本論文最主要目的是設計一波導模態共振濾波器（guided-mode resonance filter，GMR），使其具有下列三大特性：提升濾波器側帶（sideband）的穿透率（最大透射率 > 0.9）、加寬高穿透率的頻譜區域（具高透射率側帶範圍 ≥ 400 nm）、使共振線寬Δλ變窄（Δλ < 1 nm）。我們提出的結構由上往下分別為：SiNx光柵、SiNx波導、SiO2基板。我們先利用波導理論設計出波導的厚度及特徵模態，利用相位匹配求得相對應的光柵週期，接著引入等效介質理論（effective medium theory）提升側帶特性。也探討尺度因子（filling factor）與光柵深度兩結構參數對於波導模態共振濾波器弱調制（weak modulation）現象的影響。經考慮製程可行性，最後成功設計出TE（transverse electric）與TM（transverse magnetic）兩種偏振態下的波導模態共振濾波器：針對TE模態，共振波長在1550 nm、共振線寬為0.79 nm、側帶寬為668 nm、最大側帶穿透率可達0.9378；而針對TM模態，共振波長在1550 nm、共振線寬為0.77 nm、側帶寬為714.94 nm、最大側帶穿透率可達0.9362。最後，使用嚴格耦合波理論（rigorous coupled wave analysis，RCWA）模擬其頻譜側帶特性，並與等效介質理論所模擬之頻譜側帶特性做一驗證。並探討製程容忍度，光柵深度變異對於共振波長與共振線寬的影響，最後針對設計的兩波導模態共振濾波器其頻帶結構（band structure）做一學理上合理解釋。In this thesis, we show that ultranarrow-band guided-mode resonance (GMR) filters with flattened sidebands can be implemented with weakly modulated subwavelength gratings and low/high/low quarter-half-quarter dielectric thin-film stacks. These band-stop (notch) filters with characteristics of high efficiency, extended low-sideband reflection, and symmetric line shapes are designed by embedding waveguide gratings in layered structures possessing the feature of antireflection. The resonant wavelength of proposed GMR filters is precisely controlled at 1550 nm for optical communication. Furthermore, the improved spectral performance at sideband including the intensity of zero-order diffraction efficiency greater than 0.9 and the spectral range of sideband greater than 400 nm, the improved contrast between resonance peak and sideband, as well as the modulate ultra-narrow linewidth for resonance peak are demonstrated theoretically. The thickness of SiNx waveguide and its corresponding grating period are designed by using the waveguide theory and the phase-matching condition. The sideband performance can be improved by means of the effective medium theory. The effects of the grating filling factor and the grating depth on weakly-modulated GMRs are studied. The fabrication feasibility of proposed structures is considered during our design. Two GMR filters, containing the case of the transverse electric (TE) and the transverse magnetic (TM) polarization, are designed to demonstrate the concept. Under the requirement of transmission efficiency at sideband greater than 93%, resonance wavelength of 1550 nm, and its linewidth Δλ less than 0.8 nm, and sideband can extended more than 660 nm. Finally the sideband spectral response of proposed structures is compared by using the rigorous coupled wave analysis (RCWA) and the effective medium theory (EMT). The fabrication tolerance regarding grating depth, resonant peak location, and linewidth are discussed. Furthermore, the performances of ultranarrow-band guided-mode resonance filters are also studying by using band diagrams.
