Electromagnetic fields emitted by microcavities can only be analytically approached but can be computed. For complex structures such as photonic crystals, we usually only consider solutions in only two regimes: the near- field regime and the far-field regime. The near-field regime allows for example to see cavities mode shapes. In the far-field regime, where fields decreases rapidly , one can for example obtain the theoretical diffraction pattern of a laser beam. With the spherical formalism, one can develop solutions of Maxwell equations in microcavities that are dependant of a set of vector spherical harmonics. Such solutions are divided in so-called magnetic multipole and electric multipole expansions. By truncating solutions after few order in the expansions, one obtain very good approximations of fields inside microcavities.
A way to compute fields out of a photonic crystal is the use of the Finite-difference Time-Domain method, or also called FDTD. A dipole-like source inside the photonic crystal excites the structure and one computes at each time step amplitude of fields at each grid. This technique is useful to compute expansions of multipole fields.
As an illustration of multipole decompositions of fields, one computed expansion for TE modes of 2D photonic crystals with a single defect at the center. One explains far- field angular dependencies for the monopole, hexapole, doubly degenerated quadrupole and hexapole modes. The magnetic character of the monople mode and that the monopole mode mimics the theoretical dipole are shown. One can use monopole mode emitted by this kind of microcavity to create magnetic metamaterial. Using modified hexapole mode, one can create vertical emitter and dramatically reduces the number of multipole modes.