Self-focusing Effect Research Articles

Influence of spherical aberration on beam quality of high-power laser beams propagating upwards in the atmosphere

For laser ablation propulsion’s applications in space (e.g., space-debris removal, etc.), the laser power is well above the critical power for self-focusing in the atmosphere. Therefore, the self-focusing effect on the beam quality is very significant. In addition, a high-power laser beam is usually accompanied with spherical aberration due to nonlinear effects in its generation process. In this paper, the influence of spherical aberration on the beam quality of high-power laser beams propagating upwards in the atmosphere is studied by using numerical simulation. It is shown that for the large beam size case, the target intensity may be improved by applying the positive spherical aberration. However, for the small beam size case, the target intensity may be improved by using the negative spherical aberration. Furthermore, a laser beam with a large size is more suitable for laser ablation propulsion’s applications in space than that with a small size. Owing to the linear diffraction effect and the nonlinear self-focusing effect, there exists optimal beam power to maximize the target intensity. The formula of the optimal beam power is fitted for the large beam size case in this paper. On the other hand, the focal shift appears due to diffraction, self-focusing and spherical aberration, which results in a degradation of the beam quality on the target. For the large beam size case, to move the actual focus to the target and improve the beam quality on the target, the formula of the modified focal length is also derived in this paper. The results obtained in this paper are of important theoretical significance and practical value.

Temporal pulse source generating far fields with sharp optical pulse

According to the partially coherent theory for non-stationary optical fields, we introduce a novel model of partially coherent pulse sources, of which the TDOC is limited by Fractional Multi-Gaussian correlated Schell-model (FMGCSM) function. The analytical formula for the temporally mutual coherence function (TMCF) of a FMGCSM pulse beam on propagation in the presence of dispersive media is derived. The average intensity and the temporal degree of coherence (TDOC) of the FMGCSM pulse beam spreading through dispersive media are illustrated numerically. It can be seen that the pulse beam will form strongly sharp pulse intensity pattern when it propagates into far field. Moreover, the FMGCSM pulse beam propagating in dispersive media with chirp coefficient of s<0 will exhibit self-focusing effect and the focal position is controllable via the change of the source parameters. The far-field properties of the pulse beam may be useful for pulse laser shaping and material surface processing.

Propagation characteristics of focused astigmatic Gaussian beams in Kerr nonlinear media

When a powerful laser beam propagates in a Kerr nonlinear medium, the Kerr effect on the beam propagation characteristics is very significant. The astigmatic laser beams are often encountered in practice. Until now, much work has been carried out on the propagation characteristics of astigmatic laser beams in linear media, but a few researches have been reported about the propagation of astigmatic laser beams through nonlinear media. To the best of our knowledge, the propagation or the transformation of astigmatic laser beams through an optical system in a Kerr nonlinear medium has not been investigated. In this paper, the propagation characteristics of focused astigmatic Gaussian beams in a nonlinear Kerr medium are studied. The Kerr effect on the beam astigmatism and the focal shift of focused astigmatic Gaussian beams are investigated in detail, and the self-focusing focal length and focus control of focused astigmatic Gaussian beams in the Kerr nonlinear medium are also studied. For the beam spreading case, the analytical formula for each of the beam width, the beam waist position, and the focal shift of focused astigmatic Gaussian beams in the Kerr nonlinear medium is derived. It is shown that in the self-focusing medium, as the beam power increases (i.e. the self-focusing effect becomes stronger), the beam astigmatism becomes stronger, but the focal shift decreases. However, in a self-defocusing medium, as the beam power increases (i.e. the self-defocusing effect becomes stronger), the beam astigmatism becomes weaker, but the focal shift increases. On the other hand, for the beam self-focusing case, the analytical formula of the self-focusing focal length of focused astigmatic Gaussian beams in the Kerr nonlinear medium is derived. It is found that the number of foci can be controlled by applying beam astigmatism. The results obtained in this paper are of theoretical and practical significance.

Generalized Schell-model sources.

