TABLE OF CONTENTS A two-dimensional photonic crystal is a virtual two-dimensional medium whose optical index is periodically modulated: such a medium should not be confused with an object with a dimensionality reduced to 2, in a real world of dimension 3, as described in section 1.2.4.
This imaginary situation could be illustrated approximately, for example, by a dielectric material dug with a periodic lattice containing deep and parallel cylindrical holes (the depth should be much larger than the lattice constant [5]), the wave propagation being considered solely along directions normal to the holes.
A cross-section of such a periodic lattice, with discrete triangular transitional symmetry, is shown in Figure 1.24.
For the rest of this chapter we will use the triangular lattice case, which is widely used (though not exclusively so) in practice as an illustrative example.
Two of the three vectors a j( j = 1,2,3) in Figure 1.24 allow for a complete description of symmetry properties of the 2DPC in real space, and in particular of the permittivity of the periodic medium:
In the following paragraphs we will use the conceptual tools we used for the analysis of 1DPC, now applied to 2DPC.
Eigenmodes or solutions of Maxwell equations in a two dimensional periodic medium are also Bloch modes, which possess the same translational discrete periodic symmetry...
