光学微操控的物理极限：偶极子区域的最大刚度
Physical Bounds on Optical Micromanipulation: Maximal Stiffness in the Dipole Regime
AI总结：
本文建立偶极子近似下光学捕获力和刚度的理论极限框架，通过球谐函数基和孔径约束两种方法揭示稳定捕获与定向力的帕累托最优权衡，并证明优化孔径场可超越标准高斯光束的性能瓶颈。
摘要：
光学捕获和微操控依赖于精心设计的电磁场对微观粒子施加精确的力和力矩。尽管它们在生物学和纳米技术中广泛应用，但捕获性能的绝对物理极限，特别是最大可实现的光学力和捕获刚度，尚未被严格量化。本工作在偶极子近似下建立了一个通用理论框架来确定这些基本界限。通过将光学力和刚度与粒子位置处电磁场的局部泰勒展开相关联，我们将性能极限表述为二次约束二次规划的解。为了评估这些界限，我们采用了两种互补的方法。首先，我们利用矢量球面波函数的完备基来确定麦克斯韦方程在自由空间中允许的光学力和刚度的绝对理论极限，揭示了稳定约束与定向力之间的帕累托最优权衡。其次，我们引入了一种基于孔径的公式，将入射场限制为有限平面孔径可实现的场。这产生了直接适用于主要依赖电磁束的实验设置的器件一致性界限。优化后的孔径场可以通过消除严重的轴向瓶颈而优于标准高斯光束，这一发现尤为重要。通过比较这两种情况，我们识别出有助于稳定捕获的特定空间模式，并量化了物理光束整形固有的性能权衡。这种双重框架为功率归一化的光镊提供了可证明的最优界限，并作为评估实际光束设计的严格基准。
英文摘要：
Optical trapping and micromanipulation rely on carefully shaped electromagnetic fields to exert precise forces and torques on microscopic particles. Despite their widespread application in biology and nanotechnology, the absolute physical limits of trapping performance, specifically the maximum achievable optical force and trap stiffness, have not yet been rigorously quantified. This work establishes a general theoretical framework to determine these fundamental bounds in the dipole approximation. By relating the optical force and stiffness to a local Taylor expansion of the electromagnetic field at the particle location, we formulate the performance limit as a solution to a quadratically constrained quadratic program. To evaluate these bounds, we employ two complementary approaches. First, we utilize a complete basis of vector spherical wave functions to determine the absolute theoretical limits of optical force and stiffness permitted by Maxwell's equations in free space, revealing Pareto-optimal trade-offs between stable confinement and directional force. Second, we introduce an aperture-based formulation that restricts the incident fields to those realizable by finite planar apertures. This yields device-consistent bounds directly applicable to experimental setups which rely mostly on electromagnetic beams. The finding that optimized aperture fields can outperform standard Gaussian beams by removing the severe axial bottleneck is particularly important. By comparing these two regimes, we identify the specific spatial modes that contribute to stable trapping and quantify the performance trade-offs inherent to physical beam shaping. This dual framework provides provably optimal bounds for power-normalized optical tweezers and serves as a rigorous benchmark for evaluating realistic beam designs.
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