High-Speed Terahertz Modulation Signal Generation Based on Integrated LN-RMZM and CPPLN

Abstract

With the increasing communication frequencies in 6G networks, high-speed terahertz (THz) modulation signal generation has become a critical research area. This study first proposes an on-chip high-speed THz modulation signal generation system based on lithium niobate (LN), which integrates a pair of racetrack resonator-integrated Mach–Zehnder modulators (RMZMs) with a chirped periodically poled lithium niobate (CPPLN) waveguide. The on-chip system combines near-infrared electro-optic modulation and cascaded difference-frequency generation (CDFG) for high-speed THz modulation signal generation. At 300 K, utilizing two input optical waves at frequencies of 193.55 THz and 193.14 THz, this on-chip system enables high-speed THz modulation signal generation at 0.41 THz, with a 1 Gbit/s modulation rate and a 0.25 V modulation voltage. During the simulation, when the intensity of the input optical waves is 1000 MW/cm², the generated 0.41 THz signal reaches a peak intensity of 21.24 MW/cm². Furthermore, based on theoretical analysis and subsequent simulation, the on-chip system is shown to support a maximum modulation signal generation rate of 7.75 Gbit/s. These results demonstrate the potential of the proposed on-chip system as a compact and efficient solution for high-speed THz modulation signal generation.

1. Introduction

Electromagnetic waves have become the primary medium for modern information transmission. Within the electromagnetic spectrum, THz waves spanning 0.1–10.0 THz exhibit high penetration, low photon energy, and strong potential for high-speed wireless communication [1,2,3,4,5,6]. These properties make THz waves promising for advanced 6G communication and precision detection technologies [7,8,9,10,11,12,13]. Therefore, developing efficient THz modulation signal generation techniques is essential for the practical implementation of THz systems across various fields.

However, current THz modulation signal generation technologies face constraints due to the large physical size of conventional systems and the inherent limitations of modulation materials, such as low electro-optic efficiency and poor phase-matching characteristics [14,15,16]. These challenges arise from the long wavelengths of THz waves, which often require bulky and complex architectures [14]. In particular, state-of-the-art THz modulation signal generation approaches based on artificial electromagnetic metamaterials are unsuitable for on-chip integration, as they function as spatial light modulators. These approaches also face challenges, including complex structural designs, high fabrication costs, and significant insertion losses [15,16]. In contrast, on-chip THz modulation signal generation systems offer enhanced integrability but currently exhibit critical limitations. Key challenges include high modulation voltages (>6 V), limited modulation capability to kHz-range electrical signals, and relatively low generated THz signal intensity [17,18,19,20,21]. These limitations impede the widespread deployment of practical THz modulation signal generation technologies.

To address these challenges, this study first proposes an on-chip high-speed THz modulation signal generation system, which integrates near-infrared electro-optic modulation with CDFG. This on-chip system is based on LN, a material known for its high electro-optic coefficient and low optical loss [22,23]. Specifically, the proposed on-chip system consists of a pair of near-infrared RMZMs and a CPPLN waveguide. Each RMZM employs a resonator to reduce the modulation voltage. Meanwhile, the CPPLN waveguide optimizes the phase-matching conditions for CDFG, enhancing the THz signal generation intensity. At 300 K, utilizing two input optical waves at frequencies of 193.55 THz and 193.14 THz, this on-chip system enables high-speed THz modulation signal generation at 0.41 THz, with a 1 Gbit/s modulation rate and a 0.25 V modulation voltage. When the intensity of the input optical waves is 1000 MW/cm², the generated 0.41 THz signal reaches a peak intensity of 21.24 MW/cm². Theoretical analysis indicates that the maximum modulation signal generation rate supported by the on-chip system is 7.75 Gbit/s.

2. Materials and Methods

The proposed on-chip THz modulation signal generation system, depicted in Figure 1a, incorporates a compact architecture, enabling high-speed THz modulation signal generation. This on-chip system consists of two functional modules: an electro-optic modulation unit based on RMZM and a CDFG unit based on CPPLN. In the electro-optic modulation stage, two co-polarized optical waves with closely spaced frequencies (${\omega }_1=193.55\mathrm{T}\mathrm{H}\mathrm{z}$, ${\omega }_2=193.14\mathrm{T}\mathrm{H}\mathrm{z}$) are injected into separate RMZMs. Under applied voltages, the RMZMs modulate the incident optical waves. The modulated optical waves are then coupled into the CPPLN waveguide. Here, the chirped poling period compensates for the phase mismatch between cascaded optical frequency components, enabling efficient THz signal (${\omega }_T={\omega }_1-{\omega }_2=0.41\mathrm{T}\mathrm{H}\mathrm{z}$) generation. This on-chip system enables the generation of modulated THz signals by indirectly modulating two input near-infrared optical waves.

