High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire

Huangpu Han; Bingxi Xiang; Jiali Zhang; Zhixian Wei; Yunpeng Jiang

doi:10.1515/phys-2023-0178

Article Open Access

High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire

Huangpu Han , Bingxi Xiang , Jiali Zhang , Zhixian Wei and Yunpeng Jiang

Published/Copyright: January 24, 2024

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From the journal Open Physics Volume 22 Issue 1

Abstract

In this study, high-speed mid-infrared Mach–Zehnder electro-optical modulators in x-cut lithium niobate (LN) thin film on sapphire were designed, simulated, and analyzed. The main optical parameters of three types of Mach–Zehnder modulators (MZMs) (residual LN with thickness of 0, 0.5, and 1 μm) were simulated and calculated, namely, the single-mode conditions, bending loss, separation distance between electrode edge and lithium niobate waveguide edge, optical field distribution, and half-wave voltage–length product. The main radio frequency (RF) parameters of these three types of MZMs, such as characteristic impedance, attenuation constant, RF effective index, and the –3 dB modulation bandwidth were calculated depending on the dimensions of the coplanar waveguide traveling-wave electrodes. The modulations with residual LN thickness of 0, 0.5, and 1 μm were calculated with bandwidths exceeding 140, 150, and 240 GHz, respectively, and the half-wave voltage–length product achieved was 22.4, 21.6, and 15.1 V cm, respectively. By optimizing RF and optical parameters, guidelines for device design are presented, and the achievable modulation bandwidth is significantly increased.

Keywords: photonic integrated circuits; electro-optical; lithium niobate on sapphire; Mach–Zehnder modulators; mid-infrared

1 Introduction

Mid-infrared (mid-IR) photonic integrated circuits (PICs) have received increasing attention because of their applications in remote sensing [1], broadband optical communication [2,3], and defense technology [4]. With high performance, low operating cost, and compact footprint, mid-IR PICs offer the best prospect to meet the increasing demands for high data transmission capacity in communication systems [5,6]. Previous research in mid-IR PICs has utilized various silicon- and germanium-based platforms [7,8,9,10,11,12]. However, the absence of a linear E-O effect limits the application and development of silicon and germanium in high-speed optical signal modulation [13,14].

Lithium niobate (LiNbO₃, LN) thin film on sapphire (LNOS) is an option for E-O tunable mid-IR photonic devices, due to the following factors. First, LN has a high E-O coefficient (r ₃₃ = 30 pm/V at λ = 3.8 µm) in the mid-IR range [15], which enables highly efficient E-O modulation. Second, LNOS enables high-density PICs due to the high refractive index contrast between LN and sapphire. Third, the optical transmittance range of LNOS is greater than that of LN thin film on SiO₂ (LNOI) [16] because sapphire is transparent up to λ ≤ 4.6 µm and SiO₂ is opaque for λ > 3.6 µm [2].

Mach–Zehnder modulators (MZMs) are considered optimal because of their large optical bandwidth, high sensitivity, and high level of integration. Unlike microring optical modulators, the response speed of MZMs is not limited by the photon lifetime [17]. The reported high-speed MZMs have response speeds of more than 100 Gb/s at the near-infrared band [18,19,20,21]. MZMs played a crucial role in mid-IR PICs, enabling applications such as high-speed data transmission and sensitive gas sensing. Their versatility enhanced performance in mid-IR optical communication, sensing, and imaging.

In this study, we simulate, analyze, and evaluate mid-IR MZMs in LNOS with three types of waveguide structures. The mode calculation of the LNOS waveguides establishes their single-mode conditions, effective refractive indices, bending losses, and propagation losses with different separation distances between electrode edge and LN waveguide edge. The half-wave voltage–length products of the devices are also calculated. The major radio frequency (RF) parameters of such devices are calculated as a function of the coplanar waveguide electrode dimensions. At a wavelength of 3.8 μm, for MZMs with residual LN thickness of 0, 0.5, and 1 μm, the optimized bandwidths are 140, 150, and 240 GHz, respectively, and the optimized half-wave voltage–length products are 22.4, 21.6, and 15.1 V cm, respectively.

