High sensitive measurements of absorption coefficient and optical nonlinearities

Accurate knowledge of absorption coefficient of a sample is a prerequisite for measuring the third-order optical nonlinearity of materials, which can be a serious limitation for unknown samples. We introduce a method, which measures both the absorption coefficient and the third-order optical nonlinearity of materials with high sensitivity in a single experimental arrangement. We use a dual-beam pump-probe experiment and conventional single-beam z-scan under different conditions to achieve this goal with communication relevant wavelength. We also demonstrate a counterintuitive coupling of the non-interacting probe-beam with the pump-beam in pump-probe z-scan experiment.     

Diploe-allowed optical absorption of an exciton in a spherical parabolic quantum dot

A investigation of the linear and nonlinear optical properties of an exciton in a spherical parabolic quantum dot has been performed by using the matrix diagonalization method. The optical absorption coefficients between the ground state (L=0,π=+1) and the first excited state (L=1,π=-1) have been examined based on the computed energies and wave functions. The results are presented as a function of the incident photon energy for the different values of the incident optical intensity and the confinement strength. We found the optical absorption coefficient is strongly affected by the incident optical intensity and the confinement strength.     

Simultaneous estimation of optical nonlinear refractive and absorptive parameters by solvent induced changes in optical density

With picosecond pulses at the wavelength of 532 nm, we have determined the optical nonlinear refractive and absorptive parameters of the dye N,N′-bis(2,5-di-tert-butylphenyl)-3,4,9,10-perylenedicarboximide (DBPI) by a single closed-aperture (CA) Z-scan technique. This technique uses a theoretical model that elucidates the refractive and absorptive optical nonlinearity present simultaneously in the CA Z-scan profile. The observed remarkable red shift in the absorption spectrum of the dye in the acidic medium as compared to that in the polar medium has been used to vary the optical density at a single frequency. We find that the effect of saturable absorption (SA) is complete at higher concentrations. The effect of reverse saturable absorption (RSA) is dominating in dilute concentrations. The observed variations in the excited state refractive cross-section (σ_r) with the concentration and the energy have been attributed to the contributions of higher order nonlinearity along with the existing third-order nonlinearity.     

Effects of metallization and bromination on nonlinear optical properties of diphenylporphyrins

Nonlinear refraction and nonlinear absorption of diphenylporphyrins with bromination and metallization were studied by Z-scan technique in nanosecond and picosecond regimes. Results show that both metallization and bromination of diphenylporphyrins can cause the regular change of magnitude and sign of nonlinear absorption. The transition between saturable absorption and reverse saturable absorption happens as bromine increases and metal ion changes. The effect of bromination on nonlinear refraction is small, the change of nonlinear refraction is mainly attributed to the metallization. Influences of photophysical parameters on nonlinear absorption and nonlinear refraction have been elucidated using five-level models.     

Investigation of nonlinear optical properties of organic dye by Z-scan technique using He-Ne laser

The third-order nonlinear optical properties of Basic Green 1 dye were measured by the Z-scan technique and measurements were carried out at different concentrations and several incident intensities. The results showed that the Basic Green 1 dye exhibited large nonlinear refractive coefficient () and nonlinear absorption coefficient () at the wavelength 632.8 nm of He-Ne. The negative sign of the nonlinear refractive index n₂ indicates that this material exhibits self-defocusing optical nonlinearity. These results show that Basic Green 1 dye has potential applications in nonlinear optics.     

Spatial-temporal frequency band of optical parametric amplifier

The spatial-temporal frequency band of optical parametric amplifier for collinear as well as for noncollinear phase-matching is analyzed taking into account angular dispersion of amplified pulsed beam. The simple formulae are derived which make possible determination of the largest frequency bands of parametric amplifiers in noncollinear geometry. It has been demonstrated that a shape of the spatial-temporal frequency band of optical parametric amplifier essentially depends on pump and signal wavelengths, and certain angular dispersion as well as proper beamwidth of signal pulse enable amplification of ultrashort pulses with duration of a few femtoseconds.     

