Theoretical study of saturable Kerr nonlinearity using top-hat beam Z-scan technique

Saturable Kerr nonlinearity is theoretically investigated by use of the top-hat beam Z-scan technique. The saturation intensity changes the nonlinear refractive profile and decreases the sensitivity of the Z-scan measurements, which were quantitatively analyzed. An empirical formula for the saturable Kerr nonlinearity, which gave the relationship between the light intensity and the peak-valley transmittance difference, was accomplished. A high-accuracy method to determine the nonlinear refractive index and the characteristic saturation intensity was proposed.     

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.     

Birth and evolution of wave-front dislocations in a laser beam passed through a photorefractive LiNbO3: Fe crystal

We report on an experimental and numerical investigation of the process of spontaneous optical vortices nucleation in a wave front of a laser beam passed through a photorefractive LiNbO₃ : Fe crystal with self-induced nonlinear lens. The complex lens structure produces mainly defocusing of the beam passing through the crystal due to a negative variation of the refractive index, whereas side parts of the lens have a positive sign of refractive-index variation and partially focus the beam. The resulting wave-front distortions lead to a phase bifurcation occurring at a certain distance after the crystal when the amplitude of the light wave becomes zero. We study in detail the process of edge dislocation nucleation and its decay in the near field producing a pair of unity-charged opposite-sign screw dislocations. After birth, they spread along dislocation axes as stable objects.     

Measurement of nonlinear properties and optical limiting ability of Rhodamine6G doped silica and polymeric samples

The third order nonlinear optical properties of Rhodamine6G (Rh6G) doped silica and polymeric samples have been investigated using single beam z-scan technique under excitation by the second harmonic of Nd:YAG laser beam (532 nm). The nonlinear refractive index, nonlinear absorption coefficient, real and imaginary parts of third order nonlinear susceptibility in the samples of silica and poly-methylmethacrylate (PMMA) matrices are measured. Thermal contribution to the nonlinear refractive index in case of undoped silica samples has been calculated in order to have better accuracy of the material response contribution to third order nonlinearity. The comparative study of the optical limiting performance of Rh6G doped silica and polymeric samples show that Rh6G doped silica is relatively superior for optical limiting applications.     

Nonlinear responses and optical limiting behavior of Basic Violet 16 dye under CW laser illumination

Nonlinear optical properties of Basic Violet 16 dye solution in water are studied employing different optical techniques. Experiments are performed using the second harmonic of a continuous Nd-Yag laser beam at 532 nm wavelength and 100 mW power. The effect of nonlinearity of Basic Violet 16 dye in broadening the laser beam is observed. The optical limiting behavior is investigated by measuring the transmission of the samples. The third-order nonlinearity, χ³ of Basic Violet 16 dye, is measured using Z-scan data. The nonlinear absorption coefficient is calculated using the open aperture Z-scan data, while its nonlinear refractive index is measured using the closed aperture Z-scan data. All experiments are done for different concentrations and thicknesses of Basic Violet 16 dye solution. The effect of intensity of input laser beam on the nonlinear susceptibility is studied experimentally. Results indicate that Basic Violet 16 dye is a potential candidate for low-power optical limiting applications.     

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.     

Optical switching of 2-(2<Superscript>′</Superscript>-hydroxyphenyl) benzoxazole in different solvents

All-optical switching and beam deflection of 2-(2^′-hydroxyphenyl) benzoxazole (HBO) in three species of solvent (cyclohexane, ethanol and dimethyl sulfoxide) have been investigated by using third-harmonic generation (355 nm) of a mode-locked Nd:YAG laser as a pump beam and a continuous-wave He-Ne laser (632.8 nm) as a probe beam. The nonlinear refractive indices of HBO in different solvents are determined by using the Z-scan technique. The optical switching and beam-deflection effects are due to the change of the refractive index of HBO under the pump beam. Through the study of the absorption spectra and the fluorescence spectra of HBO in different solvents, we conclude that the principal reason for the change of the refractive index of HBO is not the thermal effect because of absorption of the pump beam, but the excited-state intramolecular proton-transfer (ESIPT) effect of HBO under the pump beam. As the ESIPT process is very fast, HBO might be an excellent material for high-speed optical switching. Received: 28 October 2002 / Revised version: 18 March 2003 / Published online: 2 June 2003 RID="*" ID="*"Corresponding author. Fax: +86-22/2350-1242, E-mail: zhanggl@nankai.edu.cn     

Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption

3 crystal have been measured using Z-scan technique with picosecond pulses at 532 nm. The nonlinear absorption coefficient and nonlinear refractive index are determined to be 2.5×10^-10 cm/W and 5.3×10^-15 cm²/W, respectively. Both sign and magnitude of the measured refractive nonlinearity are considerably different from the reported Z-scan results in LiNbO₃ obtained with cw laser beam at 514 nm. The nonlinearities in LiNbO₃ induced by 532 nm picosecond pulses are believed to be mainly due to two-photon absorption and bound electronic Kerr effect associated with the two-photon absorption. Received: 4 July 1996     

All-Optical Switching Based on Azo Polymer Material

Conventional all-optical switches based on azo polymer films and the all-optical switches based on the attenuated total reflection （ATR） geometry are investigated. A conventional switch system, including a pump beam of 532 nm and a probe beam of 650 nm, is based on the photoinduced birefringence effect of azo polymer. An ATR switch in a prism-multilayer configuration is achieved by changing the reflectance of the probe beam with an external pump beam. The ATR method provides the substantial improvement of the speed and the efficiency of the modulation over the conventional method. Although the azo polymer response still remains relatively slow, an enhanced nonlinear refractive index of the azo polymer film can effectively increase the modulation.     

