Self-focusing Effect Research Articles

Hard-aperture effect on self-focusing of high-power laser beams propagating in the atmosphere.

The hard-aperture effect on self-focusing of high-power laser beams propagating from the ground through the atmosphere to space orbits is studied. It is shown that the spot size on the target increases as the truncation parameter decreases and the beam power increases. However, as the truncation parameter decreases, the apertured laser beam is less affected by self-focusing. On the other hand, two effective design rules are presented to optimize the intensity on the target, i.e., the optimal power and the optimal focal length. It is proven that the self-focusing effect and the hard-aperture effect both can be compensated by applying the optimal initial beam defocusing. It is also found that the higher maximum intensity on the target will occur by applying the optimal focal length rather than the optimal power.

Anisotropy of 2PA, 3PA, and Kerr effect in nonpolar ZnO.

Anisotropic optical nonlinearity plays an important role in polarization-dependent optoelectronic devices. Taking the advantage of in-plane crystallographic axis, the polarization dependence of third- and fifth-order nonlinearity in nonpolar ZnO has been investigated by z scan. Here, we established the theory model of anisotropic relation of fifth-order nonlinearity in hexagonal wurtzite crystal. Both two-photon absorption (2PA) and three-photon absorption (3PA) coefficients exhibit anisotropic oscillations with a period of 180°, and the polarization modulation factor and anisotropy coefficient (rp,σ) are measured as (2.10, 1.84) for β2, and (1.66, 1.33) for β3, respectively. This is the first time, to the best of our knowledge, that the anisotropy of the fifth-order optical nonlinear effect has been characterized and confirmed. It is verified that the self-defocusing effect at 500 nm is isotropy, while the self-focusing effect at 800 nm exhibits significant anisotropy. The maximum value of the nonlinear figure of merit is 5.84 along the [0010] crystalline direction, nearly 1.6 times the minimum value, revealing that ZnO exhibits potential for nonlinear applications containing polarization-related all-optical switching components.

Heterobimetallic Cluster-Based Coordination Polymers: Assembly, Structures and Third-Order Nonlinear Optical Properties.

Reactions of (NH4 )2 WS4 with CuCN, CuCN/1,2-bis(4-pyridyl)propane (bppa) or [Cu(MeCN)4 ]PF6 /bppa under different reaction conditions afforded a set of two- or three-dimensional W/Cu/S cluster-based coordination polymers including {[Et4 N]2 [WS4 Cu4 (μ-CN)2 (μ-I)2 ]}n (1), [WS4 Cu4 (μ-CN)2 (bppa)2 ]n (2) and {[WS4 Cu4 (bppa)4 ](PF6 )2 }n (3), respectively. Compound 2 can be readily formed from reaction of 1 with bppa under solvothermal conditions. Compounds 1 and 2 feature two-dimensional networks with a "sql" topology, while 3 possesses a two-fold interpenetrated three-dimensional net with a rare "reo" topology. Compounds 1-3 in DMF exhibited different third-order nonlinear optical responses, and they all showed a reverse saturable absorption while 2 held a strong self-focusing effect.

Third-order nonlinear optical effects of silver nanoparticles and third harmonic generation from their plasma plumes

We investigated the third-order nonlinear optical (NLO) properties of the silver (Ag) nanoparticles (NPs) of various sizes, which were produced by disintegration of commercially available 20 and 100 nm NPs in different solvents. It is observed that NPs with the sizes less or greater than 30 nm possess saturable absorption or reverse saturable absorption (or two-photon absorption), respectively. The NPs suspensions show a self-focusing effect. In addition, the third harmonic generation from the plasma plumes produced by nanosecond laser ablation of bulk Ag and Ag NPs of 100 nm and 20 nm sizes is reported. The third harmonic efficiency from the plasmas containing NPs was higher compared with the plasmas produced on the bulk silver. Finally, the ionization probabilities of Ag atom and Ag+ were calculated.

Influence of Kerr nonlinearity on propagation characteristics of twisted Gaussian Schell-model beams.

