隨著超快雷射技術與微奈米製程技術的快速發展，雷射驅動介質加速器（Dielectric Laser Accelerator, DLA）因具有高加速梯度、微型化及晶片化等優勢，已成為新世代粒子加速器的重要研究方向。然而，傳統固定週期結構中，電子於加速過程因速度持續增加，容易與雷射電場產生相位滑移（phase slippage），使同步條件逐漸失效，進而限制有效加速距離及能量增益，因此如何維持電子與加速模態間的同步性，為提升加速效率的重要課題。
本研究利用VSim建立二維Particle-in-Cell（PIC）數值模擬模型，結合有限差分時域法（Finite-Difference Time-Domain, FDTD），分析雷射與電子束在奈米結構中的交互作用，並採用完美導體（Perfect Electric Conductor, PEC）模型探討不同結構參數對電子加速特性的影響。首先針對單一孔洞結構進行最佳化設計，比較不同孔洞長度與間隙尺寸對縱向電場分布、傳輸時間因子及加速梯度之影響；其次分析均勻多級串聯結構所產生的微觀相位滑移、全域電磁耦合及巨觀相位修正限制；最後導入漸變週期（chirped-period）結構，探討空間幾何與時間同步之耦合機制，以及不同漸變配置對電子加速效能的改善效果。
模擬結果顯示，適當的孔洞尺寸可有效提升縱向加速電場及加速梯度，但隨著均勻結構串聯級數增加，電子因速度提升導致同步條件逐漸失配，加速效率快速下降，且單純調整模組間距或光學相位無法有效克服此限制。研究亦發現，結構幾何會影響最佳共振波長，證實空間結構與雷射時間週期存在明顯的時空耦合關係；透過適當設計漸變孔洞尺寸及結構週期，可部分補償電子加速過程中的相位滑移，提升電子最終速度及整體加速梯度。研究成果除建立雷射驅動奈米電子加速器之結構設計準則外，亦驗證漸變週期結構於改善同步條件及提升加速性能上的可行性，可作為未來高梯度微型電子加速器設計與最佳化之參考。

Laser-driven dielectric accelerators (DLAs) have emerged as a promising technology for compact particle accelerators owing to their high accelerating gradients and miniaturization potential. However, conventional uniform-period structures suffer from phase slippage as electron velocity increases during acceleration, limiting energy gain. This study investigates the effects of structural parameters and evaluates the feasibility of chirped-period structures for improving acceleration performance.
A two-dimensional Particle-in-Cell (PIC) model was developed in VSim and coupled with the Finite-Difference Time-Domain (FDTD) method to simulate laser–electron interactions. A Perfect Electric Conductor (PEC) model was used to analyze the effects of cavity geometry, multistage configurations, and chirped-period designs on the accelerating field, phase synchronization, and accelerating gradient.
The results show that optimized cavity geometry enhances the longitudinal electric field and energy gain. In contrast, uniform multistage structures experience severe phase slippage and electromagnetic coupling, reducing acceleration efficiency. The simulations also reveal strong spatiotemporal coupling between structural geometry and resonant wavelength. Properly designed chirped-period structures partially compensate for phase slippage and improve electron velocity and accelerating gradient.
These results demonstrate that chirped-period structures can improve phase synchronization and provide useful design guidelines for laser-driven nanoelectron accelerators.

[1] Esarey, E., Sprangle, P., & Krall, J., “Laser acceleration of electrons in vacuum”, Physical Review E, Vol. 52, No. 5, pp. 5443-5453, 1995
[2] Kong, Q., Miyazaki, S., Kawata, S., Miyauchi, K., Nakajima, K., Masuda, S., Miyanaga, N., & Ho, Y. K., "Electron bunch acceleration and trapping by the ponderomotive force of an intense short-pulse laser", Physics of Plasmas, Vol. 10, No. 12, pp. 4605-4608, 2003.
[3] Kutsaev, S. V., "Electron bunchers for industrial RF linear accelerators: theory and design guide", The European Physical Journal Plus, Vol. 136, No. 4, p. 446, 2021.
[4] England, R. J., Noble, R. J., Bane, K., Dowell, D. H., Ng, C.-K., Spencer, J. E., Tantawi, S., et al., "Dielectric laser accelerators", Reviews of Modern Physics, Vol. 86, No. 4, pp. 1337-1389, 2014.
