微共振腔因為具有將光侷限在波長尺度模態體積的能力，因此可促進其內的光與物質交互作用。Bound states in the continuum (BIC) 因其理論上可達到極高的共振腔品質因子(Q-factor)，成為光子學領域最近受到關注的研究議題。對於光學器件應用上，提供了新穎的選擇，但在大多數的文獻中，對於BIC結構的討論與研究，多是假設無窮週期結構的前提。然而，實際應用層面希望在有限的週期內，達到與無窮週期結構接近的共振效果，因此結構微小化與探討有限週期結構是必須的。本論文運用COMSOL與FDTD進行數值電磁學模擬，研究BIC結構分別在無窮陣列與有限陣列中的光學響應，並探討有限陣列造成的影響。

Micro-cavity has the ability to confine light in wavelength-scale modal volume, it can promote the interaction of light and matter in cavity. Bound states in the continuum (BIC) become a research topic in the field of photonics recently because of its theoretically high Q-factor. For application of optical devices, BIC provided novel choice, but in most of the paper, the discussion and research on the BIC structure are mostly the premise of assuming an infinite periodic structure. However, the practical application hope to achieve a resonance effect close to the infinite period structure within a finite period. Therefore, the miniaturization of the structure and the discussion of the finite period structure are necessary. In this thesis, we use COMSOL and FDTD simulation, to study how BIC optical response in finite array and infinite array, and also discuss how Finite-size effects influence.

Key words: nano-cavity, micro-cavity, Finite-size effects, Bound states in the continuum (BIC).

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