arXiv 2406.164612024-06physics.optics

通过纳米雕刻实现光子模式体积的十倍减少

Orders-of-magnitude reduction in photonic mode volume by nano-sculpting

Technical University of Denmark（丹麦技术大学）

Rasmus E. Christiansen, Jesper Mørk, Ole Sigmund

备注：: 13 Pages, 6 Figures

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AI总结：

通过纳米雕刻技术，在介电环境中实现光子模式体积的十倍减少，并显著提升模式质量因子和Purcell因子。

摘要：

实现强光-物质相互作用对于研究和利用多种物理现象至关重要。光-物质相互作用的强度取决于相互作用区域的光场强度，通常通过 Purcell 因子来测量，对于单个发射体，该因子与光谱限制成正比，由腔体质量因子 $Q$ 表征，与光的空间局部化成反比，由光学模型体积 $V$ 表征，$F \propto \frac{Q}{V}$。虽然等离子体（金属）设备可以支持极端的空间光限制，但欧姆损耗会减少腔体寿命，从而限制可实现的光谱限制。因此，探索在（近）无损耗的介电环境中实现极端空间光限制的潜力，具有实际和基础研究的重要性。通过拓扑优化，我们探索了在允许三维雕刻介电纳米结构的情况下，介电环境中空间光限制的极限。在此，我们发现支持光学模式的结构，其模式体积在所谓的衍射极限之下三（四）个数量级，$V_{\textbf{r}_0} \approx 4 \cdot 10^{-4} \left[λ/(2 n)\right]^3 \left( V_{\textbf{r}_0} \approx 3 \cdot 10^{-5} \left[λ/2\right]^3\right)$。值得注意的是，我们进一步发现，用椭球壳包裹纳米结构可以实现模式质量因子（$Q > 10^8$ 已经通过数值方法演示）的似乎无限制增强，从而导致理论上的 Purcell 因子增强超过 $10^{11}$。建立了 $V_{\textbf{r}_0}$ 和 $Q$ 如何依赖于材料平台的选择、器件体积、最小特征尺寸和壳的数量。最后，对几何变化的敏感性研究被呈现，揭示了稳健行为。

英文摘要：

Achieving strong light-matter interaction is important for studying and exploiting several physics phenomena. The light-matter interaction strength depends on the optical field intensity in the interaction region, often measured by the Purcell factor, which for a single emitter is proportional to the spectral confinement, quantified by the cavity quality factor $Q$, and inversely proportional to the spatial localization of light, quantified by the optical model volume $V$, $F \propto \frac{Q}{V}$. While plasmonic (metallic) devices can support extreme spatial light confinement, ohmic losses reduce the cavity lifetime, thereby limiting the achievable spectral confinement. It is therefore of both practical and fundamental interest to explore the potential for achieving extreme spatial light confinement in (near) loss-less dielectric environments. Employing topology optimization we explore the limits of spatial light confinement in dielectric environments when allowing for three-dimensional sculpted dielectric nanostructures. Here we discover structures supporting optical modes that are concentrated in material (air) with mode volumes that are three (four) orders of magnitude below the so-called diffraction limit, $V_{\textbf{r}_0} \approx 4 \cdot 10^{-4} \left[λ/(2 n)\right]^3 \left( V_{\textbf{r}_0} \approx 3 \cdot 10^{-5} \left[λ/2\right]^3\right)$. Remarkably, we further discover that encapsulating the nanostructure by ellipsoidal shells enables seemingly unbounded enhancement of the mode quality factor ($Q > 10^8$ demonstrated numerically) leading to theoretical Purcell factor enhancement above $10^{11}$. It is established how $V_{\textbf{r}_0}$ and $Q$ depend on the choice of material platform, device volume, minimum feature size and the number of shells. Finally a study of sensitivity towards geometric variations is presented, revealing robust behaviour.

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