiNx}$) is detrimental to the obtainable phase-shifting performance of the LC-integrated SiN_x waveguide structure. Therefore, a suitable tapering structure is required to transfer the optical mode from the 3 µm wide SiN_x waveguide at the MMI outputs to a narrower one necessary in the LC-based phase shifter section. Figure 4b shows the linear SiN_x taper length ($L_{taper, SiNx}$) values needed to achieve 100% optical power transmission of the optical mode from the 3 µm wide SiN_x waveguide at the MMI outputs to a SiN_x waveguide with different values of $W_{SiNx}$ used at the phase shifter. To obtain ~100% optical power transmission together with a relatively compact taper ($L_{taper, SiNx}$ ≤ 50 µm), the value of $W_{SiNx}$ should not be lower than 900 nm (light blue upward-pointing triangle.) Interestingly, a 900 nm wide SiN_x waveguide results in only slightly lower phase-shifting performance than a 500 nm wide one (Figure 3a). As a result of the studies in this section, we conclude that a wideband and low-loss MMI is possible using a relatively thin SiN_x waveguide ($H_{SiNx}$~200 nm), which is required to have good phase-shifting performance in the LC-based section; however, a compromise needs to be made in terms of the SiN_x waveguide width value ($W_{SiNx}$~900 nm) in order to obtain not only competitive phase-shifting performance but also overall device compactness.

3.3. Linear Tapering of the LC Section for Optical Integration

As also shown in Figure 1, to couple light from the 900 nm wide SiN_x waveguide ($W_{SiNx}$~900 nm) to the LC-based phase shifter on the same SiN_x waveguide layer, a linear tapering of the LC section ($L_{taper,LC}$) is required to accommodate optical integration between the two sections due to the mode size and effective index mismatch. Figure 5a–d show the optical power transmission efficiency from the SiN_x waveguide to the LC-based phase shifter structure at different LC-filled trench taper length ($L_{taper,LC}$) and taper tip width ($t_{LC}$) values. According to the knowledge obtained from the results shown in Figure 3 and Figure 4, the values of other important parameters used in this investigation are as follows: $H_{SiNx}$~200 nm, $W_{LC}$~ 1500 nm, $H_{LC}$~600 nm, $D$~25 nm, $n$~2, and λ~1.55 µm. Significantly, the investigation of the optical integration performance has to be considered for LC molecule alignments both parallel (0°) and perpendicular (90°) to the SiN_x waveguide propagation direction, because the intensity modulation capability of the optical signal is obtained from the difference in the phase-shifting effect (0° and 90°) between the two arms of the Mach–Zehnder interferometer (MZI). In Figure 5, as expected, larger $L_{taper,LC}$ values lead to higher optical power transmission efficiency values, and an $L_{taper,LC}$ of ~50 µm is required to obtain the maximum optical transmission efficiency from the SiN_x waveguide to the LC-based phase shifter structure. Interestingly, we find that using a lower taper tip width value ($t_{LC}$~50 or 100 nm) can help make the optical transmission performance of the integration scheme become more comparable between the parallel (0°) and perpendicular (90°) LC molecular alignments despite the difference in the effective index values between the two cases, e.g., as shown in Figure 2b,c. This is crucial, as too much variation in the optical intensity levels between the two arms of an MZI could lead to a spurious intensity modulation that can degrade the optical modulator performance [31]. Additionally, it should be noted that a trench width of 50 or 100 nm at the taper tip ($t_{LC}$) with a trench height $H_{LC}$ of 600 nm would result in a trench aspect ratio of 6–12, which is still compatible with available advanced high-aspect-ratio SiO₂ etching processes [32].

