Two-dimensional Periodic Surface Research Articles

Sub-THz and THz Cherenkov radiation source with two-dimensional periodic surface lattice and multistage depressed collector

We present the theory, concept and design of an efficient, megawatt coherent Cherenkov radiation source based on a two-dimensional periodic surface lattice (2D-PSL) cavity combined with a novel energy recovery system for the generation of highly efficient (> 50%) single-frequency radiation. We demonstrate the scalability of the transverse dimension of the 2D-PSL cavity of the Cherenkov source and thus the potential for efficient, continuous-wave, high-power (> 1 MW) operation; fundamental to the eventual realization of clean, fusion energy. These new sources, with the capacity to operate in the 0.1-10THz range, hold strong promise to address the long-standing “Terahertz gap”. By combining a Cherenkov oscillator driven by a non-gyrating beam with an innovative four-stage depressed collector energy recovery system, the overall device efficiency can be increased to be competitive with gyrotrons in the requirements for heating and current drive in fusion plasma. In these Cherenkov devices, the frequency independence of the magnetic guide field enables advantageous frequency scaling without deployment constraints, making them especially attractive for high-impact applications in fusion science, turbulence diagnostics, non-destructive testing and biochemical spectroscopy. The novel energy recovery techniques presented in this paper have broad applicability to many electron-beam driven devices, bringing revolutionary potential to future THz source technologies.

Nanoripples evolution on tungsten surface induced by two-pulse configuration

Tuneable shapes and uniformity of the laser-induced periodic surface structures (LIPSS) attract interest because of their diverse applications in both scientific research and technological advancements. In this work, we investigate the progression of regular one-dimensional (1D) LIPSS on a tungsten surface, examining its evolution based on the time delay between two laser pulses that initiate the formation of nanoripples. 1D-LIPSS were formed in the case of single-beam laser ablation with approximately 84 laser pulses. Two-dimensional (2D) LIPSS, including triangle, hexagonal, and square shapes, were generated by employing two cross-polarized laser beams (with wavelengths of 1030 nm and pulse durations of 40 fs) with no delay between the pulses. However, introducing a time delay of 2 picoseconds (ps) between the two cross-polarized laser pulses resulted in the division of the initially cross-oriented 2D-LIPSS into square-shaped structures, particularly along the spatially overlapped region of the laser beams. The emergence of triangle- and hexagonal-shaped two-dimensional laser-induced periodic surface structures (2D-LIPSS) is analyzed within the framework of a self-organization model, particularly in the context of solidifying the molten layer under cold temperature conditions on the tungsten surface. We examine the formation mechanism of LIPSS, attributing it to a combination of the self-organization/hydrodynamic mechanism initially, which transitions to the electromagnetic mechanism as the effective number of pulses increases.

Two-dimensional periodic surface nanotexturing of 6H-SiC by ultrashort laser pulses

Circularly polarized femtosecond laser pulses have successfully promoted the formation of Two-Dimensional Laser Induced Periodic Surface Structures (2D-LIPSS) exhibiting a sub-wavelength periodicity of 150 ± 20 nm on semi-insulating 6H-SiC samples. The main objective of this study was to discern the formation of two-dimensional LIPSS depending on the single pulse energy and the number of pulses released per unit area. The experimental laser system used in this study generates pulses with a duration of 100 fs, a wavelength of 800 nm, and operates at a repetition rate of 1 kHz.Micro-Raman spectroscopy confirms the presence of the characteristic 6H-SiC peaks across all irradiated samples, indicating that the processing technique does not induce significant compositional variations. Nonetheless, the analysis reveals the induction of compressive stress within the lattice structure.Samples treated across the entire surface were characterized by using optical analysis in order to assess the induced variations in absorptance and emittance due to laser irradiation. The treated samples exhibit solar absorptance values of approximately 75 % and a high spectral selectivity up to 2.0 for temperatures higher than 1000 K. This highlights the potential of fs-laser surface textured 6H-SiC plates as viable selective solar absorbers for energy conversion devices operating at elevated temperatures.

