Composite spatial solitons in a saturable nonlinear bulk medium

We review the generation of the recently predicted multi-component spatial optical solitons in a saturable nonlinear bulk medium. We present numerical simulations for an effectively isotropic model and experimental results for a set of different combinations of a Gaussian beam co-propagating incoherently with a beam of a more complex internal structure, such as a higher order transverse laser mode. We discuss the different formation processes and the general properties of a variety of different dipole-mode composite solitons and expand our investigations to the generation of a quadrupole-mode composite soliton. Received: 1 December 2000 / Revised version: 12 January 2001 / Published online: 21 March 2001     

Selective laser heating and nonlinear light scattering in a homogeneous medium

Observation of light scattering on the laser-produced temperature inhomogeneities, the centres of which are connected with some absorbing molecules, is reported. The experimentally observed scattering intensity agrees well theory.     

Wavefront study in a Gaussian beam passed through a nonlinear optical medium

We present a numerical model to study the wavefront of a Gaussian laser beam propagated through a nonlinear Kerr media. The model is based on the Gaussian decomposition method. The interaction between a laser beam and a self-focusing or self-defocusing media is discussed from the viewpoint of wavefront distortion. The method is useful for simulation of the wavefront of the beam next to the sample. We also compare our results with those obtained from z-scan method. There is a quite good agreement between data from z-scan method and our results.     

Planar spatiotemporal solitons in a quadratic nonlinear medium

The averaged Lagrangian method has been used to derive an analytical solution in the form of planar light bullets for the system of equations describing the second-harmonic generation in a medium with anomalous dispersion. The stability of this solution is confirmed by the simulation for different relations between the nonlinearity, diffraction, and dispersion in the cases of input pulses at both frequencies and at only the fundamental frequency.     

Calculation of nonlinear optical polarization and phase matching in biaxial crystals

We present a general, analytical formula for the calculation of the unit vectors of the direction of vibration of the electric field strength in biaxial crystals. By means of this formula it is possible to calculate the effective nonlinearity for second-order nonlinear optical frequency conversion processes in biaxial crystals. For two highly efficient nonlinear optical crystals we have calculated the effective nonlinear susceptibility and walk-off angles. The results have been compared with numerical as well as experimental data of previous papers.     

Effective medium approximation for optical bistability in nonlinear metal-dielectric composites

A general theory based on the spectral representation method and effective medium approximation is adopted to investigate the optical bistable behavior in a nonlinear two-phase composite with symmetrical microstructure, in which the metal particles of the volume fraction p and the dielectric particles of the volume fraction 1−p are randomly dispersed but oriented with respect to one another. The relation between the spatial average of local field squared and the external applied field is established through the spectral density function m(x), obtained from the modified Bruggeman effective medium approximation. We find that the optical bistability (OB) is dependent on the depolarization factor L of the components and the volume fraction p. For a given p, we predict that OB can be observed only when L is larger than the critical value L_c, and bistable behavior is more pronounced at large L. Moreover, numerical results show that both the upper threshold field and the width of OB region increase monotonically as L increases. The field-dependent reflectance at normal incidence R in random composites is also investigated.     

P-polarized nonlinear surface polaritons near the surface of a saturable self-defocusing medium: Threshold case

We have obtained the solution of the stationary problem for P-polarized nonlinear surface polaritons (NLSP) near the interface of two media, one of which is optically linear and the other having an optical nonlinearity with saturation and a dielectric function of the form: =_xx=_zz=₀+a|E|²/(1+b|E|²), where E is the amplitude of the electric field. On this basis the NLSP energy and propagation properties, the polarization structure and the localization depth of the NLSP field as well as the physically allowed region in the parameter space have been investigated for the case in which the parameter ₀ is positive, b is non-negative, and a and ₁ are negative (₁ is the dielectric function of the linear medium); ₀>|₁|.     

Exact spatial soliton solution for nonlinear Schrödinger equation with a type of transverse nonperiodic modulation

In this paper, we analyze (2 + 1)D nonlinear Schrödinger (NLS) equation based on a type of nonperiodic modulation of linear refractive index in the transverse direction. We obtain an exact solution in explicit form for the (2 + 1)D nonlinear Schrödinger (NLS) equation with the nonperiodic modulation. Finally, the stability of the solution is discussed numerically, and the results reveal that the solution is stable to the finite initial perturbations.     

