A precise data processing method for extracting χ from Z-scan technique

We present a precise data processing method, in the Z-scan experiments using a Gaussian beam and trimmed Airy beam, for directly extracting nonlinear refraction from the closed aperture Z-scan trace with the aid of the open aperture Z-scan trace when the materials exhibit nonlinear refraction and nonlinear absorption simultaneously. This method is still applicable when the nonlinear absorption is dominant and the closed aperture Z-scan curve degenerates into a single valley configuration, which is a salient advantage over other methods. In addition, we give gracefully empirical formulas with very high precision, which have good practicability for characterizing the optical nonlinearities of materials by use of the Gaussian beam and trimmed Airy beam Z-scan technique, respectively.     

Z-scan determination of third-order nonlinear optical nonlinearity of three azobenzenes doped polymer films

The third-order nonlinear response of methyl red (MR), methyl orange (MO) and p-dimethylamino benzene arsenic acid (PDBAA) doped polyvinyl alcohol (PVA) films are studied by using the Z-scan technique under 532 nm and 1064 nm excitations. The larger third-order nonlinear refractive index of PDBAA doped PVA film is discussed in terms of fall of the energy level in excited state for the effect of heavy-atom arsenic. At the end, the second hyperpolarizabilities of the films are estimated and the figures of merit are evaluated for their value of applications in ultra-fast all-optical devices.     

Enhanced sensitivity of Z-scan technique by use of flat-topped beam

Based on the Huygens–Fresnel diffraction integral method, we report a theoretical investigation on the closed-aperture Z-scan technique by using the flat-topped beam. The sensitivity of the flat-topped beam Z-scan technique, which can be enhanced with the increase of the flatness order N for the flat-topped beam, is greatly higher than of the Gaussian beam. Some salient characteristics of the flat-topped beam Z-scan traces are addressed. The flat-topped beam Z-scan technique for characterizing the instantaneous nonlinearity is also presented.     

Laser Mode-Dependent Size of Plasma Zones Induced by Femtosecond Laser Pulses in Fused Silica

We carry out the numerical simulations of femtosecond laser propagation with TEMoo mode, TEM10 mode and a beam combining both the modes in fused silica. It is found that the transverse size of plasma zones induced by laser pulses with the TEM10 mode is smaller than that induced by the TEM00 mode, while the longitudinal size is almost the same, and the saturated plasma density is higher. The transverse size, the longitudinal size and the ratio of the longitudinal to transverse size, for the beam combining both the modes, all could be reduced at the same time in comparison with the TEM00 mode under the same focusing conditions.     

Velocity of pulse propagation in media with amplitude nonlinearity

The propagation velocity of optical wave fronts can be accelerated by the influence of gain saturation. We report systematic measurements for the specific case of Brillouin gain in optical fibers. A simplified analytic rate equation approach permits a qualitative understanding of the observations in terms of a pure amplitude nonlinearity. We point out that there is a close analogy to a mode-locked laser with gain saturation. Pursuing this analogy, we can explain why the changes in propagation velocity are hardly measurable for synchronously pumped lasers, but easily amount to several percent for amplifiers or lasers based on stimulated Brillouin scattering.     

Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam

We calculate the radiation force that is exerted by a focused continuous-wave Gaussian beam of wavelength λ on a non-absorbing nonlinear particle of radius a ? 50λ/π. The refractive index of the mechanically-rigid particle is proportional to the incident intensity according to the electro-optic Kerr effect. The force consists of two components representing the contributions of the electromagnetic field gradient and the light scattered by the Kerr particle. The focused intensity distribution is determined using expressions for the six electromagnetic components that are corrected to the fifth order in the numerical aperture (NA) of the focusing objective lens. We found that for particles with a < λ/21.28, the trapping force is dominated by the gradient force and the axial trapping force is symmetric about the geometrical focus. The two contributions are comparable with larger particles and the axial trapping force becomes asymmetric with its zero location displaced away from the focus and towards the beam propagation direction. We study the trapping force behavior versus incident beam power, NA, λ, and relative refractive index between the surrounding liquid and the particle. We also examine the confinement of a Kerr particle that exhibits Brownian motion in a focused beam. Numerical results show that the Kerr effect increases the trapping force strength and significantly improves the confinement of Brownian particles.     

