Research Team Collaborates to Fabricate High-Speed Mach-Zehnder Modulators Based on Nonlinear Optics and Complex Band Structures

Research Background 

High-speed optical modulators are core components in modern high-capacity optical communications, massively parallel computing, and photonic artificial intelligence. Among them, traveling-wave Mach-Zehnder modulators (TW-MZMs) are widely used due to their advantages of high speed, high efficiency, and low thermal sensitivity, and have been realized on various integrated material platforms such as silicon and lithium niobate. However, existing design and simulation methods for TW-MZMs heavily rely on electrical characteristic models of specific materials (e.g., the nonlinear I-V relationship of silicon p-n junctions, the Kubo formula for graphene, etc.), inevitably requiring the construction of complex equivalent circuit models. These models not only differ significantly but also suffer from drastically reduced simulation efficiency, difficult-to-guarantee accuracy, and enormous computational consumption as modulator length increases and modulation speeds rise (towards millimeter-wave and terahertz bands), becoming a major bottleneck for the development of high-performance modulators.

Research Highlights

The core innovation of this work lies in proposing a novel design theory and simulation framework, achieving three key breakthroughs. First, it realizes a paradigm shift from circuit models to an electromagnetic-wave perspective: Abandoning traditional circuit models, it innovatively treats the TW-MZM as a "nonlinear radio-frequency subwavelength grating waveguide" (Figs.1 a-d). This perspective based on Maxwell's equations can naturally incorporate material dispersion and nonlinear effects, offering high universality and applicability to various platforms including silicon, lithium niobate, lithium tantalate, III-V semiconductors, electro-optic polymers, and even two-dimensional materials. Second, it pioneers the introduction of complex band structure theory into the RF design domain: This theory, originally used to analyze optical modes in photonic crystals, is applied in this study to analyze RF modes in periodic T-shaped RF electrodes. By solving the eigenmodes of the electrode unit cell, key parameters determining modulator bandwidth (RF phase refractive index, group refractive index, impedance, loss) can be obtained directly and efficiently. For example, for a 500 GHz lithium niobate modulator, this method can increase electrode simulation speed by over a hundredfold (compared to traditional methods requiring simulation of a 1000 μm long electrode). Third, it establishes a unified model based on nonlinear optics: Using nonlinear optics theory, temporal coupled-mode equations are constructed to describe the nonlinear interaction between RF waves (pump) and optical waves (signal). For silicon-based p-n junction modulators, this method cleverly replaces the complex p-n junction I-V equation description with an equivalent nonlinear RF material model, avoiding time-consuming convolution calculations and thereby enabling high-speed optoelectronic co-simulation.

The research team completed the entire design and simulation process for both silicon and lithium niobate TW-MZMs. A silicon photonic modulator was fabricated through a commercial silicon photonics foundry process (Figs.1 e-h), and comprehensive experimental validation, including eye diagram measurements, was performed. The results show excellent agreement between simulation and experiment, strongly proving the accuracy and reliability of the method.

Fig. 1. (a, c) Cross-section of Si and LiNbO₃ TW-MZMs; (b, d) Schematic and layout of Si and LiNbO₃ TW-MZMs; (e) Optical microscope image of a Si TW-MZM; (f-h) Magnified views of the Si TW-MZM.

Conclusion and Outlook 

The novel perspective based on nonlinear optics and complex band structures presented in this work opens an efficient, accurate, and universal path for the design and simulation of high-speed TW-MZMs. Its all-electromagnetic-wave model fundamentally overcomes the limitations of traditional circuit models, achieving unification of the design process and a leap in simulation efficiency. Experimental validation fully demonstrates the successful application of this method on mainstream silicon and lithium niobate platforms. With the maturity of high-frequency electrode design (>500 GHz) and optoelectronic co-simulation technology, this method lays a solid technical foundation and provides a feasible technical route for developing high-performance photonic integrated devices for future high-speed millimeter-wave and terahertz applications (e.g., 6G communications, ultra-high-speed computing, quantum systems). Its core concept based on all-electromagnetic-wave simulation and modeling will also strongly promote deep synergy and convergence between electronics and photonics.

Publication

High-speed Mach-Zehnder modulators based on nonlinear optics and complex band structures,  Physical Review Applied  24, 014021 (2025). Original link: https://doi.org/10.1103/f5v4-n5dw