<p>Intense developments in optical metamaterials have led to a renaissance in several optics fields. Metamaterials, artificially structured media, provide several additional degrees of freedom that cannot be accessed with conventional materials. For example, metamaterials offer a convenient and precise way to explore a wide range of refractive indices, including negative values. </p><p>In this dissertation, I introduce the idea of metamaterial based diffractive optics. Merging diffractive optics with metamaterials has several benefits, including access to almost continuous phase profiles and a wide range of available controlled anisotropy. I demonstrate this concept with several examples. I begin with an example of metamaterial based blazed diffraction grating using gradient index metamaterials for <em>f</em>É = 10.6 <em>f</em>Êm. A series of non-resonant metamaterial elements were designed and fabricated to mimic a saw-tooth refractive index profile with a linear index variation of . The linear gradient profile is repeated periodically to form the equivalent of a blazed grating, with the gradient occurring across a spatial distance of 61 <em>f</em>Êm. The index gradient is confirmed by comparing the measured magnitudes of the -1, 0 and +1 diffracted orders to those obtained from full wave simulations. </p><p>In addition to a metamaterial grating, a metamaterial based computer-generated phase hologram was designed by implementing the Gerchberg-Saxton (GS) iterative algorithm to form a 2D phase panel. A three layer metamaterial hologram was fabricated, with the size of 750 <em>f</em>Êm ~ 750 <em>f</em>Êm. Each pixel is comprised of metamaterial elements. This simple demonstration shows the potential for practical applications of metamaterial based diffractive optics.</p><p>The demand for compact and integrated optoelectronic systems increases the urgency for optical components that can simultaneously perform various functions. This dissertation also presents an optical element capable of multiplexing two diffraction patterns for two orthogonal linear polarizations, based on the use of non-resonant metamaterial cross elements. The metamaterial cross elements provide unique building blocks for engineering arbitrary birefringence. As a proof-of-concept demonstration, I present the design and experimental characterization of a polarization multiplexed blazed diffraction grating and a polarization multiplexed computer-generated hologram, for the telecommunication wavelength of <em>f</em>É = 1.55 <em>f</em>Êm. A quantitative study of the polarization multiplexed grating reveals that this approach yields a very large polarization contrast ratio. The results show that metamaterials can form the basis for a versatile and compact platform useful in the design of multi-functional photonic devices. </p><p>The examples I have mentioned only provide a glimpse of the opportunities for metamaterials. I envision more compact optical devices, with greater functionality, being realized with metamaterials.</p> / Dissertation