论文标题
线性时变媒体的Kramers-Kronig关系的概括
A Generalization of the Kramers-Kronig Relations for Linear Time-Varying Media
论文作者
论文摘要
我们探讨了数学理论，以严格描述具有线性时变的，通常分散的电磁本构参数的介质的响应。我们表明，即使时间不均匀性在时间尺度上发生或短于驾驶场的时间段，仍然可以定义一个物理上有意义的时间变化的分散体。因此，研究了一组广义的kramers-kronig关系，以将表征培养基构成响应的时变频分散光谱的真实和虚构部分联系起来。除其他外，我们研究了Lorentzian介电响应的案例，以及可极化原子的时变量密度，并呈现了管理微分方程的各种循环等效物，这反过来又使我们能够使用依赖时间依赖的电阻器和coscicor和capcicor和capsicator和capsicor和capsicator和capsicator和coscicator和coscicator和coscicator和cossication。
We explore the mathematical theory to rigorously describe the response of media with linear time-varying, generally dispersive, electromagnetic constitutive parameters. We show that even when the temporal inhomogeneity takes place on a time scale comparable or shorter than the driving fields' time period, one can still define a physically meaningful time-varying dispersion. Accordingly, a generalized set of Kramers-Kronig relations is investigated to link the real and imaginary parts of the time-varying frequency-dispersive spectra characterizing the medium's constitutive response. Among others, we study the case of a Lorentzian dielectric response with time-varying volumetric density of polarizable atoms and present the varying circuital equivalents of the governing differential equation, which in turn allow us to use the notion of generalized time-varying impedances/admittances of a time-dependent resistor, inductor and capacitor.
