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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.
Date of Publication: July1, 2011