High-Efficiency Lithium Niobate Electro-Optic Modulator with Barium Titanate Cladding on Quartz

Abstract

The thin-film lithium niobate (TFLN)-based electro-optic (EO) modulator is one of the most important devices for optical communications in terms of the advantages of low voltages and large bandwidth. However, the large size of devices limits their applicability in large-scale integrated optical systems, posing a key challenge in maintaining performance advantages under restricted design space. In this paper, we propose a novel TFLN modulator on a quartz substrate incorporating barium titanate (BaTiO₃, BTO) as the cladding material. The device is designed with silicon–lithium niobate (Si-LN) hybrid waveguides for operation at a wavelength of 1.55 µm. After theoretical analysis and parameter optimization, the proposed 10 mm long modulator demonstrates high-efficiency modulation, featuring a low half-wave voltage-length product of 1.39 V·cm, a broad 3 dB EO bandwidth of 152 GHz, and low optical loss. This theoretical model provides a novel design solution for TFLN modulators on quartz substrates. Moreover, it is a promising solution for enhancing the integration of photonic devices on the TFLN platform.

1. Introduction

The AI-driven computing demand surge highlights the potential of optical computing in the post-Moore’s law era, leveraging low latency and high bandwidth [1]. Photonic integrated circuits (PICs) integrate electro-optic (EO) modulators [2] with photonic devices, enabling efficient optoelectronic chips for AI acceleration. With the continuous development of optical communication and integrated photonic systems, there is an increasing demand for low-power-consuming and miniaturized EO modulators [3,4,5,6,7]. Lithium niobate (LiNbO₃, LN) is widely recognized as the main photonic material because of its large Pockels effect (γ₃₃ = 30.8 pm/V) and fast EO response, as well as its low absorption in the wavelength range of optical communication [8]. Thin-film LN (TFLN) modulators based on a Mach–Zehnder interferometer (MZI) have been widely demonstrated in optical communication systems [9,10]. Etched LN and hybrid waveguides are two common types of TFLN-based waveguides [11,12]. Specifically, hybrid waveguides are fabricated by the process of ribbing a TFLN slab using other materials, such as Si [13]. The Si-LN hybrid waveguide is frequently employed in TFLN modulators on Si substrates because it avoids the issues associated with LN etching and front-end processing. Furthermore, the design facilitates the scalability of the integrated photonic platform, offering a simple and scalable way of integrating ultrahigh-bandwidth EO modulators with other optics [14,15,16,17].

Recently, TFLN modulators with sub-1.5 V voltage and 110 GHz bandwidth have emerged on quartz substrates [18]. In contrast, achieving such levels of performance with TFLN modulators on traditional Si substrates is challenging. This is because quartz substrates have near-ideal microwave properties, with a low dielectric constant (ε_Quartz = 4.5) and microwave absorption tangent (<10⁻⁴) [19], which dramatically reduce radio frequency (RF) losses. However, coplanar waveguide (CPW) electrodes on a low-permittivity substrate exhibit a lower RF effective index. In the case of x-cut LN films with a thickness of 600 nm on quartz substrates, the RF effective index of CPW electrodes in ground–signal–ground (G-S-G) structures ranges from 1.7 to 1.9, which is significantly lower than the typical optical group index of 2.2 to 2.3 observed in etched LN waveguides [20,21]. In particular, the optical group index of Si−LN hybrid waveguides generally is approximately 2.4 [13,14,15,16], which consequently leads to a more pronounced velocity mismatch and a limited bandwidth within this structure. At present, the main solution to the velocity mismatch of TFLN modulators on quartz substrates is the use of segmented electrodes and etched LN waveguides [18,21,22]. However, these designs typically achieve a modulation efficiency of approximately 2.3 V·cm [18,21], requiring a device length longer than 20 mm to realize a half-wave voltage near 1 V. To simultaneously achieve both low half-wave voltage and a compact footprint, it becomes imperative to improve modulation efficiency through innovative approaches. Notably, significantly high modulation efficiency has been demonstrated in a silicon–organic hybrid Mach–Zehnder modulator using amorphous barium titanate (BaTiO₃, BTO) cladding [23,24]. Amorphous BTO is suitable as a cladding material due to its high dielectric constant (ε_BTO = 50) and relatively low index (n_BTO = 1.85) [23,24], which contribute to considerable improvements in the electric field strength of the waveguides and enhance the overlap between the electric and optical fields. We apply this method to the modulators based on the TFLN platform to address the aforementioned issues.

