任意层排列介质多层膜和阶梯势垒中传输、色散和态密度的约束
Constraints on transmission, dispersion, and density of states in dielectric multilayers and stepwise potential barriers with arbitrary layer arrangement
摘要：
研究了非隧穿区光学多层膜和一维阶梯势垒的正入射透射和色散特性。多层膜结构中各组成层的光路以及阶梯势垒的每一步的参数都受到广义四分之一波长条件的约束。对结构几何形状没有其他限制，即，这些层可以任意排列。我们表明，态密度（DOS）谱的多层或障碍的问题受到积分守恒规则类似的Barnett-Loudon求和规则，但发生在一个有限的频率或能量区间。在光学情况下，这些频率间隔是规则的。对于势垒，只有非周期性的能量间隔可以存在于任何给定结构的光谱中，并且只有当组成势阶的参数被适当地选择时。用解析方法导出的积分守恒关系也得到了数值验证。该关系可用于色散工程多层基器件，例如，超短脉冲压缩器或超紧凑光学延迟线，以及设计多量子阱电子异质结构与工程DOS。
英文摘要：
Normal-incidence transmission and dispersion properties of optical multilayers and one-dimensional stepwise potential barriers in the non-tunneling regime are analytically investigated. The optical paths of every constituent layer in a multilayer structure, as well as the parameters of every step of the stepwise potential barrier, are constrained by a generalized quarter-wave condition. No other restrictions on the structure geometry is imposed, i.e., the layers are arranged arbitrarily. We show that the density of states (DOS) spectra of the multilayer or barrier in question are subject to integral conservation rules similar to the Barnett-Loudon sum rule but ocurring within a finite frequency or energy interval. In the optical case, these frequency intervals are regular. For the potential barriers, only non-periodic energy intervals can be present in the spectrum of any given structure, and only if the parameters of constituent potential steps are properly chosen. Abstract The integral conservation relations derived analytically have also been verified numerically. The relations can be used in dispersion-engineered multilayer-based devices, e.g., ultrashort pulse compressors or ultracompact optical delay lines, as well as to design multiple-quantum-well electronic heterostructures with engineered DOS.
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