We have developed a rigorous scattering matrix theory of light emission from periodically structured media using a Green’s function approach. We computationally simulate the spectral power inside the structure, incorporating Purcell factor enhancements, and find internal waveguiding modes and plasmonic losses. We simulate the light-outcoupling factor ${\eta _{\text{out}}}$ and describe how corrugations and structured media can enhance ${\eta _{\text{out}}}$. We have extended our framework to describe non-periodic disordered arrays as well as aperiodic quasi-crystalline arrays. Flat organic light-emitting diodes (OLEDs) have low outcoupling with ${\eta _{\text{out}}} \sim{20}\%$ since most of the light is trapped in waveguided modes in higher index layers or lost to plasmonic excitations at the metal cathode. Periodically corrugated OLEDs can achieve highly enhanced ${\eta _{\text{out}}} \sim {65}\% {-} {70}\%$ for pitch values between 1000 and 2000 nm, representing an enhancement factor $ \gt {3}$ over planar structures. Periodic corrugations strongly diffract trapped waveguided and plasmonic modes to the emissive air cone. Disordered templates also can cause significant enhanced outcoupling with ${\eta _{\text{out}}} \sim {50}\% {-} {55}\%$ for smaller nearest-neighbor separations of 300–400 nm. Quasi-crystalline tilings can also lead to enhancements of ${\eta _{\text{out}}} \sim {50}\% {-} {55}\%$. This framework can be utilized to design novel structured media that can generate high light extraction.

中文翻译：

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模拟从周期性、无序和准周期性 OLED 结构中增强的光提取

我们使用格林函数方法开发了周期性结构化介质的光发射的严格散射矩阵理论。我们通过计算模拟结构内部的光谱功率，结合 Purcell 因子增强，并找到内部波导模式和等离子体损失。我们模拟光输出耦合因子${\eta _{\text{out}}}$并描述波纹和结构化介质如何增强${\eta _{\text{out}}}$。我们扩展了我们的框架来描述非周期性无序阵列以及非周期性准晶体阵列。平面有机发光二极管 (OLED) 与${\eta _{\text{out}}} \sim{20}\%$具有低耦合因为大部分光被捕获在更高折射率层的波导模式中，或者被金属阴极的等离子体激发丢失。周期性波纹 OLED 可以实现高度增强${\eta _{\text{out}}} \sim {65}\% {-} {70}\%$对于 1000 到 2000 nm 之间的间距值，代表增强因子$ \gt {3}$在平面结构上。周期性波纹将捕获的波导和等离子体模式强烈衍射到发射空气锥。对于 300–400 nm 的较小最近邻分离，无序模板也会导致${\eta _{\text{out}}} \sim {50}\% {-} {55}\%$显着增强的外耦合。准结晶瓷砖也可以导致${\eta _{\text{out}}} \sim {50}\% {-} {55}\%$. 该框架可用于设计可产生高光提取的新型结构化介质。