In this paper, we propose a novel hybrid TFLN modulator on a quartz substrate with amorphous BTO as cladding. This design not only achieves a good match between the RF effective index and optical group index, but also improves modulation efficiency. After parameter optimization and numerical simulation, the proposed modulator achieves a half-wave voltage of 1.39 V and a broad 3 dB EO bandwidth of 152 GHz, while maintaining low optical loss. This design provides a unique and practical solution for integrating Si-LN hybrid waveguides in TFLN modulators on quartz substrates.

2. Principle and Design

2.1. Device Design

The structure of the proposed device is shown in Figure 1. The traveling-wave electrodes in a G-S-G structure are placed directly above an X-cut TFLN layer of 600 nm thickness. The electrodes are made of traditional rectangular CPW transmission lines, which can decrease the difficulty of fabrication. A 4.7 µm SiO₂ layer and a 500 µm quartz substrate are located below the TFLN wafer. The waveguide core is composed of a Si-LN combination, with Si waveguides formed at the bottom of an unetched TFLN layer. The optical mode is controllably distributed between the TFLN layer and the Si waveguide. However, the index contrast between LN (n_LN = 2.21) and BTO (n_BTO = 1.85) at 1550 nm is low, and it is difficult to form a strong confinement within the core region of the LN, which results in an increase in metal absorption loss. Therefore, a portion of SiO₂ is added on top of the TFLN to form a cladding of the proposed modulator, in which the BTO material is deposited on both sides of the SiO₂ part. As a result, the BTO material acts as a cladding layer that can significantly enhance the strength of the electrostatic field within the core region of the LN waveguide. The basic structural parameters include Si waveguide width (w_Si), electrode gap (G), SiO₂ cladding width (w_SiO₂), signal electrode width (w_s), and signal electrode thickness (h_Au).

Figure 2a illustrates the coupling section from the transition waveguide to the hybrid waveguide. A gradual reduction in the width of the Si waveguides allows for the transition of the light from the Si waveguides to the LN layer. This transition is quantified by the fraction (Γ_LN) of the integral over the cross-sectional profile of the Poynting power that resides in the LN region. Figure 2d depicts the correlation between w_Si and the Γ_LN and Γ_Si parameters, with the calculations performed at an h_Si value of 150 nm and an h_cmp value of 20 nm. In the hybrid waveguide, we chose w_Si = 320 nm after weighing up the options. Therefore, the majority of the light is confined within the TFLN, with only 6% of the Poynting vector located in the Si compared to 75% in the TFLN, and the remainder distributed in the cladding, as shown in Figure 2c. The high value of Γ_LN is typically maintained at approximately 80% in the hybrid mode [13,14,15], and the w_Si is not reduced any further, in order to have a laterally confined optical mode. In this case, there is no high optical loss from the metal electrodes, and the transition loss is kept low [13]. Furthermore, a high value of Γ_LN and low optical loss may also be attained with different Si waveguide and h_cmp sizes. A large amount of related research on Si-LN hybrid waveguides has already been published [13,14,15,25], and the parameters of the Si waveguide used in this paper are only a common example.

