Haakestad Magnus, Skaar Johannes
Opt Express. 2005 Nov 28;13(24):9922-34. doi: 10.1364/opex.13.009922.
Starting from the condition that optical signals propagate causally, we derive Kramers-Kronig relations for waveguides. For hollow waveguides with perfectly conductive walls, the modes propagate causally and Kramers-Kronig relations between the real and imaginary part of the mode indices exist. For dielectric waveguides, there exists a Kramers-Kronig type relation between the real mode index of a guided mode and the imaginary mode indices associated with the evanescent modes. For weakly guiding waveguides, the Kramers-Kronig relations are particularly simple, as the modal dispersion is determined solely from the profile of the corresponding mode field.
从光信号因果传播的条件出发，我们推导了波导的克拉默斯 - 克勒尼希关系。对于具有理想导电壁的空心波导，模式因果传播，且模式指数的实部和虚部之间存在克拉默斯 - 克勒尼希关系。对于介质波导，导模的实模式指数与消逝模相关的虚模式指数之间存在克拉默斯 - 克勒尼希型关系。对于弱导波导，克拉默斯 - 克勒尼希关系特别简单，因为模式色散仅由相应模式场的分布决定。
