Ultrafast dynamics of femtosecond laser-induced high spatial frequency periodic structures on silicon surfaces

Femtosecond laser-induced periodic surface structures(LIPSS)have been extensively studied over the past few decades.In particular,the period and groove width of high-spatial-frequency LIPSS(HSFL)is much smaller than the diffraction limit,making it a useful method for efficient nanomanufacturing.However,compared with the low-spatial-frequency LIPSS(LSFL),the structure size of the HSFL is smaller,and it is more easily submerged.Therefore,the formation mechanism of HSFL is complex and has always been a research hotspot in this field.In this study,regular LSFL with a period of 760 nm was fabricated in advance on a silicon surface with two-beam interference using an 800 nm,50 fs femtosecond laser.The ultrafast dynamics of HSFL formation on the silicon surface of prefabricated LSFL under single femtosecond laser pulse irradiation were observed and analyzed for the first time using collinear pump-probe imaging method.In general,the evolution of the surface structure undergoes five sequential stages:the LSFL begins to split,becomes uniform HSFL,degenerates into an irregular LSFL,undergoes secondary splitting into a weakly uniform HSFL,and evolves into an irregular LSFL or is submerged.The results indicate that the local enhancement of the submerged nanocavity,or the nanoplasma,in the prefabricated LSFL ridge led to the splitting of the LSFL,and the thermodynamic effect drove the homogenization of the splitting LSFL,which evolved into HSFL.

Elastic wave insulation and propagation control based on the programmable curved-beam periodic structure

Curved-beams can be used to design modular multistable metamaterials(MMMs)with reprogrammable material properties,i.e.,programmable curved-beam periodic structure(PCBPS),which is promising for controlling the elastic wave propagation.The PCBPS is theoretically equivalent to a spring-oscillator system to investigate the mechanism of bandgap,analyze the wave propagation mechanisms,and further form its geometrical and physical criteria for tuning the elastic wave propagation.With the equivalent model,we calculate the analytical solutions of the dispersion relations to demonstrate its adjustability,and investigate the wave propagation characteristics through the PCBPS.To validate the equivalent system,the finite element method(FEM)is employed.It is revealed that the bandgaps of the PCBPS can be turned on-and-off and shifted by varying its physical and geometrical characteristics.The findings are highly promising for advancing the practical application of periodic structures in wave insulation and propagation control.

Two-dimensional laser-induced periodic surface structures formed on crystalline silicon by GHz burst mode femtosecond laser pulses

Femtosecond laser pulses with GHz burst mode that consist of a series of trains of ultrashort laser pulses with a pulse interval of several hundred picoseconds offer distinct features in material processing that cannot be obtained by the conventional irradiation scheme of femtosecond laser pulses(single-pulse mode).However,most studies using the GHz burst mode femtosecond laser pulses focus on ablation of materials to achieve high-efficiency and high-quality material removal.In this study,we explore the ability of the GHz burst mode femtosecond laser processing to form laser-induced periodic surface structures(LIPSS)on silicon.It is well known that the direction of LIPSS formed by the single-pulse mode with linearly polarized laser pulses is typically perpendicular to the laser polarization direction.In contrast,we find that the GHz burst mode femtosecond laser(wavelength:1030 nm,intra-pulse duration:220 fs,intra-pulse interval time(intra-pulse repetition rate):205 ps(4.88 GHz),burst pulse repetition rate:200 kHz)creates unique two-dimensional(2D)LIPSS.We regard the formation mechanism of 2D LIPSS as the synergetic contribution of the electromagnetic mechanism and the hydrodynamic mechanism.Specifically,generation of hot spots with highly enhanced electric fields by the localized surface plasmon resonance of subsequent pulses in the bursts within the nanogrooves of one-dimensional LIPSS formed by the preceding pulses creates 2D LIPSS.Additionally,hydrodynamic instability including convection flow determines the final structure of 2D LIPSS.

