Physics Colloquium – March 2, 2012 – George Barbasthasis (MIT)
Hamiltonian Optical Machines:
Insights, Design and Experimental Implementation
Prof. George Barbastathis
MIT Mechanical Engineering and SMART Centre
In his undergraduate thesis entitled Theory of Systems of Rays, Sir William Rowan Hamilton (1805-1865) developed the set of equations that bear his name to model trajectories of the rays of light through media of GRadient INdex of refraction (GRIN). In 1832, he also recognized that the same set of equations is applicable to other conservative physical systems. Hamiltonian methods became commonplace in classical and quantum mechanics but fell somewhat out of fashion in optics since off-the-shelf GRIN elements did not become widely available until the 1960’s and, even then, the available GRIN modulations were too limiting for the full force of the formulation to become evident.
Recently, arbitrary GRINs have become feasible by subwavelength patterning (“nanopatterning”) of ordinary materials. Moreover, new more rigorous methods of analysis such as adiabatically variant bandgap theory and transformation optics have created possibilities of controlling light by GRINs with unprecedented degrees of freedom, leading to applications such as optical cloaking and imaging with resolution far below the nominal diffraction limit.
In this seminar, I will first review the basic Hamiltonian formulation as it emerges from the Fermat-Lagrangian path minimization principle via a Legendre transformation. I will then give some analogous examples from optics and mechanics as well as detailed examples of subwavelength-patterned GRIN analysis, design, and experimental implementation.