本研究旨在探討表面電漿奈米粒子（Localized Surface Plasmon Resonance, LSPR Nanoparticles）在光聲訊號增強中的物理機制與數值模擬分析[1-9]。光聲效應為一種將光能轉換為熱能並進一步產生聲波的能量轉換過程，廣泛應用於生醫成像、熱療與奈米材料檢測等領域。其中，奈米粒子因具備獨特的局域表面電漿共振效應，能顯著提升光吸收效率，進而增強光聲訊號。然而，光聲訊號的產生不僅與光吸收能力相關，亦涉及熱傳導、熱膨脹與聲波產生的多重物理過程，尤其在奈米尺度下，熱擴散行為、時間延遲效應與空間異向性現象更為複雜。
研究結果顯示奈米粒子的幾何形狀、材料性質與表面電漿共振特性[30]，均會影響熱擴散與光聲訊號強度。特別是在近場區域，聲壓場展現出明顯的空間異向性與方向性輻射特徵[33]，並可透過激發光參數與粒子結構設計進行調控。此外，本研究亦初步分析熱擴散與聲波產生之間的耦合關係，作為後續深入探討奈米尺度下多物理交互行為的基礎。
本研究首先以理論公式計算奈米粒子的瞬間溫度上升，作為數值模擬的基礎條件。接著利用 COMSOL Multiphysics 軟體進行熱擴散模擬，分析奈米粒子及其周圍介質中的熱傳導行為，並輸出溫度場與時間二階導數數據。最後，將模擬數據匯入 MATLAB ，透過有限差分法（FDM）求解光聲波動方程，重現光聲壓力場的時間演化與空間分佈。建立了一套結合理論推導、數值模擬與訊號分析的完整流程，能有效預測與分析表面電漿奈米粒子增強光聲訊號的物理行為，為奈米材料光聲應用設計與高效光聲造影劑開發提供理論基礎與技術參考。

This study explores the mechanisms and numerical modeling of photoacoustic signal enhancement induced by localized surface plasmon resonance (LSPR) nanoparticles. The photoacoustic effect converts optical energy into heat and subsequently generates acoustic waves, widely applied in biomedical imaging and nanomaterial characterization. LSPR nanoparticles enhance optical absorption and thus amplify photoacoustic signals, while nanoscale effects such as thermal diffusion, temporal delays, and spatial anisotropy further influence signal generation.
The workflow involves: (1) theoretical estimation of nanoparticle temperature rise, (2) thermal diffusion simulations in COMSOL Multiphysics, and (3) solving the photoacoustic wave equation in MATLAB using the finite difference method (FDM).
This integrated approach provides predictive insights into photoacoustic enhancement and serves as a reference for designing plasmonic nanomaterials and developing efficient photoacoustic contrast agents.

[1] Bell, A. G. "LXVIII. Upon the Production of Sound by Radiant Energy." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 11(71), 510–528 (1881)
[2] West, G. A.; Barrett, J. J.; Siebert, D. R.; Reddy, K. V. "Photoacoustic Spectroscopy." Review of Scientific Instruments 54, 797–817 (1983).
[3] Miklos, A.; Hess, P.; Bozoki, Z. "Application of Acoustic Resonators in Photoacoustic Trace Gas Analysis and Metrology." Review of Scientific Instruments 72, 1937–1955 (2001).
[4] Kosterev, A. A.; Bakhirkin, Y. A.; Curl, R. F.; Tittel, F. K. "Quartz-Enhanced Photoacoustic Spectroscopy." Optics Letters 27, 1902–1904 (2002).
[5] Czuchnowski, J.; Prevedel, R. "Photoacoustics: Seeing with Sound." Science in School 47, 14–18 (2019).
[6] Ashkin, A. "Acceleration and Trapping of Particles by Radiation Pressure." Physical Review Letters 24, 156 (1970).
[7] Righini, M.; Zelenina, A. S.; Girard, C.; Quidant, R. "Parallel and Selective Trapping in a Patterned Plasmonic Landscape." Nature Physics 3, 477–480 (2007).
[8] Shi, Y.; Polat, B.; Huang, Q.; Sirbuly, D. J. "Nanoscale Fiber-Optic Force Sensors for Mechanical Probing at the Molecular and Cellular Level." Nature Protocols 13, 2714–2739 (2018).
[9] Wang, M. M.; et al. "Microfluidic Sorting of Mammalian Cells by Optical Force Switching." Nature Biotechnology 23, 83–87 (2005).
[10] Eckerskorn, N.; et al. "Optically Induced Forces Imposed in an Optical Funnel on a Stream of Particles in Air or Vacuum." Physical Review Applied 4, 064001 (2015).
[11] Nowak, D.; et al. "Nanoscale Chemical Imaging by Photoinduced Force Microscopy." Science Advances 2, e1501571 (2016).
[12] Attia, A. B. E.; et al. "A Review of Clinical Photoacoustic Imaging: Current and Future Trends." Photoacoustics 16, 100144 (2019).
[13] Wang, L. H. V.; Hu, S. "Photoacoustic Tomography: In Vivo Imaging from Organelles to Organs." Science 335, 1458–1462 (2012).
[14] De La Zerda, A.; et al. "Carbon Nanotubes as Photoacoustic Molecular Imaging Agents in Living Mice." Nature Nanotechnology 3, 557–562 (2008).