We evaluate the modes for generalized Schell-model planar source whose complex degree of coherence (CDC) is a function of the n-th power difference of two position coordinates instead of their direct distance between two source points. We discuss through two examples how new classes of CDCs can be devised and how they affect the radiation fields. It is demonstrated that the light beams generated by these families of sources carry interesting propagation characteristics, such as the lateral self-shifting and the self-focusing effect with controllable focal length determined by the non-trivial phase, power n and other source parameters.

Cu-doped ZnO synthesis by ionothermal method: Morphology and optical properties

Zinc oxide (ZnO) and Cu-doped ZnO nanostructures having different morphologies such as nanorod, nanosheet and flower like have been synthesized via a one-step, eco-friendly ionothermal synthetic method at ambient pressure using [OMIM]Br and [C8DABCO]Br ionic liquids in terms of solvent and template. The dopant contents in the samples were 3%. The synthesized nanomaterials were examined by using scanning electron microscopy (SEM), X-ray diffraction (XRD), UV–Visible absorption spectroscopy, and Z-scan technique. The results show that ILs and Cu2+ play on significant role on morphology of nanostructures. The average crystal size of ZnO was found to be in the range of 15.5–17 nm. Also doped in different ILs are effect on bandgap of products. The third order nonlinear absorption coefficient and refractive index were calculated and increased due to the enhancement of polarizability by the doping ions (Cu2+). Open and closed aperture of Z-scan method revealed two photon absorption and self-focusing (n2 > 0) effect in the samples. Third order nonlinear susceptibility of samples is in order of 10−7(cm2/W). As a result, Cu dopant of ZnO samples are more effective than their morphology in nonlinear coefficient results. The synthesized samples are proposed as a new-type nonlinear optical materials for optical applications.

Measurement of the Kerr nonlinear refractive index of the Rb vapor based on an optical frequency comb using the z-scan method.

We report the measurement of the Kerr nonlinear refractive index of the rubidium vapor via the high sensitivity z-scan method by using an optical frequency comb. The novel self-focusing and self-defocusing effects of the vapor are presented with red and blue detunings of the laser frequency. The optical nonlinear characteristics of the rubidium vapor are clearly interpreted under different experimental parameters. Furthermore, the Kerr nonlinear refractive index n2 is obtained from the measured dispersion curve, and it basically occurs on the order of 10-6 cm2/W. The evolutions of the Kerr nonlinear coefficient n2 with the laser power and frequency detuning, respectively, are studied. To the best of our knowledge, the use of pulsed lasers to measure the Kerr nonlinear refractive index n2 of atomic vapor has not been reported yet. The direct measurement of the Kerr nonlinear coefficient will greatly help us understand and optimize nonlinear optical processes and find its more potential applications in quantum optics.

A Mathematical Modelling with Zakharov System for Langmuir Wave in Unmagnetized Plasma

In this article we present a discussion and overview of mathematical result of the self-focusing of a Langmuir wave which governs Zakharov system and has studied the self- focusing of a Langmuir wave following by Gaussian distribution. Langmuir wave propagates through uncharged plasma which governed by Zakharov systems. The phenomenon plays a vital role in the Dynamics. We present the article mathematical model with effect of Landou damping. Relativistic mass oscillation and ponderomotive force on electrons of the ionized plasma encouraged the Langmuir wave which resists the self-focusing effect when damping is ignored. The Beam radius gets narrow. when it further propagates considering the paraxial ray’s approximation, the self-focusing length Rn. It shows that characteristics of varying bandwidth distance of propagation in relativistic plasma.

