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The study is being applied to a model involving silane and on cyclopentasilane graph. We consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of cyclopentasilane. In this paper, we first study the existence of solutions to fractional conformable boundary value problem on the cyclopentasilane graph by applying Scheafer and Krasnoselskii fixed point theorems. Furthermore, we investigate different kinds of Ulam stability such as Ulam-Hyers stable, generalized Ulam-Hyers stable, Ulam-Hyers-Rassias stable and generalized Ulam-Hyers-Rassias stable for the given problem. Finally, we give an example to support our important results.
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This study enhances the ultrafast photonics application of tin selenide (SnSe) nanoflakes via copper (Cu) functionalization to overcome challenges such as low conductivity and weak near-infrared (NIR) absorption. Cu functionalization enhances concentration, induces strain, and reduces the bandgap through Sn substitution and Sn vacancy filling with Cu ions. Demonstrated by density functional theory calculations and experimental analyses, Cu-functionalized SnSe exhibits improved NIR optical absorption and superior third-order nonlinear optical properties. Z-scan measurements and femtosecond transient absorption spectroscopy reveal better performance of Cu-functionalized SnSe in terms of nonlinear optical properties and shorter carrier relaxation times compared to pristine SnSe. Furthermore, saturable absorbers based on both SnSe types, when integrated into an erbium-doped fiber laser, show that Cu functionalization leads to a decrease in pulse duration to 798 fs and an increase in 3 dB spectral bandwidth to 3.44 nm. Additionally, it enables stable harmonic mode-locking of bound-state solitons. This work suggests a new direction for improving wide bandgap 2D materials by highlighting the enhanced nonlinear optical properties and potential of Cu-functionalized SnSe in ultrafast photonics.
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Phase transition is a physical phenomenon that attracts great interest of researchers. Although the theory of second-order phase transitions is well-established, their atomic-scale dynamics in polycrystalline materials remains elusive. In this work, second-order phase transitions in polycrystalline Cu2 Se at the transition temperature are directly observed by in situ aberration-corrected transmission electron microscopy. Phase transitions in microcrystalline Cu2 Se start at the grain boundaries and extend inside the grains. This phenomenon is more pronounced in nanosized grains. Analysis of phase transitions in nanocrystalline Cu2 Se with different grain boundaries demonstrates that grain boundary energy dominates unsynchronized phase transition behavior. This suggests that the energy of grain boundaries is the key factor influencing the energetic barrier for initiation of phase transition. The findings advance atomic-scale understanding of second-order phase transitions, which is crucial for the control of this process in polycrystalline materials.
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Discovering high-performance near-room-temperature thermoelectric materials is extremely imperative to widen the practical application in thermoelectric power generation and refrigeration. Here, ternary Ag2Se1-xTex (x = 0.1, 0.2, 0.3, 0.4, and 0.5) materials are prepared via the wet-mechanical alloying and spark plasma sintering process to investigate their near-room-temperature thermoelectric properties. From density functional theory calculation and single-parabolic-band modeling study, we found that the reduced contribution of Se 4p orbitals to the total density of states decreases the carrier effective mass with increasing Te content, which should enhance the theoretically maximum zT. These calculation results are also verified by the experimental results. Meanwhile, complex microstructures including dislocations, nanograins, high-density boundaries, TeSe substitution, lattice distortions, and localized strain have been observed in ternary Ag2Se1-xTex. These complex microstructures strengthen phonon scattering and in turn lead to ultralow lattice thermal conductivity in the range of 0.21-0.31 W m-1 K-1 in ternary Ag2Se1-xTex at 300 K. Although the increased deformation potential suppresses the carrier mobility, benefiting from the engineered band structures and ultralow lattice thermal conductivity, a high zT of >1 can be potentially obtained in the ternary Ag2Se1-xTex with appropriate carrier concentration. This study indicates that ternary Ag2Se1-xTex is a promising candidate for near-room-temperature thermoelectric applications.
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Depressed-index buried and surface channel waveguides (type III) are produced in a bulk 3.5 at.% Tm3+:CALGO crystal by femtosecond direct-laser-writing at kHz repetition rate. The waveguides are characterized by confocal microscopy and µ-Raman spectroscopy. Under in-band-pumping at 1679 nm (3H6 â 3F4 transition) by a Raman fiber laser, the buried channel waveguide laser with a circular cladding (diameter: 60 µm) generated a continuous-wave output power of 0.81 W at 1866-1947 nm with a slope efficiency of 71.2% (versus the absorbed pump power) and showed a laser threshold of 200â mW. The waveguide propagation losses were as low as 0.3 ± 0.2â dB/cm. The laser performance under in-band pumping was superior compared pumping at â¼800â nm (3H6 â 3H4 transition), i.e., the convetional pump wavelength. Vibronic laser emission from the WG laser above 2 µm is also achieved. The low-loss behavior, the broadband emission properties and good power scaling capabilities indicate the suitability of Tm3+:CALGO waveguides for mode-locked laser operation at â¼2 µm.
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We report on the crystal growth, spectroscopy characterization and first laser operation of a new tetragonal disordered "mixed" calcium aluminate crystal, Tm:Ca(Gd,Lu)AlO4. The introduction of Lu3+ leads to an additional inhomogeneous broadening of Tm3+ absorption and emission spectra compared to the well-known Tm:CaGdAlO4. The maximum stimulated-emission cross-section for the 3F4 â 3H6 Tm3+ transition is 0.91 × 10-20 cm2 at 1813 nm for σ-polarization, and the emission bandwidth is more than 200 nm. A continuous-wave diode-pumped Tm:Ca(Gd,Lu)AlO4 laser generates 1.82 W at 1945 nm with a slope efficiency of 29%. Under Ti:Sapphire laser pumping, a continuous tuning of the laser wavelength from 1836 to 2083 nm (tuning range: 247 nm) is demonstrated. The Tm:Ca(Gd,Lu)AlO4 crystal is promising for tunable/femtosecond lasers at ~2 µm.
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We report on a mode-locked Tm,Ho:CLNGG laser emitting in the 2 µm spectral range using single-walled carbon nanotubes (SWCNTs) as a saturable absorber (SA). Pulses with duration of 98 fs are generated at 99.28 MHz repetition rate with an average output power of 123 mW, yielding a pulse energy of 1.24 nJ. Using a 0.5% output coupling, pulses as short as 67 fs, i.e., 10 optical cycles, are produced after extracavity compression with a 3-mm-thick ZnS plate.
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We demonstrate a mode-locked (ML) femtosecond laser based on the disordered garnet crystal Tm,Ho:CNGG. Employing a single-walled carbon nanotube saturable absorber, pulses as short as 83 and 76 fs at 2081 nm are achieved without and with external compression, respectively. The latter represents, to the best of our knowledge, the shortest pulse duration obtained from any Ho-doped or Tm,Ho-codoped laser. The average power amounts to 67 mW at a repetition rate of 102 MHz. By analyzing the soliton ML regime, the nonlinear refractive index of Tm,Ho:CNGG is estimated to be â¼1.1×10-19 m2/W.
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We experimentally demonstrated a diode-pumped sub-50 fs Yb,Na:CNGG disordered crystal laser. Pumped by a 980 nm distributed Bragg-reflector tapered diode laser and passively mode-locked with a semiconductor saturable absorber mirror (SESAM), soliton pulses as short as 62 fs and 45 fs were obtained without and with external compression, respectively. The ultrashort pulses had a repetition rate of ~104 MHz at the central wavelength of 1061 nm. To the best of our knowledge, this is the first demonstration of sub-50 fs pulses from the Yb3+-doped CNGG type disordered crystal lasers.