2.1. Electro-Optic Modulation

To minimize on-chip system footprint and power consumption [24,25], this study employs an RMZM architecture for the electro-optic modulation unit, as shown in Figure 2a. The RMZM is implemented on a x-cut thin-film LN layer integrated into a LN-on-insulator platform. The design parameters of the RMZM include a microring radius of 4 mm and a modulation length of 2 cm, the gap of the electrode is 1.8 um. The RMZM enables electro-optic modulation by dynamically tuning the coupling state of the racetrack resonator through an applied voltage $V_f$.

First, under critical coupling conditions (Figure 2b), the input optical wave is almost completely absorbed by the resonator, resulting in near-zero transmission at the resonant wavelength. Upon application of a control voltage, the RMZM is progressively tuned from critical coupling to the zero-coupling regime (Figure 2c), where decoupling of the optical field between the bus waveguide and the racetrack resonator eliminates resonant interactions.

The integrated Mach–Zehnder interferometer operates in a push–pull configuration with complementary phase modulation in its dual arms, enabling rapid suppression of optical transmission through voltage reversal. The applied voltage induces refractive index modulation in the LN waveguide, dynamically altering the resonator coupling conditions. As shown in Figure 3, at $V_f=0.25\mathrm{V}$, the RMZM enables zero-coupling operation with nearly 100% transmission efficiency; at $V_f=0\mathrm{V}$, the RMZM establishes critical coupling with nearly 0% transmission. With a modulation length of 2 cm, the electro-optic modulation section gets a $V_{\pi }\cdot L$ of 0.5 V·cm.

2.2. CDFG of THz Signals

Following electro-optic modulation, the two modulated optical waves are coupled into a shared CPPLN waveguide, enabling the generation of a 0.41 THz difference-frequency signal. As depicted in Figure 4, the CDFG process begins with two input optical waves at frequencies ${\omega }_1$ and ${\omega }_2$. Through sequential nonlinear interactions, these optical waves generate a series of progressively downshifted optical waves. At each cascaded stage, a frequency difference corresponding to the target THz signal is produced (${\omega }_T={\omega }_1-{\omega }_2$, ${\omega }_T={\omega }_3-{\omega }_4$), with each new wave inheriting the THz frequency offset from its adjacent stages (${\omega }_3={\omega }_2-{\omega }_T$, ${\omega }_4={\omega }_3-{\omega }_T$, ${\omega }_5={\omega }_4-{\omega }_T$).

In this process, photons from preceding stages interact to generate a new photon with a frequency reduced by ${\omega }_T$, enabling cumulative energy transfer across stages. This mechanism amplifies the energy of the target THz signal, ultimately yielding a high-energy THz signal with enhanced conversion efficiency. In contrast, conventional difference-frequency generation (DFG) schemes (First stage in Figure 4) rely on single-pass nonlinear conversion, theoretically limited by the Manley–Rowe efficiency limits [26].

The cascaded nonlinear interactions necessitate strict adherence to frequency and wave vector matching conditions for all participating optical fields during the parametric conversion process:

$${\omega }_{m+1}={\omega }_m-{\omega }_T,$$

(1)

$${\omega }_T={\omega }_m-{\omega }_{m+1},$$

(2)

$$\mathrm{\Delta }{k}_m=k_m-k_{m+1}-k_T,$$

(3)

where ${\omega }_i$ and $k_i$ represent the frequency and wave vector of the cascaded optical waves, respectively. The subscript m denotes the cascaded optical sequence, ${\omega }_T$ represents the frequency of the THz signal generated by the DFG process, $\mathrm{\Delta }k$ represents the phase mismatch.

To compensate for the phase mismatch $\mathrm{\Delta }k$ caused by dispersion, a fixed-period PPLN structure is conventionally employed to introduce a wave vector $k_{\mathrm{\Lambda }}=\mathrm{\Delta }k$, ensuring momentum conservation. As the cascaded order increases, the frequency of cascaded optical waves decreases while phase mismatch accumulates. Fixed-period poling structures cannot compensate for higher-order phase mismatch, leading to frequency upconversion and reduced THz signal conversion efficiency [16]. To address this issue, we employ a CPPLN structure with spatially changing poling periods, as shown in Figure 5a. This variation in poling period introduces a polarization inversion wave vector that sequentially compensates for the phase mismatch values across each stage of the CDFG process.