[15] Liu, Y. J.; Bhattarai, P.; Dai, Z. F.; Chen, X. Y. "Photothermal Therapy and Photoacoustic Imaging via Nanotheranostics in Fighting Cancer." Chemical Society Reviews 48, 2053–2108 (2019).
[16] Ntziachristos, V. "Going Deeper Than Microscopy: The Optical Imaging Frontier in Biology." Nature Methods 7, 603–614 (2010).
[17] Emelianov, S. Y.; Li, P.-C.; O’Donnell, M. "Photoacoustics for Molecular Imaging and Therapy." Physics Today 62, 34 (2009)
[18] Wang, X.; Yan, X.; Min, Q. "Mass Transfer of Microbubble in Liquid under Multifrequency Acoustic Excitation – A Theoretical Study." Ultrasonics Sonochemistry 102, 106760 (2024).
[19] Wang, H.; Brandl, D. W.; Nordlander, P.; Halas, N. J. "Plasmonic Nanostructures: Artificial Molecules." Accounts of Chemical Research 40, 53–62 (2007).
[20] Lohse, S. E.; Murphy, C. J. "The Quest for Shape Control: A History of Gold Nanorod Synthesis." Chemistry of Materials 25, 1250–1261 (2013).
[21] Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. "The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment." Journal of Physical Chemistry B 107, 668–677 (2003).
[22] Daniel, M. C.; Astruc, D. "Gold Nanoparticles: Assembly, Supramolecular Chemistry, Quantum-Size-Related Properties, and Applications Toward Biology, Catalysis, and Nanotechnology." Chemical Reviews 104, 293–346 (2004).
[23] Weber, J.; Beard, P. C.; Bohndiek, S. E. "Contrast Agents for Molecular Photoacoustic Imaging." Nature Methods 13, 639–650 (2016).
[24] Tsai, M.-F.; et al. "Au Nanorod Design as Light-Absorber in the First and Second Biological Near-Infrared Windows for In Vivo Photothermal Therapy." ACS Nano 7, 5330–5342 (2013).
[25] García-Álvarez, R.; Chen, L.; Nedilko, A.; Sánchez-Iglesias, A.; Rix, A.; Lederle, W.; Pathak, V.; Lammers, T.; von Plessen, G.; Kostarelos, K.; Liz-Marzán, L. M.; Kuehne, A. J. C.; Chigrin, D. N. "Optimizing the Geometry of Photoacoustically Active Gold Nanoparticles for Biomedical Applications." ACS Photonics 7(3), 646–654 (2020).
[26] Weber, J.; Beard, P. C.; Bohndiek, S. E. "Contrast Agents for Molecular Photoacoustic Imaging." Nature Methods 13, 639–650 (2016).
[27] Chen, Y.-S.; Zhao, Y.; Yoon, S. J.; Gambhir, S. S.; Emelianov, S. "Miniature Gold Nanorods for Photoacoustic Molecular Imaging in the Second Near-Infrared Optical Window." Nature Nanotechnology 14, 465–472 (2019).
[28] Chen, Y.-S.; et al. "Silica-Coated Gold Nanorods as Photoacoustic Signal Nanoamplifiers." Nano Letters 11, 348–354 (2011).
[29] Chen, Y.-S.; Frey, W.; Aglyamov, S.; Emelianov, S. "Environment-Dependent Generation of Photoacoustic Waves from Plasmonic Nanoparticles." Small 8(1), 47–52 (2012).
[30] Homan, K.; Shah, V.; Gomez, J.; Gensler, H.; Karpiouk, A.; Brannon-Peppas, L.; Emelianov, S. "Silver Nanosystems for Photoacoustic Imaging and Image-Guided Therapy." Journal of Biomedical Optics 15(2), 021316 (2010).
[31] Mallidi, S.; Larson, T.; Tam, J.; Joshi, P. P.; Karpiouk, A.; Sokolov, K.; Emelianov, S. "Multiwavelength Photoacoustic Imaging and Plasmon Resonance Coupling of Gold Nanoparticles for Selective Detection of Cancer." Nano Letters 9(8), 2825–2831 (2009).
[32] Li, W.; Chen, X. "Gold Nanoparticles for Photoacoustic Imaging." Nanomedicine (London) 10(2), 299–320 (2015).
[33] Lapotko, D. "Plasmonic Nanobubbles as Tunable Cellular Probes for Cancer Theranostics." Cancers 3(1), 802–840 (2011).
[34] Chen, Y.-S.; Frey, W.; Kim, S.; Kruizinga, P.; Homan, K.; Emelianov, S. "Silica-Coated Gold Nanorods as Photoacoustic Signal Nanoamplifiers." Nano Letters 11(1), 348–354 (2011)
[35] Wang, H.; Meyer, S. M.; Murphy, C. J.; Chen, Y.-S.; Zhao, Y. "Visualizing Ultrafast Photothermal Dynamics with Decoupled Optical Force Nanoscopy." Nature Communications 14, 7267 (2023).
[36] Wang, H.; Chen, Y.-S.; Zhao, Y. "Understanding the Near-Field Photoacoustic Spatiotemporal Profile from Nanostructures." Photoacoustics 28, 100425 (2022).