The study of the nonlinear absorption in the nonlinear-imaging technique with phase object

The nonlinear absorption can produce a nonlinear image very similar with the one created by the nonlinear refraction when using the nonlinear-imaging technique with phase object to measure the third-order nonlinearity of materials, but the principles of them are different. The formation of the nonlinear absorption image is explained, and the condition that the highest sensitivity of the nonlinear absorption measurement can be reached is deduced. For the materials with both nonlinear absorption and refraction, we find a proper phase shift of the phase object where the effect of the nonlinear refraction to the measured signal can be eliminated. The nonlinear absorption and refraction are numerically simulated when the phase shift of phase object to be π/2 that is normally used. The qualitative tendency of the signal variation is presented.     

Strong nonlinear optical refractive effect of self-assembled multilayer films containing tetrasulfonated iron phthalocyanine

Multilayer films containing anionic iron phthalocyanine tetrasulfonate (FePcTsNa₄) and cationic poly(diallydimethyl ammonium chloride) were prepared using electrostatic self-assembled layer-by-layer technique. The growth of the film was monitored by ultraviolet-visible absorption spectroscopy, and the morphology of the film was characterized by atomic force microscopy. Polarized visible spectra showed that macrocycles of FePcTsNa₄ in the film presented a flat orientation relative to the plane of the solid substrates. The third-order nonlinear optical properties of the film were studied by using Z-scan technique with laser duration of 21 ps at the wavelength of 532 nm. The FePcTsNa₄/PDDA film exhibited strong self-focusing effect with n₂ value of 4.13 × 10⁻¹⁵ m²/W, which is 4 orders larger than that of FePcTsNa₄ aqueous solution.     

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.     

Optical vortices in self-focusing Kerr nonlinear media

In this work we numerically compare the interaction of optical vortices (OVs) in self-defocusing and self-focusing Kerr nonlinear media. We find that the basic scenarios (attraction/repulsion, translation/rotation vs. background) in the interaction of two and three vortices with equal and alternative topological charges (TCs) are the same in both media. However, the vortex dynamics under self-focusing conditions is influenced by the reshaping of the surrounding part of the background. Square structure of OVs with alternating TCs is found to be stable with respect to the vortex positions in self-focusing media. This elementary cell is successfully generalized in a large square array of OVs with alternative TCs which brings ordering in the multiple filamentation of the background beam in self-focusing conditions.     

Anisotropy in the nonlinear absorption of elongated silver nanoparticles in silica, probed by femtosecond pulses

We present measurements of the anisotropy of the nonlinear absorption of a silica matrix doped with aligned spheroidal silver nanoparticles, produced by a double ion-implantation process of silver nanoparticles followed by an irradiation with Si ions. The nonlinear response was studied using the z-scan technique with fs pulses at 530 nm, which lies very close to the surface-plasmon absorption peak of the sample. The observed saturable absorption is studied for different angles of the input linear polarization of the pulses, showing a strong anisotropy, which is consistent with the fact that the nanorods are aligned.     

Abnormal properties of spontaneous emission in a Kerr nonlinear blackbody

We reexamine the atomic spontaneous decay in a Kerr nonlinear blackbody by contrast with our previous paper [M. Yin, Z. Cheng, Phys. Rev. A 78 (2008) 063829]. In the process of deriving the atomic decay rate, we use the temperature-dependent velocity of photons to take the full nonlinearity of a KNB into account. It is found that below a transition temperature T_c, the atomic spontaneous emission in a KNB might be enhanced or inhibited compared with that in a normal blackbody whose interior is filled with a nonabsorbing linear medium. The physical origin of the enhancement and inhibition of spontaneous emission is also discussed.     

Statistical properties of thermal radiation in a Kerr nonlinear blackbody

We study the statistical properties of thermal radiation in a Kerr nonlinear blackbody in which bare photons with opposite wave vectors and helities are bound into pairs and unpaired photons are transformed into a different kind of quasiparticle, the nonpolariton. This paper investigates the statistical properties of the photon blackbody field by using the second-order correlation function, the phase space distribution function, the photon number distribution and the nonclassical depth. The numerical computation and a discussion of the results are present.     