2.2. Principle of Improved Modulation Efficiency

A common approach to modulator design is to have the gap between the electrodes and the waveguide completely covered by SiO₂ [21], which is categorized as a cladding configuration with a low relative dielectric constant. In order to facilitate a comparison of the effects of low- and high-dielectric-constant cladding, the electric field intensity distribution and optical field distribution were calculated for both structures under identical parameters. Both structures adopted signal electrodes with a width of 20 µm and ground electrodes with a width of 100 µm. For SiO₂ cladding, the parameters were h_Au = h_SiO₂ = 1.5 µm and G = 7 µm. In the case of BTO cladding, the BTO layer had a thickness of 1.5 µm and a width of 2 µm, while maintaining the same values of h_Au = 1.5 µm, h_SiO₂ = 1.5 µm, and G = 7 µm as the SiO₂ structure. An additional geometric parameter, w_SiO₂ = 3 µm, was introduced in the BTO cladding structure. Figure 3a,c show the electric field distributions under a 1 V applied voltage. In the low-dielectric-constant cladding modulator, the relative dielectric constant of SiO₂ is considerably lower than that of TFLN, resulting in the electric field concentrating within the SiO₂ cladding and remaining weak within the TFLN waveguide. In contrast, the modulator with BTO cladding reduces the field strength in the cladding due to its high dielectric constant, while significantly enhancing it in the LN waveguide. This is explained by Gauss’s law, where the electric field satisfies Maxwell’s equations at boundaries with differing ε, as follows:

$$D={\epsilon }_{\mathrm{BTO}}{E}_{\mathrm{BTO}}={\epsilon }_{\mathrm{Si}{\mathrm{O}}_2}{E}_{\mathrm{Si}{\mathrm{O}}_2}$$

(1)

where ε_SiO₂ and ε_LN denote the relative permittivity of SiO₂ and LN, respectively, and E_SiO₂ and E_LN denote the respective electric field strength therein.

As quantitatively illustrated in Figure 3, the electro-optic interaction region (delineated by the yellow dotted box) exhibits remarkable field enhancement when employing the BTO cladding configuration. Numerical simulations reveal that the maximum electric field intensity within the LN waveguide core reaches approximately 2.5 × 10⁵ V/m under BTO cladding, representing an enhancement of roughly two times compared to the common SiO₂ cladding configuration (~1.2 × 10⁵ V/m). This substantial field amplification can be primarily attributed to the unique dielectric properties of BTO, which establishes favorable boundary conditions for electromagnetic field confinement through its high-permittivity contrast with LN.

In order to analyze the optical mode distribution and calculate propagation loss, simulations based on COMSOL Multiphysics were employed to compare the features of the two structures. The transmitted fundamental mode field at 1550 nm is illustrated in Figure 3b,d, respectively. The designed structure can confine the optical field as effectively as the structure completely covered by SiO₂ cladding. To compare the effect of the cladding on the modulation efficiency, the half-wave voltage-length product (V_π·L) was calculated by the following Equation [16]:

$${\mathrm{V}}_{\mathrm{\pi }}·\mathrm{L}={\displaystyle \frac{n_{\mathrm{eff}}\mathrm{\lambda }G}{2{n_{\mathrm{e}}}^4{r}_{33}{\mathsf{\Gamma }}_{\mathrm{m}\mathrm{o}}}}$$

(2)

where n_eff is the effective index of the optical mode field, λ is the modulator operating wavelength (in vacuum), n_e is the unusual index of the LN, and r₃₃ is the linear (Pockels) EO coefficient in the Z-direction of the crystal. Furthermore, Γ_mo is computed by the following equation:

$${\mathsf{\Gamma }}_{\mathrm{mo}}={\displaystyle \frac{G}{\mathrm{V}}}{\displaystyle \frac{{\displaystyle {\iint }_{\mathrm{L}\mathrm{N}}{E}_{\mathrm{o}\mathrm{p}}^2(\mathrm{x},\mathrm{z})E_{\mathrm{e}\mathrm{s}}(\mathrm{x},\mathrm{z})\mathrm{d}\mathrm{x}\mathrm{d}\mathrm{z}}}{{\displaystyle {\iint }_{\mathsf{\Omega }}{E}_{\mathrm{o}\mathrm{p}}^2(\mathrm{x},\mathrm{z})\mathrm{d}\mathrm{x}\mathrm{d}\mathrm{z}}}}$$

(3)

where V is the applied voltage of the modulator, E_{op(x, z)} is the electric field distribution of the optical field, E_{es(x, z)} is the electrostatic field, and the integral domains of the numerator and denominator are the LN region and the entire cross-section of the waveguide.

