Stability of temporal solitons in uniform and “managed” quadratic nonlinear media with opposite group-velocity dispersions at fundamental and second harmonics

The problem of the stability of solitons in second-harmonic-generating media with normal group-velocity dispersion (GVD) in the second-harmonic (SH) field, which is generic to available χ⁽²⁾ materials, is revisited. Using an iterative numerical scheme to construct stationary soliton solutions, and direct simulations to test their stability, we identify a full soliton-stability range in the space of the system’s parameters, including the coefficient of the group-velocity-mismatch (GVM). The soliton stability is limited by an abrupt onset of growth of tails in the SH component, the relevant stability region being defined as that in which the energy loss to the tail generation is negligible under experimentally relevant conditions. We demonstrate that the stability domain can be readily expanded with the help of two “management” techniques (spatially periodic compensation of destabilizing effects) - the dispersion management (DM) and GVM management. In comparison with their counterparts in optical fibers, DM solitons in the χ⁽²⁾ medium feature very weak intrinsic oscillations.     

Multidimensional semi-gap solitons in a periodic potential

The existence, stability and other dynamical properties of a new type of multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional (1D or 2D, respectively) periodic potential in the nonlinear Schr?dinger equation with the self-defocusing cubic nonlinearity are studied. The equation describes propagation of light in a medium with normal group-velocity dispersion (GVD). Strictly speaking, solitons cannot exist in the model, as its spectrum does not support a true bandgap. Nevertheless, the variational approximation (VA) and numerical computations reveal stable solutions that seem as completely localized ones, an explanation to which is given. The solutions are of the gap-soliton type in the transverse direction(s), in which the periodic potential acts in combination with the diffraction and self-defocusing nonlinearity. Simultaneously, in the longitudinal (temporal) direction these are ordinary solitons, supported by the balance of the normal GVD and defocusing nonlinearity. Stability of the solitons is predicted by the VA, and corroborated by direct simulations.     

Interactions between two-dimensional solitons in the diffractive-diffusive Ginzburg-Landau equation with the cubic-quintic nonlinearity

We report the results of systematic numerical analysis of collisions between two and three stable dissipative solitons in the two-dimensional (2D) complex Ginzburg-Landau equation (CGLE) with the cubic-quintic (CQ) combination of gain and loss terms. The equation may be realized as a model of a laser cavity which includes the spatial diffraction, together with the anomalous group-velocity dispersion (GVD) and spectral filtering acting in the temporal direction. Collisions between solitons are possible due to the Galilean invariance along the spatial axis. Outcomes of the collisions are identified by varying the GVD coefficient, β, and the collision “velocity” (actually, it is the spatial slope of the soliton’s trajectory). At small velocities, two or three in-phase solitons merge into a single standing one. At larger velocities, both in-phase soliton pairs and pairs of solitons with opposite signs suffer a transition into a delocalized chaotic state. At still larger velocities, all collisions become quasi-elastic. A new outcome is revealed by collisions between slow solitons with opposite signs: they self-trap into persistent wobbling dipoles, which are found in two modifications — horizontal at smaller β, and vertical if β is larger (the horizontal ones resemble “zigzag” bound states of two solitons known in the 1D CGL equation of the CQ type). Collisions between solitons with a finite mismatch between their trajectories are studied too.     

Two-color pulse compression in aperiodically-poled lithium niobate

We experimentally demonstrate engineerable compression of two-colored pulses in a linearly-chirped quasi-phase-matching grating. Quadratic solitons generated from fundamental input are reshaped through cascaded parametric processes of second-harmonic generation (SHG) and the back-conversion. We use type-I (e: o + o) SHG geometry in a 50-mm-long aperiodically-poled MgO:LiNbO₃ device to satisfy the group-velocity matching condition. Simultaneously compressed fundamental and SH pulses of about 55-fs duration with small pedestal are generated from the fundamental input pulses of 95-fs duration.     