Concatenation of plasma filaments created in air by femtosecond infrared laser pulses

We report the first observation of the attachment of two single plasma filaments created collinearly in the atmosphere by IR femtosecond laser pulses. The linked filamentary structure is electrically conductive and emits sub-THz radiation over its entire length. Concatenation is achieved only for a specific time ordering between the two initial laser pulses. The pulse producing the filament closer to the laser source must be retarded with respect to the other pulse. This special time ordering is attributed to the acceleration of light in a self-guided pulse. Received: 4 March 2003 / Published online: 14 May 2003 RID="*" ID="*"Corresponding author. Fax: +33-1/6931-9996, E-mail: stzortz@ensta.fr     

Modulational instability in one-dimensional saturable waveguide arrays: Comparison with Kerr nonlinearity

Discrete modulational instability within the first band of uniform one-dimensional waveguide arrays possessing a saturable self-defocusing nonlinearity is investigated in detail within the coupled mode approach. Explicit analytical results for both the threshold and the maximal gain of instability are compared with the corresponding data from waveguide arrays exhibiting Kerr nonlinearity. We find that saturation bounds the interval of existence of discrete modulational instability, stabilizes the frequency region of perturbations around ±π/2 and decreases both gain and critical spatial frequency of perturbations.     

I-scan thermal lens experiment in the pulse regime for measuring two-photon absorption coefficient

We present a new pump-probe mode-mismatched thermal lens method for pulse excitation aimed to the measurement of nonlinear absorption coefficient in optical materials. We develop a theoretical model based on the Fresnel diffraction approximation and their predictions are verified experimentally with samples of Rhodamine 6G and Rhodamine B in ethanol solution. The principal advantage of this technique is that it does not require any mechanical movement during measurement. Below we perform the new type of thermal lens experiment in the pulse regime for the measurement of nonlinear absorption coefficient in transparent samples and we demonstrate the validity of theoretical predictions using an alternative method to the classical thermal lens technique.     

<Emphasis Type="Italic">Z</Emphasis>-scan technique through beam radius measurements

A modification to the well-known z-scan technique for measuring optical non-linearities is introduced. It is based on directly measuring the beam radius in the far field instead of the transmittance of the irradiance through an aperture, as in the original version. It has the advantage of being insensitive to beam pointing instability and is almost insensitive to power fluctuations. Furthermore, the calculations required for the determination of the non-linear parameters are simplified. For demonstrating the advantages of the modified method, beam radius and transmittance measurements were simultaneously taken in the standard non-linear optical material CS₂. Separate fittings of these measurements gave almost the same values for the non-linearities, quite similar to those in the literature. A common fitting has been applied to both sets of measurements, enhancing the accuracy of the method. Received: 8 July 2002 / Revised version: 18 October 2002 / Published online: 8 January 2003 RID="*" ID="*"Corresponding author. Fax: +30-2610/997470, E-mail: gianetas@physics.upatras.gr     

Theoretical study on stability of Z-scan technique by use of quasi-one-dimensional slit beam

The modified Z-scan technique using the quasi-one-dimensional slit (QODS) beam for characterizing the third-order optical nonlinearity has been reported recently. In the present work, we investigate the effect of the finite length of the slit in the QODS beam Z-scan for the practical experimental conditions, and then give an empirical expression that allows the direct estimation of nonlinear refraction coefficient from the measured normalized peak-valley transmittance difference. In particular, we explore relatively in detail the influences of the sample imperfection on the Z-scan traces, such as the hollow hole of the sample and the nonuniform nonlinearity. Compared with the other Z-scan techniques, such as the top-hat and Gaussian-beam Z-scans, we find that the QODS beam Z-scan has the great improvement for the sample imperfections. The results suggest that the QODS beam Z-scan is a more promising and useful technique for characterizing the optical nonlinearity of an imperfect sample.     

Formation of Hot Images in Laser Beams through a Self-defocusing Kerr Medium Slab

A nonlinear hot image is usually thought as of a special case of self-focusing, and thus occurs when a laser beam propagates through a slab of self-focusing medium. Here we show theoretically that a hot image may also be formed by a thin slab of self-defocusing medium. The physical origin for this hot image formation is akin to the in-line volume-phase holographic imaging due to the intensity-dependent refractive-index modulation of the self- defocusing medium. NumericM simulations confirm the theoretical prediction and further identify the dependence of the hot image on the beam power, the modulation depth of obscuration and the thickness of self-defocusing medium. The analysis presented here brings new insight into the physics of hot image formation in the high power laser system.     

Quasi-stable propagation of vortices and soliton clusters in saturable Kerr media with square-root nonlinearity

Analytical and numerical investigation of the propagation of optical beams in Kerr-like saturable photorefractive media is carried out, utilizing a novel model for the local isotropic part of the space-charge field generated in the medium. Using a variational technique, optimal propagation parameters for the most stable propagation of otherwise unstable single Gaussian, single vortex, and optical soliton cluster beams are determined. Analogy between a ring of identical weakly overlapping solitons and a vortex of the same topological charge is explored.     