Enhanced optical limiting properties in suspensions of CdO nanowires

Optical limiting (OL) properties of CdO nanowires in water and ethanol were investigated by using nanosecond laser pulses at 532 nm. Experimental results show that suspension of CdO nanowires in ethanol exhibits better OL property than solution of C₆₀ in toluene and suspension of CdO nanowires in water. The dominant mechanism for the observed enhanced optical limiting in ethanol suspensions of CdO nanowires is due to nonlinear scattering.     

Widely tunable femtosecond fiber optical parametric oscillator

The phase-matching condition in a fiber is discussed. A balance among the different orders of fiber dispersion can be found to achieve a widely tuning modulation instability gain for pumping around the normal dispersion regime. Three coupled nonlinear wave equations are used to simulate the femtosecond fiber optical parametric oscillator. The numerical results show that, through appropriate choice of dispersion, femtosecond pulses with a 180-nm tunable range can be generated when pump wavelength near a fiber’s zero-dispersion wavelength is tuned only 7 nm. Further tuning is limited by the walk-off between the pump and the signal pulses.     

Strong optical limiting property of a ball-type supramolecular zinc-phthalocyanine in polymer-phthalocyanine composite film

The nonlinear absorption and optical limiting (OL) performance of a supramolecular hexa-phthalocyaninato-hexazinc (II) with hexylthio substituents in solution and in the solid-state have been described using the open-aperture Z-scan technique. The measurements were performed using collimated 4 ns pulses generated from a frequency-doubled Nd:YAG laser at 532 nm wavelength. The results indicated that OL performance of the investigated compound in the polymeric film is much better compared to properties in solution. With the excellent combination of OL parameters the investigated compound in the solid-state is a candidate for the use as optical limiter.     

Third order nonlinear optical studies of bromocresol purple in liquid and solid media

The quest for materials exhibiting high nonlinear refraction and absorption are required for photonic device application. In this paper we report a simplified Z-scan technique, to study the optical nonlinearity of the dye bromocresol purple in methanol and ethanol for different concentration and dye doped polymer film at the wavelength 532 nm of Nd:YAG laser. The experimental results show that the investigated organic dye molecule exhibits saturation absorption and negative nonlinearity. The nonlinear absorption co-efficient and the nonlinear refractive index were measured for the dye doped film, and for dye in methanol and ethanol at the concentration of 0.03 mM and 0.05 mM. The measured third order susceptibility was found to be of the order of 10⁻⁶ e.s.u. in both solid and liquid medium. The result shows that the dye has potential applications in nonlinear optics.     

Nonlinear mixing between the emission of a cw laser and a femtosecond laser

We mix the emission of a femtosecond Ti:sapphire laser with the emission of a continuous wave infrared laser in a beta-barium borate crystal. Green light with a center wavelength of 527 nm and a spectral width of 2.5 nm resulting from sum frequency generation is detected. An intensity study verifies that a nonlinear χ⁽²⁾ process is at the origin of the green light generation. The experimentally obtained conversion efficiency of 7 × 10⁻¹⁰ is in good agreement to simple theoretical considerations.     

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     

Azimuthal modulational instability of vortices in the nonlinear Schrödinger equation

We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schrödinger (NLS) equation. The method of studying the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal equation of motion, and then applying a stability analysis in Fourier space of the azimuthal modes. We formulate predictions of growth rates of individual modes and find that vortices are unstable below a critical azimuthal wave number. Steady-state vortex solutions are found by first using a variational approach to obtain an asymptotic analytical ansatz, and then using it as an initial condition to a numerical optimization routine. The stability analysis predictions are corroborated by direct numerical simulations of the NLS. We briefly show how to extend the method to encompass nonlocal nonlinearities that tend to stabilize such solutions.