Applied Mathematics and Mechanics

, Volume 40, Issue 1, pp 139–152 | Cite as

Nonlinear dynamic analysis of a photonic crystal nanocavity resonator

  • Fengrui Liu
  • Han Yan
  • Wenming ZhangEmail author


A nonlinear dynamic model of a one-dimensional photonic crystal nanocavity resonator is presented. It considers the internal tensile stress and the geometric characteristics of a photonic crystal with rectangular (and circular) holes. The solution of the dynamic model shows that the internal tensile stress can suppress the hardening and softening behaviors of the resonator. However, the stress can reduce the amplitude, which is not conducive to an improvement of the sensitivity of the sensor. It is demonstrated that with an optimized beam length, the normalized frequency drift of the beam can be stabilized within 1% when the optical power increases from 2 mW to 6 mW. When the hole size of the resonator beam is close to the beam width, its increase can lead to a sharp rise of the resonant frequency and the promotion of hardening behavior. Moreover, the increase in the optical power initially leads to the softening behavior of the resonator followed by an intensification of the hardening behavior. These theoretical and numerical results are helpful in understanding the intrinsic mechanism of the nonlinear response of an optomechanical resonator, with the objective of avoiding the nonlinear phenomena by optimizing key parameters.

Key words

nonlinear dynamic resonator photonic crystal softening and hardening behaviors 

Chinese Library Classification


2010 Mathematics Subject Classification



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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanical System and Vibration, School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiChina

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