The analytical propagation formulae of twisted Gaussian Schell-model (TGSM) beams through nonlinear Kerr media are derived. It is found that a TGSM beam is less sensitive to Kerr nonlinearity than a Gaussian Schell-model (GSM) beam. Furthermore, the propagation characteristics of TGSM beams with stronger twist and worse spatial coherence are less affected by Kerr nonlinearity. The self-focusing effect enhances the beam twist, but degrades the beam spatial coherence. In the atmosphere (one kind of self-focusing media), a TGSM beam has greater resistance to self-focusing effects and atmospheric turbulence effects than a GSM beam or an ideal Gaussian beam.

Optimal power of laser beams propagating from the ground through the atmosphere to space orbits

It is shown that, when a high-power laser beam propagates from the ground through the atmosphere to space orbits, there is an optimal beam power that maximizes the target intensity due to self-focusing effect in the atmosphere, even if the atmospheric extinction exists. The B integral is an important parameter to describe self-focusing effect quantitatively. It is found that the value of B integral corresponding to optimal beam power is a constant. Based on this characteristic of the optimal B integral and the concept of the equivalent atmospheric extinction coefficient proposed in this paper, we derive the analytical formula of the optimal beam power, which presents an effective design rule to optimize the target intensity. In addition, it is shown that the optimal beam power increases as the initial beam radius, the wavelength, the atmospheric extinction coefficient, and the aerosol scale height increase.

Systematic investigation of terahertz wave generation from liquid water lines.

Understanding the process of terahertz (THz) wave generation from liquid water is crucial for further developing liquid THz sources. We present a systematic investigation of THz wave generated from laser-irradiated water lines. We show that water line in the diameter range of 0.1-0.2 mm generates the strongest THz wave, and THz frequency red shift is observed when diameter of the water line increases. The pump pulse energy dependence is decoupled from self-focusing effect by compensating the focal point displacement. As the pump pulse energy increases, saturation effect in THz peak electric field is observed, which can be mainly attributed to the intensity clamping effect inside the plasma and have never been reported previously, using water line or water film as the THz source. The proposed mechanism for saturation is supported by an independent measurement of laser pulse spectrum broadening. This work may help to further understand the laser-liquid interaction in THz generation process.

Three dimensional wave group dynamics of ion acoustic waves in electron–positron–ion plasmas in the presence of an external uniform magnetic field

Three dimensional (3D) wave group dynamics of ion acoustic wave is studied in electron–positron–ion (EPI) plasmas incorporating the effects of an external uniform magnetic field through the Laedke–Spatschek equation. In the presence of self-interaction (self-focusing effect), the wave group dynamics is shown to be governed by a (3 + 1) nonlinear Schrödinger equation. The derived nonlinear equations are solved analytically and the solutions predict a wide class of nonlinear structures in EPI plasma in the presence of magnetic field. The boundaries of stable and unstable solutions are also specified in parametric space. The results are expected to provide deeper insights into the ionic processes occurring in both astrophysical and laboratory plasmas.

Streamer self-focusing in an external longitudinal magnetic field.

The numerical simulation of the development of a streamer discharge in a gap with an external longitudinal magnetic field was used to demonstrate the self-focusing of such discharges. Self-focusing is caused by a sharp deceleration of the radial ionization wave due to a change in the electron energy distribution function, a decrease in the average electron energy, the rate of gas ionization, and the electron mobility in crossed electric and magnetic fields as compared to the case of the discharge development without a magnetic field. The self-focusing effect of a streamer discharge in an external longitudinal magnetic field is observed for both positive and negative pulse polarities. The paper proposes an estimate of the critical value of the magnetic field, which makes it possible to control the development of pulsed high-voltage discharges at various gas pressures.