2 Device structure and methods

The physical structure of the device studied in this work was a 2 μm thick x-cut LN thin film bonded to a sapphire substrate. The schematic for this MZM is shown in Figure 1(a) and the cross-sectional schematic of the MZM is shown in the figure’s inset. The MZM consisted of the LN optical waveguides and the coplanar waveguide electrodes. The parameters of the LN optical waveguides and coplanar waveguide electrodes are denoted by the symbols, as shown in Figure 1(b). Three waveguide types with different residual LN thicknesses T were used in the MZMs and compared in Table 1. Type I had residual LN thickness T of 0 μm (i.e., total etching); Type II had residual waveguide thickness T of 0.5 μm; and Type III had residual thickness T of 1 μm. Within an MZM optical waveguide structure, a light beam propagates along a straight waveguide and gets divided into two light beams of equal intensity and phase via a symmetric Y-junction. After propagating through the parallel-arranged reference, the recombined light waves create an interference pattern. The RF transmission line employed in the E-O modulators had a symmetric coplanar waveguide electrode structure. The signal electrode was located between two MZM phase shifters. Ground electrodes were located beside the two phase shifters. On the two arms, opposite electric fields were applied to modify the refractive index of the LN, thus changing the phase of the wave propagating through those arms. Table 2 shows the refractive indices and dielectric constants of the materials in the subsequent simulation at a wavelength of 3.8 μm.

Figure 1

(a) Schematic of the MZM in x-cut LNOS. (Inset) The cross-sectional schematic of the MZM. (b) The parameters of the LN optical waveguide and coplanar waveguide electrode.

Table 1

Three types of waveguides with different residual LN thickness

Waveguide type	Residual LN thickness T (μm)
Type I	0
Type II	0.5
Type III	1

Table 2

Refractive indices and dielectric constants of the material in simulation (λ = 3.8 µm)

Material	Refractive index		Dielectric constant
Material	Ordinary refractive index (n _o)	Extraordinary refractive index (n _e)	Dielectric constant
LN [15]	2.122	2.063	28.4
Sapphire [22]	1.681		9.5

Based on a full-vectorial finite-difference (FVFD) method [23,24], the optical parameters were simulated using the commercial software “Lumerical: Mode Solutions.” The FVFD method calculated the frequency dependence and spatial profile by solving Maxwell’s equations on the waveguide cross-sectional grid, thus obtaining the effective refractive index, mode profile, and propagation loss. Based on a finite element method (FEM), the electric field distribution and RF parameters were simulated using the commercial software “Comsol Multiphysics” [25] and “High Frequency Structure Simulator (HFSS)” [26], respectively. The FEM is a numerical method for solving complex mathematical problems and a computational technique for approximate solutions to boundary value problems in engineering. The entire solution domain must be discretized into simply shaped subdomains, known as elements.

3 Results and discussion

The exploration of single-mode conditions was initiated due to several compelling advantages. First, it ensured that there was no energy transformation occurring between different modes, maintaining the integrity of the signal transmission. This absence of mode-to-mode energy conversion contributed to the overall efficiency of the optical waveguide system. Second, single-mode operation mitigated the potential signal distortion that could result from the simultaneous transmission of multiple modes at varying speeds. This distortion reduction was particularly crucial in maintaining the fidelity and quality of data transmission within the waveguide. Thus, the investigation into single-mode conditions not only enhanced the efficiency but also ensured the reliability of optical waveguide systems [27]. Single-mode ridge optical waveguides that also possess large cross-sectional dimensions were particularly desirable [28]. Consequently, a criterion should be determined for the dimensions of the waveguide to ensure single-mode propagation. To make full use of r ₃₃ in an x-cut LNOI, only the transverse electric (TE) mode was calculated in the following simulation. Figure 2(a) shows the cutoff dimensions of the three types of waveguides, with residual LN thickness T values of 0, 0.5, and 1 μm for the TE mode between the single- and multi-mode conditions at the wavelength of λ = 3.8 μm. These curves represent the smallest dimensions at which the corresponding mode disappears. As the width W increased, the height H decreased to maintain single-mode operation. At a given height H of the LN thin film, the width W of the LN waveguide should be less than this critical value to ensure that only one electric field intensity peak exists in the LN waveguide. At the same height H, the cutoff width of single-mode conditions decreased in the following order: Type III, Type I, and Type II. The cutoff width of mode disappeared in the following order: Type I, Type II, and Type III. Figure 2(b) shows the effective indices of the TE mode as a function of the waveguide width W (H = 2 μm) for residual waveguide thickness T values of 0, 0.5, and 1 μm, respectively. TE₀ and TE₁ represent the fundamental and first-order TE modes, respectively. As the width W increased, the TE₀ and TE₁ modes appeared gradually, and the effective refractive index increased. At the same width W, the effective refractive index decreased in the following order: Type III, Type II, and Type I. In the following simulation, the width W and height H of the three types of LN waveguides were set at 2.5 and 2 μm, respectively. The critical parameters are marked with stars in Figure 2(a) and (b).

