Amplifying properties of two-dimensional photonic-crystal structures that contain active media O. N. Kozina a Saratov Branch, V. A. Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov L. A. Mel’nikov Saratov Branch, V. A. Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov; Saratov State University, Saratov Submitted March 26, 2009 Opticheski Zhurnal 76, 17–21 November 2009 This paper theoretically investigates and numerically models the optical properties of an artificial two-dimensional photonic crystal formed by glass nanofilaments doped with Nd ions and periodi- cally ordered in a dielectric matrix. This investigation is based on two different methods: the method of transfer matrices, and the method of expanding the field in plane waves. The main optical characteristics that make it possible to judge the amplifying properties of a photonic crystal—the transmission and reflection spectra—are studied in detail. It is shown that the lasing- threshold conditions of the structures investigated here are achieved by choosing their optical characteristics. © 2009 Optical Society of America. INTRODUCTION The possibility of controlling the transmittance charac- teristics and properties of photonic-crystal structures— periodic and microstructured media based on dielectrics 1 —have made it possible to speak of a new spe- cialization in optics. The optical phenomena in photonic- crystal structures make it possible to advance to a new level of methods for generating, transforming, modulating, and transporting radiation; i.e., they create a set of components that can be used in virtually all areas of modern science and engineering—the communication and storage of information- and in laser systems. 1–3 The presence of absorption or amplification in the mate- rial from which a photonic crystal is made alters the wave- propagation characteristics. 2,3 The estimates and calculations of the amplification characteristics in photonic-crystal struc- tures presented in Refs. 2, 3, 5, and 6 showed that it is pos- sible to significantly increase, by more than a factor of five, the amplification at the edges of the absorption band, and this is evidence that it is promising to use photonic crystals in the construction of a new generation of quantum devices. Photonic-crystal lasers and high-power amplifiers have been developed, using microstructure fibers based on fused quartz. 7 The doping of a photonic-crystal fiber PCF with erbium, ytterbium, or neodymium makes it possible to am- plify optical radiation and even to use this type of fibers as the active elements of fiber lasers. 8 Neodymium PCFs with compensation of the dispersion at 1060 nm were used in a laser with passive mode-locking. 7 There is special interest in studying the amplifying and generator properties of active photonic-crystal structures in which radiation propagates across the structure. With such an approach, it becomes pos- sible to create distributed-feedback photonic-crystal microla- sers, operating under optical pumping. It is suitable to fabri- cate such lasers by a glass-fiber method consisting of repeated drawing of preforms assembled from glass tubes. This method makes it possible to fabricate two-dimensional periodic structures with submicron elements. The authors earlier presented the results of studies for one-dimensional and two-dimensional photonic crystals PCs of infinite length and one-dimensional PC structures of finite size, containing amplifying layers, 4–6,9 where it was shown that, when radiation propagates across the layers of the structure, the reflection and transmission spectra undergo significant modulations close to the limits of the transmission bands. A change of the transmission spectrum is noted under certain conditions, showing that it is possible to reach the lasing threshold. A criterion for satisfying the threshold con- dition for lasing in one-dimensional PC structures was for- mulated in Ref. 6. This article is devoted to a theoretical investigation of the laser effect in two-dimensional PC structures containing active media when radiation propagates across the structure. The calculations were carried out by the method of transfer matrices 4,6 and the method of plane waves. 10 The amplifica- tion of the medium was modelled by a negative imaginary part of the complex refractive index of the dielectric. With such a method of introducing the amplification, the effect is absent by which the amplification is increased by suppress- ing the spontaneous emission in a periodic medium, de- scribed by the appearance of group velocity in the denomi- nator of the expression for the gain. 5 THE AMPLIFYING CHARACTERISTICS OF A PC STRUCTURE CONTAINING ACTIVE LAYERS, CALCULATED BY THE METHOD OF TRANSFER MATRICES The authors earlier presented the results of an investiga- tion of a one-dimensional PC structure of finite size, consist- ing of layers of glass doped with Nd 3+ ions and layers of air, alternating in the transverse direction. 4 The method of trans- fer matrices was used for that paper. A detailed study of the 685 685 J. Opt. Technol. 76 11, November 2009 1070-9762/2009/110685-04$15.00 © 2009 Optical Society of America