Solid Thin Plates Research Articles

Clean hundred-µJ-level sub-6-fs blue pulses generated with helium-assisted solid thin plates.

In this work, 85 µJ, 5.5 fs pulses spanning 350-500 nm with 96% energy concentrated on the main pulse are generated by pulse compression using a helium-assisted, two-stage solid thin plate apparatus. To the best of our knowledge, these are the highest energy sub-6 fs blue pulses obtained to date. Furthermore, during the spectral broadening process, we observe that solid thin plates are much more easily damaged by blue pulses in a vacuum than in a gas-filled environment at the same field intensity. Helium, with the highest ionization energy and extremely low material dispersion, is adopted to create a gas-filled environment. Thus, the damage to solid thin plates is eliminated, and high-energy, clean pulses can be obtained with only two commercially available chirped mirrors in a chamber. Furthermore, the excellent output power stability of 0.39% root mean square (rms) fluctuations over 1 h is maintained. We believe that few-cycle blue pulses at the hundred-µJ level can open the door to numerous new ultrafast and strong-field applications in this spectral region.

Temporal contrast enhancement via nonlinear elliptical polarization rotation in a solid thin plate.

We demonstrate the simultaneous temporal contrast enhancement and spectral broadening via nonlinear elliptical polarization rotation in a solid thin plate. The efficiency, temporal contrast enhancement, spectral broadening, pulse compression and power stability are experimentally investigated. With this simple and efficient scheme, the temporal cleaned pulses with energy of 325 µJ and total efficiency of 30% are obtained. The temporal contrast and spectral bandwidth of the filtered pulse are 1011 and 104 nm, respectively. The pulse compressed from 180 fs to 45.8 fs is realized by utilizing chirped mirrors, corresponding to a compression factor of 3.93. With stable output power, presented scheme could be implemented in the ultra-intense femtosecond laser facilities.

Few-cycle mid-infrared laser based on nonlinear self-compression in solid thin plates.

A few-cycle mid-infrared (MIR) laser is demonstrated via nonlinear self-compression in solid thin plates. In this novel solution, the anomalous material dispersion in the MIR band and the chirp induced by self-phase modulation are mutually compensated, which can achieve self-compression. Finally, with the 4 µm laser injection with 4.8 mJ/155 fs and few-cycle pulses with 3.44 mJ, 29.4 fs are generated with a high efficiency of 71.7%, and the system maintains very good spectral stability in 10 days. Compared with other post-compression methods, this self-compression technique has the advantages of high efficiency and robust and large energy expansion scale, which can be further extended to MIR lasers with other wavelengths and higher peak power.

Generation of annular femtosecond few-cycle pulses by self-compression and spatial filtering in solid thin plates.

Annular-shaped femtosecond few-cycle pulses are generated by 40fs laser pulses propagating through 6 solid thin plates in numerical simulations as well as in experiments. The generation of such pulses takes advantage of the conical emission caused by plasma effect, which introduces continuously varying off-axis plasma density along the radial direction of the propagating beam. The negative dispersion induced by the plasma causes the pulse at particular radial location to be self-compressed and to form an annular beam of short pulse, which can be extracted simply by spatial filtering. Meanwhile, by adjusting the input pulse energy and position of each thin plate relative to the laser focus, we control the plasma density in thin plates which changes the ratio between ionization and effects providing positive dispersion, and obtain a higher compression ratio indicating that the scheme of solid thin plates has the flexibility to regulate the laser intensity so as to plasma density, thus the negative dispersion the pulse experiences during propagation. Few-cycle pulses as short as 8.8 fs are generated in experiments, meanwhile the shortest pulse duration found in the simulations is 5.0 fs, which corresponds to two optical cycles at its central wavelength 761 nm. This method has great potential in high-power few-cycle pulse generation.

Variation of electron density in spectral broadening process in solid thin plates at 400 nm* *Project supported by the National Key Research and Development Program of China (Grant No. 2017YFB0405202), the Major Program of the National Natural Science Foundation of China (Grant No. 61690221), and the General Program of the National Natural Science Foundation of China (Grant No. 11774277).

The generation of continuous spectrum centered at 400 nm from solid thin plates is demonstrated in this work. A continuum covering 365 nm to 445 nm is obtained when 125-μJ frequency-doubled Ti:sapphire laser pulses are applied to six thin fused silica plates at 1-kHz repetition rate. The generalized nonlinear Schrödinger equation simplified for forward propagation is solved numerically, the spectral broadening with the experimental parameters is simulated, and good agreement between simulated result and experimental measurement is achieved. The variation of electron density in the thin plate and the advantage of a low electron density in the spectral broadening process are discussed.