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 electrostatic response of strongly correlated one-dimensional electron systems

We investigate the nonlinear response of the strongly correlated one-dimensional electron systems to the static electric field with using the one-dimensional Hubbard model in the half-filled case. We adopt the variational Monte Carlo method with the Gutzwiller wave function to describe the strong correlation effects. In the weak correlation region U/t≤4, where U is the one-site Coulomb repulsion energy and t is the transfer integral between the nearest neighbor sites, the response can be described within the band picture, and the third order nonlinear susceptibility χ⁽³⁾ increases slowly with increasing U/t. For U/t≤4, χ⁽³⁾ increases rapidly with increasing U/t, and χ⁽³⁾ at U/t=10 is more than ten times larger than that at U/t=2. This large value of χ⁽³⁾ originates from the exotic properties of carriers in the strongly correlated one-dimensional electron systems.     

Theoretical and experimental studies on laser-induced transient gratings in laser dyes

Laser-induced transient grating technique has been used to measure the diffraction efficiency (η) and calculate the third-order nonlinear susceptibility (χ⁽³⁾) of some laser dyes. Theoretical simulations have been carried out on η and χ⁽³⁾ as a function of wavelength covering the spectral range corresponding to the first excited singlet state of the dyes. Theoretically simulated values have been found in agreement to those observed experimentally. The decay profiles for these dyes have been measured by using diffraction of a delayed probe laser pulse to estimate the relaxation times in the excited state.     

Single- and multi-peak solitons in two-component models of metamaterials and photonic crystals

We report results of the study of solitons in a system of two nonlinear-Schrödinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials (MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations with equal GVD coefficients, which generate only simple single-peak solitons, the present model gives rise to families of solitons with complex shapes, which feature extended oscillatory tails and/or a double-peak structure at the center. Regions of existence are identified for single- and double-peak bimodal solitons, demonstrating a broad bistability in the system. Behind the existence border, they degenerate into single-component solutions. Direct simulations demonstrate stability of the solitons in the entire existence regions. Effects of the group-velocity mismatch (GVM) and optical loss are considered too. It is demonstrated that the solitons can be stabilized against the GVM by means of the respective “management” scheme. Under the action of the loss, complex shapes of the solitons degenerate into simple ones, but periodic compensation of the loss supports the complexity.     

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.     

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.     

Soliton stability against polarization-mode-dispersion in dispersion-managed systems

We study the dynamics of two-component solitons in a dispersion-managed (DM) system, built as a periodic concatenation of segments of optical fibers with anomalous and normal group-velocity dispersion (GVD). The model includes, in addition to the usual GVD and nonlinear terms, birefringence and polarization-mode-dispersion (PMD), in the form of the polarization scrambling (random rotation of the polarization) taking place at randomly distributed defects. We propose a numerical algorithm for finding optimized DM solitons in such a system, which secure stable transmission over a large distance. The analysis includes effects of the PMD-induced noise, together with the noise due to the spontaneous amplifier emission, and the input-source noise. It is concluded that, if the group-velocity birefringence is not excessively large, the use of the optimized solitons makes it possible to tolerate the PMD effects in the long-haul DM link.     

TEMPORAL OPTICAL SOLITONS VIA MULTISTEP χ(2) CASCADING

We consider a multistep χ⁽²⁾ cascading for light pulses with the dispersion of the system taken into account. Using the method of multiple scales we derive a set of coupled envelope equations governing the nonlinear evolution of the fundamental, second and third harmonic waves involved simultaneously in two nonlinear optical processes, i.e. second harmonic generation and sum frequency mixing. We show that three-wave temporal optical solitons are possible in three-and four-step cascading in the presence of a group-velocity mismatch between different pulses.     