Microstructure and tribological behavior of Mg-Gd-Zn-Zr alloy with LPSO structure

A Mg-14.28Gd-2.44Zn-0.54Zr （mass fraction, %） alloy was prepared by conventional ingot metallurgy （I/M）. The microstructure differences in as-cast and solution-treated alloys were investigated. Sliding tribological behaviors of the as-cast and solution-treated alloys were investigated under oil lubricant condition by pin-on-disc configuration. The wear loss and friction coefficients were measured at a load of 40 N and sliding speeds of 30-300 mm/s with a sliding distance of 5000 m at room temperature. The results show that the as-cast alloy is mainly composed ofα-Mg solid solution, the lamellar 14H-type long period stacking ordered （LPSO） structure within matrix, andβ-[（Mg,Zn）3Gd] phase. However, most of theβ-phase transforms to X-phase with 14H-type LPSO structure after solution heat treatment at 773 K for 35 h （T4）. The solution-treated alloy presents low wear-resistance, because the hard β-phase is converted into thermally-stable, ductile and soft X-Mg12GdZn phase with LPSO structure in the alloy.

Structural color of metallic glass through picosecond laser

The alteration in surface color of metallic glasses(MGs)holds great significance in the context of microstructuredesign and commercial utility.It is essential to accurately describe the structures that are formed during the laser and colorseparation processes in order to develop practical laser coloring applications.Due to the high oxidation sensitivity of Labasedmetallic glass,it can broaden the color range but make it more complex.Structure coloring by laser processing on thesurface of La-based metallic glass can be conducted after thermoplastic forming.It is particularly important to clarify therole of structure and composition in the surface coloring process.The aim is to study the relationship between amorphoussurface structural color,surface geometry,and oxide formation by laser processing in metallic glasses.The findings revealedthat the periodic structure primarily determines the surface color at laser energy densities below 1.0 J/mm^(2).In contrast,thesurface color predominantly depends on the proportion of oxides that are formed when energy densities exceed 1.0 J/mm^(2).Consequently,this study provides a novel concept for the fundamental investigation of laser coloring and establishes a newavenue for practical application.

Formation mechanism of periodic layered structure in Ni_3Si/Zn system

The formation of periodic layered structure in Ni3Si/Zn diffusion couples with Zn in vapor or liquid state was investigated by SEM-EDS, FESEM and XRD. The results show that the diffusion path in solid-liquid reaction is Ni3Si/（T＋γ）/γ/…T/γ/Ni4Zn12Si3/γ/…Ni4Zn12Si3/γ/Ni4Zn12Si3/δ…/Ni4Zn12Si3/δ/liquid-Zn, and the diffusion path in solid-vapor reaction is Ni3Si/θ/（T＋γ）/γ/…/T/γ/…T/γ/vapor-Zn. With increasing Zn diffusion flux, the diffusion reaction path moves toward the Zn-rich direction, and the distance from the Ni3Si substrate to the periodic layer pair nearest to the interface decreases. In the initial stage of both reactions,γphase nucleates and grows within T matrix phase at first, and then conjuncts together to form a band to reduce the surface energy. Based on the experimental results and diffusion kinetics analysis, the microstructure differences were compared and the formation mechanism of the periodic layered structure in Ni3Si/Zn system was discussed.

MULTI-SCALE FE COMPUTATION FOR THE STRUCTURES OF COMPOSITE MATERIALS WITH SMALL PERIODIC CONFIGURATION UNDER CONDITION OF COUPLED THERMOELASTICITY

In this paper,the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic(TSA)expression of the displacement and the increment of temperature for composite materials with a small periodic configuration under the condition of thermoelasticity are briefly shown at first,then the multi-scale finite element algorithms based on TSA are discussed.Finally the numerical results evaluated by the multi-scale computational method are shown.It demonstrates that the basic configuration and the increment of temperature strongly influence the local strains and local stresses inside a basic cell.

Wave propagation control in periodic track structure through local resonance mechanism

Excessive vibration and noise radiation of the track structure can be caused by the operation of high speed trains.Though the track structure is characterized by obvious periodic properties and band gaps,the bandwidth is narrow and the elastic wave attenuation capability within the band gap is weak.In order to effectively control the vibration and noise of track structure,the local resonance mechanism is introduced to broaden the band gap and realize wave propagation control.The locally resonant units are attached periodically on the rail,forming a new locally resonant phononic crystal structure.Then the tuning of the elastic wave band gaps of track structure is discussed,and the formation mechanism of the band gap is explicated.The research results show that a new wide and adjustable locally resonant band gap is formed after the resonant units are introduced.The phenomenon of coupling and transition can be observed between the new locally resonant band gap and the original band gap of the periodic track structure with the band gap width reaching the maximum at the coupling position.The broader band gap can be applied for vibration and noise reduction in high speed railway track structure.

