The so-called magnonic crystals (MCs), the new metamaterial struc- tures made of periodic variations in geometric parameters and/or properties of magnetic materials, are being actively studied worldwide. In contrast to the well-established photonic crystals (PCs), MCs possess the capability of controlling the generation and transmission of information-carrying magnetostatic waves (MSWs) at microwave fre- quencies by a bias magnetic field. A new theoretical approach based on Walker's equation which is capable of efficiently analyzing mag- netostatic volume waves (MSVWs) propagation characteristics in one-dimensional (1-D) and two-dimensional (2-D) MCs was developed through this dissertation research. The validity of this theoretical approach was subsequently verified by extensive experimental results with excellent agreements.

MC-based tunable microwave devices were also envisaged and realized. Specifically, the performance characteristics of wideband tunable microwave filters and phase shifters, and waveguides, are detailed in this dissertation. In device fabrication, both the 1-D MC consisting of pe- riodic channels and the 2-D MC consisting of periodic holes in square lattices were prepared by wet etching technique. The magnetically-tuned bandgaps created in the 1-D and 2-D MCs were shown to func- tion as tunable band stop filters (BSFs). Furthermore, the large phase shifts associated with the left and right flat passbands of the bandgap facilitated construction of tunable wideband microwave phase shifters. Compared to all existing magnetically-tuned phase shifters, the MC-based phase shifters are significantly smaller in dimension and possess much larger phase tuning rate and phase shifts. Finally, confinement of magnetostatic forward volume waves (MSFVWs) was demonstrated both theoretically and experimentally.