Narrow pass-band and narrow transmission-angle filter by photonic heterostructures containing negative-index materials

We propose a type of photonic heterostructure by combining two one dimensional (1D) defective photonic crystals (PCs) containing negative-index materials (NIMs). It is demonstrated by transfer matrix method that the proposed structure can achieve the integrated functions of narrow passband (NPB) frequency filtering and narrow transmission-angle (NTA) direction filtering. The key in designing such a structure is first to make the frequencies of the defect modes the same in the sub-PCs at a certain angle, and secondly to make the dispersion deviation of the defect modes as large as possible between the sub-PCs. This kind of structure is useful for medical sensing, and designing filters with the functions of NPB and NTA.