Reducing the electrode gap can enhance the electric field, but this method has an upper limit for improving the modulation efficiency. This is because the metal electrodes can absorb the light that leaks out of the waveguide, and a narrow gap will result in a high light absorption loss. Figure 4 shows the simulated V_π·L and optical loss of the modulators as the gap between the electrodes varies, with or without BTO cladding. At the same gap, the proposed modulator exhibits slightly larger optical losses compared to the common design. This primarily stems from the reduced index contrast between the LN core and the BTO cladding compared to common structures. When the gap between the electrodes narrows, the modulator becomes more efficient, and the optical loss increases exponentially. When the optical loss is approximately 1.0 dB/cm (point C) in the normal modulator design, the voltage-length product is 2.08 V·cm (point D). However, the modulation efficiency of modulators with BTO cladding can reach 1.67 V·cm (point B) when the optical loss is 1.0 dB/cm (point A). The result shows that the high-dielectric-constant cladding provides a significant improvement in modulation efficiency, as we expected, demonstrating superior performance over the common design under equivalent optical loss conditions.

2.3. Cladding Structure Optimization

Since the gap variation monotonically affects modulation efficiency and optical loss, it does not alter the trend observed with the BTO cladding. Therefore, we fixed the electrode gap at 7 µm in simulations to determine how changes in the size of the BTO cladding structure affect modulation efficiency and optical loss. With the w_SiO₂ fixed at 3 µm, the modulation efficiency and the metal absorption loss, with variation in the heights of SiO₂ (h_SiO₂) and BTO (h_BTO) within the range from 0.5 to 2.5 µm, were calculated, as depicted in Figure 5a,b, respectively. It was found that a lower V_π·L could be achieved when h_SiO₂ ≈ h_BTO ≥ 1.5 µm. Furthermore, the propagation loss could also be realized to be less than 1.6 dB/cm. Considering the challenges associated with depositing thick BTO cladding layers, where achieving greater thickness currently requires extended deposition time at the expense of production efficiency, we intentionally selected h_SiO₂ = h_BTO = 1.5 µm as a representative case to investigate the structural dependence. This thickness value serves as a practical compromise between device performance and fabrication feasibility. Based on this thickness configuration, taking the case of h_SiO₂ = h_BTO = 1.5 µm as an example, the impact of w_SiO₂ on the modulation efficiency and metal absorption loss is also shown in Figure 5c. Here, the w_SiO₂ is varied between 1.0 and 5.5 µm, and the width of BTO on both sides of the cladding layer is in one-to-one correspondence with the width of SiO₂, namely, w_BTO = (G − w_SiO₂)/2. It can be observed that V_π·L can reach a low point of 1.39 V∙cm, with a propagation loss of 3.2 dB/cm, when w_SiO₂ = 1.9 µm.

