Boston University, Department of Electrical and Computer Engineering and Photonics Center, 8 Saint Mary's Street, Boston, Massachusetts, 02215, United States of America.
Boston University, Division of Materials Science and Engineering, 15 Saint Mary's Street, Brookline, Massachusetts, 02446, United States of America.
Sci Rep. 2017 May 23;7(1):2259. doi: 10.1038/s41598-017-02170-9.
The propagation of optical pulses through primary types of deterministic aperiodic structures is numerically studied in time domain using the rigorous transfer matrix method in combination with analytical fractional transport models. We demonstrate tunable anomalous photon transport, including the elusive logarithmic Sinai sub-diffusion in photonic systems for the first time. Our results are in excellent agreement with the scaling theory of transport in aperiodic media with fractal spectra, and additionally demonstrate logarithmic sub-diffusion in the presence of multifractality. Moreover, we establish a fruitful connection between tunable photon diffusion and fractional dynamics, which provides analytical insights into the asymptotic transport regime of optical media with deterministic aperiodic order. The demonstration of tunable sub-diffusion and logarithmic photon transport in deterministic aperiodic structures can open novel and fascinating scenarios for the engineering of wave propagation and light-matter interaction phenomena beyond the conventional diffusive regime.
本文通过严格的传递矩阵方法与解析分数传输模型相结合，在时域内对光脉冲在主要类型确定性非周期结构中的传播进行了数值研究。我们首次在光子系统中展示了可调反常光子输运，包括难以捉摸的对数 Sinai 亚扩散。我们的结果与分形谱非周期介质中输运的标度理论非常吻合，并且在多重分形存在的情况下还证明了对数亚扩散。此外，我们在可调光子扩散和分数动力学之间建立了有益的联系，为具有确定性非周期序的光学介质的渐近输运状态提供了分析见解。在确定性非周期结构中实现可调亚扩散和对数光子输运，为超越传统扩散范围的波传播和光物质相互作用现象的工程设计开辟了新颖而迷人的场景。
