Lasing and Amplified Spontaneous Emission in Periodic and Quasi-Periodic Photonic Band Gap Materials Julian Kuerti Photonic Band Gap materials (or PBGs) were first fabricated less than 20 years ago, and currently enjoy considerable popularity among a growing number of quantum optic experimentalists and theorists. In the upcoming 'conference', I will present the theory and experimental results regarding the construction of lasers in periodic and quasi-periodic photonic band gap materials. The simplest PBG is fabricated by creating cylindrical air 'wells' in a thin substrate such as silicon or aluminum oxide. These holes are usually of the order of ~ 1 micron in diameter, ~ 100 microns in length and with lattice constant ~ 1 micron, and are usually arranged in a hexagonal lattice structure. Viewed from the side, the structure presents a 2-D photonic lattice, which, depending on the difference in refractive index between the air and the substrate material (and further geometrical considerations), may exhibit a photonic band gap. Quasi-periodic PBG materials are similar to periodic PBGs, the difference being that the lattice is not macroscopically ordered, but on a microscopic scale approximates its periodic cousin fairly closely. These materials have many applications in the construction of ultra low-loss optical wave guides, photonic filters/polarizers and other optical devices. One such application (which, strangely enough does not explicitly utilize the band gap properties) is the construction of a 2-D lasing medium. By filling the pores with a fluorescing dye, and pumping the material from the top, lasing was observed in the periodic lattice (as per Inoue et al, IQEC'98/Tuesday Morning). Recently, the experimental and theoretical results of amplified spontaneous emission have been detailed (see Lawandy et al, Optics Letters, Vol. 20 No. 11, June 1, 1995 and Nature, Vol. 368, March 31, 1994 as well as S. John and G. Pang, Phys. Rev. A, Vol. 54 No. 4, October 1996) in the case of a 3-D non-periodic scattering medium (dubbed 'laser paint'). Finally, the outline of the current experiment involving quasi-periodic lasing in a 2-D substrate will be given and discussed.