Third-order optical nonlinear properties of Co-doped V2O5 nanoparticles

The Co-doped vanadium pentoxide nanoparticles with Co concentrations up to 20 wt. % were synthesized via a gelatin-based sol–gel route. The effect of Co substitution was investigated on the microstructural and nonlinear optical characteristics of the synthesized particles through X-ray diffraction, field effect scanning electron microscopy and Z-scan technique. The results showed that the synthesized particles consist mainly of crystalline α-V 2 O 5 phase. Co substitution results in expansion of the orthorhombic unit cell and growth of particle size from about 36–45 nm. On increasing the dopant concentration, the nonlinearity was enhanced due of the improved crystallinity, more porosity, and the increased carrier concentration. The optical nonlinearity was intensified by the power of incident laser radiation, as well. The nonlinear refractive (NLR) index, nonlinear absorption (NLA) coefficient, and nonlinear optical susceptibility are of 10 − 8 ( c m 2 / W ) , 10 − 4 ( c m / W ) , and 10 − 8 ( c m 2 / W ) order, respectively. The positive NLR index of samples originates from the self-focusing effect. Furthermore, the involved NLA coefficients are mainly related to the saturable absorption. The encouraging nonlinear optical results of V 2-x Co x O 5 suggests that this system is a promising candidate for nonlinear optical applications.

Laser wakefield acceleration driven by a few-terawatt laser pulse in a sub-mm nitrogen gas jet

Quasi-monoenergetic electron bunches with energies peaked in 10–20 MeV are generated from laser wakefield acceleration (LWFA) by focusing few-TW laser pulses onto a sub-mm gas jet of dense nitrogen. A 152-μm diameter orifice is used to produce transient (≤20 ms), free-flow nitrogen jets, while the plasma electrons with a 860-μm wide Gaussian density profile and a density up to ∼2.8 × 1019 cm−3 enable self-focusing effect and self-modulation instability to develop on the pump pulse, resulting in a high intensity to drive the LWFA. Meanwhile, this Gaussian nitrogen plasma facilitates ionization-induced injection and density down-ramp injection throughout the acceleration process and consequently improves the energy and charge stabilities of output electrons. When 40-fs, 3.2-TW, 810-nm pump pulses are applied, output electrons with a peak energy ∼11 MeV and a charge ∼20 pC are routinely generated with ≤20% energy and charge stabilities, ∼20 mrad divergence, and ∼10 mrad pointing variation. A large electron energy spread is attributed to the dominant mechanisms of ionization and down-ramp injections. This scheme represents a viable approach for implementing a high-repetition-rate LWFA, from which stable tens-of-MeV electrons can be generated with less than 150 mJ of on-target laser energy.

Imitation in one's own presence: No specific effect of self-focus on imitation

Previous studies have reported that imitative responses may be modulated by top-down social factors such as self-focus. However, growing evidence suggests that such social factors may actually modulate domain-general processes such as spatially compatible responding, rather than specifically social processes such as imitation. In this study, we aimed to identify the cognitive processes being modulated under conditions of heightened or diminished self-focus. Participants performed a stimulus-response compatibility task which independently measures both spatial and imitative response tendencies, under two conditions: heightened self-focus, where the task was performed in the presence of two mirrors; and diminished self-focus, where the mirrors were covered. While participants were faster to respond to compatible trials than to incompatible trials, both imitatively and spatially, there was no significant modulation of either spatial or imitative compatibility by self-focus; although the magnitude of the modulation of spatial compatibility was numerically similar to the effect of self-focus on imitation found in previous studies. These results provide no evidence for an effect of self-focus on either social-specific, or domain-general, processes.

Performance effects of self-focus

ABSTRACT IS AVAILABLE IN THE PDF

Characteristics of high-power partially coherent laser beams propagating upwards in the turbulent atmosphere.

The characteristics of high-power partially coherent laser beams propagating upwards in the turbulent atmosphere are studied, where the principal features of diffraction, nonlinear self-focusing and turbulence are considered. Based on the "thin window" model, the analytical propagation formulae are derived by using the quadratic approximation of the nonlinear phase shift. It is found that the turbulence effect plays an important role in beam propagation characteristics. But the turbulence and self-focusing effects can be suppressed by increasing the laser elevation. Furthermore, the influence of laser elevation on the turbulence effect is stronger than that on the self-focusing effect, and influence of laser elevation on the self-focusing effect is stronger than that on the diffraction effect. In particular, the optimal focal length and wavelength are proposed to decrease the beam spot size on the target.

Defect edge steepness dependence of multiple nonlinear hot-image formation from a single phase defect.

