Mathematical models of elastic structures have become very sophisticated: given the crucial material properties (mass density and the several elastic moduli), computer-based techniques can be used to construct exotic finite element models. By contrast, the modeling of damping is usually very primitive, often consisting of no more than mere guesses at “modal damping factors.” The aim of this paper is to raise the modeling of viscoelastic structures to a level consistent with the modeling of elastic structures. Appropriate material properties are identified which permit the standard finite element formulations used for undamped structures to be extended to viscoelastic structures. Through the use of “dissipation” coordinates, the canonical “M, K” form of the undamped motion equations is expanded to encompass viscoelastic damping. With this formulation finite element analysis can be used to model viscoelastic damping accurately.

Optical reflectivity contrast provides a simple, fast and noninvasive method for characterization of few monolayer samples of two-dimensional materials. Here we apply this technique to measure the thickness of thin flakes of hexagonal Boron Nitride (hBN), which is a material of increasing interest in nanodevice fabrication. The optical contrast shows a strong negative peak at short wavelengths and zero contrast at a thickness dependent wavelength. The optical contrast varies linearly for 1-80 layers of hBN, which permits easy calibration of thickness. We demonstrate the applicability of this quick characterization method by comparing atomic force microscopy and optical contrast results.Hexagonal Boron Nitride (hBN) has a planar hexagonal structure similar to graphite and has proven to be an excellent substrate for graphene based electronic and opto-electronic devices. It has been shown that graphene devices on hBN substrates show enhanced performance like increased carrier mobility and reduced charge fluctuations 1-3 . Graphene sheets conform to atomically flat hBN resulting in reduced roughness and charge puddle formation as compared to other common substrates such as Si/SiO 2 2,3 . Thin hBN flakes have also proven to be an excellent dielectric or tunnel barrier for device applications 4-7 and can modify graphene's band structure 8 . A large direct bandgap makes hBN attractive for compact UV laser applications 9 . Interestingly, the success of hBN in graphene electronics is now also being mirrored in the development of other two dimensional materials such as transition metal dichalcogenides (TMD) (e.g. MoS 2 , MoSe 2 , WS 2 etc.) devices, where hBN substrates have led to 10 times better photoluminescence quantum yields than Si/SiO 2 . 10 It is anticipated that hBN will be an essential constituent for future graphene and TMD heterostructure devices in many roles ranging from a tunnel barrier to a gate dielectric. Hence, it is very important to have methods for quick, economical and non-invasive characterization of hBN flakes, specifically, the exact number of hBN monolayers and its flatness over the size of the device. In that regards optical reflection microscopy has proven to be a highly useful tool. Optical contrast measurement have been used to identify mono and few layered graphene on various substrates 11-13 . Identification of monolayer and bilayer hBN has also been reported using reflectivity contrast 14 . In this paper, we characterize hBN flakes deposited on a SiO 2 /Si substrate. We establish parameters which can enable quick identification for hBN flakes varying from a few to 100 layers. We also show that this approach is sensitive to optical thickness changes as small as 1-2 layers allowing the identification of steps in flakes which appear flat under white light illumination.The sample geometry is shown schematically in the inset of figure 1. Few layer hBN flakes were prepared by FIG. 1. The optical contrast of hBN on SiO2/Si substrate as a function of the wavelength of light. Different curves corre...