Wave localization in randomly disordered periodic layered piezoelectric structures

Considering the mechnoelectrical coupling, the localization of SH-waves in disordered periodic layered piezoelectric structures is studied. The waves propagating in directions normal and tangential to the layers are considered. The transfer matrices between two consecutive unit cells are obtained according to the continuity conditions. The expressions of localization factor and localization length in the disordered periodic structures are presented. For the disordered periodic piezoelectric structures, the numerical results of localization factor and localization length are presented and discussed. It can be seen from the results that the frequency passbands and stopbands appear for the ordered periodic structures and the wave localization phenomenon occurs in the disordered periodic ones, and the larger the coefficient of variation is, the greater the degree of wave localization is. The widths of stopbands in the ordered periodic structures are very narrow when the properties of the consecutive piezoelectric materials are similar and the intervals of stopbands become broader when a certain material parameter has large changes. For the wave propagating in the direction normal to the layers the localization length has less dependence on the frequency, but for the wave propagating in the direction tangential to the layers the localization length is strongly dependent on the frequency.

ELASTIC WAVE LOCALIZATION IN TWO-DIMENSIONAL PHONONIC CRYSTALS WITH ONE-DIMENSIONAL QUASI-PERIODICITY AND RANDOM DISORDER

The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the quasi-periodicity as the deviation from the periodicity in a special way, two kinds of quasi phononic crystal that has quasi-periodicity （Fibonacci sequence） in one direction and translational symmetry in the other direction are considered and the band structures are characterized by using localization factors. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional perfect, randomly disordered and quasi-periodic phononic crystals. Band structures of the phononic crystals can be tuned by different random disorder or changing quasi-periodic parameters. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.

Large-area straight,regular periodic surface structures produced on fused silica by the interference of two femtosecond laser beams through cylindrical lens

Inhomogeneity and low efficiency are two important factors that limit the application of laser-induced periodic surface structures(LIPSSs),especially on glass surfaces.In this study,two-beam interference(TBI)of femtosecond lasers was used to produce large-area straight LIPSSs on fused silica using cylindrical lenses.Compared with those produced us-ing a single circular or cylindrical lens,the LIPSSs produced by TBI are much straighter and more regular.Depending on the laser fluence and scanning velocity,LIPSSs with grating-like or spaced LIPSSs are produced on the fused silica sur-face.Their structural colors are blue,green,and red,and only green and red,respectively.Grating-like LIPSS patterns oriented in different directions are obtained and exhibit bright and vivid colors,indicating potential applications in surface coloring and anti-counterfeiting logos.

P-Δ effect on inelastic displacement ratio spectra for inelastic structures

For the evaluation of structures with known ductility demands,the constant-ductility displacement ratio spectra(CDDRS) are particularly useful for providing inelastic displacement ratios to estimate maximum lateral inelastic displacement demands from maximum elastic displacement demands.The CDDRS are computed for single-degree-of-freedom systems(SDOF) by considering or ignoring P-Δ effect for different ductility levels when subjected to 344 earthquake ground motions recorded in four site classes.The modified expressions of CDDRS for P-Δ effect are proposed.It is concluded that the P-Δ effect on CDDRS is significant,and the effect increases with the increase of ductility level.In the long-period region,the CDDRS ignoring P-Δ effect almost conforms to the equal-displacement rule.But in the case of higher ductility level,the CDDRS considering P-Δ effect are much higher than 1.0,which do not conform to the equal-displacement rule.