$Figure 2 (a) Cutoff dimensions of the three types of waveguides for the TE mode as a function of width W and height H. (b) Effective refractive indices of the three types of waveguides for the TE mode as a function of the width W.$

Figure 2

(a) Cutoff dimensions of the three types of waveguides for the TE mode as a function of width W and height H. (b) Effective refractive indices of the three types of waveguides for the TE mode as a function of the width W.

Propagation losses of MZM are caused by the following three main factors: (1) electromagnetic fields leaking to the substrate during the light propagation, (2) radiation losses of the curved waveguide, and (3) metal-induced loss introduced by the electrode near optical waveguide [29]. The losses can be measured by using perfectly matched layer boundary conditions to absorb the radiation from the waveguide. In practical structures, the residual roughness of the waveguide etched surface causes scattering losses. Since the roughness of the etched surface is affected by the waveguide fabrication process, scattering losses are not considered in the simulations. Low bending loss is important for low power consumption devices. A small bending radius is also preferred to reduce the dimensions of the photonic devices. Figure 3 shows the relationship between the bending radius and bending loss at λ = 3.8 μm. As the bending radius decreased, the bending loss increased sharply. The bending loss was less than 0.1 dB/cm when the bending radius of the three types of waveguides with T values of 0, 0.5, and 1 μm was greater than 51, 75, and 290 μm, respectively.

Figure 3

Bending loss variation as a function of bending radius.

The separation distance S between the electrode edge and the waveguide edge greatly influenced the half-wave voltage–length product and modulation bandwidth of the MZM. The separation distance S was determined based on the propagation loss introduced by the electrode edge near the optical waveguide edge. Figure 4 shows the propagation loss with different separation distances S at the wavelength of 3.8 μm. As the separation distance S increased and the residual LN thickness decreased, the propagation loss decreased rapidly. At the same separation distance S, the propagation loss decreased in the following order: Type III, Type II, and Type I. To keep the transmission loss less than 0.1 dB/cm, the separation distance S of the three types of waveguides with residual LN thickness T values of 0, 0.5, and 1 μm was selected as 1.03, 3.88, and 5 μm, respectively, in the following simulation. These values are marked with circles in Figure 4.

Figure 4

Curves of the propagation loss and the separation distance S between the electrode edge and the LN waveguide edge.

The distributions of the electric field and optical mode of the LN waveguide were simulated. A voltage of 1 V is applied between electrodes [30,31], and the distribution of the direct current (DC) electric field around the three types of optical-modulating waveguides with residual LN thickness T values of 0, 0.5, and 1 μm, and separation distance S of 1.03, 3.88, and 5 μm is shown in Figure 5(a), (c), and (e), respectively. The electric field intensities at the center of the three types of waveguides with T values of 0, 0.5, and 1 μm were 33,464, 33,665, and 42,261 V/m, respectively. With the increase in the residual LN thickness, the electric field strength in the waveguide increased. The TE mode distributions in the optical-modulating waveguide with residual LN thickness T values of 0, 0.5, and 1 μm are shown in Figure 5(b), (d), and (f), respectively. Most of the optical power of the three waveguide types was confined within the LN core. Strong E-O interaction remained in the optical-modulating waveguide. Due to the existence of evanescent waves, a small part of the energy interacts with the Au electrode to produce a surface Plasmon effect. However, due to the weak interaction, the surface plasmon effect can be neglected [32,33].