Self-ordered dendrimers based on multi-octupolar ruthenium complexes for quadratic nonlinear optics

A quasi-optimized supramolecular octupolar ordering has been achieved in a metallodendrimer made of several ruthenium tris-bipyridine complexes displaying high nonlinear optical efficiency. This acentric organization is evidenced by Harmonic Light scattering at 1.9 μm, where a coherent second harmonic emission from each dendrimer unit is compared to the fully incoherent harmonic signal from a disordered linear polymer containing the same nonlinear complexes. These results show the interest of a controlled coordination strategy to build supramolecules and dendritic structures, with promising perspectives towards nanoscale applications in photonics.     

Spatial filtering in the detection of thermal transverse phase modulation of laser beams

We study the application of spatial filtering to the far field detection of a probe beam with transverse phase modulation induced by the refractive index distribution generated in an optically thin film by the steady state absorption of a pump beam. To this end we introduce a mathematical model able to describe the phenomenon and we study the dependence of the detected signal on the radius and the position of a circular stop operating as a spatial filter. We show, by computer calculations, that spatial filtering allows enhancement of signal/background ratio as has already been shown for the case of pulsed thermal lens spectroscopy. We give an explicit expression of the detected signal as a function of sample properties that can be used for the interpretation of measurements.     

Cross phase modulation in a five–level atomic medium: semiclassical theory

The interaction of a five-level atomic system involving electromagnetically induced transparency with four light fields is investigated. Two different light-atom configurations are considered, and their efficiency in generating large nonlinear cross-phase shifts compared. The dispersive properties of those schemes are analyzed in detail, and the conditions leading to group velocity matching for two of the light fields are identified. An analytical treatment based on amplitude equations is used in order to obtain approximate solutions for the susceptibilities, which are shown to fit well with the numerical solution of the full Bloch equations in a large parameter region.     

Numerical study of energy transfer between a beam and its internal reflection component in a nonlinear medium

A theoretical study is presented of a special case of stationary energy transfer in degenerate two-wave mixing in a reflection geometry. The two interacting beams consist of a beam and its first-order internal reflection component created at the boundary of a nonlinear medium. Numerical results obtained from the computer calculations are presented as graphs. It is found that, under suitable conditions, this phenomenon can be used to eliminate the multiple internal reflections.     

The spectral broadening of a blue optical pulse and the modulation of a pulse waveform in a photonic crystal fiber by induced-phase modulation

By copropagating a fundamental pulse and a blue second-harmonic pulse from a Ti:Sapphire oscillator in a photonic crystal fiber (PCF), the spectral broadening of the blue second-harmonic pulse from 380 to 600 nm has been observed by use of induced-phase modulation (IPM) at a 78-MHz repetition rate. From the experimental and the calculated delay time dependence of spectral intensities, it was inferred that the largest spectral broadening was observed when the second-harmonic pulse interacted with the fundamental pulse near the input end of a PCF, where the fundamental pulse was compressed temporally due to self-phase modulation and negative group velocity dispersion. From the simulation, the mechanism of spectral broadening was clarified and the fission process of the fundamental pulse was shown to be influenced strongly by IPM.     

Optical modes in a nonlinear double-channel waveguide

We analytically address different types of optical modes in a coupler composed by two nonlinear optical waveguides. It is shown that the coupler not only supports symmetry-preserving modes but also symmetry-breaking modes. In addition, the properties on the existence and bifurcation of those modes are analyzed in detail.     

Threshold of oscillation in a ring-loop phase conjugator as a second-order optical phase transition

The threshold behavior is studied for a ring-loop coherent oscillator with a photorefractive strontium barium niobate (SBN) sample. A soft onset of oscillation is revealed and critical slowing down is observed in the temporal development of light-induced scattering below the threshold, thus pointing to a similarity with a second-order phase transition. Received: 10 July 2000 / Published online: 20 September 2000     

Analytical functions for the optimization of second-harmonic generation and parametric generation by focused Gaussian beams

An analytical function involving four parameters is proposed to express the second-harmonic generation efficiency as well as the parametric generation gain coefficient in the Boyd–Kleinman theory. The analytical function clearly reveals the dependence of conversion efficiency on the focusing parameter and the walk-off parameter. Moreover, the optimum focusing parameter and its corresponding maximum efficiency are explicitly given in the analytical function, leading to a straightforward evaluation of a given crystal performance. Received: 20 January 2003 / Published online: 22 May 2003 RID="*" ID="*"Corresponding author. Fax: +886-35/7291-34, E-mail: yfchen@cc.nctu.edu.tw