In this paper, we propose a novel approach to enhance the efficiency of the two-photon spontaneous emission process that is driven by the multifractal optical mode density of photonic structures based on the aperiodic distributions of Eisenstein and Gaussian primes. In particular, using the accurate Mie–Lorenz multipolar theory in combination with multifractal detrended fluctuation analysis, we compute the local density of states of periodic and aperiodic systems and demonstrate the formation of complete bandgaps with distinctive fractal scaling behavior for scattering arrays of dielectric nanocylinders. Moreover, we systematically study the Purcell enhancement and the most localized optical mode resonances in these novel aperiodic photonic systems and compute their two-photon spontaneous emission rates based on the general Green’s tensor approach. Our results demonstrate that excitation of the highly resonant critical states of Eisenstein and Gaussian photonic arrays across broadband multifractal spectra gives rise to significantly enhanced emission rates compared to what is possible at the band edges of periodic structures with comparable size. Besides defining a novel approach for enhanced quantum two-photon sources on the chip, the engineering of aperiodic bandgap structures with multifractal mode density may provide access to novel electromagnetic resonant phenomena in a multi-scale-invariant vacuum for quantum nanophotonics applications.

中文翻译：

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用于增强型量子双光子源的非周期性带隙结构

在本文中，我们提出了一种新方法来提高双光子自发发射过程的效率，该过程由基于爱森斯坦和高斯素数的非周期分布的光子结构的多重分形光学模式密度驱动。特别是，使用精确的 Mie-Lorenz 多极理论结合多重分形去趋势涨落分析，我们计算了周期性和非周期性系统的局部状态密度，并证明了具有独特分形缩放行为的完整带隙的形成，用于电介质纳米圆柱的散射阵列。此外，我们系统地研究了这些新型非周期性光子系统中的 Purcell 增强和最局部的光学模式共振，并基于一般格林张量方法计算了它们的双光子自发发射率。我们的结果表明，与具有可比尺寸的周期性结构的带边可能发生的发射率相比，跨越宽带多重分形光谱激发爱森斯坦和高斯光子阵列的高共振临界状态会显着提高发射率。除了定义芯片上增强型量子双光子源的新方法外，具有多重分形模式密度的非周期性带隙结构的工程可以为量子纳米光子学应用提供多尺度不变真空中的新型电磁谐振现象。