Highly sensitive refractometer with photonic crystal fiber long-period grating

We present highly sensitive refractometers based on a long-period grating in a large mode area PCF. The maximum sensitivity is 1500 nm/RIU at a refractive index of 1.33, the highest reported for any fiber grating. The minimal detectable index change is $2\times 10^{-5}$. The high sensitivity is obtained by infiltrating the sample into the holes of the photonic crystal fiber to give a strong interaction between the sample and the probing field.Comment: 4 pages, 3 figures, journal paper, submitte

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.Comment: 4 pages with 6 figure

Nonlocal incoherent solitons

We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons.Comment: 5 pages, 3 figure

Fusion, collapse, and stationary bound states of incoherently coupled waves in bulk cubic media

We study the interaction between two localized waves that propagate in a bulk (two transverse dimensions) Kerr medium, while being incoherently coupled through cross-phase modulation. The different types of stationary solitary wave solutions are found and their stability is discussed. The results of numerical simulations suggest that the solitary waves are unstable. We derive sufficient conditions for when the wave function is bound to collapse or spread out, and we develop a theory to describe the regions of different dynamical behavior. For localized waves with the same center we confirm these sufficient conditions numerically and show that only when the equations and the initial conditions are symmetric are they also close to being necessary conditions. Using Gaussian initial conditions we predict and confirm numerically the power-dependent characteristic initial separations that divide the phase space into collapsing and diffracting solutions, and further divide each of these regions into subregions of coupled (fusion) and uncoupled dynamics. Finally we illustrate how, close to the threshold of collapse, the waves can cross several times before eventually collapsing or diffracting

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.Comment: V1: 4 pages, 4 figures. V2: Accepted for publication in Physical Review E. 5 pages, 4 figures. Fig. 2 changed to be for fixed soliton width and to show soliton power. New simple relations in terms of power and pahse mismatch are include

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.Comment: 9 pages, 5 figure

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 $\pi$, 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.Comment: 3 pages with 3 figure

Directional supercontinuum generation: the role of the soliton

In this paper we numerically study supercontinuum generation by pumping a silicon nitride waveguide, with two zero-dispersion wavelengths, with femtosecond pulses. The waveguide dispersion is designed so that the pump pulse is in the normal-dispersion regime. We show that because of self-phase modulation, the initial pulse broadens into the anomalous-dispersion regime, which is sandwiched between the two normal-dispersion regimes, and here a soliton is formed. The interaction of the soliton and the broadened pulse in the normal-dispersion regime causes additional spectral broadening through formation of dispersive waves by non-degenerate four-wave mixing and cross-phase modulation. This broadening occurs mainly towards the second normal-dispersion regime. We show that pumping in either normal-dispersion regime allows broadening towards the other normal-dispersion regime. This ability to steer the continuum extension towards the direction of the other normal-dispersion regime beyond the sandwiched anomalous-dispersion regime underlies the directional supercontinuum notation. We numerically confirm the approach in a standard silica microstructured fiber geometry with two zero-dispersion wavelengths

The complete modulational instability gain spectrum of nonlinear QPM gratings

We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phase-matching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher order gain bands.Comment: 4 pages, 3 figures expanded with more explanation and mathematical detai