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Analysis of periodicity-induced attenuation effect in a nonlinear waveguide by means of the method of polynomial system resultants
摘要： This paper addresses the application of the novel method of polynomial system resultants for solving two problems governed by systems of cubic equations. Both problems emerge in analysis of stationary dynamics of a periodic waveguide, which consists of linearly elastic continuous rods with nonlinear springs between them. The first one is the classical problem of finding “backbone curves” for free nonlinear vibrations of a symmetric unit periodicity cell of the waveguide. The second one is the problem of finding the Insertion Losses for a semi-infinite waveguide with several periodicity cells. Similarly to the canonical linear case, a very good agreement between boundaries of high attenuation frequency ranges and eigenfrequencies of a unit cell is demonstrated.
关键词： Periodicity,Nonlinear waveguide,Insertion losses,Method of polynomial system resultants,Eigenfrequencies
更新于2025-09-23 15:21:01
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Integrated Raman Laser: A Review of the Last Two Decades
摘要： Important accomplishments concerning an integrated laser source based on stimulated Raman scattering (SRS) have been achieved in the last two decades in the fields of photonics, microphotonics and nanophotonics. In 2005, the first integrated silicon laser based upon SRS was realized in the nonlinear waveguide. This breakthrough promoted an intense research activity addressed to the realization of integrated Raman sources in photonics microstructures, like microcavities and photonics crystals. In 2012, a giant Raman gain in silicon nanocrystals was measured for the first time. Starting from this impressive result, some promising devices have recently been realized combining nanocrystals and microphotonics structures. Of course, the development of integrated Raman sources has been influenced by the trend of photonics towards the nano-world, which started from the nonlinear waveguide, going through microphotonics structures, and finally coming to nanophotonics. Therefore, in this review, the challenges, achievements and perspectives of an integrated laser source based on SRS in the last two decades are reviewed, side by side with the trend towards nanophotonics. The reported results point out promising perspectives for integrated micro- and/or nano-Raman lasers.
关键词： nonlinear waveguide,lasers,microphotonics,nanophotonics,stimulated Raman scattering,optical microcavity,photonics crystals,nonlinear optics,nanocrystals
更新于2025-09-23 15:19:57
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Nonlinear propagation of coupled surface TE and leaky TM electromagnetic waves
摘要： Propagation of the coupled electromagnetic wave, which is a superposition of TE surface and TM leaky waves, in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is studied (if the permittivity is linear, the coupled wave does not exist). Nonlinear coupled TE–TM wave is characterised by two (independent) frequencies and two (coupled) propagation constants (propagation constants). The physical problem is reduced to a nonlinear two-parameter transmission eigenvalue problem for Maxwell’s equations. Existence of coupled TE–TM waves is proved. Intervals of localisation of propagation constants are found.
关键词： nonlinear waveguide,Nonlinear coupled TE–TM waves,Kerr nonlinearity,Maxwell’s equations,two-parameter eigenvalue problem,coupled propagation constants
更新于2025-09-16 10:30:52
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Problem of Coupled Electromagnetic TE-TE Wave Propagation in a Layer Filled with Nonlinear Medium with Saturation
摘要： Propagation of coupled electromagnetic TE-TE wave in a nonlinear plane layer is considered. The layer is located between two half-spaces with constant permittivities. The permittivity in the layer is described by nonlinearity with saturation. The physical problem is reduced to a nonlinear two-parameter eigenvalue problem for a system of (nonlinear) ordinary differential equations. Existence and uniqueness of solution to the two-parameter eigenvalue problem is proved. Iteration method for solving given problem is presented. Convergence theorem of the iteration method is proved.
关键词： wave propagation,perturbation method,saturated nonlinearity,plane nonlinear waveguide,Maxwell’s equations
更新于2025-09-16 10:30:52