Quantitative analysis method for extraordinary optical transmission of thin microcavity by the catastrophic theory

School of Mechanical Engineering, Xi'an Jiaotong University - Xi'an 710049, China and State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University Xi'an 710049, China

^(a) E-mail: zhlforever@stu.xjtu.edu.cn
^(b) E-mail: ejhwu@mail.xjtu.edu.cn (corresponding author)

Received: 16 November 2022
Accepted: 4 May 2023

Abstract

Extraordinary optical transmission (EOT) can be regarded as a phase transition process based on the variation of the aperture of the thin microcavity by the published results. Considering that the catastrophe theory could describe quantitatively any phase transition process, a novel method is proposed to analyze the EOT transition quantitatively based on a cusp catastrophic model with dimensionless analysis. The quantitative relationship of transmitted energy spectral density is fully obtained, which is also related to the aperture radius and incident electromagnetic frequency. Furthermore, from this method, a quantum transition factor is derived strictly to describe the EOT transition process, which can be divided into wave region, wave-particle duality region and quantum region with the factor increasing from 0 to 1, and Bethe's aperture theory stating that transmission is proportional to is only one of our special cases in the wave region. Finally, the influence of the aperture and the frequency of incident wave on the EOT transmittance is analysed, and the catastrophic model is verified by previous experiments. The novel method of transition analysis provides a new insight into the EOT.