Formation of two-dimensional laser-induced periodic surface structures on titanium by GHz burst mode femtosecond laser pulses

GHz burst mode femtosecond (fs) laser pulses, which consist of a series of pulse trains with ultra-fast intervals of several hundred picoseconds, have offered distinct features for material processing compared to conventional irradiation of laser pulses (single-pulse mode). We apply GHz burst mode processing to fabricate laser-induced periodic surface structures (LIPSS) on the material surfaces. In our previous work for silicon (Si), we have found that GHz burst mode can create unique two-dimensional (2D) LIPSS composed of both parallel and perpendicular to the laser polarization direction. We proposed that the formation of 2D-LIPSS is attributed to the synergetic contributions of electromagnetic and hydrodynamic mechanisms. To further investigate more detailed formation mechanisms and explore practical applications, we employ titanium (Ti), whose properties are significantly different from Si. We demonstrate that GHz burst mode fs laser pulses (central wavelength: 1,030 nm, intra-pulse width: 230 fs, intra-pulse repetition rate (an intra-pulse interval): 4.88 GHz (205 ps) and burst pulse repetition rate: 10 kHz) can also fabricate 2D-LIPSS on Ti surfaces. We attribute the dominant formation mechanism of 2D-LIPSS to the generation of hot spots with highly enhanced electric fields due to transient change of material properties during GHz burst pulse irradiation. Based on this speculation, properly tailoring the shapes of the burst pulse with an optimum intra-pulse number enables the creation of well-defined 2D-LIPSS. Furthermore, essentially homogeneous 2D-LIPSS can be formed in a large area by laser scanning of a focused fs laser beam with a stage scanning speed of 5 mm/s.

Laser-driven self-organized evolution of 1D- and 2D-Nanostructures from metal thin-films on silicon: Influence of alloying and oxidation

One- and two-dimensional laser-induced periodic surface structure (LIPSS) formation of various metal (Ag, Cu, Fe, Zn, Ti) thin films on silicon wafers is achieved by irradiation with circularly polarized 532 nm nanosecond laser pulses. The occurrence and the evolution of pseudo-1D linear periodic, 2D honeycomb-like structures, and 2D periodic nanoparticle arrays were mapped for each element in dependence on the energy applied, i.e. the effective pulse number, and the metal thin film thickness. Samples series with increasing pulse counts monitor, like snapshots, the progressive pattern evolution. Because the metal thin films are of nanometer thickness only, the co-structuring of the silicon substrate must be taken into account in all cases. Even more complex are LIPSS formations on samples carrying two stacked thin films. The LIPSS formation process of thin films becomes rather complex as soon as co-structuring of the substrate, oxidation of the material, and alloy formation with substrate material or a potential second thin film layer are considered. All these effects affect the morphology of the formed LIPSS patterns.

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.

All-metal wakefield accelerator: Two-dimensional periodic surface lattices for charged particle acceleration

Interest in ``all-metal'' surface periodic structures to control charged particle beam dynamics and properties, and to generate coherent radiation in the THz frequency range has recently risen exponentially. While such structures have the benefits of metal, they are capable of providing similar properties to a dispersive dielectric. All-metal structures allow good temperature and space charge management. Transportation of high energy charge particle beams in the vicinity of the structure without risking material degradation makes them very attractive for particle acceleration and terahertz radiation generation applications. Here, the results of theoretical studies (via numerical modeling) of the electron beam dynamics and wakefield excitation and evolution along the cylindrical two-dimensional periodic surface structure will be presented, and the properties of the wakefields generated will be discussed. The wakefield acceleration of the witness bunch in the potential reaching $1\text{ }\text{ }\mathrm{GV}/\mathrm{m}$ will be demonstrated. The challenges will be identified and discussed, and the concept of the cascade accelerator based on such all-metal wakefield accelerator (AMWA) structures will be presented.

Efficient, 0.35-THz Overmoded Oscillator Based on a Two-Dimensional Periodic Surface Lattice

We present the theory, design, and numerical modeling of a cylindrical, two-dimensional periodic surface lattice (2D-PSL) intended for use as the interaction region of an electron beam-driven, pulsed source. The production of 1.95-MW peak, pulsed 0.35-THz radiation with an electronic efficiency of 24% is reported. Mode selection in the oversized cavity, where the diameter D is almost <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.5\times $ </tex-math></inline-formula> larger than the operating wavelength <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> , is achieved by coupling volume and surface fields to form a coupled cavity eigenmode. We demonstrate the advantages (including enhanced output power and improved spectral purity) of using a 2D-PSL over a simpler 1-D structure. The cylindrical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${D}/\lambda \sim {3.5} 2\text{D}$ </tex-math></inline-formula> -PSL demonstrates the “proof-of-principle” high-order mode coupling with the potential to increase <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${D}/\lambda $ </tex-math></inline-formula> to values of 20 or more for the realization of CW 2D-PSL sources or very powerful pulsed sources. The theory is applicable over a broad frequency range.

