Find an interesting photonic-crystal phenomenon, such as one described by a published paper. Replicate the results using the MIT numerical software, and then extend them in some interesting way: for example, look at a different range of parameters, demonstrate the same phenomenon in an alternative photonic-crystal context, or include some optimization. Write up a review of the literature, an analysis of the phenomenon, and a summary of your results in the form of a 5-10 page paper, formatted as for a publication (including references, figures, etcetera).
In the interest of time, students are encouraged to restrict themselves to two-dimensional calculations, either by starting with two-dimensional phenomena or by looking at 2d analogues to 3d phenomena.
"Photonic crystal superlensing and local density of states" - demonstrates flat-lens imaging and "superlensing" in a 2d photonic crystal, and correlates this phenomenon with the effect on the local density of states.
"Simulation of nonlinear effects in the 2d photonic bandgap fiber by MPB and MEEP" - frequency- and time-domain modelling of cutoff solitons and optical bistability in a 2d Fabry-Perot waveguide.
"Two-dimensional analysis of a channel drop filter in a triangular lattice" - demonstrates and analyses channel-drop tunnelling between two waveguides in a triangular-hole lattice crystal in 2d, mediated by a pair of cavities formed of three missing holes in the crystal.
"Exploiting multipole-cancellation for development of high Q cavities in photonic bandgap systems" - demonstration and multi-parameter optimization of multipole-cancellation phenomenon in a novel 2d cavity structure, and application to Fano-resonance filter.
"Guiding radiation from a point source in an OmniGuide fiber" - demonstrates how a point source inside a cylindrical hollow fiber surrounded by omnidirectional mirrors leads to radiation that is guided almost entirely within the fiber core.
"Towards effective modeling of mode coupling by collinear surface acoustic wave pattern" - design and analysis of a surface-wave grating coupler to convert a TE-polarized slab-waveguide mode into a leaky TM-polarized mode.
"Localized propagation modes guided by shear discontinuities in photonic crystals and tunable group velocity in a coupled-resonator optical waveguide (CROW) formed by shear discontinuities in a photonic crystal" - demonstrates how a tunable slow-light group velocity is achieved by a glide-symmetric shear defect in a 2d photonic crystal.