At present, an important research area is the search for materials that are compatible with CMOS technology and achieve a satisfactory response rate and modulation efficiency. A strong local field of graphene surface plasmon polariton (SPP) can increase the interaction between light and graphene, reduce device size, and facilitate the integration of materials with CMOS. In this study, we design a new modulator of SPP-based cycle branch graphene waveguide. The structure comprises a primary waveguide of graphene–LiNbO3–graphene, and a secondary cycle branch waveguide is etched on the surface of LiNbO3. Part of the incident light in the primary waveguide enters the secondary waveguide, thus leading to a phase difference with the primary waveguide as reflected at the end of the branch and interaction coupling to enhance output light intensity. Through feature analysis, we discover that the area of the secondary waveguide shows significant localized fields and SPPs. Moreover, the cycle branch graphene waveguide can realize gain compensation, reduce transmission loss, and increase transmission distance. Numerical simulations show that the minimum effective mode field area is about 0.0130l2, the gain coefficient is about 700 cm–1, and the quality factor can reach 150. The structure can realize the mode field limits of deep subwavelength and achieve a good comprehensive performance.

Abstract
 1. Introduction
 2. Experimental
  2.1. Structure design
  2.2. Propagation analysis
 3. Results and Discussion
  3.1. Analysis of SPP
  3.2. Analysis of cycle branch
 4. Conclusions
 Conflict of Interest
 Acknowledgements
 References

• Jun Zhu(College of Electronic Engineering, Guangxi Normal University, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin University of Electronic Technology) Corresponding Author
• Zhengjie Xu(College of Electronic Engineering, Guangxi Normal University)
• Wenju Xu(College of Electronic Engineering, Guangxi Normal University)
• Duqu Wei(College of Electronic Engineering, Guangxi Normal University)