On the stability of the zero solution of a periodic reversible second-order differential equation

The problem of the stability of the zero solution of the second-order differential equation describing the periodic perturbations of an oscillator with a nonlinear reducing force is studied. The problem in the autonomous case was solved by A.M. Lyapunov. The so called transcendental case when all members of the decomposition of the right part of the differential equation into series are to be taken into account, is considered. This case takes place for reversible differential equations, i. e. equations that do not change when time is replaced by the opposite value. The problem is solved by the methods of the KAM theory, according to which in any neighborhood of the equilibrium position at the origin of the phase plane there are periodic invariant two-dimensional tori that separate the three-dimensional configuration space. These tori are considered as two-dimensional periodic invariant surfaces covering the time axis from where the stability (non-asymptotic) of the zero solution followed. The problem to be solved is characterized by the fact that the unperturbed part of the equation contains a dissipative term (a term dependent on velocity) which has the same order of smallness as the restoring force. It is established that if a dissipative part of the perturbation is small enough then the unperturbed movement is stable according to Lyapunov.

Two-dimensional suprawavelength periodic surface structuring of a ZnO single crystal with a UV femtosecond laser.

Herein, we report on the one-step formation of a novel microstructure on the surface of crystalline ZnO in ambient air excited by a single femtosecond laser beam (central wavelength 400 nm, pulse duration 35fs), which has photon energy close to the bandgap of ZnO. A two-dimensional surface structure with a controlled period of ∼2-6 μm is observed, with its orientation independent on the status of laser polarization (linear, circular, or elliptical polarization). We find that the orientation of this two-dimensional structure is defined by the direction of the crystal a and c axes. This structural period of ∼2-6 micrometers and the independence of its orientation on the laser polarization are in sharp contrast with the traditional laser induced periodic surface structure (LIPSS). In the meantime, surface cracks with a feature size of ∼30 nm are observed at the bottom of the valley of the two-dimensional structure and theoretical results show there exists strong electric field enhancement on the cracks under 400 nm femtosecond laser irradiation. In view of these unusual features, we attribute the formation of this two-dimensional structure to the mechanical cracking of the ZnO crystal along its (11-20) and (0001) planes induced by the multiple-cyclic heating due to linear absorption of the femtosecond pulses.

Deep-Subwavelength 2D Periodic Surface Nanostructures on Diamond by Double-Pulse Femtosecond Laser Irradiation.

Two-dimensional laser-induced periodic surface structures with a deep-subwavelength periodicity (80 nm ≈ λ/10) are obtained for the first time on diamond surfaces. The distinctive surface nanotexturing is achieved by employing a single step technique that relies on irradiation with two temporally delayed and cross-polarized femtosecond-laser pulses (100 fs duration, 800 nm wavelength, 1 kHz repetition rate) generated with a Michelson-like interferometer configuration, followed by chemical etching of surface debris. In this Letter, we demonstrate that, if the delay between two consecutive pulses is ≤2 ps, the 2D periodicity of nanostructures can be tuned by controlling the number of pulses irradiating the surface. Under scanning mode, the method is effective in treating uniformly large areas of diamond, so to induce remarkable antireflection properties able to enhance the absorptance in the visible up to 50 times and to pave the route toward the creation of metasurfaces for future diamond-based optoelectronic devices.

Dynamics of a collection of active particles on a two-dimensional periodic undulated surface

We study the dynamics of circular disk-shaped active particles on a two-dimensional periodic undulated surface. Each particle has an internal energy mechanism which is modeled by an active friction force and it is controlled by an activity parameter [Formula: see text]. It acts as negative friction if the speed of the particle is smaller than [Formula: see text] and normal friction otherwise. Surface undulation is modeled by the periodic undulation of fixed amplitude and wavelength. The dynamics of the particle is studied for different activities and surface undulations (SU). Three types of particle dynamic is observed on varying activity and SU: confined, early time subdiffusion to diffusion and super diffusion to late time diffusion. An effective equilibrium is established by showing the Green-Kubo relation between the effective diffusivity and the velocity auto-correlation function for all activities and small SU.

Reactive-ion-etched glass surface with 2D periodic surface texture for application in solar cells

Thin-film silicon solar cells are promising candidates for the low-cost production of electricity from sunlight. However, their efficiency remains relatively low, which is one of the major issues for their commercialisation. In the thin-film silicon technology, light trapping is an important design consideration for achieving a higher device efficiency. An advanced light-trapping technology is expected to boost the efficiency of solar cells further. Therefore, we investigated the development of an advanced light-trapping scheme in a two-dimensional periodic surface structure produced via inductively coupled plasma reactive-ion etching. The texture of the glass surface was varied under various plasma conditions. For the various shapes and sizes of the obtained surface texture, the increased height and base angle of the individual texture showed an overall increase in the diffused transmission of light. In some cases, the diffused transmission was as high as 89 % of the total light transmitted through the glass. The effect of the textured glass on a solar cell was investigated through simulation. Results show that the efficiency of a single-junction solar cell can be enhanced significantly when such a textured glass is used instead of a non-textured glass.