Attosecond pulse trains driven by IR pulses spectrally broadened via supercontinuum generation in solid thin plates**Project supported by the National Key R&D Program of China (Grant No. 2017YFB0405202), the Major Program of the National Natural Science Foundation of China (Grant No. 61690221), the Key Program of the National Natural Science Foundation of China (Grant No. 11434016), and the National Natural

We utilized a set of fused silica thin plates to broaden the spectrum of 1 kHz, 30 fs Ti:sapphire amplified laser pulses to an octave. Following the compression by chirped mirror pairs, the generated few-cycle pulses were focused onto an argon filled gas cell. We detected high order harmonics corresponding to a train of 209 as pulses, characterized by the reconstruction of attosecond beating by interference of two-photon transition (RABITT) technique. Compared with the conventional attosecond pulse trains, the broad harmonics in such pulse trains cover more energy range, so it is more efficient in studying some typical cases, such as resonances, with frequency resolved RABITT. As the solid thin plates can support high power supercontinuum generation, it is feasible to tailor the spectrum to have different central wavelength and spectral width, which will make the RABITT source work in different applications.

Determination of Natural Frequency and Mode Shape for Hollow Thin Plates

The determination of natural frequency and the mode shape of structures are important in characterizing the properties or behavior of the structures. The existing hollow in solid thin plate will change the vibration behavior in term of resonance frequency and mode behavior. A lot of structure consists of hollow space such as inner panel of car hood and bonnet. However, simplifying the model from hollow structure with solid thin plates only will resulting some difference in their vibration performance. This study begins with conducting modal analysis experiment using solid thin plate under free-free boundary condition. Next, the finite element methods were performing to compare with the experimental results. The average error of 3.96% was obtain when compared which provide a good confident level with the simulation result. Next, the study continued by finding the natural frequency and the mode shape for the thin plate under various position of hole, number of holes and shape of hole by using FEM software. Finally, finite element was also being carried out on the simplified design model of the inner panel car hood based from the real product and compared the resonance frequency from the model with some vibration reference sources. Through this study, it is found that the diversity of the hole position, the increasing number of holes and the change of the hole shape play a role in changing the natural frequencies of a thin plate. Since there is a lot of hollow thin plates in the car part, designing every parts are important to make sure the NVH quality is improve and not opposite of it.

Adaptive finite element analysis of steel girder deck pavement

This paper shows a more exact and practical finite element model of the steel girder deck pavement. Based on Mindlin thick plate theory, a 12-node solid thick plate element was constituted to analyze the pavement. The computation result was compared with that by traditional 4-node and 8-node thick plate finite element, and is satisfactory. A combined plate beam element method is presented to investigate the stiffened plate. A 6-node solid thin plate element was constituted to analyze the top plate based on Kirchhoff thin plate theory. The stiffeners acting as the vertical supporting function mainly are taken as Euler beam elements. A method of using the linear interpolation to realize the longitudinal displacement and the cubic Hermite interpolation to the vertical displacement is presented to analyze the stiffeners. In addition, it is essential to consider the displacement coordination between the top plate and stiffeners. A node-to-node contact scheme, which is applicable for three-dimensional contact analyses involving large deformations, was used to treat the contact problem between pavement and stiffened plate by Lagrange multiplier methods.

High-Efficiency Generation of 0.12 mJ, 8.6 Fs Pulses at 400nm Based on Spectral Broadening in Solid Thin Plates**Supported by the National Natural Science Foundation of China under Grant Nos 11434016, 11574384 and 11674386, and the National Key Basic Research Program of China under Grant Nos 2013CB922401 and 2013CB922402.

We demonstrate efficient generation of continuous spectrum centered at 400 nm from solid thin plates. By frequency doubling of 0.8 mJ, 30 fs Ti:sapphire laser pulses with a BBO crystal, 0.2 mJ, 33 fs laser pulses at 400 nm are generated. Focusing the 400-nm pulses into 7 thin fused silica plates, we obtain 0.15 mJ continuous spectrum covering 350–450 nm. After compressing by 3 pairs of chirped mirrors, 0.12 mJ, 8.6 fs pulses are achieved. To the best of our knowledge, this is the first time that sub-10-fs pulses centered at 400 nm are generated by solid thin plates, which shows that spectral broadening in solid-state materials works not only at 800 nm but also at different wavelengths.

High-efficiency supercontinuum generation in solid thin plates at 0.1 TW level.

Supercontinuum generation in a solid-state medium was investigated experimentally. A continuum covering 460 to 950 nm was obtained when 0.8 mJ/30 fs Ti:sapphire laser pulses were applied to seven thin fused silica plates at a 1 kHz repetition rate. The primary processes responsible for spectral broadening were self-phase modulation (SPM) and self-steepening, while SPM and self-focusing were balanced to optimize the spectral broadening and suppress the multiphoton process. The output was compressed to a 5.4 fs and a 0.68 mJ pulse, corresponding to two optical cycles and 0.13 TW of peak power.

