本研究針對電子束激發金屬光柵所產生的 Smith-Purcell 輻射進行深入探討，並提出了一種基於可調電子束頻率與速度的設計方法。利用結合有限時域差分法（FDTD）與粒子-網格法（PIC）的數值模擬，分析了輻射特性隨電子束參數變化的影響，並成功展示如何利用此調控機制來實現對輻射波長、強度及模式的靈活控制。
我們在研究過程中發現，透過調整電子束的頻率與速度，不僅能改變輻射波長，還能精確調節輻射的方向性及強度分佈，這對於太赫茲光源及高頻通訊等領域具有重要應用價值。此外，光柵結構參數的微調，如週期與材料選擇，皆為輻射效率的關鍵，進一步證明了結構設計與電子束動態調控的協同效應。
綜上所述，本研究不僅提出了一種新型的輻射源調控技術，還探索了其在多種應用領域的潛力，尤其是在光電子學、奈米材料分析、精密感測及太赫茲技術等方面。研究結果為未來高效、可調的輻射源設計提供了理論基礎和實驗指導，具有廣闊的應用前景和技術創新價值。

This study investigates the Smith-Purcell radiation generated by electron beams interacting with metallic gratings, and presents a novel design approach based on adjustable electron beam frequency and velocity. Using a combination of Finite-Difference Time-Domain (FDTD) and Particle-In-Cell (PIC) numerical simulations, we analyze the impact of variations in electron beam parameters on the radiation characteristics, and successfully demonstrate how this control mechanism can be used to flexibly adjust the radiation wavelength, intensity, and mode.
Through the course of the study, we found that by adjusting the frequency and velocity of the electron beam, not only could the radiation wavelength be altered, but also the directionality and intensity distribution of the radiation could be precisely controlled. This provides significant potential for applications in terahertz sources and high-frequency communication. Moreover, fine-tuning the grating structure parameters, such as the period and material choice, plays a critical role in enhancing radiation efficiency, further demonstrating the synergistic effect between structural design and electron beam dynamic control.
In summary, this research not only proposes a novel radiation source control technique, but also explores its potential in various application areas, particularly in photonics, nanomaterial analysis, precise sensing, and terahertz technology. The findings provide a solid theoretical foundation and experimental guidance for the design of efficient and tunable radiation sources, with broad prospects for future applications and technological innovation.

[1] C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles. John Wiley & Sons, 2008.
[2] G. P. Berlyn and J. P. Miksche, Botanical microtechnique and cytochemistry. 1976.
[3] J. D. Jackson, Classical electrodynamics. John Wiley & Sons, 2021.
[4] E. Economou, “Surface plasmons in thin films,” Physical review, vol. 182, no. 2, p. 539, 1969.
[5] A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Applied optics, vol. 37, no. 22, pp. 5271–5283, 1998.
[6] M. Kiwi and J. Rössler, “The drude model,” Revista Brasileira de Ensino de Física, vol. 46, e20240199, 2024. doi: 10.1590/1806-9126-rbef-2024-0199.
[7] S. Kaya, “Photo-thermal control of surface plasmon mode propagation at telecom wavelengths,” Ph.D. dissertation, Université de Bourgogne, 2016.
[8] D. Y. Fedyanin and A. V. Arsenin, “Semiconductor surface plasmon amplifier based on a schottky barrier diode,” in AIP Conference Proceedings, American Institute of Physics, vol. 1291, 2010, pp. 112–114.
[9] H. T. Baltar, E. M. Goldys, and K. Drozdowicz-Tomsia, Propagating surface plasmons and dispersion relations for nanoscale multilayer metallic-dielectric films. INTECH Open Access Publisher, 2012.
[10] J. C. Maxwell, “A dynamical theory of the electromagnetic field,” Philosophical Transactions of the Royal Society of London, vol. 155, pp. 459–512, 1865.
[11] F. D. Tombe, “Maxwell’s original equations,” ResearchGate, 2011.
[12] K. Yee, “Numerical solution of initial boundary value problems involving maxwell’sequations in isotropic media,” IEEE Transactions on antennas and propagation, vol. 14, no. 3, pp. 302–307, 1966.
[13] R. Courant, K. Friedrichs, and H. Lewy, “On the partial difference equations of mathematical physics,” IBM Journal of Research and Development, vol. 11, no. 2, pp. 215–234, 1928.
[14] O. Heaviside, “The stability of numerical solutions of differential equations,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 3, no. 11, pp. 324–343, 1902.
[15] S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of fdtd lattices,” IEEE transactions on Antennas and Propagation, vol. 44, no. 12, pp. 1630–1639, 1996.
[16] G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE transactions on Electromagnetic Compatibility, no. 4, pp. 377–382, 2007.
[17] J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” Journal of computational physics, vol. 114, no. 2, pp. 185–200, 1994.
[18] C. K. Birdsall, “Particle-in-cell charged-particle simulations, plus monte carlo collisions with neutral atoms, pic-mcc,” IEEE Transactions on plasma science, vol. 19, no. 2, pp. 65–85, 2002.
[19] G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE transactions on Electromagnetic Compatibility, no. 4, pp. 377–382, 2007.
[20] J. Grunwald and P. Mercorelli, “Visualization of the plasma frequency by means of a particle simulation using a normalized periodic model,” in Journal of Physics: Conference Series, IOP Publishing, vol. 2162, 2022, p. 012 016.