Fast carrier cooling is important for high power graphene based devices. Strongly Coupled Optical Phonons (SCOPs) play a major role in the relaxation of photoexcited carriers in graphene. Heterostructures of graphene and hexagonal boron nitride (hBN) have shown exceptional mobility and high saturation current, which makes them ideal for applications, but the effect of the hBN substrate on carrier cooling mechanisms is not understood.We track the cooling of hot photo-excited carriers in graphene-hBN heterostructures using ultrafast pump-probe spectroscopy. We find that the carriers cool down four times faster in the case of graphene on hBN than on a silicon oxide substrate thus overcoming the hot phonon (HP) bottleneck that plagues cooling in graphene devices.Graphene heterostructures have garnered a lot of interest in the last decade 1 . Recently developed fabrication techniques have made it possible to engineer devices with better transport, optical and thermal properties 2,3 . Hexagonal boron nitride (hBN) is a layered material with a hexagonal lattice similar to graphene with a lattice constant that is about 1.8% larger 3 . It is an insulator with a wide band gap and high dielectric constant making it a good candidate as a substrate for graphene devices. Heterostructures of graphene and hBN show much higher mobility compared to those using SiO2 as a substrate 2-4 . This improvement is a result of the hBN substrate being free of charged impurities and displacing the graphene away from the impurities in the SiO2 substrate 4 .As electronic devices continue to scale down in size and push power capabilities, heat management has become a critical issue. Relaxation dynamics of photoexcited (PE) carriers has been studied extensively by many groups using variety of techniques such as photocurrent measurement, Raman time resolved Raman spectroscopy, transport measurements and ultrafast pump-probe spectroscopy 5-7 etc. Upon photoexcitation (with an ultrafast pulse for example), electrons and holes are excited, into a highly non-thermal system. This bath of carriers exchanges energy among themselves through coulombic interactions and thermalize into a hot (~1000's K) Fermi-Dirac population

The role of many-body interactions is experimentally and theoretically investigated near the saddle point absorption peak of graphene. The time and energy-resolved differential optical transmission measurements reveal the dominant role played by electron-acoustic phonon coupling in band structure renormalization. Using a Born approximation for electron-phonon coupling and experimental estimates of the dynamic lattice temperature, we compute the differential transmission line shape. Comparing the numerical and experimental line shapes, we deduce the effective acoustic deformation potential to be D ac eff ≃ 5 eV. This value is in accord with recent theoretical predictions but differs from those extracted using electrical transport measurements. [5][6][7][8][9] can significantly alter the electronic band structure and optical properties of graphene. When a light pulse interacts with graphene, the observation of many-body effects caused by transient photoexcited carriers is limited to short, subpicosecond time scales due to high electron scattering rates and short lifetimes. Over longer time scales (1-100 ps), the photoexcitation energy is converted into heat, and band structure renormalization effects due to electron-phonon interactions and possibly thermally excited charge carriers at the elevated temperatures [10] can be measured.The long time scale electron-phonon (e-ph) interactions in graphene have numerous ramifications. The intrinsic carrier mobility in high quality graphene devices is limited by e-ph scattering [11][12][13][14][15]. Efficient optoelectronic device design also relies on the conversion of the energy of photoexcited carriers to electrical current before it dissipates through e-ph interactions [16][17][18]. Ultrafast heat generation and dissipation dynamics in devices, which is an important topic in nanoscale heat management, is also crucially dependent on the interaction of electronic excitations with phonons [19].The exact nature and strength of e-ph coupling in graphene is unclear at present. Specifically, the electronacoustic phonon interaction strength, characterized by the deformation potential D ac eff , has been controversial. The experimental estimates obtained from electrical transport measurements [13][14][15] range from 16-50 eV, while theoretical predictions indicate acoustic deformation potential in the range of ∼2.8 − 7 eV [4,11,20,21]. Since many observables are proportional to jD Here we report ultrafast pump-probe measurements of photon energy dependent differential transmission in graphene. Instead of focusing on the heavily studied K point of the graphene band structure [23][24][25][26][27][28], our study uniquely concentrates on the region near the M point. The absorption maxima associated with the van Hove singularity at the M point ( Fig. 1) enables sensitive probing of e-ph interactions through the measurement of pump-induced changes in the absorption spectrum. In contrast, the region near the K point has a relatively featureless, flat absorption profile which does not ...

We study the reflection of a Hermite-Gaussian beam at an interface between two dielectric media. We show that unlike Laguerre-Gaussian beams, Hermite-Gaussian beams undergo no significant distortion upon reflection. We report Goos-Hänchen shift for all the spots of a higherorder Hermite-Gaussian beam near the critical angle. The shift is shown to be insignificant away from the critical angle. The calculations are carried out neglecting the longitudinal component along the direction of propagation for a spatially finite, s-polarized, full 3D vector beam. We briefly discuss the difficulties associated with the paraxial approximation pertaining to a vector Gaussian beam.