Modulation instability with incoherent white light in self-defocusing photorefractive crystal

We report on the first experimental observation of modulation instability and spontaneous pattern formation with incoherent white light emitted from an incandescent lamp in self-defocusing photorefractive LiNbO₃:Fe crystal. Experimental results show that the modulation instability of white light in self-defocusing medium is related to the input intensity, illumination time and the direction of the crystalline c-axis with respect to that of the lamp filament. At the illumination time t = 0 and the steady-state of MI, we give the spatial distribution of the optical Fourier power spectrum experimentally and the corresponding Fourier transformation of the output intensity numerically, and observe the emergence of the high frequency component along the c-axis.     

Padé approximant for refractive index and nonlocal envelope equations

Padé approximation is superior to Taylor expansion when functions contain poles. This is especially important for response functions in complex frequency domain, where singularities are present and intimately related to resonances and absorption. Therefore, we introduce a rational Padé approximant for the complex medium refractive index n(ω). The approximant is calculated using only local information of medium dispersion properties close to a carrier frequency ω₀. In return it typically offers an accurate global representation of medium dispersion and absorption. Moreover, the fulfillment of the causality principle and the Kramers-Kronig relation can be established. In practice, our results are relevant if n(ω) is known only for ω?ω₀ whereas optical field is spectrally broad such that (i) the resonance absorption becomes important and (ii) a traditional polynomial dispersion operator diverges and induces huge errors. As an exemplary application we use the approximant to derive a nonlocal envelope model for ultrashort pulses. The model provides a natural bridge between the commonly used local envelope equations and the most general non-envelope models operating directly with the electric field.     

Effects on squeezing and sub-poissonian of light in fourth harmonic generation up to first-order Hamiltonian interaction

The effects on squeezing and sub-poissonian of light in fourth harmonic generation (FHG) are investigated based on the fully quantum mechanically up to the first order Hamiltonian interaction in gt, where g is the coupling constant between the modes per second and t is the interaction time between the waves during the process in a nonlinear medium. FHG is a process in which an incident laser beam of the fundamental frequency ω interacts with a nonlinear medium to produce the harmonic frequency at 4ω. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The occurrence of amplitude squeezing effects in both the quadratures of the radiation field in the fundamental mode is investigated and found to be dependent on the selective phase values of the field amplitude. The photon statistics of the pump mode in this process have also been investigated and found to be sub-poissonian in nature. It is found that there is no possibility to produce squeezed light in the harmonic mode up to first-order interaction in gt. Further, we have found the case up to second-order Hamiltonian interaction in gt that the normal squeezing in the harmonic mode is directly depends upon the fourth-order squeezing of the initial pump field. This gives a method of converting higher-order (fourth-order) squeezing into normal squeezing in the harmonic mode and vice versa.     

Temporal behavior of dark spatial solitons in closed-circuit photovoltaic media

We show that the time-dependent nonlinear wave equation in closed-circuit photovoltaic media can exhibit quasi-steady-state and steady-state spatial solitons. We demonstrate that the formation time of open-circuit quasi-steady-state and open-circuit steady-state dark solitons decreases with an increase in the intensity ratio of the soliton, which is the ratio between the soliton peak intensity and the dark irradiance. We find that for the time-dependent nonlinear wave equation that exhibits only an open-circuit steady-state dark soliton, changing the electric current density J₀ does not generate quasi-steady-state dark solitons and affects the formation time of steady-state dark solitons and that for the time-dependent nonlinear wave equation that exhibits an open-circuit quasi-steady-state dark soliton, changing J₀ gives rise to three different time evolution regimes of the full width half maximum of the soliton’s intensity. The first regime shows that the formation time of steady-state dark solitons increases with J₀ whereas the formation time of quasi-steady-state dark solitons is independent of J₀. The second regime shows that the formation time of steady-state dark solitons decreases with an increases in J₀ and the formation time of quasi-steady-state dark solitons increases with J₀. The third regime shows that changing J₀ enables only steady-state dark solitons in the time-dependent nonlinear wave equation, of which the formation time increases with J₀.     

Propagation of fs TW laser filaments in adverse atmospheric conditions

The propagation of femtosecond terawatt laser pulses at reduced pressure (0.7 atm) is investigated experimentally. In such conditions, the non-linear refractive index n ₂ is reduced by 30%, resulting in a slightly farther filamentation onset and a reduction of the filament number. However, the filamentation process, especially the filament length, is not qualitatively affected. We also show that drizzle does not prevent the filaments from forming and propagating.     

