Topic
Linear medium
About: Linear medium is a research topic. Over the lifetime, 293 publications have been published within this topic receiving 4817 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, the authors constructed the solution for a semi-infinite hydraulic crack for arbitrary toughness, which accounts for the presence of a lag of a priori unknown length between the fluid front and the crack tip.
Abstract: The focus of this paper is on constructing the solution for a semi-infinite hydraulic crack for arbitrary toughness, which accounts for the presence of a lag of a priori unknown length between the fluid front and the crack tip. First, we formulate the governing equations for a semi-infinite fluid-driven fracture propagating steadily in an impermeable linear elastic medium. Then, since the pressure in the lag zone is known, we suggest a new inversion of the integral equation from elasticity theory to express the opening in terms of the pressure. We then calculate explicitly the contribution to the opening from the loading in the lag zone, and reformulate the problem over the fluid-filled portion of the crack. The asymptotic forms of the solution near and away from the tip are then discussed, It is shown that the solution is not only consistent with the square root singularity of linear elastic fracture mechanics, but that its asymptotic behavior at infinity is actually given by the singular solution of a semi-infinite hydraulic fracture constructed on the assumption that the fluid flows to the tip of the fracture and that the solid has zero toughness. Further, the asymptotic solution for large dimensionless toughness is derived, including the explicit dependence of the solution on the toughness. The intermediate part of the solution (in the region where the solution evolves from the near tip to the far from the tip asymptote) of the problem in the general case is obtained numerically and relevant results are discussed, including the universal relation between the fluid lag and the toughness.
332 citations
TL;DR: In this article, self-trapping of a white-light beam from an incandescent source was observed in both dimensions transverse to the beam when diffraction effects are balanced exactly by self-focusing in the host photorefractive medium.
Abstract: Optical pulses—wave-packets—propagating in a linear medium have a natural tendency to broaden in time (dispersion) and space (diffraction). Such broadening can be eliminated in a nonlinear medium that modifies its refractive index in the presence of light in such a way that dispersion or diffraction effects are counteracted by light-induced lensing1,2. This can allow short pulses to propagate without changing their shape2,3, and the ‘self-trapping’ of narrow optical beams1 whereby a beam of light induces a waveguide in the host medium and guides itself in this waveguide, thus propagating without diffraction4. Self-trapped pulses in space and time have been investigated extensively in many physical systems and, as a consequence of their particle-like behaviour, are known as ‘solitons’ (ref. 5). Previous studies of this phenomenon in various nonlinear media6,7,8,9,10,11,12 have involved coherent light, the one exception being our demonstration13 of self-trapping of an optical beam that exhibited partial spatial incoherence. Here we report the observation of self-trapping of a white-light beam from an incandescent source. Self-trapping occurs in both dimensions transverse to the beam when diffraction effects are balanced exactly by self-focusing in the host photorefractive medium. To the best of our knowledge, this is the first observation of self-trapping for any wave-packet that is both temporally and spatially incoherent.
315 citations
TL;DR: This work expresses the degree of coherence of the electromagnetic beam in terms of one of the generalized Stokes parameters, which obey precise laws of propagation, both in free space and in any linear medium, whether deterministic or random.
Abstract: A generalization of the Stokes parameters of a random electromagnetic beam is introduced. Unlike the usual Stokes parameters, which depend on one spatial variable, the generalized Stokes parameters, depend on two spatial variables. They obey precise laws of propagation, both in free space and in any linear medium, whether deterministic or random. With the help of the generalized Stokes parameters, the changes in the ordinary Stokes parameters upon propagation can be determined. Numerical examples of such changes are presented. The generalized Stokes parameters contain information not only about the polarization properties of the beam but also about its coherence properties. We illustrate this fact by expressing the degree of coherence of the electromagnetic beam in terms of one of the generalized Stokes parameters.
255 citations
TL;DR: In this paper, the authors consider the evolution of ultra-short optical pulses in linear and nonlinear media and compare the predictions of the traditional nonlinear Schrodinger equation (NLSE) approximation with those of the linear short-pulse equation (SPE).
Abstract: We consider the evolution of ultra-short optical pulses in linear and nonlinear media. For the linear case, we first show that the initial-boundary value problem for Maxwell's equations in which a pulse is injected into a quiescent medium at the left endpoint can be approximated by a linear wave equation which can then be further reduced to the linear short-pulse equation (SPE). A rigorous proof is given that the solution of the SPE stays close to the solutions of the original wave equation over the time scales expected from the multiple scales derivation of the SPE. For the nonlinear case we compare the predictions of the traditional nonlinear Schrodinger equation (NLSE) approximation with those of the SPE. We show that both equations can be derived from Maxwell's equations using the renormalization group method, thus bringing out the contrasting scales. The numerical comparison of both equations with Maxwell's equations shows clearly that as the pulse length shortens, the NLSE approximation becomes steadily less accurate, while the SPE provides a better and better approximation.
227 citations
TL;DR: In this paper, the authors derived necessary and sufficient conditions which the parameters of the source must satisfy in order to generate a physically realizable beam of this type, which provided certain constraints for synthesis, simulations and any application of such beams.
158 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 4 |
| 2019 | 9 |
| 2018 | 6 |
| 2017 | 5 |
| 2016 | 10 |