Transmission properties of Fibonacci quasi-periodic one-dimensional photonic crystals containing indefinite metamaterials

The transmission properties of Fibonacci quasi-periodic one-dimensional photonic crystals (1DPCs) containing indefinite metamaterials are theoretically studied. It is found that 1DPCs can possess an omnidirectional zero average index (zero-n̅) gap which exists in all Fibonacci sequences. In contrast to Bragg gaps, such zero-n̅ gap is less sensitive to the incidence angle, the scale length and the polarizations of electromagnetic waves. When an impurity is introduced, a defect mode appears inside the zero-n̅ gap with a very weak dependence on the incidence angle and scaling.