Nonlinear hot image is one of the key elements that limit the output performance of high-power laser systems. In most hot-image researches, only one hot image peak is observed in the conjugate position for a single defect. Generally, multiple hot image peaks occur for multiple defects or cascaded nonlinear media. However, a new phenomenon is found by numerical simulation in our work: one defect can also afford two hot-image peaks near the conjugate position when considering the defect edge steepness. The super-Gaussian defect model is employed to mimic the defect edge steepness. When the super-Gaussian order is higher than one, there could be two hot image peaks under certain conditions. The formation of the double hot image peaks is primarily due to the co-effect of the hard-edge diffraction and the self-focusing effect. The influence of different factors, including the super-Gaussian order, defect size, modulation depth, and Kerr medium thickness, on the double hot image peaks intensity and location is systematically investigated. The results show that with the increase in the super-Gaussian order, the intensity of the double hot image peaks increases gradually. The defect size has a great influence on the position of the two hot image peaks. The modulation depth and thickness of the Kerr medium influence the intensity of the two hot image peaks; however, they have less impact on the peak location. Importantly, the defect edge steepness and size dependences of multiple nonlinear hot-image formation from a single-phase defect are further discussed in this paper. The two hot image peaks are fatal to optical components in high-power laser systems; in particular, the hot image peak behind the conjugate position is totally unexpected for a single defect. This research provides insights into basic physical images and hot-image formation laws. It also provides important guidance for optical defect specification evaluation and optical component layout design, as well as for beam quality control, in high-power laser systems.

Chirality-Enhanced Periodic Self-Focusing of Light in Soft Birefringent Media.

We experimentally and numerically show that chirality can play a major role in the nonlinear optical response of soft birefringent materials, by studying the nonlinear propagation of laser beams in frustrated cholesteric liquid crystal samples. Such beams exhibit a periodic nonlinear response associated with a bouncing pattern for the optical fields, as well as a self-focusing effect enhanced by the chirality of the birefringent material. Our results open new possible designs of nonlinear optical devices with low power consumption and tunable interactions with localized topological solitons.

Effect of Eu3+ in tuning the ultrafast third-order optical nonlinearity in heavy metal borate glasses

Abstract Photonic vitreous materials with high optical nonlinearities and fast response times are beneficial for designing next generation nonlinear photonic devices. Herein, large concentration of heavy metal oxide (PbO and Bi2O3) containing borate glasses activated with different Eu3+ concentrations have been designed through the melt quench technique. The non-linear optical (NLO) attributes such as nonlinear optical absorption and refractions were ascertained by utilizing the open aperture (OA) and closed aperture (CA) Z-scan techniques respectively in the spectral regions of 750–1000 nm using femtosecond laser pulses. The OA and CA Z-scan profiles demonstrated a reverse saturable absorption (RSA) nonlinearity (ascribed to two-photon absorption) and a positive nonlinear refraction nonlinearity (attributed to self-focusing effect) respectively. The NLO coefficients such as α2, n2 and χ(3) values were improved with respect to Eu3+ content in the glasses composition due to non-bridging oxygen and hyperpolarizability of Eu3+ ions. The NLO studies suggested that the examined glasses could be constructive materials for NLO device utilizations in the near infrared spectral regime.

Fabrication of Uniform Phase Structures in the Bulk of a N-BK7 Glass Using Ultrashort Laser Pulses

We study the possibility of application of direct laser writing technique for the fabrication of large-size uniform phase structures in the bulk of the borosilicate glass N-BK7. The morphology and the type of modifications induced by the sub-picosecond (500 fs) pulses are studied depending on the energy dose of irradiation. We show that with moderate focusing and at pulse energies below the threshold of self-focusing effects, it is possible to choose writing regimes (the scanning speed, the repetition rate of pulses) which allow the fabrication of extended structures with flat modification of the glass refractive index in the layer-by-layer scanning mode. At higher peak intensities of the laser, the Kerr nonlinearities affect the pulse propagation and the dynamics of the relaxation processes, and the resulting structures are essentially inhomogeneous with the alternating sign of refractive index change. To validate the approach, a buried phase structure with large dimensions was fabricated showing a rather uniform refractive index change over the entire processed range.

