Perspective of high-speed Mach-Zehnder modulators based on nonlinear optics and complex band structures

Abstract: Optical modulators are essential building blocks for high-capacity optical communication and massively parallel computing. Among all types of optical modulators, travelling-wave Mach-Zehnder modulators (TW-MZMs) featuring high speed and efficiency are widely used, and have been developed on a variety of integrated material platforms. Existing methods to design and simulate TW-MZMs so far strongly rely on the peculiar material properties, and thus inevitably involve complicated electrical-circuit models. As a result, these methods diverge significantly. In addition, they become increasingly inefficient and inaccurate for TW-MZMs with extending length and levitating modulation speed, posing formidable challenges for millimeter-wave and terahertz operation. Here, we present an innovative perspective to understand and analyze high-speed TW-MZMs. Our perspective leverages nonlinear optics and complex band structures of RF photonic crystals, and is thus entirely electromagnetic-wave-based. Under this perspective, we showcase the design, optoelectronic simulation and experimental validation of high-speed TW-MZMs based on Si and LiNbO$_3$, and further demonstrate unambiguous advantages in simplicity, accuracy and efficiency over conventional methods. Our approach can essentially be applied to nearly any integrated material platform, including those based on semiconductors and electro-absorption materials. With high-frequency electrode designs and optoelectronic co-simulation, our approach facilitates the synergy and convergence of electronics and photonics, and offers a viable route to constructing future high-speed millimeter-wave and terahertz photonics and quantum systems.

• The paper introduces a novel perspective by applying nonlinear optics and complex band structures to simulate travelling-wave Mach-Zehnder modulators, achieving bandwidths exceeding 500 GHz.
• The paper employs finite-element and Bloch’s theorem methods to generate complex band structures for RF photonic crystals, significantly accelerating simulation speeds.
• The paper validates the design through experimental CMOS-based Si fabrication and optoelectronic co-simulation, demonstrating high extinction ratios and quality factors.

Perspective of High-Speed Mach-Zehnder Modulators Based on Nonlinear Optics and Complex Band Structures

Abstract and Introduction

The paper "Perspective of high-speed Mach-Zehnder modulators based on nonlinear optics and complex band structures" (2502.14386) introduces a novel perspective to analyze travelling-wave Mach-Zehnder modulators (TW-MZMs) by leveraging nonlinear optics and complex band structures of RF photonic crystals. This approach diverges from traditional electrical-circuit-based methods, enabling simpler and more accurate simulations applicable to various integrated material platforms. TW-MZMs are crucial for optical communication, quantum information processing, and photonic computing. The discussed methodology potentially facilitates future developments in high-speed, millimeter-wave, and terahertz photonics systems.

Theoretical Framework and Design Process

The research reconceptualizes TW-MZMs from an electromagnetic perspective, regarding RF electrodes as periodic sub-wavelength grating waveguides, naturally addressing RF waveguide dispersion and eliminating complex convolution calculations. The nonlinear interaction between RF and optical waves is modeled with temporal coupled-mode equations (TCME), incorporating self-phase modulation (SPM) and cross-phase modulation (XPM). The paper showcases a unified design and simulation process for TW-MZMs using silicon (Si) and lithium niobate (LiNbO$_3$).

Figure 1: Schematics, layouts, and design process of Si and LiNbO$_3$ TW-MZMs.

Simulation Method and Complex Band Structures

The paper presents a simulation method based on complex band structures (CBS) of RF photonic crystals. Utilizing finite-element methods and Bloch’s theorem, the RF vector wave equation is solved in the weak-form, generating CBS for periodic T-shaped RF electrodes. This process significantly accelerates simulation speeds for LiNbO$_3$ TW-MZMs, achieving up to 500 GHz bandwidth.

Figure 2: Simulation models of periodic T-shaped RF electrodes for Si and LiNbO$_3$ TW-MZMs.

Figure 3: Simulation results indicating RF wave parameters across different frequencies and voltages.

Optoelectronic Co-Simulation

The research further describes an optoelectronic co-simulation framework for calculating TCME, streamlining complexity by obviating computationally heavy PN junction I-V equations. This approach reliably predicts the performance of TW-MZMs by modeling RF and optical wave interactions.

Figure 4: Optoelectronic co-simulation approach to solve TCME.

Experimental Validation and Results

The study provides experimental validation through Si TW-MZM fabrication using CMOS technology, including eye-diagram measurements under varying propagation configurations. Both simulated and experimental results demonstrate concordance in extinction ratio (ER) and quality factor (Q) metrics, confirming the method's accuracy.

Figure 5: Experimental setup and simulation flowchart for generating eye diagrams of Si TW-MZM.

Figure 6: Comparison between simulated and experimental eye diagrams under different configurations.

Conclusion

This innovative perspective on TW-MZM design and simulation offers substantial improvements in efficiency, accuracy, and simplicity over traditional approaches. By applying nonlinear optics and CBS, the method accommodates diverse integrated platforms and supports frequencies exceeding 500 GHz. This provides a clear pathway towards the construction of future high-speed photonics systems capable of millimeter-wave and terahertz operations, promoting the synergy between electronics and photonics for advanced applications in AI acceleration and quantum systems.