Metamaterials open unparalleled opportunities for "engineering" previously inaccessible values of refractive indices from positive to near-zero and even negative values, as well as new avenues for light manipulation. While enormous progress has been made in the field of linear optics of uniform metamaterials, including a negative index of refraction, magnetism in optics, and subwavelength focusing, light interactions with graded-index and nonlinear metamaterials is a fascinating, relatively new, and highly unexplored branch of metamaterials research. In this talk, I will discuss new phenomena that we predicted in so-called "transition metamaterials", or materials with the refractive index gradually changing from positive to negative values, and in nonlinear guided-wave metamaterial structures.
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