3.4. Modulation Efficiency

It is also important to consider the magnitude of the electric field across the LC-filled region. As indicated in [33], an electric field of ~0.2 × 10⁴ V/cm would be required to obtain a nematic LC 4-n-pentyl-4′-cyanobiphenyl (5CB) molecular orientation from parallel (0°) to perpendicular (90°). Moreover, to take into account the additional electric field needed to overcome the mechanical anchoring strength of the alignment layer [9], a total electric field of ~0.4 × 10⁴ V/cm would be necessary to have a perpendicular LC molecule orientation. Figure 6b shows the minimum electric field obtained in the LC-filled trench region with different reverse bias voltage values between the two aluminum (Al) contacts placed between the LC-filled trench at various distances between the Al contact and the trench, $S$; as in Figure 6a, $W_{SiNx}$~900 nm, $H_{SiNx}$~200 nm, $W_{LC}$~1500 nm, $H_{LC}$~600 nm, $D$~25 nm, $n$~2, and λ~1.55 µm, according to the results shown in Figure 3, Figure 4 and Figure 5. As shown in Figure 6b, lower values of $S$ lead to higher values of the obtainable minimum electric field in the LC-filled trench region. Significantly, a reverse bias as low as ~1 V (resp. 2 V) can be used to obtain a perpendicular LC molecule orientation using a moderate $S$ distance value of 0.5 µm (resp. 1 µm), which is compatible with the available drivable voltage (e.g., ≤2 V [34]) from Si-based complementary metal-oxide semiconductor (CMOS) circuits. Figure 6c shows that the electric field can be effectively and uniformly applied across the LC-filled trench region with 1 V. It is important to note that the Al contact needs to be placed slightly lower than the LC-filled trench region by ~0.2 µm, as indicated in Figure 6a, in order to have a relatively well distributed electric field across the LC-filled trench. Last but not least, to determine the modulation performance of an optical modulator based on an LC phase shifter on a SiN_x waveguide, a common Figures of Merit (FoM) when using MZI is the modulation efficiency, $V_{\pi }{L}_{\pi }$, which is the product between the voltage and the length needed to obtain a π phase shift [35].

$$V_{\pi }{L}_{\pi }=V_{\pi }·{\displaystyle \frac{\lambda }{2∆n_{eff}\left(V_{\pi }\right)}}$$

where $∆n_{eff}\left(V_{\pi }\right)$ is the change in the effective refractive index of the phase shifter structure between no bias voltage (LC molecules oriented in parallel (0°)) in one arm of the MZI and $V_{\pi }$ (LC molecules oriented perpendicularly (90°)) in the other arm. Figure 6d shows that a $V_{\pi }{L}_{\pi }$ of ~$0.3 \times {10}^{-2} V·cm$ can be expected; this is one order of magnitude less than that typically obtainable with forward-biased silicon Mach-Zehnder modulators [36,37], and it is consistent with previous data reported in a recent demonstration of an LC-based optical modulator [9], indicating that our simulation is well calibrated. To reliably evaluate the extinction ratio (ER) and overall insertion loss (IL) of the LC-based MZI optical modulator, we perform a 3D-FDTD simulation of the entire structure from the SiN_x input to the SiN_x output waveguide, including two MMIs, the linear tapering of the LC section, and the two arms of the LC-based phase shifter integrated with the SiN_x waveguide, as shown in Figure 7a,b for ON-mode (constructive interference at the output) and OFF-mode (destructive interference at the output) operations at λ~1.55 µm with an LC section length ($L_{LC}$) of 30 µm. It is important to note that another linear SiN_x taper length ($L_{taper, SiNx}$ = 50 µm) is required in the output section to suppress the higher-order mode excited at the 3 µm wide SiN_x waveguide at the MMI output and to allow for only the fundamental mode to be transferred to the single-mode 0.9 µm wide SiN_x waveguide, at which the output of the entire structure is evaluated. In the 3D-FDTD simulation of the entire structure, a competitive ER of ~15 dB and an IL lower than ~1 dB are obtained, confirming the potential of a low-voltage LC-based MZI optical modulator for high extinction and low optical loss usage. It is worth mentioning that all optical losses, including material absorption together with the reflection and scattering losses at each optical component and interface, are taken into account in the 3D-FDTD simulation [38]. As each dB loss in optical power requires a dB increase in laser power [39], a low-loss optical modulator plays a crucial role in achieving a low-power optical interconnection with a good signal-to-noise level. Based on

Table 1. Comparison of the designed LC-based MZI optical modulators with recently published state-of-the-art works.