High harmonic generation experiments based on solid-state supercontinuum

Intense few-cycle pulses are widely used in transient light synthesis,high harmonic generation (HHG) and especially in isolated attosecond pulse generation.To obtain intense few-cycle pulses,the intense supercontinuum is needed.The traditional way to generate intense supercontinuum is using rare gas filled hollow-core fibers.Since the input energy of hollow-core fiber system is limited to a level of tens of mJ,it is necessary to find new ways to achieve energy scaling.In this paper we demonstrate the efficient generation of supercontinuum by solid thin plates,compression and its application in HHG. The Ti:sapphire laser used in the present experiment emits 0.8 mJ in energy with a duration of 30 fs at 1 kHz.After passing through a 3:1 telescope,the beam has a diameter changed from 12 mm to 4 mm.Then the laser is focused by an f=2000 mm lens into a 600 m-diameter spot.After propagating through 7 fused silica plates placed at Brewster's angle (55.5) with a thickness of 0.1 mm,the 0.7 mJ octave spanning supercontinuum is achieved,corresponding to an efficiency of 87.5%.The first three plates are placed at 31,11,2.5 mm in front of the beam waist,and the last four plates are placed at 2,7,12,17 mm behind the beam waist respectively.With a pair of wedges and 4 pairs of chirped mirrors,the 0.68 mJ supercontinuum is compressed to a duration of 6.3 fs,which is measured by TG-FROG. The 0.5 mJ,6.3 fs pulse is used to perform high-harmonic generation experiment.The beam diameter is 150 m when focused by an f=400 mm lens,with a laser intensity of 8.11014 W/cm2.The 1 mm Ne gas jet is used to perform HHG experiment with a back pressure of 300 mbar.To block the near-infrared light,a 150 m Zirconium foil is placed behind the gas jet.Then the XUV spectrum is detected by a spectrometer,which consists of a flat field grating and a CCD camera.For driving pulses of few-cycle regime without dispersion,the cutoff spectrum of HHG is continuous.But when the pulse is stretched by positive or negative dispersion,the cutoff spectrum turns discrete.The HHG result is that the cutoff region is continuous when the wedge is in a certain place.Then by increasing or reducing the insertion of the wedge,the cutoff spectrum becomes discrete.Our result is consistent with HHG generated by few-cycle pulses. In conclusion,we demonstrate high-harmonic generation based on supercontinuum generated by solid thin plates. The 0.7 mJ supercontinuum is achieved when 0.8 mJ pulses are injected to 7 thin fused silica plates.The supercontinuum is compressed to 0.68 mJ,6.3 fs.The 0.5 mJ,6.3 fs pulse is used to perform HHG experiments.The HHG result was consistent with few-cycle driving pulses.Our research indicates that solid state supercontinuum has great potential applications in HHG and isolated attosecond pulse generation.

Exact Solutions for Free-Vibration Analysis of Rectangular Plates Using Bessel Functions

A novel Bessel function method is proposed to obtain the exact solutions for the free-vibration analysis of rectangular thin plates with three edge conditions: (i) fully simply supported; (ii) fully clamped, and (iii) two opposite edges simply supported and the other two edges clamped. Because Bessel functions satisfy the biharmonic differential equation of solid thin plate, the basic idea of the method is to superpose different Bessel functions to satisfy the edge conditions such that the governing differential equation and the boundary conditions of the thin plate are exactly satisfied. It is shown that the proposed method provides simple, direct, and highly accurate solutions for this family of problems. Examples are demonstrated by calculating the natural frequencies and the vibration modes for a square plate with all edges simply supported and clamped.

Nonlinear Equivalent Plate Modeling of Wing-Box Structures

AMA-99-1 234 Nonlinear Equivalent Plate Modeling of W ing Box Structures Eli Livne* and Israel Navarro* * University of Washington, Seattle, WA 98 195-2400 Abstract A geometrically nonlinear moderate-deformation equivalent plate modeling capability for wing structures is developed. It is a generalization of the successful simplepolynomial based equivalent plate modeling techniques for linear wing structures. The formulation allows First Order Shear Deformation Plate Theory or Classical Plate Theory to be used for modeling solid thin plates as well as typical wing box structures made of cover skins and an array of spars and ribs, Mass and stiffness matrix contributions of different wing box elements are presented. Stiff springs are included to enforce a variety of boundary conditions. The resulting nonlinear equations can be solved for static and dynamic structural response. The new nonlinear equivalent plate modeling technique was validated by comparing its results with those of nonlinear finite element models and results of analyses published previously by different authors. It is expected to lead to efficient nonlinear aeroelastic analysis of wings subject to in-plane compressive forces such as the rear wings in joined-wing airplane configurations. List of Symbols

Vibration response of perforated thin plates

The vibration behavior of perforated metal thin plates is studied here. In order to highlight specific phenomena, a rather simple experiment has been researched. While covering a large range of frequencies, a sinusoidally varying point force has been applied to a free boundary circular plate at its midpoint. In that case, the plate vibrations obtained are of an axial symmetry type; for that geometry the first symmetrical modes only are excited. The driving-point mechanical impedance is measured. For a plane stress problem, the perforated plate vibration response is evaluated by assimilating perforated plates to equivalent solid thin plates whose effective elastic constants are determined with the help of Meijers’ theory [Ph.D. thesis, University of Delft, Holland, 1967]. First of all, the numerical simulation is validated by comparing theoretical impedance results to those obtained experimentally. Then, the use of double exposure holographic laser interferometry permits one to verify that modes observed on photographs correspond in general to theoretical ones. Initially developed for the study of perforated plate static behavior, that theory can certainly be used for the dynamic study of various geometry perforated plates.