56 K.Busch et al. tering resonances from individual elements of the periodic array and Bragg scattering from the corresponding lattice leads to the formation of a photonic bandstructure.In particular,the flexibility in material composition,lattice periodicity,symmetry,and topology of PCs allows one to tailor the photonic dispersion relations to almost any need.The most dramatic modification of the photonic dispersion in these systems occurs when suitably engineered PCs exhibit frequency ranges over which the light propagation is forbidden irrespective of direction [4.3,4.4].The existence of these so-called complete Photonic Band Gaps (PBGs)allows one to eliminate the problem of light leakage from sharply bent optical fibers and ridge waveguides.Indeed,using a PC with a complete PBG as a background material and embedding into such a PC a circuit of properly engineered waveguiding channels permits to create an optical micro-circuit inside a perfect optical insulator,i.e.an optical analogue of the customary electronic micro-circuit.In addition,the absence of photon states for frequencies in a complete PBG allows one to suppress the emission of optically active materials embedded in PCs.Furthermore, the multi-branch nature of the photonic bandstructure and low group veloc- ities associated with fat bands near a photonic band edge may be utilized to realize phase-matching for nonlinear optical processes and to enhance the interaction between electromagnetic waves and nonlinear and/or optically active material. These prospects have triggered enormous experimental activities aimed at the fabrication of two-dimensional(2D)as well as three-dimensional (3D) PC structures for telecommunication applications with PBGs in the near in- frared frequency range.Considering that the first Bragg resonance occurs when the lattice constant equals half the wavelength of light,fabrication of PCs with bandgaps in the near IR requires substantial technological re- sources.For 2D PCs,advanced planar microstructuring techniques borrowed from semiconductor technology can greatly simplify the fabrication process and high-quality PCs with embedded defects and waveguides have been fab- ricated in various material systems such as semiconductors [4.5-4.10,poly- mers [4.11,4.12],and glasses [4.13,4.14].In these structures,light experiences PBG effects in the plane of propagation,while the confinement in the third direction is achieved through index guiding.This suggests that fabricational imperfections in bulk 2D PCs as well deliberately embedding defect struc- tures such as cavities and waveguide bends into 2D PCs will inevitably lead to radiation losses into the third dimension.Therefore,it is still an open ques- tion as to whether devices with acceptable radiation losses can be designed and realized in 2D PCs.However,radiation losses can be avoided altogether if light is guided within the comlete PBG of 3D PCs and,therefore,the past years have seen substantial efforts towards the manufacturing of suitable 3D PCs.These structures include layer-by-layer structures [4.15,4.16,inverse opals [4.17-4.19]as well as the fabrication of templates via laser hologra- phy [4.20,4.21]and two-photon polymerization (sometimes also referred to as stereo-lithography)[4.22-4.24].56 K. Busch et al. tering resonances from individual elements of the periodic array and Bragg scattering from the corresponding lattice leads to the formation of a photonic bandstructure. In particular, the flexibility in material composition, lattice periodicity, symmetry, and topology of PCs allows one to tailor the photonic dispersion relations to almost any need. The most dramatic modification of the photonic dispersion in these systems occurs when suitably engineered PCs exhibit frequency ranges over which the light propagation is forbidden irrespective of direction [4.3, 4.4]. The existence of these so-called complete Photonic Band Gaps (PBGs) allows one to eliminate the problem of light leakage from sharply bent optical fibers and ridge waveguides. Indeed, using a PC with a complete PBG as a background material and embedding into such a PC a circuit of properly engineered waveguiding channels permits to create an optical micro-circuit inside a perfect optical insulator, i.e. an optical analogue of the customary electronic micro-circuit. In addition, the absence of photon states for frequencies in a complete PBG allows one to suppress the emission of optically active materials embedded in PCs. Furthermore, the multi-branch nature of the photonic bandstructure and low group veloc￾ities associated with flat bands near a photonic band edge may be utilized to realize phase-matching for nonlinear optical processes and to enhance the interaction between electromagnetic waves and nonlinear and/or optically active material. These prospects have triggered enormous experimental activities aimed at the fabrication of two-dimensional (2D) as well as three-dimensional (3D) PC structures for telecommunication applications with PBGs in the near in￾frared frequency range. Considering that the first Bragg resonance occurs when the lattice constant equals half the wavelength of light, fabrication of PCs with bandgaps in the near IR requires substantial technological re￾sources. For 2D PCs, advanced planar microstructuring techniques borrowed from semiconductor technology can greatly simplify the fabrication process and high-quality PCs with embedded defects and waveguides have been fab￾ricated in various material systems such as semiconductors [4.5–4.10], poly￾mers [4.11,4.12], and glasses [4.13,4.14]. In these structures, light experiences PBG effects in the plane of propagation, while the confinement in the third direction is achieved through index guiding. This suggests that fabricational imperfections in bulk 2D PCs as well deliberately embedding defect struc￾tures such as cavities and waveguide bends into 2D PCs will inevitably lead to radiation losses into the third dimension. Therefore, it is still an open ques￾tion as to whether devices with acceptable radiation losses can be designed and realized in 2D PCs. However, radiation losses can be avoided altogether if light is guided within the comlete PBG of 3D PCs and, therefore, the past years have seen substantial efforts towards the manufacturing of suitable 3D PCs. These structures include layer-by-layer structures [4.15, 4.16], inverse opals [4.17–4.19] as well as the fabrication of templates via laser hologra￾phy [4.20, 4.21] and two-photon polymerization (sometimes also referred to as stereo-lithography) [4.22–4.24]