Structure of liquid crystals

Ostrovskiǐ, B. I.

doi:10.1070/pu1987v030n08abeh002943

Cited by 36 publications

(45 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Conversely, the existence of stable dark solitons requires the absence of MI of the constant intensity background. The phenomenon of MI has been identified and studied in various physical systems, such as fluids [20], plasma [21], nonlinear optics [22], discrete nonlinear systems [23], waveguide arrays, and Fermi-resonant interfaces [24]. It has been shown that MI is strongly affected by mechanisms such as saturation of the nonlinearity [25], coherence properties of optical beams [26], and linear and nonlinear gratings [27].…”

Section: Modulational Instabilitymentioning

confidence: 99%

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

Królikowski

Bang

Nikolov

et al. 2004

J. Opt. B: Quantum Semiclass. Opt.

399

322

View full text Add to dashboard Cite

show abstract

Section: Modulational Instabilitymentioning

confidence: 99%

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

Królikowski

Bang

Nikolov

et al. 2004

J. Opt. B: Quantum Semiclass. Opt.

399

322

View full text Add to dashboard Cite

show abstract

“…The MI is a general feature of continuum as well as discrete nonlinear wave equations and its demonstrations span a diverse set of disciplines, ranging from fluid dynamics [9] (where it is usually referred to as the Benjamin-Feir instability) and nonlinear optics [10] to plasma physics [11]. Additionally, the MI has been examined recently in the context of optical lattices in BECs both in one-dimensional and quasi-one dimensional systems, as well as in multiple dimensions.…”

Section: Introductionmentioning

confidence: 99%

Modulational instability of Gross-Pitaevskii-type equations in1+1dimensions

et al. 2003

View full text Add to dashboard Cite

The modulational stability of the nonlinear Schrödinger (NLS) equation is examined in the case with a quadratic external potential. This study is motivated by recent experimental studies in the context of matter waves in Bose-Einstein condensates (BECs). The theoretical analysis invokes a lens-type transformation that converts the Gross-Pitaevskii into a regular NLS equation with an additional growth term. This analysis suggests the particular interest of a specific time-varying potential (∼ (t + t ⋆ ) −2 ). We examine both this potential, as well as the time independent one numerically and conclude by suggesting experiments for the production of solitonic wave-trains in BEC.

show abstract

“…It involves the exponential growth of weak perturbations through the amplification of sideband frequencies, which causes a destructive modulation of the carrier wave. Many diverse physical systems exhibit MI, e.g., fluids [1], plasmas [2], nonlinear optics [3], molecular chains [4], and Fermi-resonant interface waves and waveguide arrays [5]. In nonlinear optics MI may appear as a transverse instability that breaks up a broad optical beam, thereby acting as a precursor for the formation of stable bright spatial solitons [6].…”

mentioning

confidence: 99%

Modulational Instability in Periodic Quadratic Nonlinear Materials

Corney

Bang

2001

Phys. Rev. Lett.

View full text Add to dashboard Cite

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature. DOI: 10.1103/PhysRevLett.87.133901 PACS numbers: 42.65.Tg, 42.65.Jx, 42.65.Ky The modulational instability (MI) of waveforms is a fundamental phenomenon in nonlinear media and is closely associated with the concept of self-localized waves, or solitons. Similar to solitons, MI occurs due to an interplay between nonlinear and dispersive or diffractive effects. It involves the exponential growth of weak perturbations through the amplification of sideband frequencies, which causes a destructive modulation of the carrier wave. In nonlinear optics MI may appear as a transverse instability that breaks up a broad optical beam, thereby acting as a precursor for the formation of stable bright spatial solitons [6]. Conversely, the stable propagation of dark solitons relies on the stability of the constant-intensity background and thus requires the absence of MI [7].Here we study optical media with a purely quadratic (x ͑2͒ ) nonlinearity. These materials are of significant technological interest due to their strong and fast cascaded nonlinearities [8], which can support stable bright solitons in all dimensions [9]. Moreover, they provide the most general means of studying nonlinear processes, because varying the phase mismatch between the fundamental and second-harmonic (SH) waves changes the nonlinearity from being distinctly quadratic to effectively cubic. The generality is further enhanced when the properties of the medium are modulated with long-period quasi-phase-matching (QPM) gratings. This periodicity not only allows one to tune the effective mismatch, but it also induces effective cubic nonlinearities [10,11], which may be engineered to different strengths and signs [12].Except in special cases, MI is unavoidable in x ͑2͒ materials. Optical pulses can be stable if the dispersion has opposite sign at the fundamental and SH frequencies [13]. Transverse inhomogeneities, as in x ͑2͒ waveguide arrays [5], and spatial incoherence [14] also eliminate MI. However, coherent cw beams propagating in pure homogeneous x ͑2͒ materials are always unstable [7]. Naturally, a cubic (Kerr) nonlinearity is always present in x ͑2͒ materials, and, if defocusing and sufficiently strong, it may eliminate MI [15]. Unfortunately, the cubic nonlinearity in conventional x ͑2͒ materials is usually focusing, though it may be a factor in the recent observation of apparently stable quadratic optical vortex solitons [16].We consider transverse MI of coherent cw ...

show abstract

Structure of liquid crystals

Cited by 36 publications

References 0 publications

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

Modulational instability of Gross-Pitaevskii-type equations in1+1dimensions

Modulational Instability in Periodic Quadratic Nonlinear Materials

Contact Info

Product

Resources

About