Ref.	Integration Approach	Wavelength	Total Footprint (2 MMIs, Integration Structures, and MZI)	${\mathit{V}}_{\mathit{\pi }}{\mathit{L}}_{\mathit{\pi }}$	ER/IL
M. Notaros et al. [9]	Two different SiNx layers for passive optical components and active phase shifter LC region	632 nm (visible light)	N/A (dimensions of MMIs and integration structures were not available)	~$0.5\times {10}^{-2}$ $V·cm$	N/A
This work	Same SiNx layer for passive optical components and active phase shifter LC region	1530–1565 nm (C-band)	20 $\times$ 600 µm2 (Figure 7a)	~$0.3\times {10}^{-2}$ $V·cm$	~15

, we can project that a SiN_x waveguide-integrated LC-based MZI optical modulator with a modulation efficiency ($V_{\pi }{L}_{\pi }$) comparable to that of the previous demonstration could be obtained while using only one SiNx waveguide layer for both the passive and active regions. It is important to note that, in the first demonstration work, information on the MMI and integration structure dimensions and the ER/IL values was not available. Significantly, Figure 7c reports the ER and IL values of the LC-based MZI optical modulators with LC section lengths ($L_{LC}$) of 30 and 50 µm at different C-band wavelengths. We find that it is critical to carefully determine the phase shifter length of LC-based MZI optical modulators. A too-long phase shifter length can contradictorily worsen the optical modulation, as the phase shifter length required to obtain a π phase shift can be as low as ∼15–20 µm (previous investigation shown in Figure 3g). To illustrate, our analysis shows that an LC-based MZI with a 30 µm long phase shifter length will instead have a superior optical modulation performance to the one with a 50 µm long phase shifter length. While the LC-based MZIs with 30 and 50 µm long phase shifters have identical IL values (pink and purple data points), the ER values are significantly better when using the shorter phase shifter of 30 µm (destructive interference; blue data points) than when using the longer phase shifter of 50 µm (constructive interference; green data points). Additionally, regarding the potential device rapidity, it is important to mention that, although the typical response time of LC molecules can be expected to fall within the millisecond range, a response time within ten nanoseconds has been demonstrated to be possible using a twisted-nematic 5CB LC [40]. It is worth noting that, to couple the investigated SiN_x waveguide-integrated LC-based MZI optical modulator with an off-chip optical source, a SiN_x spot-size converter could be employed [41,42] to enable a low-loss optical interconnection.

4. Conclusions

In conclusion, we thoroughly investigated the potential of employing a SiN_x waveguide platform to enable the use of liquid-crystal-based phase shifters for on-chip optical modulators using optical 3D-FDTD and electrical simulations. Contrary to previous demonstrations, we chose to focus on using only one SiN_x waveguide layer for the entire device in both the passive and active regions in order to achieve a potentially simpler fabrication process. The entire structure of the liquid-crystal-based MZI optical modulator, comprising mainly MMI splitters, linear tapers to transfer the optical mode between different structures, and LC-based phase shifters integrated on a SiN_x waveguide, was systematically investigated. The trade-offs between several important parameters in each part were discussed in order to holistically consider the obtainable phase-shifting performance, single-mode propagation, compact integration, and fabrication tolerance. Based on the investigations, out of eleven studied parameters, we project that a wideband, relatively compact, high-extinction ratio, and low-voltage SiN_x waveguide-integrated MZI optical modulator can be obtained while using only one SiN_x waveguide layer for both the passive and active regions by carrying out the following: (1) employing a relatively thin SiN_x layer ($H_{SiNx}$) with a moderately high refractive index value ($n$) of stoichiometric Si₃N₄ to enhance optical overlapping with the LC region; (2) using a relatively large MMI access waveguide width ($W_{SiNx,MMI}$) to obtain wideband and low-loss operation; (3) utilizing a narrow width for the tip of the LC-filled trench taper ($t_{LC}$) to obtain a low-loss and comparable optical coupling in both arms of the MZI with LC molecules aligned parallelly (0°) and perpendicularly (90°) to avoid a spurious intensity modulation that can degrade the optical modulation; (4) maintaining compromising values of the SiN_x waveguide width ($W_{SiNx}$), LC-filled trench width ($W_{LC}$), and height ($H_{LC}$) to retain device compactness and single-mode operation; (5) carefully positioning the metal contacts with respect to the LC-filled trench ($S$) to ensure a homogeneous and high field in the LC trench with a bias voltage potentially as low as 1 V; and (6) attentively determining the phase shifter length of the LC-based MZI optical modulators to obtain proper destructive and constructive interference at the modulator outputs, as a too-long phase shifter length can contradictorily worsen the optical modulation. Via well-calibrated finite-difference time-domain techniques, together with electrical simulation, this work contributes toward obtaining a deeper and holistic understanding of the potential, limitations, and design rules to achieve a competitive LC-based Mach–Zehnder interferometer (MZI) optical modulator for compact, wideband, and low-voltage on-chip optical modulation.