Liu Hsi-Chun, Yariv Amnon
Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
Opt Express. 2012 Apr 9;20(8):9249-63. doi: 10.1364/OE.20.009249.
We present a systematic design of coupled-resonator optical waveguides (CROWs) based on high-Q tapered grating-defect resonators. The formalism is based on coupled-mode theory where forward and backward waveguide modes are coupled by the grating. Although applied to strong gratings (periodic air holes in single-mode silicon-on-insulator waveguides), coupled-mode theory is shown to be valid, since the spatial Fourier transform of the resonant mode is engineered to minimize the coupling to radiation modes and thus the propagation loss. We demonstrate the numerical characterization of strong gratings, the design of high-Q tapered grating-defect resonators (Q>2 × 10⁶, modal volume = 0.38·(λ/n)³), and the control of inter-resonator coupling for CROWs. Furthermore, we design Butterworth and Bessel filters by tailoring the numbers of holes between adjacent defects. We show with numerical simulation that Butterworth CROWs are more tolerant against fabrication disorder than CROWs with uniform coupling coefficient.
我们展示了基于高Q值锥形光栅缺陷谐振器的耦合谐振器光波导（CROW）的系统设计。该形式体系基于耦合模理论，其中前向和后向波导模式通过光栅耦合。尽管应用于强光栅（单模绝缘体上硅波导中的周期性气孔），但耦合模理论被证明是有效的，因为谐振模式的空间傅里叶变换经过设计，可将与辐射模式的耦合降至最低，从而降低传播损耗。我们展示了强光栅的数值表征、高Q值锥形光栅缺陷谐振器（Q>2×10⁶，模态体积 = 0.38·(λ/n)³）的设计以及CROW的谐振器间耦合控制。此外，我们通过调整相邻缺陷之间的孔数来设计巴特沃斯滤波器和贝塞尔滤波器。我们通过数值模拟表明，巴特沃斯CROW比具有均匀耦合系数的CROW对制造无序更具容忍性。