Dependence of high-energy proton acceleration in TNSA regime by fs laser on the laser pulse shape

TNSA regime is employed to accelerate protons from gold foils up to 20 MeV. Measurements were performed using a fs-pulsed laser at about 4× 1018 W/cm2. The laser source is characterized by a low contrast, high pre-pulse duration, main pulse within 40÷120 fs and presence of a second main pulse. The proton energy appears high compared to the values reported in the literature under similar experimental conditions, but the results can be explained by taking into account different mechanisms. The self-focusing effect, for instance, can produce increases in intensity of the main pulse. PIC simulations are used to account for these effects. The maximum electric field of ion acceleration, electron density as a function of space and time, and plasma temperature, are evaluated. The theoretical calculation is compared with the experimental measurements, confirming the very high proton acceleration under particular conditions of the laser parameters, irradiation conditions and target properties.

Evolution of rectangular and triangular initial beam profiles in positive Kerr local medium

The hyperbolic secant (Sech) shape, as the initial beam profile, is the well-know profile that compensates the diffraction and self-focusing effect during propagation in Kerr medium, and evolves as the bright spatial soliton. The Sech beam can be confined in the Kerr medium andinduces its own waveguide. In this work, two initial beam profiles, rectangular and triangular functions, that are different than Sech profile, are considered, and the propagation of these beam profiles in third-order nonlinear (Kerr) medium is investigated. As a result, the initialbeam-width played an important role in confining the beam profiles in direction of propagation. In addition, the intensity profiles change to the Sech profile after some initial step of propagation. All the calculations and simulations have been done by the Split-Step numericalmethod with MATLAB program.

Transport of intense particle beams in large-scale plasmas.

Transport of particle beams in plasmas is widely employed in fundamental research, industry, and medicine. Due to the high inertia of ion beams, their transport in plasmas is usually assumed to be stable. Here we report the focusing and flapping of intense slab proton beams transporting through large-scale plasmas by using a recently developed kinetic particle-in-cell simulation code. The beam self-focusing effect in the simulation is prominent and agrees well with previous experiments and theories. Moreover, the beam can curve and flap like turbulence as the beam density increases. Simulation and analysis indicate that the self-generated magnetic fields, produced by movement of collisional plasmas, are the dominant driver of such behaviors. By analyzing the spatial growth rate of magnetic energy and energy deposition of injected proton beams, it is found that the focusing and flapping are significantly determined by the injected beam densities and energies. In addition, a remarkable nonlinear beam energy loss is observed. Our research might find application in inertial confinement fusion and also might be of interest to the laboratory astrophysics community.

Influences of Fe3+ ions on rapid growth and laser-induced nonlinear refraction of potassium dihydrogen phosphate crystal

For rapidly grown KDP crystal, the whole growth zone is composed of prismatic- and pyramidal-sector. In order to further understand the distinctions between them, KDP crystals doped with Fe3+ in trace amount were selected to explore the influences of metal cation with high-valence on growth characteristics, Optical quality and nonlinear refraction. The growth characteristics for as-grown crystals indicate that the growth rate of prismatic sector can be obviously inhibited by Fe3+ ions with less than 15 ppm due to the stronger electronegativity of (100) face. With the increase of Fe3+, the crystal and optical qualities show significantly lower trends, especially for the prismatic sector. The influence of Fe3+ ions on nonlinear refraction was observed by Z-scan technique, which shows that self-focusing effect could be caused in high-intensity laser system because of the nonlinear refractive index obtained with a positive sign. Specially, nonlinear refraction effects along II-type and z-cut in prismatic area both show a significant variation with increase of Fe3+, while a negligible effect on nonlinear refraction is proved for pyramidal sector. Additionally, the generation of nonlinear refraction is mainly attributed to the electron-cloud distortion of H2PO4− groups, and the changes in prismatic sector may be due to the existence of (FeO4)2- groups.