The calculation formula for the changing poling periods ${\mathrm{\Lambda }}_N$ of CPPLN waveguide material is given by [27]:

$${\mathrm{\Lambda }}_N\left(z\right)={\displaystyle \frac{c}{-n_{z\times \raisebox{1ex}{$\mathrm{N}$}\!\left/ \!\raisebox{-1ex}{$L$}\right.}+L\times {\omega }_{z\times \raisebox{1ex}{$\mathrm{N}$}\!\left/ \!\raisebox{-1ex}{$L$}\right.}+n_{z\times \raisebox{1ex}{$\mathrm{N}$}\!\left/ \!\raisebox{-1ex}{$L$}\right.+1}\times {\omega }_{z\times \raisebox{1ex}{$\mathrm{N}$}\!\left/ \!\raisebox{-1ex}{$L$}\right.+1}+n_T\times {\omega }_T}}$$

(4)

where N represents the number of cascaded stages, and L denotes the maximum waveguide length. The changing poling periods ${\mathrm{\Lambda }}_N$ introduces a quasi-phase-matching (QPM) wavevector $k_{\mathrm{\Lambda }}$, as illustrated in Equation (5):

$$k_{\mathrm{\Lambda }}\left(z\right)={\displaystyle \frac{2\mathrm{\pi }}{{\mathrm{\Lambda }}_N\left(z\right)}},$$

(5)

Through chirped poling, CPPLN dynamically adjusts the QPM wavevector $k_{\mathrm{\Lambda }}$, enabling effective phase-mismatch compensation for $\mathrm{\Delta }{k}_{\mathrm{m}}$ at each stage. This phase-mismatch compensation mechanism is one of the key advantages of CPPLN over fixed-period PPLN, especially for THz generation via the CDFG process.

Figure 5b shows the change of the CPPLN poling period along the waveguide length. The total length of the CPPLN waveguide is 6 mm. As the optical waves propagate through the waveguide, the poling period changes gradually from 225.42 μm at the waveguide position z = 0 mm to 225.18 μm at z = 6 mm.

In the CDFG process, the propagation of each cascaded optical wave within the waveguide is governed by the interaction between the electromagnetic field and the internal polarization field, as described by the coupled wave equations [26]:

$${\displaystyle \frac{d{E}_T}{dz}}=-{\displaystyle \frac{{\alpha }_T}{2}}{E}_T+j{\kappa }_T{\displaystyle \sum _{-\infty }^{\infty }{E}_m}{E}_{m+1}^{*}{e}^{j\mathrm{\Delta }{k}_{m}z}$$

(6)

$${\displaystyle \frac{d{E}_m}{dz}}=-{\displaystyle \frac{{\alpha }_m}{2}}{E}_m+j{\kappa }_m\left[E_{m-1}{E}_T^{*}{e}^{j\mathrm{\Delta }{k}_{m-1}z}+E_{m+1}{E}_T{e}^{-j\mathrm{\Delta }{k}_{m}z}\right]$$

(7)

where $E$ represents the electric field strength, $\alpha$ is the absorption coefficient, $\kappa$ denotes the coupling coefficient between the optical wave and the waveguide, and $z$ signifies the propagation distance of the optical wave within the waveguide. $dE/dz$ indicates the spatial variation of the electric field $E$ of frequency ${\omega }_T$ or ${\omega }_m$ passing through the nonlinear crystal. The first term on the right side of Equation (6) represents the material absorption of the THz wave at the frequency ${\omega }_T$, and the second term describes the nonlinear interaction between the optical waves at frequencies ${\omega }_m$ and ${\omega }_{m+1}$, which generates the THz wave at frequency ${\omega }_T$ in the CDFG process. The first term on the right side of Equation (7) signifies the material’s absorption of near-infrared waves at frequencies ${\omega }_m$ and ${\omega }_{m+1}$ during the cascaded process, while the second terms indicate the nonlinear interactions among the cascaded optical waves at frequencies ${\omega }_m$, ${\omega }_{m+1}$ and ${\omega }_T$.

The calculation formulas for the coupling coefficients ${\kappa }_m$ and ${\kappa }_T$ are presented below [26]:

$${\kappa }_i={\displaystyle \frac{{\omega }_i{d}_{eff}}{c\cdot n_i}},$$

(8)

where i represents T or m, which correspond to the THz and near-infrared waves, respectively. $d_{eff}$ is the effective nonlinear coefficient of the crystal, $n_i$ denotes the refractive index at the corresponding optical frequency, and $c$ is the speed of light in vacuum.