Surface field excitation by an obliquely incident wave

Observation of surface field excitation by an obliquely incident wave inside a cylindrical two-dimensional periodic surface lattice is a step forward toward THz Cherenkov amplifiers. Here we observe and discuss this phenomenon, investigating it using different approaches. The results are compared, and it is shown that an increase in the lattice contrast results in excitation of surface fields by an obliquely incident wave resulting in the eigenmode formation. Measurements were conducted by studying forward transmission of the signal, and it is shown that the measured gaps in the spectra are associated with the eigenmode formation rather than band gap establishment.

Efficiency Enhancement of Organic Solar Cells by Fabricating Periodic Surface Textures using Direct Laser Interference Patterning

Direct laser interference patterning (DLIP) is used to fabricate large area, two-dimensional periodic surface patterns on polyethylene terephthalate (PET) substrates to enhance the performance of ZnPc:C60 solar cells by light concentration in the absorber layer. Comparing the power conversion efficiencies to the reference cell on flat PET, a relative increase of 21% is observed for the hexagonal pattern with 0.7 μm period, depicted in the figure.

Surface waves on steady perfect‐fluid flows with vorticity

AbstractThis is a theory of two‐dimensional steady periodic surface waves on flows under gravity in which the given data are three quantities that are independent of time in the corresponding evolution problem: the volume of fluid per period, the circulation per period on the free stream line, and the rearrangement class (equivalently, the distribution function) of the vorticity field. A minimizer of the total energy per period among flows satisfying these three constraints is shown to be a weak solution of the surface wave problem for which the vorticity is a decreasing function of the stream function. This decreasing function can be thought of as an infinite‐dimensional Lagrange multiplier corresponding to the vorticity rearrangement class being specified in the minimization problem. (Note that functional dependence of vorticity on the stream function was not specified a priori but is part of the solution to the problem and ensures the flow is steady.) To illustrate the idea with a minimum of technical difficulties, the existence of nontrivial waves on the surface of a fluid flowing with a prescribed distribution of vorticity and confined beneath an elastic sheet is proved. The theory applies equally to irrotational flows and to flows with locally square‐integrable vorticity. © 2011 Wiley Periodicals, Inc.

Small-amplitude capillary-gravity water waves: Exact solutions and particle motion beneath such waves

Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, we find the exact solutions of the nonlinear differential equation system which describes the particle motion in the considered case, and we describe the possible particle trajectories. The required computations involve elliptic integrals of the first kind, the Legendre normal form and a solvable Abel differential equation of the second kind. Some graphs of the results are included.

Direct Observation of Twisted Grain Boundary in a Block Copolymer Lamellar Nanostructure

The grain boundary morphology of a lamella-forming poly(styrene-b-isoprene) (SI) diblock copolymer was investigated by transmission electron microtomography. The twist grain boundary, at which two lamellar nanodomains orthogonally intersect, was successfully observed in three dimensions (3D). A two-dimensional periodic minimal surface, the Scherk's first surface, was once hypothesized as a model of such a grain boundary morphology but never experimentally ascertained. The area-averaged curvatures of the interface between the PI and PS nanodomains as well as the interfacial area per unit volume suggested that the grain boundary morphology had characteristics of the saddlelike hyperbolic surface and was found to be quite similar to Scherk's first surface.

Grating diffraction and Wood's anomalies at two-dimensionally periodic impedance surfaces.

We address the problem of plane-wave scattering and Wood's anomalies at two-dimensional (2-D) periodic surfaces by employing a simplified grating model given by a planar surface whose impedance varies sinusoidally along two orthogonal directions. We obtain a rigorous solution to the corresponding boundary-value problem in terms of an infinite set of coupled recurrence equations. When truncated for computational purposes, this solution is in the form of a banded matrix, which we solve by direct methods and also by a highly efficient iterated matrix procedure. Numerical results are presented for symmetric and nonsymmetric incidence cases, and we show that certain diffracted fields do not depolarize in the former case. The expected Wood's anomalies of both Rayleigh and leaky-wave types are confirmed, and their location in wavelength space is numerically demonstrated for 2-D periodic configurations.

Sub-micron patterning of solid materials with ultraviolet femtosecond pulses

The treatment of solid materials using subpicosecond laser pulses at 248 nm is studied. The potential of the combination of femtosecond pulse durations with ultraviolet wavelengths for precise material processing is demonstrated. Imaging techniques combined with diffractive optical elements are exploited for the fabrication of nanometer-scale features on practically all classes of materials including metals, semiconductors, and dielectrics. Two-dimensional periodic surface structures with excellent quality and reproducibility over large areas with feature sizes down to the 100 nm range are reached .