标题： 复杂共振介质中的开放通道和捕获通道 显示英文标题

标题： Open and trapping channels in complex resonant media

摘要： 我们对由谐振子组成的无序介质中的传输矩阵和驻留时间矩阵进行了统计研究，重点关注频率失谐如何影响它们的特征值分布。我们的分析表明，随着频率接近粒子的共振频率，传输特征值的分布经历了从单峰到双峰再回到单峰的变化。此外，在共振附近，驻留时间特征值的分布显著变宽，最长寿命比中位数高出几个数量级。通过检查频率$\omega$如何影响光的传输平均自由程$\ell(\omega)$和能量传输速度$v_E(\omega)$，这些结果得到了解释，而这些参数又塑造了观察到的分布。我们展示了波前整形在增强共振无序介质中的传输和能量存储方面具有巨大的潜力。在扩散区域，当系统厚度$L$超过平均自由程时，使用具有最大特征值的波前代替平面波可以将传输和驻留时间提高一个因子$\varpropto L/\ell(\omega) \gg 1$。 在局域化区域，增强效应对于传输变为$\varpropto Ne^{2L/\xi}$，对于驻留时间变为$\varpropto N\xi /L$，其中$\xi$是局域化长度，$N$是受控散射通道的数量。 最后，我们展示使用高$Q$振荡器而不是低$Q$振荡器可以在介质中增加能量存储，这一增加在扩散区域和局域化区域都是$\varpropto Q/k\ell(\omega)$倍。 显示英文摘要

摘要： We present a statistical study of the transmission and dwell-time matrices in disordered media composed of resonators, focusing on how frequency detuning influences their eigenvalue distributions. Our analysis reveals that the distribution of transmission eigenvalues undergoes a transition from a monomodal to a bimodal profile, and back to monomodal, as the frequency approaches the resonant frequency of the particles. Moreover, the distribution of dwell-time eigenvalues broadens significantly near resonance, with the longest lifetimes exceeding the median by several orders of magnitude. These results are explained by examining how frequency $\omega$ affects the transport mean free path of light, $\ell(\omega)$, and the energy transport velocity, $v_E(\omega)$, which in turn shape the observed distributions. We demonstrate the strong potential of wavefront shaping to enhance both transmission and energy storage in resonant disordered media. In the diffusive regime, where the system thickness $L$ exceeds the mean free path, both transmission and dwell time can be enhanced by a factor $\varpropto L/\ell(\omega) \gg 1$ when using wavefronts associated with the largest eigenvalues instead of plane waves. In the localized regime, the enhancements become $\varpropto Ne^{2L/\xi}$ for transmission and $\varpropto N\xi /L$ for dwell time, where $\xi$ is the localization length and $N$ is the number of controlled scattering channels. Finally, we show that employing high-$Q$ resonators instead of low-$Q$ ones increases energy storage within the medium by a factor of $\varpropto Q/k\ell(\omega)$, in both the diffusive and localized regimes.