Parametric dispersion and amplification in semiconductor plasmas: Effects of carrier heating

Using the hydrodynamic model of a semiconductor plasma, the influence of carrier heating on the parametric dispersion and amplification has been analytically investigated in a doped III-V semiconductor, viz. n-InSb. The origin of the phenomena lies in the effective second-order optical susceptibility (χ_e⁽²⁾) arising due to the induced nonlinear current density of the medium. Using the coupled-mode theory, the threshold value of pump electric field (|E_0T|_para) and parametric gain coefficient (α_para) are obtained via χ_e⁽²⁾. The relevant experiment has not been performed. Proper selection of the doping level not only lowers |E_0T|_para required for the onset of parametric excitation but also enhances α_para. The carrier heating induced by the intense pump modifies the electron collision frequency and hence the nonlinearity of the medium, which in turn further lowers |E_0T|_para and enhances α_para by a factor of ∼10³ and ∼2×10², respectively. The results strongly suggest that the incorporation of carrier heating by the pump in the analysis leads to a better understanding of parametric processes in solids and gaseous plasmas, which can be of great use in the generation of squeezed states.     

Generation of quadratic spatial dark soliton in periodically poled lithium niobate

In this paper, we report the evolution of quadratic spatial dark soliton in periodically poled lithium niobate (PPLN). The generation of solitons pairs by wavefront modulation methods is investigated in both numerical simulations and experiments. We found that quadratic dark spatial solitons have analogue performances compared with that in χ⁽³⁾ defocusing Kerr media.     

Bright entanglement and the Einstein-Podolsky-Rosen paradox with coupled parametric oscillators

We show that two evanescently coupled χ⁽²⁾ parametric oscillators provide a tunable bright source of quadrature squeezed light, Einstein-Podolsky-Rosen correlations and quantum entanglement. Analysing the system in the above threshold regime, we demonstrate that these properties can be controlled by adjusting the coupling strengths and the cavity detunings. As this can be implemented with integrated optics, it provides a possible route to rugged and stable EPR sources.     

Light bullets in quadratic media with normal dispersion at the second harmonic

Stable two- and three-dimensional spatiotemporal solitons (STSs) in second-harmonic-generating media are found in the case of normal dispersion at the second-harmonic (SH). This result, surprising from the theoretical viewpoint, opens the way for experimental realization of STSs. An analytical estimate for the existence of STSs is derived, and full results, including a complete stability diagram, are obtained in numerical form. STSs withstand not only the normal SH dispersion, but also finite walk-off between the harmonics, and readily self-trap from a Gaussian pulse launched at the fundamental frequency.     

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.     

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.     

Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams

Second harmonic generation microscopy was conducted on rat-tail tendons with linearly and radially polarized beams. Transverse and axial field components were generated in the focal region through tight focusing of linearly and radially polarized. It was found that the generated SHG signals could not be qualitatively explained with a scalar approximation to the electric field at the focus. Only by accounting for the interactions of the axial and transverse components of the electric field interacting through the nonlinear susceptibility χ⁽²⁾ tensor could the SHG images be explained. For the case of collagen we find that the SHG signal varies as a function of the analyzer angle with a cos² or sin² dependency for linearly polarized beams. For tightly focused radially polarized beams we find that the output SHG is radially polarized after collimation and is independent of the analyzer angle.     

Solitons in a linearly coupled system with separated dispersion and nonlinearity

We introduce a model of dual-core waveguide with the cubic nonlinearity and group-velocity dispersion (GVD) confined to different cores, with the linear coupling between them. The model can be realized in terms of photonic-crystal fibers. It opens a way to understand how solitons are sustained by the interplay between the nonlinearity and GVD which are not "mixed" in a single nonlinear Schrodinger (NLS) equation, but are instead separated and mix indirectly, through the linear coupling between the two cores. The spectrum of the system contains two gaps, semi-infinite and finite ones. In the case of anomalous GVD in the dispersive core, the solitons fill the semi-infinite gap, leaving the finite one empty. This soliton family is entirely stable, and is qualitatively similar to the ordinary NLS solitons, although shapes of the soliton's components in the nonlinear and dispersive cores are very different, the latter one being much weaker and broader. In the case of the normal GVD, the situation is completely different: the semi-infinite gap is empty, but the finite one is filled with a family of stable gap solitons featuring a two-tier shape, with a sharp peak on top of a broad "pedestal." This case has no counterpart in the usual NLS model. An extended system, including weak GVD in the nonlinear core, is analyzed too. In either case, when the solitons reside in the semi-infinite or finite gap, they persist if the extra GVD is anomalous, and completely disappear if it is normal.