Discussion on structural, optical, thermal, mechanical, dielectric and third-order NLO properties of 3-Nitroanilinium chloride single crystals for optoelectronic applications

Preferable, third-order nonlinear optical (NLO) single crystal, 3-Nitroanilinium chloride (3NACL) was auspiciously synthesised by slow evaporation technique. The crystal system of the synthesised 3NACL crystal was triclinic with centrosymmetric space group \({\text{P}}\bar{1}\) was identified by single-crystal XRD studies. All the functional groups present in the sample and its respective vibrations were analysed through FTIR analysis. UV–Vis transmittance spectrum revealed that the synthesised material showed 83% transmittance and its cut-off wavelength was 281 nm. The mechanical stability and thermal property of the grown 3NACL crystals were ascertained by Vickers microhardness analysis and TG/DTA analysis. The intermolecular interaction of the 3NACL was scrutinized by Hirshfeld surface analysis. Dielectric studies revealed that dielectric constant and dielectric loss were high at lower frequency region due to the space charge polarization. Inclusion-free 3NACL crystal was used to analyse the Laser damage threshold (LDT) studies and its calculated LDT value was 4.3 GW/cm2. The third-order NLO parameters (β = 7.5472 × 10–12 m/W, η2 = 5.6931 × 10–19 m2/W, χ3 = 2.9491 × 10–13 esu) of the 3NACL material were statutorily evaluated by Z-scan studies. Here, β and η2 were positive, due to the saturated absorption and self-focusing effect as observed in open and closed aperture z-scan curve. Above all these findings, 3NACL was a suitable material for NLO and optoelectronic applications.

Investigation on third-order nonlinear parameters, mechanical and dielectric behavior of alkali metal-organic C2HLiO4 H2O single crystal

A metal-organic lithium hydrogen oxalate hydrate single crystal was developed using the solution growth method. The single-crystal XRD analysis confirmed the triclinic structure and space group P1 along with the lattice parameters a = 3.439 Å, b = 5.097 Å, c = 6.141 Å, α = 78.50°, β = 84.89°, and γ = 81.41° of the grown crystal. The average crystallite size and strain within the material were calculated and compared using Debye Scherrer and Williamson-Hall method. The existence of diverse functional groups in the LHOH crystal was verified with the help of the FTIR analysis. The Z-scan method was carried out to acquire information about the developed material's third-order nonlinear characteristics that showed the material's self-focusing effect. The dielectric behavior of the compound was studied for various temperatures and frequencies. The Vicker’s microhardness analysis was carried out to collect information about the hardness number, yield strength, elastic stiffness, brittle index and fracture toughness of the grown crystal. The hardness number decreased when the applied load was increased, which indicated the normal indentation effect of the material.

Beam Quality of Annular Pulsed Laser Beams Propagating Through the Nonlinear and Dispersive Atmosphere

The Kerr self-focusing and group-velocity dispersion (GVD) effects play important roles when a high-power pulsed laser beam propagates from the ground through the nonlinear and dispersive atmosphere to space orbits. For an annular pulsed laser beam, the Kerr self-focusing and GVD effects on the beam quality on the target is studied in this paper. Due to self-focusing, the maximum intensity I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> on the target arrives when the beam power P = P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> is called the optimal beam power), and the intensity on the target will decrease as the beam power P increases further when P > P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> . The P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> of nanosecond and picosecond pulsed beams is lower than that of femtosecond pulsed beams, while the maximum intensity I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> on the target of nanosecond and picosecond pulsed beams is higher than that of femtosecond pulsed beams. The P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> and I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> of annular pulsed beams are higher than those of Gaussian pulsed beams. In addition, the B integral and the Strehl ratio are also adopted to describe the beam quality on the target. On the other hand, because of the interplay of Kerr self-focusing and GVD effects, the temporal pulse splitting and self-healing may take place on propagation, and the temporal pulse splitting may take place more than once. The results obtained in this paper are useful for laser ablation propulsion's applications in space.