This work employs a magnesium oxide-doped chirped periodically poled lithium niobate (MgO:CPPLN) crystal for CDFG process. In such lithium niobate-based applications, temperature directly affects the terahertz absorption coefficient ${\alpha }_T$. In this work, the system is set to operate at 300 K, corresponding to room-temperature conditions. Previous studies have shown that decreasing the temperature can significantly reduce the terahertz absorption coefficient of lithium niobate [17]. This reduction would lower propagation losses within the CPPLN waveguide in the on-chip system, thereby enhancing the overall conversion efficiency.

Based on its Sellmeier dispersion equation [28], the refractive indices at 300 K are calculated as $n_m\approx 2.14$ for the near-infrared band and $n_T\approx 5.20$ for the 0.41 THz band [29,30]. The absorption coefficients at cascaded optical frequencies and the THz frequency are about 0 cm⁻¹ and 16 cm⁻¹ at 300 K [31,32]. The nonlinear coefficient of MgO:CPPLN at 0.41 THz is 336 pm/V [33].

The calculation formulas for the intensity of the generated THz wave and the energy conversion efficiency $\eta$ are given by Equations (8) and (9) [26]:

$$I={\displaystyle \frac{1}{2}}nc{\epsilon }_0|E_T{|}^2,$$

(9)

$$\eta ={\displaystyle \frac{n_T|E_T\left({\omega }_T,x\right){|}^2}{{\displaystyle \sum _{-\infty }^{+\infty }{n}_{\mathrm{m}}|E_{\mathrm{m}}\left({\omega }_{\mathrm{m}},0\right){|}^2}}},$$

(10)

where ${\epsilon }_0$ is the vacuum permittivity.

In the ideal CDFG process, which disregards material absorption and coupling losses, the impact of the signal wave intensity ratio $I_{{\omega }_1}:I_{{\omega }_2}$ on THz energy conversion efficiency is demonstrated in Figure 6a. The ideal energy conversion efficiency for THz wave generation peaks when $I_{{\omega }_1}:I_{{\omega }_2}=1:1$. Consequently, this on-chip system employs two equal-power optical waves modulated by the RMZMs for the CDFG process.

As shown in Figure 6b, in the CPPLN waveguide specifically designed for the CDFG process, the conversion efficiency increases with the waveguide length, reaching a maximum of 3.5% at 6 mm. This result demonstrates an improvement in conversion efficiency from 0.33% in conventional single-stage DFG approaches [26] and 1.8% in previous CDFG schemes based on 6 mm PPLN [34] to 3.5%, which confirms the cumulative advantage of the CPPLN-based CDFG scheme. For the on-chip THz modulation signal generation system, due to the existing losses in various components, the total conversion efficiency will be lower than 3.5%.

3. Results

Based on the RMZM and CPPLN, an on-chip THz modulation signal generation system is constructed. Its performance is evaluated through a simulation model, as illustrated in Figure 7. Initially, two optical waves with frequencies of 193.55 THz and 193.14 THz are passed through a polarization controller to adjust their polarization states. They are then amplified by an erbium-doped fiber amplifier (EDFA) before being injected into the on-chip system. Under the application of a modulation voltage signal $V_f$, the RMZM modulators perform high-speed electro-optic modulation on the two input optical waves (${\omega }_A$ and ${\omega }_B$). The modulated signals (${\omega }_1$ and ${\omega }_2$) are subsequently coupled into a CPPLN waveguide via a Y-branch structure, enabling the generation of a 0.41 THz modulated signal (${\omega }_T$) through the cascaded difference-frequency generation process. Finally, the system output is characterized using both an optical spectrum analyzer (OSA) and an electronic spectrum analyzer (ESA).

As shown in Figure 8a, the applied modulation voltage signal is an electrical pulse signal with an amplitude of 0.25 V. When the voltage changes from 0.25 V to 0 V, the racetrack resonator transitions from the zero-coupling state to the critical coupling state, causing the generated THz modulation signal to rapidly decrease to zero. Conversely, when the voltage changes from 0 V to 0.25 V, the racetrack resonator returns to the zero-coupling state, allowing the generated THz modulation signal to reach its peak intensity.

