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.     

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.     

Ultra fast third-order non-linear response of amino-triazole donor-acceptor derivatives by optical Kerr effect

We report the study of the temporal dependence of the non-linear optical response of novel organic materials in solution. The experimental results of the optical Kerr gate using 70 fs pulses show a quasi-instantaneous response for three derivatives of an amino-triazole donor-acceptor system. The non-linearity of the compounds is identified as arising from the electronic contribution to the third-order non-linear susceptibility. The non-linear parameters of each sample were obtained using the optical Kerr response of CS₂ as reference.     

Propagation of Gaussian beams in negative-index metamaterials with cubic nonlinearity

Propagation of Gaussian beams in the negative-index metamaterials (NIMs) with cubic nonlinearities is investigated, both theoretically and numerically. The role of the status of the incident Gaussian beam, which is scaled by a converging parameter in this paper, in beam self-focusing and self-defocusing in NIMs is specially identified. The expressions for beam self-focusing and self-defocusing for different converging parameter cases, and the dependence of the critical power and the focus location of self-focusing in NIMs on the converging parameter are obtained. It is found that it is the divergent rather than convergent incident beams which are self-focused more quickly in NIMs with defocusing nonlinearities, in sharp contrast with the propagation property of Gaussian beams in conventional Kerr media, in which beam self-focusing only occurs in the media with focusing nonlinearities and a convergent incident beam self-focuses more quickly than a divergent one. By adjusting the converging parameter of incident Gaussian beam or the controllable magnetic permeability of NIM, or both, one can manipulate the beam self-focusing in NIMs at will.     

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.     

Comparative analysis of multi-wave mixing and measurements of the higher-order nonlinearities in resonant media

The features of degenerate multi-wave mixing in resonant media (dye solutions) have been studied theoretically and experimentally. It has been demonstrated that thermal nonlinearity due to the induced absorption from the excited level contributes significantly to the efficiency of four-wave mixing, but results in lower efficiency of higher-order interactions. The measurement results obtained for the energy efficiency of four-, six- and eight-wave mixing enable calculations of the third-, fifth- and seventh-order nonlinear optical susceptibilities, respectively. Experimentally, the method proposed for measurements of the higher-order nonlinearities has been realized with the use of the multi-wave mixing at second harmonic λ = 532 nm of monopulse YAG:Nd³⁺ laser radiation in a Rhodamine 6G dye solution. The ratios ∣χ⁽⁵⁾∣/∣χ⁽³⁾∣ and ∣χ⁽⁷⁾∣/∣χ⁽⁵⁾∣ are determined to be of the order of 10⁻⁵ cm³/erg.     

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.     

Broadband four-wave optical parametric amplification in bulk isotropic media in the ultraviolet

We report on four-wave optical parametric amplification of the ultrashort ultraviolet light pulses in bulk fused silica and CaF₂. Exact phase-matching in these isotropic media is achieved by means of non-collinear interaction with cylindrical beam focusing. Four-wave optical parametric amplifier efficiently operates in the UV spectral range with 1-ps laser pulses, delivering amplified signal energy exceeding 50 μJ using millijoule pump pulses in the visible (527 nm). Results of scanning of the parametric gain profile suggest that broad amplification bandwidth as wide as ∼20 nm (at FWHM) under these experimental settings is achieved, which might support amplification of sub-10-fs ultraviolet pulses with central wavelength around 330 nm. It is also shown experimentally and verified theoretically that the parametric gain profile exposes a distinct inhomogeneity and its bandwidth notably broadens due to effects of self- and cross-phase modulation imposed by the intense pump beam.     

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.     

Generalised dispersive phase and its effect on four wave mixing in fibers

A generalised method of calculating the efficiency of four wave mixing products in an optical fiber is presented in this paper. Apart from indicating the insufficiency of the existing theoretical model, this work brings out the importance of calculating the dispersive phase shift more precisely in combination with the nonlinear phase shift to predict the efficiencies of sideband generation. The experimental results for the generation of the first and second order sidebands are analysed. Contrary to expectations, higher powers and longer lengths of fiber do not result in larger number of sidebands. An attempt is made to understand this aspect as well as the experimentally observed fluctuations in the four wave mixing products.     

Nonlinear three-wave interaction in photonic crystals

We present a multi-scale analysis of nonlinear three-wave-interaction processes in photonic crystals. Based on photonic Bloch functions as carrier waves, we derive the effective nonlinear coupled wave equations that govern pulse propagation in these systems and obtain the corresponding effective photonic crystal parameters directly from photonic band-structure computations. As an illustration, we show how hitherto inaccessible radiation-conversion processes such as wave-front reversal of optical pulses can be realized. Furthermore, we describe a novel regime of nonlinear three-wave interaction in photonic crystals associated with the nearly degenerate case and show how these results may be utilized to study experimentally certain problems from plasma physics and hydrodynamics in the context of nonlinear photonic crystals.     

