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.

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.

THE MUTUAL VARIATIONAL PRINCIPLE OF FREE WAVE PROPAGATION IN PERIODIC STRUCTURES

By taking infinite periodic beams as examples,the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propaga- tion constant in the present paper,and the corresponding hierarchical finite element formulation is then de- rived.Thus,it provides the numerical analysis of that problem with a firm theoretical basis of variational prin- ciples,with which one may conveniently illustrate the mathematical and physical mechanisms of the wave prop- agation in periodic structures and the relationship with the natural vibration.The solution is discussed and ex- amples are given.

DISCRETE SINGULAR CONVOLUTION METHOD WITH PERFECTLY MATCHED ABSORBING LAYERS FOR THE WAVE SCATTERING BY PERIODIC STRUCTURES

A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem.

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.

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.

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.

NUMERICAL ANALYSIS OF BIFURCATION BUCKLING FOR ROTATIONALLY PERIODIC STRUCTURES UNDER ROTATIONALLY PERIODIC LOADS

By considering the characteristics of deformation of rotationally periodic structures under rotationally periodic loads, the periodic structure is divided into some identical substructures in this study. The degrees-of-freedom (DOFs) of joint nodes between the neighboring substructures are classified as master and slave ones. The stress and strain conditions of the whole structure are obtained by solving the elastic static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method is used to get the bifurcation buckling load and mode for the whole rotationally periodic structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. The finite element (FE) formulation of shell element of relative degrees of freedom (SERDF) in the buckling analysis is derived. Different measures of tackling internal degrees of freedom for different kinds of buckling problems and different stages of numerical analysis are presented. Some numerical examples are given to illustrate the high efficiency and validity of this method.

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.

Impact of flm thickness in laser‑induced periodic structures on amorphous Si flms

We report self-organized periodic nanostructures on amorphous silicon thin flms by femtosecond laser-induced oxidation.The dependence of structural periodicity on the thickness of silicon flms and the substrate materials is investigated.The results reveal that when silicon flm is 200 nm,the period of self-organized nanostructures is close to the laser wavelength and is insensitive to the substrates.In contrast,when the silicon flm is 50 nm,the period of nanostructures is much shorter than the laser wavelength,and is dependent on the substrates.Furthermore,we demonstrate that,for the thick silicon flms,quasi-cylindrical waves dominate the formation of periodic nanostructures,while for the thin silicon flms,the formation originates from slab waveguide modes.Finite-diference time-domain method-based numerical simulations support the experimental discoveries.

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.

Fast SSED-MoM /FEM Analysis for Electromagnetic Scattering of Large-Scale Periodic Dielectric Structures

A hybrid method combining simplified sub-entire domain basis function method of moment with finite element method( SSED-MoM /FEM) is accelerated for electromagnetic( EM) scattering analysis of large-scale periodic structures.The unknowns are reduced sharply with non-uniform mesh in FEM. The computational complexity of the hybrid method is dramatically declined by applying conjugate gradient-fast Fourier transform( CG-FFT) to the integral equations of both electric field and magnetic field. The efficiency is further improved by using OpenMP technique. Numerical results demonstrate that the SSED-MoM /FEM method can be accelerated for more than three thousand times with large-scale periodic structures.

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 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.

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.

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.

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.

Enhancement of photocatalytic activity by femtosecond-laser induced periodic surface structures of Si

Laser induced periodic surface structures(LIPSS)represent a kind of top down approach to produce highly reproducible nano/microstructures without going for any sophisticated process of lithography.This method is much simpler and cost effective.In this work,LIPSS on Si surfaces were generated using femtosecond laser pulses of 800 nm wavelength.Photocatalytic substrates were prepared by depositing TiO2 thin films on top of the structured and unstructured Si wafer.The coatings were produced by sputtering from a Ti target in two different types of oxygen atmospheres.In first case,the oxygen pressure within the sputtering chamber was chosen to be high(3×10^–2 mbar)whereas it was one order of magnitude lower in second case(2.1×10^–3 mbar).In photocatalytic dye decomposition study of Methylene blue dye it was found that in the presence of LIPSS the activity can be enhanced by 2.1 and 3.3 times with high pressure and low pressure grown TiO2 thin films,respectively.The increase in photocatalytic activity is attributed to the enlargement of effective surface area.In comparative study,the dye decomposition rates of TiO2 thin films grown on LIPSS are found to be much higher than the value for standard reference thin film material Pilkington Activ^TM.

Determination of Random Periodic Structures in Transverse Magnetic Polarization

Consider an inverse problem that aims to identify key statistical pro-perties of the profile for the unknown random perfectly conducting grating structure by boundary measurements of the diffracted fields in transverse mag-netic polarization.The method proposed in this paper is based on a novel combination of the Monte Carlo technique,a continuation method and the Karhunen-Loève expansion for the uncertainty quantification of the random structure.Numerical results are presented to demonstrate the effectiveness of the proposed method.

The Problem of Quasiperiodic Photonic Structures Solved by Considering the Cut of 2D Periodic Structure

The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.