Ultrafast third-order nonlinear optical properties of self-assembled poly[[4,4-bis(4-sulphobutyl)-4H-cyclopenta[2,1-b:3,4-b’]dithiophene-2,6-diyl]-1,4-phenylene sodium sa multilayer films

An ultrathin multilayer film with well-defined structure containing anionic Poly[[4,4-bis(4-sulphobutyl)-4H-cyclopenta[2,1-b:3,4-b’]dithiophene-2,6-diyl]-1,4-phenylene sodium sa (PCPDTPhSO3Na) and cationic poly(diallydimethyl ammonium chloride) (PDDA) was prepared using layer-by-layer assembly technique. The growth of the film was monitored by UV–Vis absorption spectroscopy, showing regularly consecutive adsorption. The ultrafast third-order nonlinear optical (NLO) properties of the multilayer film were investigated via the 4f coherent imaging measurement with phase object with 190 fs laser pulses at both 400 and 532 nm. The results demonstrate that PCPDTPhSO3Na/PDDA film exhibited excellent self-focusing effect (n 2 ∼2.42 × 10−16 m2/W) and reverse saturable absorption properties (β ∼6.34 × 10−10 m/W) at 400 nm. In contrast, self-focusing effect (n 2 ∼1.81 × 10−16 m2/W) and saturable absorption properties (β ∼−8.02 × 10−10 m/W) are observed when the laser wavelength (532 nm) is near-resonant with the absorption peak (470 nm). Our studies indicate that the PCPDTPhSO3Na/PDDA film is a promising candidate for applications in NLO devices.

Effect of orbital angular momentum of light on self-action effects of Laguerre Gaussian laser beams in collisionless plasmas

Nonlinear optical self-action effects like self-focusing, self-trapping of intense laser beams propagating through underdense plasmas have been investigated theoretically. The optical nonlinearity of the plasma has been modelled by ponderomotive force originating through intensity gradient over the cross section of the laser beam. In order to investigate the effect of orbital angular momentum of the photons on propagation characteristics of the laser beam, the irradiance over the cross section of the beam has been considered to be Laguerre Gaussian (LG). Effect of self-focusing of the laser beam on the evolution of its axial phase also has been investigated. Formulation is based on finding semi-analytical solution for the wave equation for the field of laser beam with the help of moment theory approach.

Z-scan investigation to evaluate the third-order nonlinear optical properties of cauliflower-like VS2 structures

V S 2 was prepared via the hydrothermal method and changing the reaction time and employing surfactant. The microstructural characterizations show the control of sheet dimensions and growth of crystal planes. The Z-scan study demonstrates the positive nonlinear n 2 due to the self-focusing effect and the two-photon absorption for nonlinear absorption. These results imply the effect of lateral dimensions of sheets in cauliflower-like structures on nonlinear optical responses. Also, the nonlinear optical susceptibility χ ( 3 ) is as high as 1 0 − 10 (esu). This study shows that the V S 2 flower-like structure and its similar nanostructures are promising materials for nonlinear optical applications and further considerations.

Investigation on millijoule femtosecond laser spiral drilling of micro-deep holes in thermal barrier coated alloys

Ultra-short laser drilling of micro-holes with high quality and high processing efficiency in the aviation industry is urgently needed. This study reported the fabrication of micro-deep holes on thermal barrier coated alloys through millijoule femtosecond laser beam irradiation. The self-focusing effect (Kerr effect induced by the intense beam itself) and waveguide effect (reflections induced by the sidewall) on beam propagation behavior inside the micro-deep hole were investigated. The experimental results showed the number of spiral orbits required for through holes has little change within a certain defocus range. Combined with the simulation analyses, it reveals that self-focusing can reinforce the laser intensity in the deep of micro-holes, preventing the beam energy attenuation as the depth of hole increases. Additionally, the guidance and reflection of the sidewall will also make the beam self-converge and enhance its intensity. The enhancement of the laser intensity in the hole cavity can help shorten the processing time. Furthermore, as the aperture increases, the self-focusing still has the noteworthy effect on the intensity enhancement inside the cavity, while the waveguide effect of the sidewall on the intensity enhancement will be weakened. The section profile of holes was analyzed, delamination-free was achieved, and no recast layer was found.

