ISSN 1063-7842, Technical Physics, 2006, Vol. 51, No. 8, pp. 1030–1034. © Pleiades Publishing, Inc., 2006. Original Russian Text © J.Kh. Nurligareev, K.M. Golant, V.A. Sychugov, B.A. Usievich, 2006, published in Zhurnal Tekhnicheskoœ Fiziki, 2006, Vol. 76, No. 8, pp. 68–72. 1030 INTRODUCTION Interest in light generation and amplification in tun- nel-coupled waveguides has considerably grown in recent years primarily because of the need to improve the performance of fiber and semiconductor lasers [1, 2]. However, a better understanding of the physics of channel-waveguide-based passive devices also requires a deeper insight into light propagation in them [3, 4]. Systems of channel waveguides can be catego- rized as homogeneous and inhomogeneous. While the former have been explored comprehensively, the latter have been the subject of investigation in only three works [5–7]. In this article, we study the propagation of pencil light beams in a system of cylindrical waveguides. INHOMOGENEOUS SYSTEM OF COUPLED WAVEGUIDES A system of channel waveguides is called inhomo- geneous if the light propagation constant varies from waveguide to waveguide by a certain law. We will con- sider the simplest case when the propagation constant varies linearly. In other words, propagation constant β changes from waveguide to waveguide by a constant amount, ∆β = γ. It was found [5, 6] that light introduced into one waveguide of an inhomogeneous system does not spread throughout the system (as in the case of a homo- geneous system) but concentrates within several waveguides (W ≅ , where W is the number of con- centrating waveguides and χ is the coefficient of cou- pling between the waveguides). Moreover, in such a 8 χ γ ------ waveguide system, the light returns to the initially excited waveguide and concentrates at distances z, 2z 0 , 3z 0 , … (z 0 = ) from the entrance. Such a pattern is caused by the interference of equi- distant (∆β = γ = const) eigenmodes present in an inho- mogeneous system of channel waveguides. In [5, 6], two ways of creating the inhomogeneous system of channel waveguides were suggested and light focusing in it was demonstrated. We would like to call the reader’s attention to a simple waveguide system of this type comprising single-mode waveguides identical in parameters that are equidistantly placed on concen- tric circles with a sufficiently large radius [7]. Under the assumption that the propagation constants within the waveguides remain the same and all the waveguides, being excited in phase, start on one radius of curvature and end on the other, the signal passing from waveguide to waveguide will be delayed in phase at the exit of the system. This delay may be thought of as being related to a change in the light propagation constant in each waveguide relative to its neighbor. Such an approach to the problem of light propagation in a curved system of channel waveguides allows one to establish a relation- ship between the inhomogeneous system of rectilinear waveguides and the system of identical curvilinear waveguides [7], (1) where R is the radius of curvature of a waveguide with effective refractive index n*, ∆R is the difference 2 π γ ------ ∆β l β∆ l , ≈ ∆β k ∆ n * kn * ∆ R R ------- , = = Propagation of a Focused Light Beam in a Circuital System of Tunnel-Coupled Waveguides J. Kh. Nurligareev, K. M. Golant, V. A. Sychugov, and B. A. Usievich Prokhorov General Physics Institute, Russian Academy of Sciences, ul. Vavilova 38, Moscow, 119991 Russia e-mail: borisu@kapella.gpi.ru Received November 22, 2005 Abstract—The propagation of a pencil beam in a circuital system of tunnel-coupled waveguides is considered. It is shown that the beam periodically focuses into a point when moving along the trajectory. A maximal number of waveguides supporting the propagation of the beam can be estimated in simple terms. The cross-sectional area of the waveguides can be subdivided into three zone with the beam pulsing only in the central one. PACS numbers: 42.25.Bs DOI: 10.1134/S1063784206080123 OPTICS, QUANTUM ELECTRONICS