The Transmission Properties Of Photonic Crystals Containing Metamaterials

Photonic crystals (PCs), also called photonic band gap (PBG) materials, are artificial materials which possess a periodic modulation of permittivity or permeability. The most important feature of PCs is the PBG. Electromagnetic (EM) waves with frequencies within the band gap cannot propagate through the PCs. Utilizing the effect of PBGs, the propagation of EM waves can be controlled by introducing the defect into the PCs. Metamaterials are a type of artificial EM materials with different EM properties from the ordinary materials, such as negative index, negative permittivity or negative permeability. When the EM waves pass through the metamaterials, there will be a lot of unusual phenomenon, such as converse Doppler Effect, converse Cerenkov Effect and unusual light pressure.Due to the unusual EM properties of metamaterials, if we introduce the metamaterials into PCs, there will be a lot of new rules and phenomenon. In this thesis, we investigate the transmission properties of PCs containing metamaterials. The major contents are given as follows.1. The reflection phase properties in the omnidirectional gap by one-dimensional PCs containing metamaterials are investigated. We consider three types of structure:'mu-negative positive-index PC','epsilon-negatvie positive-index PC', and'mu-negative epsilon-negative PC'. The properties of reflection phase versus the incident angle, the scaling factor of layer thickness and the periodic numbers are studied. These results can help us to have a better understanding of the reflection phase properties in one-dimensional PCs containing metamaterials, and valuable in designing phase compensator and dispersion compensator.2. A type of photonic heterostructure containing left-hand materials is studied, from which the polarization-independent and omnidirectional defect mode can be obtained. Firstly, we get the omnidirectional defect mode for TE wave from the one-dimensional defective PC containing left-hand materials by the use of the eigenfrequency equation of the defect mode. Then, according to the symmetry of Maxwell's wave equations in electric and magnetic vectors, we found that the dielectric one-dimensional defective PC benefits to achieve the omnidirectional defect mode for TE waves, while the magnetic one-dimensional defective PC benefits for TM waves. By combining dielectric one-dimensional defective PC and magnetic one-dimensional defective PC, we get the polarization-independent and omnidirectional defect mode. Finally, the field distributions are also calculated and the results prove our deduction.3. A type of photonic heterostructure containing left-hand materials is investigated. The structure is made of two one-dimensional defective PCs: the first one consists of alternating positive-index material layers with a positive-index material defect; the second one consists of the same alternating positive-index material layers with a left-hand materials defect. The results show that the proposed structure can achieve the integrated functions of narrow pass-band frequency filtering and narrow transmission-angle direction filtering at a certain angle. 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. The results also show that the proposed structure can get more narrow pass-band and more narrow transmission-angle than the similar structure only containing ordinary materials.4. A type of photonic quantum well containing negative-index materials is studied. The structure is made of two different PCs with negative-index materials and positive-index materials. The left and right side PCs in the proposed heterostructure serve as photonic barriers, and the middle PC works as a well. When the passband of the well PC just locates inside the gap of the barrier PC, the condition of forming the photonic quantum well can be satisfied. Just like the electrons in the semiconductor quantum well, the waves can pass through the barrier PCs by the way of tunneling owing to the photonic confinement effects. The tunneling modes vary with different number of periods in the well PC and the number of modes is just the same as the number of periods in the well PC. Moreover, these types of modes are insensitive to the incident angle as well as the scaling of the barrier PC.