**3.3 Computational methods and fabrication techniques**

Substantial work has been done to provide numerical solution of Maxwell equations. In this subsection a rough idea on the different computational methods to solve photonic crystal problems is given, for a broader notion we refer the reader to (Joannopoulus et al., 2008).

As a first approach, one can divide computational methods in frequency domain methods and time-domain methods, each of them useful for solving different problems typologies. Frequency domain methods are used to solve problems such as the computation of band diagrams and stationary mode profiles. On the other side, time-domain methods are better suited to perform computations involving time evolution of fields, such as transmission and reflection spectra or resonant cavities decay in time. Numerical methods can be alternatively classified on the basis of the used discretization schemes in: finite differences, finite elements, boundary-element and spectral methods.

Several commercial and open-source software packages implementing different numerical methods are available for computational photonics. Just to cite a few of these free-software products we will mention MPB (using plane wave expansion frequency-domain method) and Meep (implementing finite differences in time domain) MIT's packages and CAMFR (based in eigenmode expansion and advanced boundary conditions like perfectly matched layers).

Next, a coarse notion on the fabrication techniques to synthesize photonic crystals is given. A good set of references about 3D and 2D photonic crystal fabrication techniques is given in (Skorobogatiy & Yang, 2009). It has to be noticed that, in spite of its outstanding potential, photonic crystals mostly remain at research stage and this is mostly due to current technological limitations of fabrication techniques. Focused Ion Beam (FIB) and electron beam (e-beam) lithography combined with reactive ion-etching (RIE) are two the methods used in laboratories for high accuracy and high-resolution fabrication of planar 2D photonic crystals. However, it is necessary to start moving photonic crystal technology out of the laboratory and onto the production floor for building photonic devices for practical applications. Recent advances in nano-imprint lithography are fulfilling this goal (Kreindl et al., 2010).
