Microwave propagation guided by one dimensional array of strongly coupled split ring resonators

摘要 本實驗是研究以雙分裂環(DSRR)與互補雙分裂環(CSRR)作為一維陣列的微波傳輸特性。將一個DSRR與一個CSRR作為一維系統的基礎單元，DSRR和CSRR使用標準黃光製程製作在印刷電路板兩側。在共振器陣列兩端分別耦合至兩條微帶線藉以量測S參數。實驗量測結果與高頻電磁模擬軟體(HFSS)比較。為了比較共振器之間的耦合強度，使用了方形與圓形兩種共振器，方形共振器大小6.9 mm與圓形共振器大小7.6 mm，其共振頻率皆約為3 GHz。在圓形共振器的實驗中，固定共振器單元間距d=10 m, 改變不同的單元數量N，傳輸振幅從N=5的-22dB變化至N=30的-56dB。在相同的間距d=10 mm與單元數量N=10時，方形共振器的傳輸振幅-30dB與頻寬0.34GHz，相比圓形共振器的傳輸振幅-18dB與頻寬0.27GHz較大，此特性與共振器之間的耦合強度有關。由於傳輸振幅與頻寬受到共振器之間的耦合影響，我們研究這些傳輸特性如何受到共振器間距d和環方向的影響，而方向參數由共振器面向的角度θ決定。結果發現較小的間距d產生較大的傳輸振幅與頻寬，但是當d <11mm時差異不明顯。另一方面，實驗和模擬都顯示方向可以對傳輸造成巨大影響，在CSRR與DSRR方向角度為90°具有最大的傳輸振幅-7.9dB與頻寬0.25GHz，而當CSRR方向角度在240° (或 300° )時，具有最小的傳輸振幅-29.7dB與頻寬0.17GHz。模擬上在方向角度為240°處，傳輸頻帶分成兩個子頻帶。 這個結果顯示改變環形共振器的方向可用於控制波導行為。Abstract We experimentally study microwave transmission guided by one dimensional (1D) array of coupled double split ring resonators (DSRR) and complementary split ring resonators (CSRR). Dimer of double split ring resonators (DSRR) and complementary split ring resonator (CSRR) are used as the building blocks of the 1D system. DSRRs and CSRRs are respectively fabricated on the front- and back-sides of a printed circuit board by using standard photolithography. The resonator array is coupled to two microstrips at each end for S-parameter measurement. Results are compared with simulation using High Frequency Structural Simulator (HFSS). For changing the inter-resonator coupling strength, arrays composed of circular and rectangular resonators are made and compared. The sizes of circular and rectangular resonators are respectively 7.6mm and 6.9mm for providing the same resonance frequency of about 3 GHz, which were confirmed in transmission spectroscopy. For circular resonators with inter-resonator distance d=10 mm, the transmission amplitude in dB scale at resonance frequency decreases linearly with dimer number N from -22 dB to -56 dB respectively,for N=5 and 30. With the same d=10mm and dimer number N=10, a larger transmission amplitude (from -30 dB to -18.8 dB) and greater bandwidth (from 0.27 GHz to 0.34 GHz) are founded for rectangular case than circular case, probably due to stronger inter-resonator coupling. The transmission amplitude and bandwidth strongly depends on the inter-resonator coupling between a DSRR and a CSRR. We investigate how these transmission properties are affected by inter-resonator distance d and ring orientation, which is parameterized by an angle θ to the array direction. A smaller d yields a larger transmission amplitude and larger bandwidth but the difference is not significant when d