Photorefractive four-wave mixing in a high-contrast regime

The effect of high contrast in photorefractive four-wave mixing is studied using a recently proposed empirical formula for the grating amplitude. An analytical solution to the coupled-wave equation is obtained and its properties are discussed in the case of a double-phase-conjugate mirror and semilinear phase-conjugate mirror.     

Single photon self-interference via inelastic two-wave mixing in a coherently prepared cold medium

We investigate a coherently prepared cold medium for efficient single-photon inelastic two-wave mixing (ITWM), maximum Fock state entanglement and single photon self-interference. We show the possibility of generating maximally entangled single-photon state, and near 100% conversion efficiency for generating a frequency shifted TWM photon by proper choice of medium length and concentration. In addition, we demonstrate a new type of transparency effect produced by an efficient single photon self-interference, a transparency effect that is very different from the conventional electromagnetically induced transparency (EIT) process.     

Thermodynamics of Phase Transitions of a Kerr Nonlinear Blackbody

We study the thermodynamics of phase transitions of a blackbody whose interior is filled by a Kerr nonlinear crystal. There is a transition temperature To, above which the Kerr nonlinear blackbody is in the normal thermal radiation state, and below which it is in the squeezed thermal radiation state. At To, the Gibbs free energy of the two phases is continuous but the entropy density of the two phases is discontinuous. Hence, there is a jump in the entropy density and this leads to a latent heat density. The photon system undergoes a first-order phase transition from the normal to the squeezed thermal radiation state.     

Highly efficient inelastic four-wave mixing using dual induced transparency and coherently prepared states

We investigate a life time broadened and coherently prepared five-state system for multi-wave mixing processes. We show that very efficient wave mixing occurs, producing an unconventional mixing wave that has the characteristics of both conventional four-wave mixing (FWM) and stimulated hyper-Raman (SHR) emission. In addition, we show interesting multiple simultaneous multi-photon interference effects at large propagation distances and demonstrate more than 10 orders of magnitude suppression of populations of the probe wave terminal state and the near three-photon resonance mixing wave generating state. These new type of multi-photon interference based induced transparency effects, which are critically dependent on two distinctive relaxation processes involving both an external supplied and an internally generated fields, are fundamentally different from the conventional three-state electromagnetically induced transparency effect which does not depend on propagation. As a consequence, both the probe and the wave-mixing field to propagate nearly free of absorption and distortions in a highly dispersive medium.     

Beam-size effect in time-delayed laser-induced double gratings

We have studied theoretically the effect of the probe-beam size on time-delayed laser-induced double gratings by assuming that the probe beam is described as a Gaussian beam. LettingE _s1 andE _s2 be the Four-Wave Mixing (FWM) signals originating from the diffraction of the probe beam by the gratings, the condition for the occurrence of the FWM signal modulation is that the divergence angle ofE _s1 andE _s2 is larger than half of the intersection angle between the propagation directions ofE _s1 andE _s2. We have also proposed methods to increase the modulation contrast.     

Direct measurement of free carrier nonlinearity in semiconductor-doped glass with picosecond pump-probe Z-scan experiment

We report the direct measurement of free carrier nonlinearity in a semiconductor-doped glass with picosecond pump-probe Z-scan experiment. A strong Z-scan signal from a weak and time delayed probe beam is observed. The probe beam Z-scan signal is comparable in magnitude to the Z-scan signal of the intense pump beam, clearly showing the dominance of the effective fifth order nonlinearity due to the pump beam generated free carriers in the overall nonlinear response of semiconductor-doped glass. The estimated magnitude of the fifth order nonlinearity is consistent with that obtained from earlier reported experiments.     

Reducing pulse distortion in fast-light pulse propagation through an erbium-doped fiber amplifier using a mutually incoherent background field

It was reported earlier that it is possible to obtain large pulse advancement with minimum pulse distortion in fast-light propagation through an erbium-doped fiber amplifier by placing the pulse on top of a mutually coherent constant background field. Here we show that comparable distortion reduction can be obtained through use of a mutually incoherent background field, a procedure that could be much more readily implemented under many circumstances. We also show that further improvement can be obtained by means of adjusting the pulse power, and for a pulse-power of the distortion decreases about 56% from 0.56 with no background while the fractional advancement decreases only about 3% from 0.16.