Figure 8b illustrates the temporal waveform of the generated THz electric field under 1 Gbit/s electrical modulation, clearly tracking the variation of the applied modulation voltage signal. Figure 8c shows the generated THz signal spectrum, which exhibits a distinct main peak and symmetrically distributed sidebands near 0.41 THz. The absence of significant spurious components or noise interference confirms high signal purity at the target terahertz frequency. During the simulation, the maximum output intensity reached 21.24 MW/cm², while the minimum was 4.045 × 10⁻³⁸ MW/cm², resulting in a calculated modulation depth close to 100%.

During the CDFG process within the CPPLN waveguide, the propagation velocity of optical waves results in an additional delay in the generated THz modulation signal. At $t_1=L/(c/n_m)=42\mathrm{ps}$, the modulated optical waves reach the waveguide exit, initiating the generation of a modulated THz signal. At a temperature of 300 K and an input optical intensity of 1000 MW/cm² for both optical waves, the on-chip system experiences a delay of approximately 50 ps. This delay is due to the combined effects of various system components. Consequently, the on-chip system generates a modulated THz signal with a peak intensity of 21.24 MW/cm², as shown in Figure 8d.

The maximum modulation signal generation rate $v$ supported by the on-chip system is inversely proportional to the total response time T, which can be expressed as:

$$v={\displaystyle \frac{1}{T}},$$

(11)

$$T=t_{re}+t_s,$$

(12)

where $t_{re}$ is the material response time, and $t_s$ is the stabilization time of the on-chip system.

Simulation results for the stabilization time of the on-chip system are shown in Figure 8d, indicating a stabilization time of 129 ps. Considering the fast response time (<1 ps) of the electro-optic effect in LN [35], the material response time is negligible; thus, the total response time of the on-chip system is approximately 129 ps. This stabilization time mainly includes the time required for the modulation process to stabilize and the build-up time of the THz cascaded difference-frequency generation process. Consequently, the maximum modulation signal generation rate supported by this on-chip system is calculated to be 7.75 Gbit/s according to Equation (11). Figure 9a illustrates the temporal waveform of the generated THz electric field at a 7.75 Gbit/s modulation rate. Figure 9b presents the generated THz signal spectrum at the same rate, exhibiting a pronounced peak at 0.41 THz. This result indicates that the on-chip system can support a maximum modulation signal generation rate of 7.75 Gbit/s. The simulation results indicate that the on-chip system supports a maximum modulation rate of 7.75 Gbit/s.

Compared to existing THz generation systems, the LN-based system offers distinct advantages for on-chip integration. While Si-based systems benefit from mature fabrication processes, they are constrained by high power consumption and limited modulation rates [17]. III–V semiconductor-based systems suffer from significant optical losses and integration challenges [36]. In contrast, the LN-based on-chip system combines a high electro-optic coefficient, strong nonlinear efficiency, and low optical loss, supporting high-speed modulation signal generation under low-voltage operating conditions. In addition, the current system is a single-frequency THz generation system, focused on the commonly used 0.41 THz signal in the THz communication window. By altering the input optical frequency and optimizing the structural parameters of the corresponding system components, the system can be adapted to generate signals at different frequency bands. Furthermore, the system architecture can be extended to support multi-frequency outputs by incorporating multi-wavelength inputs and parallel CPPLN waveguide arrays. This extension would enable broader spectral coverage and greater flexibility in THz modulation signal generation, addressing the demands of future multi-carrier THz communication systems. In practical applications, scaling the on-chip system to high-power operation may introduce challenges such as thermal effects caused by high input optical intensities. These thermal effects could affect the stability of the refractive index, the terahertz absorption coefficient, and phase-matching conditions. Additionally, achieving the designed poling periods of the CPPLN structure with high precision remains a fabrication challenge, particularly for long waveguides. These challenges can be addressed by incorporating additional thermal control modules and employing high-precision lithography techniques.

4. Conclusions

This study first proposes an on-chip THz modulation signal generation system that integrates RMZMs with a CPPLN waveguide. The on-chip system reduces the required modulation voltage and enhances THz signal intensity, while enabling high-speed THz modulation signal generation. Driven by two input optical waves at 193.55 THz and 193.14 THz, this on-chip system generates a modulated THz signal at 0.41 THz, with a 1 Gbit/s modulation rate and a 0.25 V modulation voltage. At an input optical wave intensity of 1000 MW/cm² and a temperature of 300 K, the generated THz signal intensity reaches 21.24 MW/cm². According to theoretical analysis, the maximum modulation signal generation rate supported by the on-chip system is 7.75 Gbit/s. In summary, the proposed on-chip system provides a compact and efficient solution for THz modulation signal generation. It shows strong potential for future applications in high-speed communication, real-time imaging, and integrated THz photonics.