Figure 5

Electrostatic field distribution of the three types of waveguides with residual LN thickness T values of (a) 0, (c) 0.5, and (e) 1 μm after a 1 V voltage was applied, and optical field distribution of the waveguide with residual LN thickness of (b) 0, (d) 0.5, and (f) 1 μm.

The change in the extraordinary refractive index of the LN film (Δn _e) after application of an electrostatic field is [34]

(1) Δ n e = − 1 2 n e 3 γ 33 E x ,

where E _x is the electric field component along the x direction.

Using the distribution of the DC electric field, the distribution of the refractive index of the LN waveguide was calculated using Eq. (1). The effective refractive index change (Δn _eff) of TE mode is the difference between effective refractive index with and without the applied voltage. Figure 6 shows Δn _eff at λ = 3.8 µm when E _x varies from 0 to 14 V/μm. The change in refractive index results in a phase shift Δφ given by the following equation [18,34]:

(2) Δ φ = 2 π λ Δ n eff L = Δ V V π π 2 ,

$Figure 6 The change in the effective refractive index Δn eff for a single waveguide under applied voltage.$

Figure 6

The change in the effective refractive index Δn _eff for a single waveguide under applied voltage.

where L is the interaction length in the optical-modulating waveguide, ΔV is the change in applied voltage, and V _π is the half-wave voltage. The half-wave voltage–length product (V _π ·L) of the three types of MZMs with residual LN thickness T values of 0, 0.5, and 1 μm were calculated to be 22.4, 21.6, and 15.1 V·cm, respectively.

Low voltage and wide broadband are essential for high signal quality E-O modulators. The electrode structure was designed to obtain high frequency performance. Figure 7 shows the RF properties simulated by HFSS as a function of electrode dimensions that are performed at 100 GHz. For each electrode height H _e, the width W _e of the signal electrode was first adjusted to ensure the characteristic impedance is 50 Ω at the frequency of 100 GHz. These curves are shown in Figure 7(a). A narrow signal electrode width requires greater thickness to achieve impedance matching. For each combination of electrode height H _e and width W _e, the RF effective mode index and RF attenuation of the coplanar waveguide electrode are further analyzed in Figure 7(b) and (c). The group index of the optical mode of the LN waveguide is also marked in Figure 7(c). For RF attenuation, the loss decreased as the electrode height H _e increased. The decrease in RF waveguide loss saturated when the electrode height H _e was larger than 0.6 μm. In the following simulation, considering the RF attenuation and matching the effective refractive indices with optical mode, the electrode height H _e of the three types of MZM with T values of 0, 0.5, and 1 μm were set at 1 μm, and the electrode width W _e was set at 4.3, 11.4, and 12.3 μm, respectively.

Figure 7

The curves between the signal electrode height and (a) electrode width, (b) RF attenuation α _m, and (c) RF effective mode index n _m of the coplanar waveguide electrode, when the real part of the characteristic impedance was kept at 50 Ω.

The RF E-O frequency response m(ω) can be modeled as [35] follows:

(3) m ( ω ) = R L + R G R L Z in Z in + Z G × ( Z L + Z 0 ) F ( u + ) + ( Z L − Z 0 ) F ( u − ) ( Z L + Z 0 ) e γ m L + ( Z L − Z 0 ) e − γ m L ,

where R _L and R _G are the load and generator resistances, respectively. Here Z _in is the modulator input impedance.

(4) Z in = Z 0 Z L + Z 0 tanh ( γ m L ) Z 0 + Z L tanh ( γ m L ) ,

where Z _G and Z _L are the generator and load impedance, Z ₀ is the characteristic impedance, F ( u ± ) = ( 1 − e u ± ) / u ± , where u ± = ± α m L + j ω ( ± n m − n g ) L / c 0 , and γ m = α m + j ω n m / c 0 is the propagation constant. Here n _m and α _m are the RF effective mode index and RF attenuation, the unit of α _m is Np/cm, and 1 Np/cm equals 8.68 dB/cm. We assume R _L = R _G = Z _G = Z _L = 50 Ω. The modulation bandwidth is then determined by the RF properties (Z ₀, α _m, and n _m) and the optical group index n _g.

