Third-Order Optical Nonlinearity in Novel Porphyrin Dimers

We investigate the third-order optical nonlinearities in four novel porphyrin dimers （dimers A to D） and a monomeric porphyrin H2 CPTPP measured by using the single-beam z-scan technique with a pulsed Q-switched Nd：YAG nanosecond laser at 532nm. All the samples show strong excited state absorption （ESA） and high value of Х^（3） in the ns domain at this wavelength. We perform a comparison between dimer A and its monomer H2 CPTPP in their third-order optical nonlinearity, and discuss the relationships between the values of Х^（3） and the different bridging groups for all the dimers.     

Optical beams in lossy non-local Kerr media

It is discussed that optical beams propagate in non-local Kerr medium waveguides with losses. A variational principle is carried out for the 1 + 1-D non-local non-linear Schrödinger equation in the presence of the losses. In the strongly non-local case, the approximate analytical solutions are obtained. The lossy soliton solution shows that, Unlike its local counterpart, such lossy strongly non-local soliton does not possess the adiabatic property anymore. In addition, the general approximate results for non-soliton cases are gained. The comparisons between our approximate analytic solutions and numerical simulations confirm our variational approximate solutions.     

Optical beams in sub-strongly non-local nonlinear media: A variational solution

Discussed is the propagation of optical beams in non-local nonlinear media modelled by 1 + 1D non-local nonlinear Schrödinger equation (NNLSE). In the sub-strongly non-local case, an approximate analytical solution is obtained for an arbitrary response function by a variational approach. Described by a combination of the Jacobian elliptic functions, the solution is periodic, and its period depends on not only the input power but also the initial beam width, which is confirmed by the numerical simulation of the NNLSE.     

Self-action effects in ionization and fragmentation of toluene by femtosecond laser pulses

Occurrence and influence of several self-action effects, induced in the entrance window of a time-of-flight interaction chamber, on the ion and fragment yields of the toluene molecule in the focus of a Ti:sapphire laser pulse are analyzed. Experimental data are obtained using different focusing geometries and are compared with results from numerical simulations using a nonlinear pulse propagation model as well as those from the strong-field S-matrix theory. It is shown that (a) self-focusing leads to a displacement of the focus while amplified small perturbations of the input beam result in hot spots in the spatial distribution and in an energy-dependent focus area, (b) small self-phase modulation changes the form of the spectrum and broadens it slightly. A strong increase of the toluene fragmentation appears to correlate to linear and nonlinear changes in the focal spot area, while the scenario of excitation of Raman modes proposed in an earlier publication is ruled out as the dominant effect.This revised version was published online in March 2005. In the previous version, the published online date was missing     

Optical limiting behavior of Sudan III dye doped polymer

The optical limiting performance of Sudan III dye doped into ethylene propylene diene polymethylene polymer (EPDM) is investigated using 532 nm, 10 ns pulses from a frequency-doubled Nd-YAG laser. The optical limiting behavior is investigated by transmission measurement through the sample at different concentrations. Our results show that the optical limiting efficiency is concentration dependent.     

Transformation of Sign of Nonlinear Refraction between Mo（W）/S/Cu Planar Metal Clusters

Optical nonlinear refractive properties of a series of Mo（W）/S/Cu planar square clusters are investigated using the Z-scan technique with the ns laser pulses at the wavelength of 532 nm. The result shows that the planar metal clusters containing the halogen ligands demonstrate the self-focusing effect, and the other planar metal dusters demonstrate the self-defocusing effect. These facts indicate that the halogen ligands can act as crucial factors in determining the sign of the nonlinear refraction of the Mo（W）/S/Cu planar metal clusters. The analysis of the experimental data shows that the planar clusters with halogen ligands possess greater refraction volume of the excited state than that of the ground state, while the other planar clusters possess the smaller refraction volume of the excited state than that of the ground state.     

