Diffraction Management

Eisenberg, Henryk; Silberberg, Yaron; Morandotti, Roberto; Aitchison, J. S.

doi:10.1103/physrevlett.85.1863

Cited by 519 publications

(410 citation statements)

References 21 publications

Supporting

Mentioning

395

Contrasting

Unclassified

Order By: Relevance

“…The result of this check is summarized in Fig.4.c where a clear separation of the central peaks of the pulses is visible in propagation, while the shapes of the individual pulses distort negligibly. , by solving numerically (7). We note that the fringes appear both in the initial superposition pattern as well as in propagated pattern, which is due to nonuniform phases of the constituent pulses.…”

Section: Fig2mentioning

confidence: 96%

“…We searched for particular spatio-temporal shapes of the pulses which are invariant under the propagation described by (7). The pulse propagating invariantly with the group velocity 1 V is obtained directly from (6):…”

Section: Fig2mentioning

confidence: 99%

“…The vanishing of the diffraction has been shown for the arrays of waveguides in [7], and more recently for 2-and 3-dimensional PCs [8]. The vanishing of diffraction means, that at some particular point of parameter space, and for a given frequency, the curvature of the spatial dispersion curve…”

mentioning

confidence: 95%

See 2 more Smart Citations

Subdiffractive light pulses in photonic crystals

et al. 2006

View full text Add to dashboard Cite

show abstract

Section: Fig2mentioning

confidence: 96%

Section: Fig2mentioning

confidence: 99%

See 1 more Smart Citation

Subdiffractive light pulses in photonic crystals

et al. 2006

View full text Add to dashboard Cite

show abstract

“…A great deal of attention has also been recently attracted to more special cases, when the diffraction is subject to various forms of management, so that the diffraction coefficient gradually vanishes or periodically changes its sign [1]. In particular, it was shown in Ref.…”

Section: Introductionmentioning

confidence: 99%

Spatial solitons under competing linear and nonlinear diffractions

et al. 2012

View full text Add to dashboard Cite

We introduce a general model which augments the one-dimensional nonlinear Schrödinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a Hamiltonian representation in a form natural for optical media. The equation serves as a model for spatial solitons near the supercollimation point in nonlinear photonic crystals. In the framework of this model, a detailed analysis of the fundamental solitary waves is reported, including the variational approximation (VA), exact analytical results, and systematic numerical computations. The Vakhitov-Kolokolov (VK) criterion is used to precisely predict the stability border for the solitons, which is found in an exact analytical form, along with the largest total power (norm) that the waves may possess. Past a critical point, collapse effects are observed, caused by suitable perturbations. Interactions between two identical parallel solitary beams are explored by dint of direct numerical simulations. It is found that in-phase solitons merge into robust or collapsing pulsons, depending on the strength of the nonlinear diffraction.

show abstract

“…In the most typical experimental situation, with the power of light beams 500 − 1000 W, the nonlinearity length in AlGaAs waveguides (whose nonlinearity is 500 time stronger than that of fused silica glass) takes values ∼ 1 − 2 mm, and the coupling length is ∼ 1 mm [11,12]. In fact, L coupl may vary in broad limits, as it exponentially depends on the separation h between the waveguides: for instance, L coupl decreases by a factor of 1.6 as h increases from 9 µm to 11 µm [11].…”

Section: Introductionmentioning

confidence: 99%

Domain walls in two-component dynamical lattices

2003

View full text Add to dashboard Cite

We introduce domain-wall (DW) states in the bimodal discrete nonlinear Schrödinger equation, in which the modes are coupled by cross phase modulation (XPM). The results apply to an array of nonlinear optical waveguides carrying two different polarizations of light, or two different wavelengths, with anomalous intrinsic diffraction controlled by direction of the light beam, and to a string of drops of a binary Bose-Einstein condensate, trapped in an optical lattice. By means of continuation from various initial patterns taken in the anti-continuum (AC) limit, we find a number of different solutions of the DW type, for which different stability scenarios are identified. In the case of strong XPM coupling, DW configurations contain a single mode at each end of the chain. The most fundamental solution of this type is found to be always stable. Another solution, which is generated by a different AC pattern, demonstrates behavior which is unusual for nonlinear dynamical lattices: it is unstable for small values of the coupling constant C (which measures the ratio of the nonlinearity and coupling lengths), and becomes stable at larger C. Stable bound states of DWs are also found. DW configurations generated by more sophisticated AC patterns are identified as well, but they are either completely unstable, or are stable only at small values of C. In the case of weak XPM, a natural DW solution is the one which contains a combination of both polarizations, with the phase difference between them 0 and π at the opposite ends of the lattice. This solution is unstable at all values of C, but the instability is very weak for large C, indicating stabilization as the continuum limit is approached. The stability of DWs is also verified by direct simulations, and the evolution of unstable DWs is simulated too; in particular, it is found that, in the weak-XPM system, the instability may give rise to a moving DW. The DW states can be observed experimentally in the same parameter range where discrete solitons have been found in the lattice setting.

show abstract

Diffraction Management

Cited by 519 publications

References 21 publications

Subdiffractive light pulses in photonic crystals

Subdiffractive light pulses in photonic crystals

Spatial solitons under competing linear and nonlinear diffractions

Domain walls in two-component dynamical lattices

Contact Info

Product

Resources

About