Short-Wavelength Light Propagation in Graded Photonic Crystals

Control of electromagnetic fields using graded photonic crystals (GPhCs) is explored using equations of Hamiltonian optics. Contrary to previous works devoted to the long-wavelength regime enabling homogenization of photonic metamaterials, attention is paid to short-wavelength light propagation for the possible use of dispersive phenomena and light path reconfiguring with wavelength. An analytical description of the dispersion diagram of a square PhCs is extracted using plane wave expansion calculations, making possible the description of arbitrary light paths in 2-D GPhC structures and fast optimization to find the conditions suited to make light follow prescribed paths. The validity of the approach is validated by comparison with finite-difference time-domain simulation. For purpose and illustration, a wavelength demultiplexing structure with four channels and an overall surface of 60 μm × 60 μm is proposed. The described methodology is applicable to the generalized 2-D chirp of PhC lattice or filling ratio parameters for electromagnetic field shaping.