White-Light Nonlinear Photonic Lattices in Self-Defocusing Media

Using fully incoherent white light emitted from an incandescent lamp and amplitude mask, we experimentally investigate the influence of several factors on the fabrication of the lattice in photovoltaic self-defocusing LiNbO3：Fe crystal, the factors include the orientation of the crystalline c axis relative to the principal axis of the photonic lattice and the filament, the diameter of input dark spot and the separation of the adjacent input dark spots. Experimental results reveal that the best fabricating condition of photonic lattices is that the principal axis of lattice is tilted for 45^o relative to the crystalline c axis which is parallel to the filament of the lamp. In addition, it is necessary that the diameter of the input dark spot is larger than the half of their separation.     

Dynamic hysteresis of magnetic aggregates with non-integer dimension

We investigate the dynamic hysteresis of nanoscale magnetic aggregates by employing Monte Carlo simulation, based on Ising model in non-integer dimensional space. The diffusion-limited aggregation (DLA) model with adjustable sticking probability is used to generate magnetic aggregates with different fractal dimension D. It is revealed that the exponential scaling law A(H₀, ω)∼H₀^α·ω^β, where A is the hysteresis area, H₀ and ω the amplitude and frequency of external magnetic field, applies to both the low-ω and high-ω regimes, while exponents α and β decrease with increasing D in the low-ω regime and keep invariant in the high-ω regime. A mean-field approach is developed to explain the simulated results.     

Waveguides induced by steady-state gray solitons in biased photorefractive-photovoltaic crystals

We carry out a theoretical investigation of the properties of waveguides induced by photorefractive one-dimensional steady-state gray spatial solitons (i.e., screening solitons, photovoltaic solitons, and screening-photovoltaic solitons). We demonstrate that waveguides induced by photorefractive steady-state gray spatial solitons are only a single guided mode for both all soliton graynesses and all values of ρ, where ρ is the ratio between the soliton peak intensity and the dark irradiance, and moreover, waveguides induced by gray photovoltaic solitons for closed-circuit condition are also only a single guided mode for all electric current densities. We find that the confined energy near the center of a photorefractive steady-state gray spatial soliton increases with ρ and decreases with an increase in the soliton grayness. We also find that the confined energy near the center of a gray photovoltaic soliton for closed-circuit condition increases with the electric current density. On the other hand, waveguides induced by gray screening-photovoltaic solitons are gray screening soliton-induced waveguides when the bulk photovoltaic effect is neglectable and are gray photovoltaic soliton-induced waveguides when the external bias field is absent.     

Inertia of the bound-electron Kerr-type optical nonlinearity in transparent solids

The inertia of the Kerr-type nonlinear-optical response of bound electrons in solids is analyzed. It is shown that, in the case of wide-gap materials, away from the mid-gap frequency E_g/2?, E_g being the band gap, the inertia of this response becomes noticeable only for attosecond pulse features. However, near E_g/2?, where the inertia of bound-electron Kerr-type optical nonlinearity is enhanced by a strong dispersion of two-photon absorption and where the nonlinear refraction is especially strong, light pulses as long as tens and even hundreds of femtoseconds are expected to experience self-steepening and an asymmetric spectral broadening due to the retarded Kerr effect.     

Incoherent solitons in strongly nonlocal media: The coherent density theory

We study the properties of one dimension incoherent accessible solitons in strongly nonlocal media with noninstantaneous Kerr nonlinearity. Following the coherent density theory, we obtain an exact solution of such incoherent solitons. The spatial width of the incoherent solitons is related to the incoherent angular power spectrum θ₀ as well as the incident power. The evolution properties of the intensity profile and the coherence characteristics are also discussed in detail when the solitons undergo periodic harmonic oscillation.     

On the visibility of electron-electron interaction effects in field emission spectra

One of the most convenient methods to obtain information about the energy distribution function of electrons in conducting materials is the measurement of the energy resolved current j(ω) in field emission (FE) experiments. Its high energy tail j_>(ω) (above the Fermi edge) contains invaluable information about the nature of the electron-electron interactions inside the emitter. Thus far, j_>(ω) has been calculated to second order in the tunnelling probability, and it turns out to be divergent toward the Fermi edge for a wide variety of emitters. The extraction of the correlation properties from real experiments can potentially be obscured by the eventually more divergent contributions of higher orders as well as by thermal smearing around E_F. We present an analysis of both factors and make predictions for the energy window where only the second order tunnelling events dominate the behaviour of j_>(ω). We apply our results to the FE from Luttinger liquids and single-wall carbon nanotubes.     

