Band structure and broadband compensation of absorption by amplification in layered optical metamaterials
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OLECULES, OPTICS
Band Structure and Broadband Compensation of Absorption by Amplification in Layered Optical Metamaterials N. N. Rozanova,b,*, S. V. Fedorova,b, R. S. Savel’eva, A. A. Sukhorukova,c, and Yu. S. Kivshara,c a
St. Petersburg State University of Information Technologies, Mechanics and Optics, St. Petersburg, 197101 Russia b Vavilov State Optical Institute, Federal State Unitary Enterprise, St. Petersburg, 199034 Russia cNonlinear Physics Center, Australian National University, ACT 0200, Canberra, Australia email: [email protected] Received August 14, 2011
Abstract—The frequency dependence of the gain required to compensate for absorption is determined for a layered structure consisting of alternating absorbing and amplifying layers. It is shown that the fulfillment of the same conditions is required for the existence of a band structure consisting of alternating bands allowed and forbidden for optical radiation propagation in the frequency–wave vector parametric region. Conditions are found under which the gain required for compensation is smaller than thresholds for absolute (parasitic lasing) and convective (waveguide amplification of radiation) instabilities. DOI: 10.1134/S1063776112040140
1. INTRODUCTION Both classical (electrodynamic, acoustic, etc.) and quantum (electron wavefunction in crystals) waves propagating in media periodic in one or several direc tions acquire new properties which differ fundamen tally from those inherent in homogeneous media. One of the main properties is the appearance of allowed bands and forbidden gaps for the propagation of waves in the frequency–generalized wave vector dependen cies [1]. Studies in this direction have been mainly performed for transparent media; however, the con sideration of absorption and/or amplification in peri odic media is quite important for optics. Examples are distributed feedback lasers [2] and active waveguide periodic structures in which dissipative Bragg solitons can be formed [3]. Of special interest are photonic crystals and layered materials whose efficient opera tion is restricted by considerable losses, which should be compensated by introducing amplification [4]. Currently, considerable success has been achieved in the development of methods for introducing amplify ing layers into metamaterials [5–8], which motivates further investigations of schemes with active metama terials. In this paper, we analyze the linear propagation of optical radiation in a system consisting of alternating absorbing and amplifying layers. Linearity of the regime is achieved if the radiation intensity in the medium is lower than the saturation intensity in this medium, and such regimes are required for a number of metamaterial applications, including superresolu tion [5]. As we will see, the presence of dissipation– absorption and amplification fundamentally changes the type of propagation of waves in such media and, in
particular, the concept of allowed and forbidden bands itself. We will show that bands with the zero attenua tion coeffic
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