Light Propagation In Metamaterials Research Articles

Fermat Principle, Ramsey Theory and Metamaterials.

Reinterpretation of the Fermat principle governing the propagation of light in media within the Ramsey theory is suggested. Complete bi-colored graphs corresponding to light propagation in media are considered. The vertices of the graphs correspond to the points in real physical space in which the light sources or sensors are placed. Red links in the graphs correspond to the actual optical paths, emerging from the Fermat principle. A variety of optical events, such as refraction and reflection, may be involved in light propagation. Green links, in turn, denote the trial/virtual optical paths, which actually do not occur. The Ramsey theorem states that within the graph containing six points, inevitably, the actual or virtual optical cycle will be present. The implementation of the Ramsey theorem with regard to light propagation in metamaterials is discussed. The Fermat principle states that in metamaterials, a light ray, in going from point S to point P, must traverse an optical path length L that is stationary with respect to variations of this path. Thus, bi-colored graphs consisting of links corresponding to maxima or minima of the optical paths become possible. The graphs, comprising six vertices, will inevitably demonstrate optical cycles consisting of the mono-colored links corresponding to the maxima or minima of the optical path. The notion of the "inverse graph" is introduced and discussed. The total number of triangles in the "direct" (source) and "inverse" Ramsey optical graphs is the same. The applications of "Ramsey optics" are discussed, and an optical interpretation of the infinite Ramsey theorem is suggested.

Resilience of symmetry against stochasticity in a gain-loss balanced oscillator

We investigate the effects of dichotomous noise added to a classical harmonic oscillator in the form of stochastic time-dependent gain and loss states, whose durations are sampled from two distinct exponential waiting time distributions. Despite the stochasticity, stability criteria can be formulated when averaging over many realizations in the asymptotic time limit and serve to determine the boundary line in parameter space that separates regions of growing amplitudes from those of decaying ones. Furthermore, the concept of symmetry remains applicable for such a stochastic oscillator and we use it to distinguish between an underdamped symmetric phase and an overdamped asymmetric phase. In the former case, the limit of stability is marked by the same average duration for the gain and loss states, while in the the latter case, a higher duration of the loss state is necessary to keep the system stable. The overdamped phase has an ordered structure imposing a position-velocity ratio locking and is viewed as a phase transition from the underdamped phase, which instead displays a broad and more disordered, but nevertheless, symmetric structure. We also address the short time limit and the dynamics of the moments of the position and the velocity with the aim of revealing the extremely rich dynamics offered by this apparently quite simple mechanical system. The notions established so far may be extended and applied in the stabilization of light propagation in metamaterials and optical fibres with randomly distributed regions of asymmetric active and passive media.

Light propagation in a fishnet metamaterial

We derive the dispersion relation of Bloch modes in a fishnet metamaterial in the optical frequency domain. The dependence of the longitudinal wave vector component on the transverse one and the frequency, which governs diffraction and dispersive spreading of localized light excitations, respectively, are analyzed. We show that this type of metamaterial exhibits an involved anisotropic behavior with diffraction changing the sign in passing even a zero diffraction point. For completeness we derive furthermore a formal angle-dependent effective refractive index which exhibits discontinuities. Thus we conclude that an effective refractive index tends to get meaningless and that only the dispersion relation predicts reliably light propagation in metamaterials. The results are double checked with those obtained from a retrieval algorithm based on angular resolved reflection/transmission data of a finite slab. Excellent agreement is observed.