arXiv subjects

Ole Bang

Publications and source records attributed to Ole Bang.

51 records · Page 3Linked to original sources

arXiv2002

Engineering of spatial solitons in two-period QPM structures

We report on a scheme which might make it practically possible to engineer the effective competing nonlinearities that on average govern the light propagation in quasi-phase-matching (QPM) gratings. Modulation of the QPM period with a second longer period, introduces an extra degree of freedom, which can be used to engineer the effective quadratic and induced cubic nonlinearity. However, in contrast to former work here we use a simple phase-reversal grating for the modulation, which is practically realizable and has already been fabricated. Furthermore, we develop the theory for arbitrary relative lengths of the two periods and we consider the effect on solitons and the bandwidth for their generation. We derive an expression for the bandwidth of multicolor soliton generation in two-period QPM samples and we predict and confirm numerically that the bandwidth is broader in the two-period QPM sample than in homogeneous structures.

nlin.PS↗

arXiv2002

Collapse arrest and soliton stabilization in nonlocal nonlinear media

We investigate the properties of localized waves in systems governed by nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric, but can be of completely arbitrary shape. We use variational techniques to find the soliton solutions and illustrate the stabilizing effect of nonlocality.

nlin.PS↗

arXiv2001

Escape angles in bulk chi(2) soliton interactions

We develop a theory for non-planar interaction between two identical type I spatial solitons propagating at opposite, but arbitrary transverse angles in quadratic nonlinear (or so-called chi(2)) bulk media. We predict quantitatively the outwards escape angle, below which the solitons turn around and collide, and above which they continue to move away from each other. For in-plane interaction the theory allows prediction of the outcome of a collision through the inwards escape angle, i.e. whether the solitons fuse or cross. We find an analytical expression determining the inwards escape angle using Gaussian approximations for the solitons. The theory is verified numerically.

nlin.PS↗

arXiv2001

Generic features of modulational instability in nonlocal Kerr media

The modulational instability (MI) of plane waves in nonlocal Kerr media is studied for a general, localized, response function. It is shown that there always exists a finite number of well-separated MI gain bands, with each of them characterised by a unique maximal growth rate. This is a general property and is demonstrated here for the Gaussian, exponential, and rectangular response functions. In case of a focusing nonlinearity it is shown that although the nonlocality tends to suppress MI, it can never remove it completely, irrespectively of the particular shape of the response function. For a defocusing nonlinearity the stability properties depend sensitively on the profile of the response function. It is shown that plane waves are always stable for response functions with a positive-definite spectrum, such as Gaussians and exponentials. On the other hand, response functions whose spectra change sign (e.g., rectangular) will lead to MI in the high wavenumber regime, provided the typical length scale of the response function exceeds a certain threshold. Finally, we address the case of generalized multi-component response functions consisting of a weighted sum of N response functions with known properties.

nlin.PS↗

arXiv2001

Modulational instability in periodic quadratic nonlinear materials

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.

nlin.PS↗

arXiv2001

Modulational instability in nonlocal nonlinear Kerr media

We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespectively of the particular profile of the nonlocal response function. For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose-Einstein condensates.

nlin.PS↗

arXiv2001

Accurate switching intensities and length scales in quasi-phase-matched materials

We consider unseeded Type I second-harmonic generation in quasi-phase-matched (QPM) quadratic nonlinear materials and derive an accurate analytical expression for the evolution of the average intensity. The intensity-dependent nonlinear phase mismatch due to the QPM induced cubic nonlinearity is found. The equivalent formula for the intensity for maximum conversion, the crossing of which changes the nonlinear phase-shift of the fundamental over a period abruptly by $π$, corrects earlier estimates by more than a factor of 5. We find the crystal lengths necessary to obtain an optimal flat phase versus intensity response on either side of this separatrix intensity.

nlin.PS↗

arXiv2000

Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of nonlinear impurity modes --- one- and two-hump symmetric localized modes and asymmetric localized modes --- for both focusing and defocusing nonlinearity and two different (attractive or repulsive) types of impurity. We obtain an analytical stability criterion for the nonlinear localized modes and consider the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site.

nlin.PS↗

arXiv2000

Solitons in quadratic nonlinear photonic crystals

We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities and numerically find previously unknown soliton families. The inclusion of the induced cubic terms enables us to show that solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons are stable under propagation.

nlin.PS↗

arXiv2000

Robustness of Quadratic Solitons with Periodic Gain

We address the robustness of quadratic solitons with periodic non-conservative perturbations. We find the evolution equations for guiding-center solitons under conditions for second-harmonic generation in the presence of periodic multi-band loss and gain. Under proper conditions, a robust guiding-center soliton formation is revealed.

nlin.PS↗

arXiv2000

Solitons in nonlocal nonlinear media: exact results

We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties of these solitons and show their stability.

nlin.PS↗

arXiv2000

Parametric localized modes in quadratic nonlinear photonic structures

We analyze two-color spatially localized modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi-2) nonlinear interfaces embedded into a linear layered structure --- a quasi-one-dimensional quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi-2 equations), and find, numerically and analytically, the spatially localized solutions --- discrete gap solitons. For a single nonlinear interface in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities and differences with quadratic solitons in homogeneous media.

nlin.PS↗

arXiv2000

Multi-component optical solitary waves

We discuss several novel types of multi-component (temporal and spatial) envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for high performance computer networks, multi-colour parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons due to quasi-phase-matching in Fibonacci optical superlattices.

nlin.PS↗

arXiv1999

Quasiperiodic Envelope Solitons

We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally.

patt-sol↗

arXiv1999

Two-color nonlinear localized photonic modes

We analyze second-harmonic generation (SHG) at a thin effectively quadratic nonlinear interface between two linear optical media. We predict multistability of SHG for both plane and localized waves, and also describe two-color localized photonic modes composed of a fundamental wave and its second harmonic coupled together by parametric interaction at the interface.

patt-sol↗