A coupled-line coupler comprising a microstrip line, edge-coupled to a negative-refractive-index line, exhibits co-directional phase but contra-directional Poynting vectors on the lines, leading to backward coupling. A key feature of this coupler is that it can support complex coupled modes. The resulting exponential field decay enables enhanced coupling with moderate line lengths and spacing. An example 3 dB device has been implemented and tested at 3 GHz.
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Islam et al. (2004) studied this question.
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