(1 + 2)-Dimensional sub-strongly nonlocal spatial optical solitons: Perturbation method

By extending the (1 + 1)-dimensional [(1 + 1)-D] perturbation method suggested by Ouyang et al. [S. Ouyang, Q. Guo, W. Hu, Phys. Rev. E. 74 (2006) 036622] to the (1 + 2)-D case, we obtain a fundamental soliton solution to the (1 + 2)-D nonlocal nonlinear Schrödinger equation (NNLSE) with a Gaussian-type response function for the sub-strongly nonlocal case. Numerical simulations show that the soliton solution obtained in this paper can describe the soliton states in both the sub-strongly nonlocal case and the strongly nonlocal case. It is found that the phase constant and the power of the (1 + 2)-D strongly nonlocal spatial optical soliton with a Gaussian-type response function are both in inverse proportion to the 4th power of its beam width.     

Internal vibrations of nonlocal nonlinear Schrödinger soliton

We prove that the nonlocality is a source of the internal mode generation in a bright soliton of the nonlocal nonlinear Schrödinger equation, at least in the weak nonlocality limit. The internal mode bifurcates from the edge of the continuous spectrum of the linearized eigenvalue problem into the gap of this spectrum. A dependence of the internal mode propagation constant position in the gap on the nonlocality rate is established. It is shown that the vibration amplitude of the soliton decays inversely proportional to the propagation distance, as in the local models.     

Nonlinear refraction and absorption in hetero- thiometallic planar clusters

The nonlinear absorption and refraction of the clusters [MoS₄Cu₄Br₂(py)₆] and [Et₄N]₂[MoS₄Cu₄(SCN)₄(2-pic)₄] have been investigated using the z-scan technique with a ns laser at 532 nm wavelength. They have the same planar ‘open’ structures and the same skeleton metal atoms; the only difference is that the former has halogen ligands while the latter possesses pseudo-halogen groups – SCN – as ligands. Alteration of nonlinear refractive index and enhancement of nonlinear absorption were found in these two clusters. A steady state model of excited state nonlinear refraction was proposed to explain this phenomenon. Received: 12 June 2001 / Revised version: 4 September 2001 / Published online: 29 November 2001     

Elliptic incoherent spatial solitons and their interactions in strongly nonlocal media with an anisotropic nonlocality

We investigate the propagation and interaction of elliptic incoherent spatial solitons (EISS) in strongly nonlocal kerr media with an anisotropic nonlocality based on the coherent density approach. An exact analytical solution of such EISS is obtained; the results show that such EISS can form with both isotropic and anisotropic coherence. Moreover, we find that the interaction properties of EISS are very similar to that of their coherent counterpart. Some numerical examples are presented and pertinent physics features are addressed.     

Measurement of the nonlinear refractive index of SF6 with a hollow prism

We measure the nonlinear refractive index of SF₆ at three different CO₂ laser lines. Higher terms than the cubic nonlinearity are found and the behavior of the refractive index as a function of the laser intensity depends strongly on the frequency used, reflecting the characteristic SF₆ absorption dynamics.     

Optical and nonlinear optical characteristics of the Ge and GaAs nanoparticle suspensions prepared by laser ablation

The laser ablation of Ge and GaAs targets placed in water and ethanol was carried out using the fundamental radiation of nanosecond Nd:YLF laser. The results of preparation and the optical and nonlinear optical characterization of the Ge and GaAs nanoparticle suspensions are presented. The considerable shift of the band gap energy of the nanoparticles compared to the bulk semiconductors was observed. The distribution of nanoparticle sizes was estimated in the range of 1.5-10 nm on the basis of the TEM and spectral measurements. The nonlinear refractive indices and nonlinear absorption coefficients of Ge and GaAs nanoparticles were defined by the z-scan technique using second harmonic radiation of picosecond Nd:YAG laser (λ = 532 nm).     

Large Third-Order Optical Nonlinearity of a Novel Copper Phthalocyanine--Ferrocene Dyad

Third-order optical nonlinearity of a novel copper phthalocyanine-ferrocene dyad is measured by femtosecond forward degenerate four-wave mixing （DFWM） technique at 800 nm. The second-order hyperpolarizability of the novel copper phthalocyanine-ferrocene dyad is measured to be 1.74 ×10^-30 esu. This large and ultrafast thirdorder optical nonlinear response is mainly enhanced by the formation of intramolecular charge-transfer which can enhance the delocalized movements of the large π-electrons in the molecules.     