Effects of relativistic and ponderomotive nonlinearities on the interaction of high-power laser beam with an inhomogeneous warm plasma

The influence of relativistic-ponderomotive nonlinearities and the plasma inhomogeneity on the nonlinear interaction between a high-power laser beam and a warm underdense plasma are studied. It is clear that the relativistic ponderomotive force and the electron temperature modify the electron density distribution and consequently change the dielectric permittivity of the plasma. Therefore, by presenting the modified electron density and the nonlinear dielectric permittivity of the warm plasma, the electromagnetic wave equation for the propagation of intense laser beam through the plasma is derived. This nonlinear equation is numerically solved and the distributions of electromagnetic fields in the plasma, the variations of electron density, and plasma refractive index are investigated for two different background electron density profiles. The results show that the amplitude of the electric field and electron density oscillations gradually increase and decrease, during propagation in the inhomogeneous warm plasma with linear and exponential density profiles, respectively, and the distribution of electron density becomes extremely sharp in the presence of intense laser beam. It is also indicated that the electron temperature and initial electron density have an impact on the propagation of the laser beam in the plasma and change the plasma refractive index and the oscillations' amplitude and frequency. The obtained results indicate the importance of a proper choice of laser and plasma parameters on the electromagnetic field distributions, density steepening, and plasma refractive index variations in the interaction of an intense laser beam with an inhomogeneous warm plasma.     

Measurement of nonlinear refractive index of ethyl red by interference of capillary

Using the intensity distribution of interference fringes formed by a capillary filled with transparent liquid, the variations in refractive index (RI) of nonlinear optical materials, corresponding to change of the intensity at the centre of fringes for a period, were deduced. With this conclusion, we measured variations in RI of ethyl red (ER) solution excited by a 535-nm-15 mW-laser, and found that the change of RI is 0.00504 and the corresponding effective index of refraction is −1.06 × 10⁻⁹, for which the order of magnitude is same as that measured by Z-scan. The influences on the accuracy of the method, such as temperature, beam and fringe contrast, were analyzed. This is a novel and simple method for measuring the RI of nonlinear optical materials.     

Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines

We report direct measurements of the excited singlet state absorption cross section and the associated nonlinear refractive cross section using picosecond pulses at 532 nm in solutions of phthalocyanine and naphthalocyanine dyes. By monitoring the transmittance and far field spatial beam distortion for different pulsewidths in the picosecond regime, we determine that both the nonlinear absorption and refraction are fluence (energy per unit area) rather than irradiance dependent. Thus, excited state absorption (ESA) is the dominant nonlinear absorption process, and the observed nonlinear refraction is also due to real population excitation.     

Third-Order Nonlinear Optical Susceptibility of Indium Phosphide Nanocrystals

InP nanocrystals synthesized by refluxing and annealing of organic solvent are determined from XRD measurements to have an averse granularity of 25 nm. The nonlinear optical properties of the InP nanocrystals studied by using laser Z-scan technique with 50 ps pulses at 532nm are found to reveal strong nonlinear optical properties and two-photon absorption phenomenon. Also, the nonlinear absorption coeffcient, the nonlinear refractive index and the third-order nonlinear optical susceptibility are determined by experiments, in which the nonlinear refractive index is three orders of magnitude larger than that of bulk InP.     

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.     

Nonparaxial propagation of Hermite-Laguerre-Gaussian beams in uniaxial crystal orthogonal to the optical axis

Analytical expressions for the three components of the nonparaxial propagation of a Hermite-Laguerre-Gaussian （HLG） beam in uniaxial crystal orthogonal to the optical axis are derived. The intensity distribution of an HLG beam and its three components propagating in a uniaxial crystal orthogonal to the optical axis are demonstrated by numerical examples. Although the y and z components of an HLG beam in the incident plane are both equal to zero, they emerge upon propagation inside the uniaxial crystal. Moreover, the beam profile of the x component is relatively stable and the beam profiles of the y and z components have the same evolution law. If the ratio of the extraordinary refractive index to the ordinary refractive index is larger than unity, the beam profile of the HLG beam is elongated in the x direction and generally rotates clockwise. Otherwise, the beam profile of the HLG beam is elongated in the y direction and generally rotates anticlockwise. This research is beneficial to the optical trapping and nonlinear optics involved in the rotation of a beam profile.     

Conditional phase-shifter in refractive index enhancement scheme

We propose a conditional phase-shifter between two weak laser beams in an alkali vapor. We begin by enhancing the refractive index of a weak, far-detuned probe beam while maintaining vanishing absorption. The enhancement is a result of interfering an absorptive and an amplifying Raman resonance in a four-level atomic system. Then, a conditional switching beam ac stark shifts the narrow Raman resonances, modifying the phase accumulation experienced by the probe beam. We find that the scheme works with acceptable fidelity at the tens of photons level, and that the energy requirement can be reduced further at the expense of noise.     

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.     

Modal Characterization of a Planar Waveguide in Bismuth Borate Crystal

We report on the fabrication and modal property studies of planar waveguide structure in x-cut bismuth borate biaxial crystal formed by He ion implantation with triple energies. The prism coupling method is used to measure the effective refractive indices of this waveguide. We reconstruct the refractive index distribution of this waveguide by the reflectivity calculation method. Our results indicate that a broadened optical barrier is produced by the multiple He ion implantations. The so-called tunneling effect of the non-stationary mode in this type of barrier waveguide is presented by the well-known finite difference beam propagation method.     

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.