About the modeling of light beam self-focusing in plasma at the irradiation of the target by power UV laser

The peculiarities of light beam expansion in plasma upon irradiation of condensed targets with a powerful UV laser pulse are studied with the help of mathematical modeling. Experiments were carried out at the Lebedev Physical Institute of the Russian Academy of Sciences with the use of GARPUN installation: a powerful KrF laser that irradiated two-layer targets consisting of aluminum foil and a plexiglass layer. Channels stretched along the direction of incidence of the laser beam were found at the bottom of the crater. It was shown on the basis of experimental and calculated data that selffocusing of the laser beam developed in the plasma. As a result, hot spots were produced in vicinity of the plasma critical density, and fast (superthermal) electron flows were generated. The electron flows could produce the channels in the plexiglas. In order to describe the self-focusing effect a physicalmathematical model was developed, and “FOCUS” program was created at the Russian Technological University (MIREA). Numerical simulations were carried out on the gas-dynamic profiles (linear and exponential). It was shown that thermal self-focusing could develop at the conditions of “GARPUN” experiments (~ 1 mm longitudinal plasma, moderate radiation intensity: 1011–1012(W/cm2) × µm2). The parameters of dangerous modes of laser beam perturbations were estimated. The interest in the experimental and mathematical modelling results is related to the laser thermonuclear fusion (LTF) research. Although Nd glass lasers are the basic installations for LTF research, UV gas eximer lasers have some advantages as drivers for future thermonuclear fusion reactors. The interaction of UV laser radiation with plasma has some peculiarities. Thus, developing physical-mathematical models and creating new programs required for the interpretation of modern UV laser – plasma coupling experiments and for the design of large scale facilities based on eximer drivers is a topical problem.

New vision for the soliton solutions to the complex Hirota-dynamical model

In this paper, the nonlinear complex Hirota-dynamical model NLCHM in which the third derivative term represents the self-interaction in the high-frequency subsystem is established. This model plays a vital role in plasma physics because there are agreements between the self-interaction in the high-frequency and the well- known self-focusing effect in plasma. Many soliton solutions to this equation model have been achieved perfectly using the solitary wave ansatz method (SWAM). Furthermore, in the same vein and related subject the extended simple equation method (ESEM) has been applied perfectly to achieve new perception of soliton solutions to this model. A good isomorphic between the achieved results and that achieved previous by other authors have been listed.

Fabrication of self-aligning convergent waveguides of microlens arrays to collect and guide light.

The optical properties of microlens arrays may be significantly affected by the optical crosstalk effect between adjacent lenses. Recently, this issue has triggered increasing attention in the scientific community. In this study, an integrated microlens array (MLA) consisting of self-aligning convergent waveguides of microlenses was fabricated. The optical crosstalk effect does not influence the performance of such system. Based on the self-focusing effect principle, self-writing of the waveguide array was achieved in a photosensitive polymer. The light collection and guiding performance of the MLA with and without thermal cross-linking treatment was analyzed in depth. The relation between the stray light and the filling rate of the MLA shows that a high filling rate decreases the optical crosstalk. Finally, an integrated MLA with a large area, high uniformity, and excellent optical performance was fabricated.

Self-focusing effect on the beam quality of Hermite-Gaussian beams propagating upwards through the inhomogeneous atmosphere.

The self-focusing effect on the beam quality of Hermite-Gaussian beams propagating upwards through the inhomogeneous atmosphere is studied. The analytical formula of the beam width is derived, and its validity is confirmed. Furthermore, the analytical formulas of the actual focal length and M2-factor are also derived. It is found that the self-focusing effect in the inhomogeneous atmosphere results in beam quality degradation. Under the same initial beam width and the same beam power, as the beam order m increases, the actual focal length is farther away from the target, and the spot size on the target and the M2-factor increase; namely, the beam quality degrades further. In addition, it is shown that the beam quality can be improved by the phase compensation.