Biomedical subjects
Publications and source records attributed to Jianke Yang.
We demonstrate a ring-shaped Bessel-like photonic lattice akin to a photonic bandgap fiber with a low-index core. While the ring lattice is optically induced in a bulk crystal with a self-defocusing nonlinearity, guidance of a probe beam propagating linearly through the core is clearly observed. The possible mechanism for such guidance is also discussed.
We report the first experimental demonstration of band-gap guidance of light in an optically induced two-dimensional photonic lattice with a single-site negative defect (akin to a low-index core in photonic-crystal fibers). We discuss the difference between spatial guidance at a regular and a defect site, and show that the guided beam through the defect displays fine structures such as vortex cells that arise from defect modes excited at higher band gaps. Defect modes at different wavelengths are also observed.
Nonlinear defect modes (defect solitons) and their stability in one-dimensional photonic lattices with focusing saturable nonlinearity are investigated. It is shown that defect solitons bifurcate out from every infinitesimal linear defect mode. Low-power defect solitons are linearly stable in lower bandgaps but unstable in higher bandgaps. At higher powers, defect solitons become unstable in attractive defects, but can remain stable in repulsive defects. Furthermore, for high-power solitons in attractive defects, we found a type of Vakhitov-Kolokolov (VK) instability which is different from the usual VK instability based on the sign of the slope in the power curve. Lastly, we demonstrate that in each bandgap, in addition to defect solitons which bifurcate from linear defect modes, there is also an infinite family of other defect solitons which can be stable in certain parameter regimes.
Linear defect modes in one-dimensional photonic lattices are studied theoretically. For negative (repulsive) defects, various localized defect modes are found. The strongest confinement of the defect modes appears when the lattice intensity at the defect site is nonzero rather than zero. When launched at small angles into such a defect site of the lattice, a Gaussian beam can be trapped and undergo snake oscillations under appropriate conditions.
We study the generalized third-order nonlinear Schrodinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons.
We demonstrate the formation of fundamental and dipolelike vector solitons in an optically induced two-dimensional photonic lattice. Such vector solitons are realized by mutual trapping of two beams in the lattice. Our theoretical results are in good agreement with experimental observations.
Dipole solitons in a two-dimensional optically induced photonic lattice are theoretically predicted and experimentally demonstrated for the first time to our knowledge. It is shown that such dipole solitons are stable and robust under appropriate conditions. Our experimental results are in good agreement with theoretical predictions.
Fundamental and vortex solitons in a two-dimensional optically induced waveguide array are reported. In the strong localization regime the fundamental soliton is largely confined to one lattice site, whereas the vortex state comprises four fundamental modes superimposed in a square configuration with a phase structure that is topologically equivalent to the conventional vortex. However, in the weak localization regime, both the fundamental and the vortex solitons spread over many lattice sites. We further show that fundamental and the vortex solitons are stable against small perturbations in the strong localization regime.
Stable embedded solitons are discovered in the generalized third-order nonlinear Schrödinger equation. When this equation can be reduced to a perturbed complex modified Korteweg-de Vries equation, we developed a soliton perturbation theory which shows that a continuous family of sech-shaped embedded solitons exist and are nonlinearly stable. These analytical results are confirmed by our numerical simulations. These results establish that, contrary to previous beliefs, embedded solitons can be robust despite being in resonance with the linear spectrum.
We study both analytically and numerically the existence, uniqueness, and stability of vortex and dipole vector solitons in a saturable nonlinear medium in (2+1) dimensions. We construct perturbation series expansions for the vortex and dipole vector solitons near the bifurcation point, where the vortex and dipole components are small. We show that both solutions uniquely bifurcate from the same bifurcation point. We also prove that both vortex and dipole vector solitons are linearly stable in the neighborhood of the bifurcation point. Far from the bifurcation point, the family of vortex solitons becomes linearly unstable via oscillatory instabilities, while the family of dipole solitons remains stable in the entire domain of existence. In addition, we show that an unstable vortex soliton breaks up either into a rotating dipole soliton or into two rotating fundamental solitons.
Two related problems on scalar (2+1)-dimensional solitons in a saturable nonlinear medium are investigated. The first one is the internal oscillations of fundamental (single-hump) solitons. Internal modes which cause these oscillations, both with and without angular dependence, are discovered. The visual effect of angle-dependent internal modes on the soliton can be a rotation or spatially uneven breathing of the perturbed soliton. These internal oscillations are very robust and persist for a very long distance. The second problem is the instability of double-hump and radially symmetric solitons. Unstable eigenmodes of these solitons are presented. Contrary to intuition, the instability growth rates decrease to zero when the soliton power becomes high. Thus the instability is strongly suppressed at high powers. This phenomenon is corroborated by our direct numerical simulations.
A direct perturbation theory for solitons of the derivative nonlinear Schrödinger (DNLS) equation is developed based on a closure of eigenfunctions of the linearized DNLS equation around a one-soliton solution. The slow evolution of soliton parameters and the perturbation-induced radiation are obtained. Under the known simple gaugelike transformation, these results are transformed into those for the perturbed modified nonlinear Schrödinger (MNLS) equation describing propagation of femtosecond pulses in optical fibers. A calculation of the perturbation-induced radiation fields for the perturbed DNLS and MNLS equations is also made. Our results for the perturbed MNLS equation can be reduced perfectly to those for the perturbed nonlinear Schrödinger equation in the small nonlinear-dispersion limit.
In this paper, we study the interaction of two vector solitons in the Manakov equations that govern pulse transmission in randomly birefringent fibers. Under the assumptions that these solitons initially are well separated and having nearly the same amplitudes and velocities but arbitrary polarizations, we derive a reduced set of ordinary differential equations for both solitons' parameters. We then solve this reduced system analytically. Our analytical solutions show that, when two Manakov solitons have the same amplitude and phases, their collision distance steadily increases as their initial polarizations change from parallel to orthogonal. In particular, the collision distance at orthogonal polarizations is of the order of the square of the collision distance at parallel polarizations. When the Manakov solitons have different amplitudes, a quasiequidistant bound state can be formed. The degrees of position and amplitude oscillations in this bound state diminish as the initial polarizations change from parallel to orthogonal. With a combination of launching Manakov solitons along orthogonal polarizations and at unequal amplitudes, Manakov-soliton interference is almost completely suppressed. These theoretical results are in excellent agreement with our direct numerical simulations.