Surface defect gap solitons in superlattices with self-defocusing nonlinearity

We put forward the existence and stability of defect surface gap solitons at the interface between uniform media and an superlattice with self-defocusing nonlinearity. We reveal that the defect plays the significant role in controlling the region of solitons existing. Various solitons are found to be existed in different gaps for different defects. For positive defects, fundamental solitons can exist stably in the semi-infinite gap, and dipole solitons can exist stably in the first gap but they are unstable in the second gap. For zero or negative defects, fundamental and dipole solitons can exist stably in the first gap and the second gap, respectively.     

The origin of the super-resolution via a nonlinear thin film

In laser applications, resolutions beyond the diffraction limit can be obtained with a thin film of strong optical nonlinear effect. The optical index of the silicon thin film is modified with the incident laser beam as a function of the local field intensity n(r)∼E²(r). For ultrathin films of thickness d?λ, the transmitted light through the film forms a profile of annular rings. Therefore, the device can be related to the realization of super-resolution with annular pupils. Theoretical analysis shows that the focused light spot appears significantly reduced in comparison with the diffraction limit that is determined by the laser wavelength and the numerical aperture of the converging lens. Analysis on the additional optical transfer function due to the thin film confirms that the resolving power is improved in the high spatial frequency region.     

Femtosecond filamentation in air at low pressures: Part I: Theory and numerical simulations

We investigate numerically the influence of the pressure on femtosecond filamentation in air. We show that femtosecond filamentation occurs at low pressure and compute the features of the plasma channel generated in the wake of the pulse. We discuss the influence of the pulse duration, chirp and input beam shape on the length of the plasma channels. These calculations constitute a prerequisite for laboratory experiments over short distances as well as for vertical femtosecond filamentation at high altitude on which light detection and ranging techniques or lightning protection rely.     

Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid-crystalline polymer

The nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid-crystalline polymer were investigated. The single beam Z-scan measurement showed the polymer film possessed a value of nonlinear refractive index n₂ = −1.07 × 10⁻⁹ cm²/W under a picosecond 532 nm excitation. Photoinduced anisotropy in the polymer was studied through dichroism and photoinduced birefringence. A photoinduced birefringence value Δn ∼ 10⁻² was achieved in the polymer film. The mechanism for the nonlinear optical response and the physical process of photoinduced anisotropy in the polymer were discussed.     

Wavelength dependence of nonlinear absorption in a bis-phthalocyanine studied using the Z-scan technique

The wavelength dependence of the nonlinear absorption of a bis-phthalocyanine, Nd(Pc)₂, dissolved in dimethyl formamide was studied in the rising part of the Q-band using the open aperture Z-scan technique, to determine the wavelength region over which the nonlinear absorption changes from reverse saturable absorption to saturable absorption. It was found that the sample could be used as a reverse saturable absorber, and hence as an optical limiter, up to a wavelength of about 604 nm. The imaginary part of the third order susceptibility was also calculated for these wavelengths. Resonant enhancement of the imaginary part of the third order susceptibility was clearly observed. Received: 26 April 2002 / Revised version: 30 June 2002 / Published online: 20 December 2002 RID="*" ID="*"Corresponding author. Fax: +91-484/576-714, E-mail: kpu@cusat.ac.in RID="**" ID="**"Present address: Optical Sciences Center, University of Arizona, Tucson, USA     

Study of optical nonlinearity of functionalized multi-wall carbon nanotubes by using degenerate four wave mixing and Z-scan techniques

The phase conjugation geometry of degenerate four wave mixing (DFWM) technique has been employed to study the third-order optical nonlinear susceptibility (χ³) and second-order hyperpolarizability of multi-wall carbon nanotubes (MWCNTs). MWCNTs were grown by thermal chemical vapor deposition method and, subsequently functionalized with carboxylic acid group to improve their solubility in an organic solvent, ethylene glycol. The average hyperpolarizability for each carbon atom has been found to be 4.74 × 10⁻⁴⁶ m⁵/V² for the pump pulse of 8 ns at 532 nm. Decreasing the pulse width of the pump laser decreases the average value of hyperpolarizability. The absorption spectra show a monotonous increase from IR through visible and give an opportunity to estimate the imaginary part of the χ³ by the open aperture Z-scan technique.     

Dynamics of Incoherent Photovoltaic Spatial Solitons

Propagation properties of bright and dark incoherent beams are numerically studied in photovoltaic-photorefractive crystal by using coherent density approach for the first time. Numerical simulations not only exhibit that bright incoherent photovoltaic quasi-soliton, grey-like incoherent photovoltaic soliton, incoherent soliton doublet and triplet can be established under proper conditions, but also display that the spatial coherence properties of these incoherent beams can be significantly affected during propagation by the photovoltaic field.