Third-Order Nonlinear Optical Properties of a Series of Polythiophenes

The third-order nonlinear optical properties of a series of polythiophenes are investigated with the Z-scan method under picosecond pulse laser irradiation at 532nm. The copolymers exhibit a good nonlinear response： large nonlinear refraction coefficients without nonlinear absorption. The signs of nonlinear refraction coefficients are positive, which are opposite to the negative signs of the polythiophene reported before. The mechanism accounting for the process of nonlinear refraction under pulse laser excitation is analyzed from the viewpoint of the electrondonor/acceptor units of polythiophenes. Moreover, changes of nonlinearity according to the lengths of main chains in polythiophene molecules are discussed.     

Nonlinear Optical Properties of Novel Polymeric Rare Earth Phthalocyanine Studied Using Picosecond Z-Scan Technique

Three novel tri-dimensional phthalocyanine polymers, with lanthanum （LaPPc）, gadolinium （GdPPc） and ytterbium （YbPPc） as centric atoms, have been synthesized from a tetranuclear phthalonitrile. Third-order optical nonlinearities of these compounds in DMF solution are measured by a picosecond Z-sacn technique at 532 nm. It is found that all the compounds show reverse saturation absorption and nonlinear self-focus refraction effect. The second-order molecular hyperpolarizabilities are calculated to be 1.82×10^-23, 1.48×10^-23 and 1.45×10^-23 esu for LaPPc, GdPPc and YbPPc, respectively. The differences among their nonlinear optical properties are attributed to the special tri-dimensional structure and the variation in rare earth atoms.     

Interaction of nonlocal incoherent spatial solitons

We investigate numerically the interaction of nonlocal incoherent spatial solitons in strongly nonlocal kerr media based on the coherent density approach. Numerical simulations show that the incoherent soliton position is very similar to the case of coherent soliton, and show that the incoherence plays an important role in the soliton interaction, while the role of other parameters such as the phase difference, the separation, the extent of nonlocality and the input power play in the interaction is very similar to the case of nonlocal coherent soliton. Some interesting numerical examples are presented to illustrate their interaction behavior further. Pertinent physics features are addressed.     

Interaction of Nonlocal Incoherent White-Light Solitons

The propagation and interaction of nonlocal incoherent white-light solitons in strongly nonlocal kerr media is investigated. Numerical simulations show that the interaction properties of nonlocal incoherent white-light solitons are different from the case in local media. The interactions of nonlocal incoherent white-light solitons are always attractive independent of their relative phase, while the other parameters such as the extent of nonlocality and the input power have a great impact on the soliton interactions. Pertinent numerical examples are presented to show their propagation and interaction behaviour further.     

Optical nonlinearity enhancement for an anisotropic semiconductor–insulator composite

We investigate the effect of geometric anisotropy on the optical nonlinearity enhancement for a periodic composite with a rectangular array of elliptic semiconducting cylinders in an insulating host. By using a series expression of the space-dependent electric field obtained by a simple Fourier method in a periodic composite, we calculate the frequency dependence of the effective third-order nonlinear susceptibility as a function of anisotropy. The results show that the height of the nonlinearity enhancement peak may be increased by several orders of magnitude as the aspect ratio of the ellises is decreased or the lattice edge length ratio is increased. At resonance frequency, there exists a strong anomalous dispersion. We also investigate the effect of the volume fraction of the semiconductor phase for composites with a square array of circular semiconducting cylinders. Received: 23 November 2000 / Accepted: 2 August 2001 / Published online: 17 October 2001     

Femtosecond laser pulse filamentation versus optical breakdown in H<Subscript>2</Subscript>O

The competition between femtosecond laser pulse induced optical breakdown and femtosecond laser pulse filamentation in condensed matter is studied both experimentally and numerically using water as an example. The coexistence of filamentation and breakdown is observed under tight focusing conditions. The development of the filamentation process from the creation of a single filament to the formation of many filaments at higher pulse energy is characterized systematically. In addition, strong deflection and modulation of the supercontinuum is observed. They manifest themselves at the beginning of the filamentation process, near the highly disordered plasma created by optical breakdown at the geometrical focus. Received: 9 July 2002 / Revised version: 15 November 2002 / Published online: 19 March 2003 RID="*" ID="*"Corresponding author. Fax: +1-418/6562-623, E-mail: wliu@phy.ulaval.ca