2.4. Bandwidth Estimation and Optimization

A comparative simulation was conducted using ANSYS HFSS to verify that the proposed model achieves improved bandwidth performance compared to common designs. When the characteristic impedance of the common design model amounts to 50 Ω and n_RF is maximized to the greatest extent possible, the bandwidth of the BTO design model with the identical electrode dimensions is contrasted. At this point, w_s = 20 µm, h_Au = 1 µm, h_SiO₂ = 1.5 µm, and G = 7 µm, and the phase shifter arm length L = 10 mm. The ground electrodes are five times the width of the signal electrode, as this configuration in the CPW electrode reduces dispersion and minimizes radiation loss. The simulated RF effective index (n_RF), the RF loss, and the characteristic impedance (z₀) are depicted in Figure 6a–c, respectively. The n_RF value of the modulator with BTO is approximately 2.46, which is essentially the same as the optical group index (n_opt = 2.432). However, the n_RF value of another modulator is approximately 2.04, resulting in a velocity mismatch. The characteristic impedance of the BTO cladding modulator is marginally lower than 50 Ω. Additionally, both modulators show high similarity in RF loss, indicating that the presence of BTO does not significantly impair RF loss. Furthermore, the EO response and electrical reflections (S₁₁) were calculated over a wide frequency range. Theoretically, the bandwidth of the EO response can be calculated by the following equations [26]:

$$M(f_{\mathrm{R}\mathrm{F}})=20{\log }_{10}[{\displaystyle \frac{2\sqrt{z_0{z}_{in}}}{z_0+z_{in}}}{e}^{-{\displaystyle \frac{\alpha L}{2}}}{\left\{\left.{\displaystyle \frac{{\sinh }^2(\frac{\alpha L}{2})+{\sin }^2(\frac{bL}{2})}{{(\frac{\alpha L}{2})}^2+{(\frac{bL}{2})}^2}}\right\}\right.}^{{\displaystyle \frac{1}{2}}}]$$

(4)

$$b={\displaystyle \frac{2\pi f_{\mathrm{R}\mathrm{F}}}{c}}(n_{\mathrm{RF}}-n_{opt})$$

(5)

where L is the length of the modulation region, α is the attenuation coefficient, and z_in is the input impedance of the applied system (50 Ω). b quantifies the effect of the velocity mismatch between the modulated light and the RF on the EO response of the modulator. The obtained simulation results of the EO response are shown in Figure 6d.

Obviously, it can be seen that the 3 dB EO bandwidth of the designed modulator is demonstrably superior to that entirely covered by SiO₂, and can reach ≈ 100 GHz. In addition, the electrical reflection (S₁₁) from the electrode for both cases is maintained below −15 dB. Therefore, the designed modulator is expected to satisfy the high-speed modulation requirements.

In order to achieve a broader 3 dB EO bandwidth, the parameters of the electrode size were optimized. Additionally, altering the thickness and width of the electrode had no influence on the modulation efficiency and optical loss. Figure 7a,b presents contour maps of n_RF and z₀ as a function of the signal electrode width w_s and the thickness h_Au. The modulator parameters are set as w_SiO₂ = 1.9 µm, G = 7 µm, h_BTO = h_SiO₂ = 1.5 µm, and a phase shifter arm length of L = 10 mm. The RF effective index decreases as the signal electrode width or thickness increases. Similarly, the characteristic impedance decreases as the signal electrode width or thickness increases. It can be found that a broad 3 dB EO bandwidth of >150 GHz can be achieved when h_Au = 0.7 µm and w_s = 28 µm. This approach has the capability of achieving an operating voltage of less than 1.5 V and high-speed modulation up to 150 GHz.

3. Discussion

A comparison of the performance of a typical TFLN modulator is presented in

Table 1. Performance comparison of C-band TFLN-based MZI modulators.

Substrate	Platform	Vπ·L (V·cm)	Vπ (V)	L (mm)	Optical Loss (dB/cm)	3 dB EO Bandwidth (GHz)	Ref.
Si	Etched LN	1.2	3.0	4	6.0	40	[27]
Si	Etched LN	1.41	3.53	5	1.25	67	[28]
Si	Si-LN	3.1	6.2	5	0.6	110	[15]
Si	Si-LN	2.5	5.1	5	0.98	>70	[29]
Si	Si-LN	3.10	3.10	10	0.6	70	[16]
Si	Si-LN	2.13	1.7	12.5	<0.1	70	[14]
Quartz	Etched LN	3.8	2.53	15	7.0	<40	[15]
Quartz	Etched LN	2.3	1.15	20	1.0	180 a	[21]
Quartz	Etched LN	2.35	1.0	23.5	2.97	140 a	[18]
Quartz	Etched LN	2.04	1.02	20	<0.1	95	[22]
Quartz	Si-LN	1.39	1.39	10	3.2	152	This work a

^a simulation results.