Stabilization of spatiotemporal solitons in second-harmonic-generating media

We report the results of a systematic analysis of the existence and stability of spatiotemporal (two-dimensional) solitons (STSs) in the model of a planar waveguide with the intrinsic χ⁽²⁾ nonlinearity. Fundamental obstacles to the creation of STSs under physically realistic conditions are the normal sign of the group-velocity dispersion (GVD) at the second harmonic (SH), and the significant group-velocity mismatch (GVM) between the SH and fundamental-frequency (FF) components. To construct STS solutions in a numerical form, we adjust the iterative method, which was recently used for finding temporal (one-dimensional) χ⁽²⁾ solitons in a similar setting. We identify effective existence borders for the STSs, within which the energy loss to the generation of extended “tails” in the SH component (due to the normal sign of the GVD) is negligible. It is demonstrated that the existence region can be made much broader by means of the GVD-management and GVM-management techniques. We also explore interactions between the STSs, and find robust two-soliton bound states, with a moderate separation in the longitudinal (temporal) direction. Head-on collisions between the STSs are always destructive.     

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.     

Enhanced frequency conversion of nonadiabatic pulses in a double Λ system driven by two pumps with and without carrier beams

We show that nonadiabatic, resonant amplitude- and phase-modulated pulses can be frequency converted with greater efficiency than adiabatic resonant pulses in a double Λ system, interacting with two strong cw beams on one side of the system, and a weak pulsed probe on the other. Indeed, in this double EIT (electromagnetically induced transparency) configuration, conversion efficiencies close to unity, similar to those achieved using highly detuned pulses, can be obtained using highly nonadiabatic resonant pulses. The distance at which the maximum conversion occurs is shorter than in a coherently-prepared Λ system. This counteracts the increased absorption that occurs in the double EIT configuration, so that both produce similar conversion efficiencies. The absorption experienced by matched nonadiabatic pulses in the double EIT system, at all propagation distances, can be overcome by superimposing the nonadiabatic pulses as amplitude modulations on carrier fields. Thus we demonstrate the formation of adiabatons in the double EIT system, and of diabatons in both the coherently-prepared Λ system and the double EIT system. Both the diabatons and adiabatons satisfy pulse-matching conditions. In addition, the asymptotic amplitude of the complementary amplitude modulations is proportional to the ratio of the pump to probe carrier Rabi frequencies, and is the same in each of the configurations.     

Long-range spectrally and spatially resolved radiation from filaments in air

The distance-resolved spectral intensity distribution of the backscattered light from long filaments generated in air using ultra-short and intense laser pulses is presented. A clean fluorescence spectrum from N₂ molecules and ions, which is produced by the high peak intensity inside the plasma filament of the fundamental pulse, was clearly resolved from the backscattered supercontinuum. The supercontinuum generated by both the fundamental and the third-harmonic pulses developed progressively and became fully developed only at the end of the filamentation.     

Nonlinear optical and optical power limiting studies on a new thiophene-based conjugated polymer in solution and solid PMMA matrix

An experimental investigation of the third-order nonlinear optical properties of new poly{2-{5-[3,4-ditetradecyloxy-5-(1,3,4-oxadiazol-2-yl)thiophen-2-yl]-1,3,4-oxadiazol-2-yl}pyridine} (P) in tetrahydrofuran (THF) solution and in solid poly(methylmethacrylate) (PMMA) matrix, by Z-scan technique is reported. The Z-scan traces reveal that the composite films exhibit large negative nonlinear refractive index of the order 10⁻¹⁰ esu. The excited-state absorption cross-section was found to be larger than the ground-state absorption indicating that the operating nonlinear process is reverse saturable absorption (RSA). The new polymer P exhibits good optical power limiting properties in the nanosecond regime in solution and as well in solid PMMA matrix.     

Temperature Controlled Filamentation in Argon Gas

Temperature controlled filamentation is experimentally demonstrated in a temperature gradient gas-filled tube. The proper position of the tube is heated by a furnace and two ends of the tube are cooled by air. The experimental results show that multiple filaments are shrunken into a single filament or no filament only by increasing the temperature at the beginning of the filament. This technique offers another degree of freedom of controlling the filamentation and opens a new way for intense monocycle pulse generation through gradient temperature in a noble gas.     

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.