Figure 8(a) shows the characteristic impedance Z ₀ of three types of MZM at frequencies 0–300 GHz. The Z ₀ range of the Type I MZM was from 50 to 65 Ω, and the other two types MZMs ranged from 50 to 55 Ω. Figure 8(b) shows α _m for the three types of MZM. At frequencies from 0 to 300 GHz, α _m for Type I MZM ranged from 5 to 31 dB/cm, and the other two types of MZM had similar ranges, from 1 to 14 dB/cm. Figure 8(c) shows the RF effective index n _m at frequencies 0–300 GHz. The optical effective indices n _g at λ = 3.8 μm are marked in Figure 8(c) for comparison. Figure 8(d) shows the E-O frequency response m(ω) at frequencies 0–300 GHz. The modeled bandwidths (−3 dB) of the three types of MZM with residual LN thicknesses T values of 0, 0.5, and 1 μm exceed 140, 150, and 240 GHz, respectively.

Figure 8

(a) Characteristic impedance Z ₀, (b) RF attenuation α _m, (c) RF effective mode index n _m, and (d) modulation response m(ω) vs RF frequency.

In Table 3, we compare the V _π ·L and bandwidths of the mid-IR MZMs based on different platforms. Clearly, the present device featured the best modulation bandwidth compared among others, and to the best of our knowledge. This characteristic made the present device suitable for applications in large capacity switched optical networks. The demonstrated LNOS platform could become a paradigm for building compact and high-performance E-O modulators, providing a crucial advantage for future ultra-fast mid-IR optical communication.

Table 3

Comparison of different types of MZM modulators in the mid-IR band

Modulator type	Wavelength (μm)	V _π·L (V cm)	Bandwidth (GHz)	References
Si-on-LN	3.39	26	70	[36]
Si-on-SiO₂	2.165	0.012	/	[37]
Si-on-SiO₂	2	0.45	9.7	[38]
Ge-on-Si	3.8	0.47	0.06	[39]
LN-on-Sapphire (Type I)	3.8	22.4	140	This work
LN-on-Sapphire (Type II)	3.8	21.6	150	This work
LN-on-Sapphire (Type III)	3.8	15.1	240	This work

4 Conclusion

We demonstrated mid-IR MZMs with high-performance on LNOS. Additionally, the width W and height H of the ridge waveguides were optimized to 2.5 and 2 μm, respectively. The separation distance S between the electrode edge, as well as the waveguide edge and the bending loss were analyzed in detail. The characteristic impedance, RF effective mode index, and RF attenuation of the coplanar waveguide electrode were systematically simulated. For the three types of MZM with residual LN thickness T values of 0, 0.5, and 1 μm, the −3 dB bandwidths were calculated to beyond 140, 150, and 240 GHz, and the values of V _π ·L were calculated to be 22.4, 21.6, and 15.1 V cm, respectively. The LNOS platform resided within the realm of compact and high-performance electro-optic modulators, catering to the needs of ultra-fast mid-IR optical communication systems. Its exceptional bandwidth capabilities firmly established it as an essential resource to meet the burgeoning demands of data-intensive applications. These applications spanned across various fields, including modulation spectroscopy [40], rapid medical diagnostics [41], and free-space communication [42], where its contributions were poised to make a significant impact.

Funding information: This work was supported by the National Natural Science Foundation of China (12105190), the Shenzhen Science and Technology Planning (NO. JCYJ20190813103207106).
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: The authors state no conflict of interest.

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Received: 2023-08-27

Revised: 2023-10-16

Accepted: 2024-01-02

Published Online: 2024-01-24

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/phys-2023-0178

Keywords for this article

photonic integrated circuits; electro-optical; lithium niobate on sapphire; Mach–Zehnder modulators; mid-infrared

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