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应变诱导的PT对称耦合硅谐振器中的频率分裂

Strain-Induced Frequency Splitting in PT Symmetric Coupled Silicon Resonators.

作者信息

Wang Lifeng, Zhang Shangyang, Yuan Qunce

机构信息

Key Laboratory of MEMS of the Ministry of Education, School of Electronic Science & Engineering, Southeast University, Nanjing 210096, China.

出版信息

Micromachines (Basel). 2024 Oct 21;15(10):1278. doi: 10.3390/mi15101278.

DOI:10.3390/mi15101278
PMID:39459152
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11509901/
Abstract

When two resonators of coupled silicon resonators are identical and the gain on one side is equal to the loss on the other side, a parity-time (PT) symmetric-coupled silicon resonator is formed. As non-Hermitian systems, the PT-symmetric systems have exhibited many special properties and interesting phenomena. This paper proposes the strain-induced frequency splitting in PT symmetry-coupled silicon resonators. The frequency splitting of the PT system caused by strain perturbations is derived and simulated. Theory and simulation both indicate that the PT system is more sensitive to strain perturbation near the exceptional point (EP) point. Then, a feedback circuit is designed to achieve the negative damping required for PT symmetry. Based on a simple silicon-on-insulator (SOI) process, the silicon resonator chip is successfully fabricated. After that, the PT-symmetric-coupled silicon resonators are successfully constructed, and the frequency splitting phenomenon caused by strain is observed experimentally.

摘要

当耦合硅谐振器的两个谐振器相同时，且一侧的增益等于另一侧的损耗时，就形成了一个宇称-时间（PT）对称耦合硅谐振器。作为非厄米系统，PT对称系统展现出了许多特殊性质和有趣的现象。本文提出了PT对称耦合硅谐振器中的应变诱导频率分裂。推导并模拟了由应变微扰引起的PT系统的频率分裂。理论和模拟均表明，PT系统在例外点（EP）附近对应变微扰更为敏感。然后，设计了一个反馈电路来实现PT对称所需的负阻尼。基于简单的绝缘体上硅（SOI）工艺，成功制造出了硅谐振器芯片。之后，成功构建了PT对称耦合硅谐振器，并通过实验观察到了由应变引起的频率分裂现象。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/d91d355116dc/micromachines-15-01278-g012.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/23ab1b263b37/micromachines-15-01278-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/531022320d41/micromachines-15-01278-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/4ac94eb3a356/micromachines-15-01278-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/550a317ceace/micromachines-15-01278-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/93b92243d5b7/micromachines-15-01278-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/bf8ab251e2ca/micromachines-15-01278-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/b10f0f0ee069/micromachines-15-01278-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/d91d355116dc/micromachines-15-01278-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/aa7c694073c5/micromachines-15-01278-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/a778894b740a/micromachines-15-01278-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/14d71c04796f/micromachines-15-01278-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/869a9cf06773/micromachines-15-01278-g004a.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/23ab1b263b37/micromachines-15-01278-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/531022320d41/micromachines-15-01278-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/4ac94eb3a356/micromachines-15-01278-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/550a317ceace/micromachines-15-01278-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/93b92243d5b7/micromachines-15-01278-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/bf8ab251e2ca/micromachines-15-01278-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/b10f0f0ee069/micromachines-15-01278-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dc0/11509901/d91d355116dc/micromachines-15-01278-g012.jpg

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Utilizing the Intrinsic Mode of Weakly Coupled Resonators for Temperature Compensation.利用弱耦合谐振器的本征模式进行温度补偿。
Micromachines (Basel). 2022 Sep 1;13(9):1447. doi: 10.3390/mi13091447.
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A Low-g MEMS Accelerometer with High Sensitivity, Low Nonlinearity and Large Dynamic Range Based on Mode-Localization of 3-DoF Weakly Coupled Resonators.
一种基于三自由度弱耦合谐振器模式定位的具有高灵敏度、低非线性和大动态范围的低重力微机电系统加速度计。
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