Coupled-resonator optical waveguides hold potential for slow-light propagation of optical pulses. The dispersion properties may adequately be analyzed within the framework of coupled-mode theory. We extend the standard coupled-mode theory for such structures to also include complex-valued parameters which allows us to analyze the dispersion properties also in presence of finite Q factors for the coupled resonator states. Near the band-edge the group velocity saturates at a finite value v_g/c propto sqrt{1/Q} while in the band center, the group velocity is unaffected by a finite Q factor as compared to ideal resonators without any damping. However, the maximal group delay that can be envisioned is a balance between having a low group velocity while not jeopardizing the propagation length. We find that the maximal group delay remains roughly constant over the entire bandwidth, being given by the photon life time of the individual resonators.
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机译:耦合谐振器光波导具有使光脉冲缓慢传播的潜力。可以在耦合模式理论的框架内充分地分析色散特性。我们将此类结构的标准耦合模式理论扩展为还包括复数值参数,这使我们能够在耦合谐振器状态存在有限Q因子的情况下分析色散特性。在频带边缘附近,群速度以有限值v_g / c propto sqrt {1 / Q}饱和,而在频带中心,与理想的谐振器相比,群速度不受有限Q因子的影响,没有任何阻尼。但是,可以设想的最大群时延是在不降低传播速度的前提下具有低群速度之间的平衡。我们发现,最大群延迟在整个带宽上大致保持恒定,这由各个谐振器的光子寿命给出。
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