. Compared with these modulators on Si substrates, the demonstrated design shows the lowest V_π and the broadest 3 dB EO bandwidth, while maintaining low optical loss. Although the modulator in Ref. [27] achieves the lowest V_π·L (1.2 V·cm), its implementation is constrained by specific TFLN structural requirements and substantial optical loss. Additionally, the TFLN modulator with glycerol cladding [28] shows similar modulation efficiency (1.41 V·cm) to our design, but BTO films offer greater stability in practical applications compared to liquid glycerol. While other implementations employing shortened electrodes [15,29] achieve compact device sizes and maintain large 3 dB bandwidths, they exhibit undesirably high half-wave voltages compared to our design. A critical advantage of TFLN modulators on quartz substrates lies in their inherent potential for high-speed operation. While previous studies on quartz substrate modulators have achieved broad bandwidths exceeding 110 GHz, these modulators often require compromises between low driving voltage and device compactness. While the implementation in [21] requires 20 mm electrodes to achieve a 1.15 V half-wave voltage, our design attains a comparable 1.39 V half-wave voltage with electrodes that are half this length. As a result, the designed modulator achieves low-voltage operation while maintaining a smaller device size, which may make it a crucial part of large-scale photonic integrated circuits in the future. In addition, the proposed design provides a unique and practical solution for the integration of Si-LN hybrid waveguides and quartz substrates.

Compared to conventional TFLN modulators, the proposed modulator introduces an additional fabrication step, namely the deposition of amorphous BTO. The fabrication processes for BTO are relatively mature, with common preparation methods including RF magnetron sputtering [30], metal–organic chemical vapor deposition, and molecular beam epitaxy [31]. Amorphous BTO can be deposited by the RF magnetron sputtering method, and the sputtered BTO exhibits a relatively low refractive index (n_BTO = 1.85) at a wavelength of 1550 nm, thereby ensuring optical mode confinement within the LN waveguide core region. The required deposition temperature for amorphous BTO is relatively low, making it compatible with the pre-existing metal layers in the modulator [23,24]. Notably, this design eliminates BTO patterning processes, circumventing the inherent challenges of physical etching techniques [31] to simplify fabrication. Furthermore, by controlling the grain size and crystallinity, BTO layers with a relative permittivity ε ≥ 100 can be achieved, which could substantially reduce the V_π·L product of the device. Additionally, BTO with higher dielectric constants can be deposited through other processes, such as molecular beam epitaxy, which may further improve modulation efficiency, but there are still challenges in applying these processes to TFLN modulators. With advances in manufacturing technology, we believe that the proposed modulator structure can be easily fabricated in the future.

4. Conclusions

In summary, we propose a novel TFLN modulator on a quartz substrate, featuring an amorphous BTO cladding. This structure significantly enhances the electric field strength in the LN and increases the RF effective index of the modulator on a quartz substrate. By employing theoretical simulation, the BTO cladding structure was designed to minimize the V_π·L product while maintaining low optical loss. Additionally, the electrode structure was optimized to achieve impedance and index matching, and the 3 dB bandwidth of the designed modulator was calculated. We demonstrated a TFLN modulator with a 10 mm long device length, achieving a low half-wave voltage of 1.39 V and a wide 3 dB modulation bandwidth of 152 GHz. This theoretical model provides a novel design solution for TFLN modulators on quartz substrates, and has the potential to become a crucial part of large-scale photonic integrated circuits in the future.