[5] Bar-Lev, D., England, R. J., Wootton, K. P., Liu, W., Black, D. S., & Scheuer, J., "Design of a plasmonic metasurface laser accelerator with a tapered phase velocity for subrelativistic particles", Physical Review Accelerators and Beams, Vol. 22, No. 2, pp. 021303-1- 021303-11, 2019.
[6] Halir, R., Bock, P. J., Cheben, P., Ortega-Moñux, A., Alonso-Ramos, C., Hallynck, J.-M., et al., "Waveguide sub-wavelength structures: a review of principles and applications", Laser & Photonics Reviews, Vol. 9, No. 1, pp. 25-49, 2015.
[7] Luo, X., "Subwavelength Artificial Structures: Opening a New Era for Engineering Optics", Advanced Materials, Vol. 31, No. 4, pp. 1804680, 2019.
[8] Wang, L., Xu, B.-B., Cao, X.-W., Li, Q.-K., Tian, W.-J., Chen, Q.-D., Juodkazis, S., & Sun, H.-B., "Competition between subwavelength and deep-subwavelength structures ablated by ultrashort laser pulses", Optica, Vol. 4, No. 6, pp. 637-642, 2017.
[9] Errico, F., Ichchou, M., De Rosa, S., & Bareille, O., "Application of the Wave Finite Element Approach to the Structural Frequency Response of Stiffened Structures", Proceedings of the 6th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2017), 2017.
[10] Faisal, F. H. M., & Kamiński, J. Z., "Floquet-Bloch theory of high-harmonic generation in periodic structures", Physical Review A, Vol. 56, No. 1, pp. 748-762, 1997.
[11] McNeur, J., Kozák, M., Schönenberger, N., Leedle, K. J., Deng, H., Black, D. S., et al., "Elements of a dielectric laser accelerator", Optica, Vol. 5, No. 6, pp. 687-690, 2018.
[12] Schulenberger, J. R., "Boundary waves on perfect conductors", Journal of Mathematical Analysis and Applications, Vol. 66, No. 3, pp. 514-549, 1978.
[13] Chacón, L., & Chen, G., "Energy-conserving perfect-conductor boundary conditions for an implicit, curvilinear Darwin particle-in-cell algorithm", Journal of Computational Physics, Vol. 391, pp. 216-239, 2019.
[14] Perse, B., Kormann, K., & Sonnendrücker, E., "Perfect Conductor Boundary Conditions for Geometric Particle-in-Cell Simulations of the Vlasov–Maxwell System in Curvilinear Coordinates", arXiv:2111.08342, 2021.
[15] Cheng, D. K., "Field and Wave Electromagnetics", Addison-Wesley, Reading, Massachusetts, pp. 321-326, 1989.
[16] Tong, D., "Electromagnetism, University of Cambridge Part IB Mathematical Tripos Lecture Notes", University of Cambridge, Cambridge, UK, pp. 41-94, 2015.
[17] Yee, K. S., "Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media", IEEE Transactions on Antennas and Propagation, Vol. 14, No. 3, pp. 302-307, 1966.
[18] 藍永強、邱行偉，「電漿模擬」，物理雙月刊，Vol. 28, No. 2, pp. 497-509, 2006。
[19] Yee網格圖, https://commons.wikimedia.org/wiki/File%3AYee-cube.svg
[20] Chen, W.-K., “The Electrical Engineering Handbook”, Elsevier Academic Press, Burlington, MA, USA, pp. 629-670, 2004.
[21] Pozar, D. M., Microwave Engineering (Fourth Edition), John Wiley & Sons, Hoboken, NJ, USA, pp. 95-159, 2011.
[22] Tskhakaya, D., Matyash, K., Schneider, R., & Taccogna, F., "The Particle-In-Cell Method", Contributions to Plasma Physics, Vol. 47, No. 8-9, pp. 563-594, 2007.
[23] Birdsall, C. K., & Langdon, A. B., "Plasma Physics via Computer Simulation", IOP Publishing / Taylor & Francis, New York, p. 11, 2004.
[24] Vsim Documention, https://txcorp.com/images/docs/vsim/11/VSimUserGuide/overviewCapabilities.html