论文标题
在“因果”光学设置中的负静脉速度和侵犯Kramers-Kronig关系的侵犯
Negative superluminal velocity and violation of Kramers-Kronig relations in "causal" optical setups
论文作者
论文摘要
我们研究了不同光学设置中的折射率$ n（ω）$的非分析性（例如，零和极点）和组索引$ n_g（ω）$。我们首先证明：虽然洛伦兹介电在复杂频率平面（CFP）的上半部分没有非分析性，但其组指数（控制脉冲中心传播）违反了kramers-kronig关系（KKRS）。因此，我们将非分析性分类为（a）一阶（折射率或反射）和（b）二阶（组索引或组延迟）中的非分析性。后者包含前者的衍生物。然后，我们研究了CFP上半部分的负静脉速度与非分析性的存在之间的可能联系。我们表明，（a）（a）一阶响应和（b）二阶响应分别伴随着负（a）相速度和（b）组速度的二阶响应的CFP上半部分的存在。我们还区分了两种超浮力，$ v> c $和$ v <0 $，在其中我们表明第二种（$ v <0 $）出现在违反KKRS的情况下。
We investigate nonanalyticities (e.g., zeros and poles) of refractive index $n(ω)$ and group index $n_g(ω)$ in different optical setups. We first demonstrate that: while a Lorentzian dielectric has no nonanalyticity in the upper half of the complex frequency plane (CFP), its group index -- which governs the pulse-center propagation -- violates the Kramers-Kronig relations (KKRs). Thus, we classify the nonanalyticities as in the (a) first-order (refractive index or reflection) and (b) second-order (group index or group delay). The latter contains the derivative of the former. Then, we study a possible connection between the negative superluminal velocities and the presence of nonanalyticities in the upper half of the CFP. We show that presence of nonanalyticities in the upper half of the CFP for (a) the first-order response and (b) the second-order response are accompanied by the appearance of negative (a) phase velocity and (b) group velocity, respectively. We also distinguish between two kinds of superluminosity, $v>c$ and $v<0$, where we show that the second one ($v<0$) appears with the violation of KKRs.
