Abstract
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 x $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.
© 2011 IEEE
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