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Extra info for Design and fabrication of quasi-2D photonic crystal components based on silicon-on-insulator technology
The vast research 30 Chapter 2 _______________________________________________________________________________________ carried out in the field of diffraction gratings can be applied to modeling and design of photonic crystals. Dansas and Paraire [Dansas 1998] applied the classical rigorous coupledwave analysis (RCWA also known as “Fourier modal method” [Lalanne 2000]) to 2D PhCs, considering an arbitrary profile as a stack of lamellar gratings. But the staircase approximation of the geometrical profile raises convergence problems [Popov 2002].
Because the basis functions are scalar, the Fourier coefficients need to be vector. 1 Cartesian triad formed by propagation vector of plane wave and polarization vectors of h (see text for details) Unit vectors eˆ1G , eˆ2 G are polarization vectors. In principle they can have ( ) arbitrary orientations in the plane perpendicular to k + G , there is an unlimited number of possibilities in choosing their directions. 1, eˆ1G can be in the eˆx , eˆy plane, then eˆ2 G is in the plane ( ) spanned by eˆz and eˆkG .
7 is apparent that 6 layers give a transmittance of about 10-6, which means an attenuation of about 10dB/layer. 6. * This is the optical analogue of the phenomenon of tunneling in quantum mechanics that does not allow complete blocking by a finite potential barrier. 2. Photonic crystal slabs (PCSs) Some of the most important applications of photonic crystals are based of introducing ‘defects’ in an otherwise perfect lattice by locally breaking the translational symmetry. A point defect can be a wavelength-scale resonant cavity with small modal volume and high quality factor [Villeneuve 1996].