PROPAGATION BEHAVIORS OF SHEAR HORIZONTAL WAVES IN PIEZOELECTRIC-PIEZOMAGNETIC PERIODICALLY LAYERED STRUCTURES

This paper investigates shear horizontal （SH） waves propagating in a periodically layered structure that consists of piezoelectric （PE） layers perfectly bonded with piezomagnetic （PM） layers alternately. The explicit dispersion relations are derived for the two cases when the propagation directions of SH waves are normal to the interface and parallel to the interface, respectively. The asymptotic expressions for dispersion relations are also given when the wave number is extremely small. Numerical results for stop band effect and phase velocity are presented for a periodic system of alternating BaTiO3 and Terfenol-D layers. The influence of volume fraction on stop band effect and dispersion behaviors is discussed and revealed.

Periodic Structures of Rossby Wave under Influence of Dissipation

A simple barotropic potential vorticity equation with the influence of dissipation is applied to investigate the nonlinear Rossby wave in a shear flow in the tropical atmophere. By the reduetive perturbation method, we derive the rotational KdV （rKdV for short） equation. And then, with the help of Jaeobi elliptie functions, we obtain various periodic structures for these Rossby waves. It is shown that dissipation is very important for these periodic structures of rational form.

Attenuation of wave propagation in a novel periodic structure

A novel periodic mount was presented. A theoretical model was developed to describe the dynamics of wave propagation in the novel periodic mount. The model was derived using Hamilton's energy conservation principle. The characteristics of wave propagation in unit cell were analyzed by transfer matrix formulation. Numerical examples were given to illustrate the effectiveness of the periodic mount. The experiments were carried out to identify the predications of the theoretical model. The obtained results show that the experimental results coincide with the prediction of theoretical model. No pass bands appear in the overall frequency range measured when waves propagate in the longitude direction of the periodic mount. These dramatic results demonstrate its potential as an excellent mount in attenuating and isolating vibration transmission.

Two-scale finite element method for piezoelectric problem in periodic structure

The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.

The Two-dimensional Electromagnetic Scattering from Periodic Chiral Structures and Its Finite Element Approximation

In this paper, we consider the electromagnetic scattering from periodic chiral structures. The structure is periodic in one direction and invariant in another direction. The electromagnetic fields in the chiral medium are governed by the Maxwell equations together with the Drude-Born-Fedorov equations. We simplify the problem to a two-dimensional scattering problem and we show that for all but possibly a discrete set of wave numbers, there is a unique quasi-periodic weak solution to the diffraction problem. The diffraction problem can be solved by finite element method. We also establish uniform error estimates for the finite element method and the error estimates when the truncation of the nonlocal transparent boundary operators takes place.

A transparent electromagnetic-shielding film based on one-dimensional metal–dielectric periodic structures

In this study, we designed and fabricated optical materials consisting of alternating ITO and Ag layers. This approach is considered to be a promising way to obtain a light-weight, ultrathin and transparent shielding medium, which not only transmits visible light but also inhibits the transmission of microwaves, despite the fact that the total thickness of the Ag film is much larger than the skin depth in the visible range and less than that in the microwave region. Theoretical results suggest that a high dielectric/metal thickness ratio can enhance the broadband and improve the transmittance in the optical range. Accordingly, the central wavelength was found to be red-shifted with increasing dielectric/metal thickness ratio. A physical mechanism behind the controlling transmission of visible light is also proposed. Meanwhile, the electromagnetic shielding effectiveness of the prepared structures was found to exceed 40 dB in the range from 0.1 GHz to 18 GHz, even reaching up to 70 dB at 0.1 GHz, which is far higher than that of a single ITO film of the same thickness.

Femtosecond laser-induced periodic structures:mechanisms, techniques, and applications

Over the past two decades,femtosecond laser-induced periodic structures(femtosecond-LIPSs)have become ubiquitous in a variety of materials,including metals,semiconductors,dielectrics,and polymers.Femtosecond-LIPSs have become a useful laser processing method,with broad prospects in adjusting material properties such as structural color,data storage,light absorption,and luminescence.This review discusses the formation mechanism of LIPSs,specifically the LIPS formation processes based on the pump-probe imaging method.The pulse shaping of a femtosecond laser in terms of the time/frequency,polarization,and spatial distribution is an efficient method for fabricating high-quality LIPSs.Various LIPS applications are also briefly introduced.The last part of this paper discusses the LIPS formation mechanism,as well as the high-efficiency and high-quality processing of LIPSs using shaped ultrafast lasers and their applications.

Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures

The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.