Casimir effect of massive vector fields

Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace’s equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite’s membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

Laser shock induced lateral compression has been demonstrated to controllably flatten cylindrical silver nanowires. Nanowires with circular cross-sections of diameter 70 nm are significantly shaped laterally, which transformed them to metallic ribbons of huge width of 290 nm and of thickness down to 13 nm, amounting the aspect ratio to as high as 22, at a laser intensity of 0.30 GW cm(-2). Above the laser intensity of 0.30 GW cm(-2) though, nanowires are observed to be ruptured. Lateral deformations of nanowires are achieved without altering longitudinal dimensions. Selected area electron diffraction patterns on the laterally deformed nanowires reveal that the flattening gives rise to twinning under high strain rate deformation without actually degrading crystallinity. As the 1D nanowire turns into a 2D metallic nanoribbon, new plasmonic modes and their combinations emerge. The transverse plasmon mode does not shift substantially, whereas longitudinal modes and their combinations are greatly influenced by lateral deformation. Apart from the transverse mode, which is dominant in a 1D nanowire and diminishes heavily when lateral deformation occurs, there is a presence of several longitudinal plasmonic modes and their combinations for metallic nanoribbons, which are revealed by experimental extinction spectra and also supported by finite-difference time-domain (FDTD) simulation. Such plasmonic tuning of silver nanowires across the visible range demonstrates the capability of a laser shock induced lateral compression technique for various emerging plasmonic applications. The laser shock compression technique has the advantages of flexibility, selectivity and tunability while retaining crystallinity of metallic nanowires, all of which enable it to be a potential candidate for plasmonic tuning of nanogeometries.

The nonlocal theoretical model developed to observe current-driven low-frequency electrostatic modes in a collisional magnetized strongly coupled dusty plasma, in the strongly coupled kinetic regime ωτ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> ≫ 1 (i.e., wave frequency is much larger than the dust particle relaxation time) led to a new set of equations for dispersion relation, frequency, and the growth rate. The theoretical investigations on a cylindrical magnetized strongly coupled dusty plasma led to a current driven ion dust hybrid like longitudinal dust wave propagating nearly along radial direction and a peculiar transverse shear dust wave mode along axial direction. Dispersion properties of both longitudinal dust acoustic modes and transverse shear modes are modified in the presence of ion and dust currents and the effective perpendicular wave number provided by finite geometry of strongly coupled magnetized dusty plasma. The magnetic field has a destabilizing effect on the growth of longitudinal wave modes, while the dependence of transverse modes on the strength of magnetic field is not prominent. Transverse shear modes are characterized as the short wavelength modes with a long wavelength cutoffs. A comparison of nonlocal effects with local effects shows that in bounded magnetized strongly coupled dusty plasmas, the longitudinal wave modes need a large magnetic field and weak collisional regime to support the excitation of dust wave modes, whereas the transverse modes are a consequence of viscous and collisional damping.

We report a detailed theoretical investigation about the influence of the nanorod length and incident polarization on the far-field and near-field optical properties of Al nanorod using the discrete dipole approximation. The results show that Al nanorod has great tunability in the UV-Vis-NIR region and much stronger near-field intensity at UV and NIR wavelengths. The band position of transverse mode (TM) for the nanorod has a little blueshifted as the length increases, while that of the longitudinal mode (LM) is linearly redshifted with the size. In addition, we investigate how the incident polarization affects the extinction position and efficiency of the TM and LM. Finally, the near-field distribution dependences of the nanorod length for the TM and the LM have been analyzed. It is shown that much enhanced near-field always occur in the lateral surface of the nanorod for TM and the tip of the nanorod for the LM, respectively. The maximum local field enhancement factor of the TM is found to be about two times higher than that of the LM, which is due to close the region of interband transitions at about nm. These results would be of great potential application in localized surface plasmon resonance sensor and UV-plasmonic device.

In the modal technique for the analysis of multilayered structures, a generalized S-matrix description of each infinite, periodic, metallic screen is obtained by the Floquet mode expansion moment method. These S-matrices are then cascaded together with those of the intervening dielectric layers to form an overall S-matrix. At the input plane of the polarizer, the electric field vector of a linearly polarized incident plane of the polarizer, the electric field vector of a linearly polarized incident plane wave is inclined at 45 degrees to the meanderline line axis so that either a TE (transverse electric) or a TM (transverse magnetic) mode is present. The polarizer then provides the necessary coupling between or conversion into the TE and TM modes so that, at the output plane, a circularly polarized wave exists, consisting of a TE00 and TM00 mode, all other modes being evanescent. The S-matrix of the layered structure describes this mode conversion. By attaching an optimizer to the analysis module, a synthesis program is obtained. The dimensions of the meanderline within the cell, the cell periodicities, and the thickness of the supporting layers are manipulated to provide low axial ratio and good match over a range of frequencies and incident angles.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper we deal with the macroscopic electromagnetic response of a finite size dispersive dielectric object, in unbounded space, in the framework of quantum electrodynamics using the Heisenberg picture. We apply a Hopfield type scheme to account for the dispersion and dissipation of the matter. We provide a general expression of the polarization density field operator as functions of the initial conditions of the matter field operators and of the electromagnetic field operators. It is a linear functional whose kernel is a linear expression of the impulse response of the dielectric object that we obtain within the framework of classical electrodynamics. The electric field operator is expressed as a function of the polarization density field operator by means of the dyadic Green's function for the free space. The statistical functions of these operators are classical functionals of the statistics of the initial conditions of the matter field operators and of the electromagnetic field operators, whose kernels are linear or multilinear expressions of the impulse response of the dielectric object. We keep the polarization and the electromagnetic field distinct to enable the treatment of the polarization and electromagnetic fluctuations on equal footing. We expand the polarization density field operator in terms of the static longitudinal and transverse modes of the object to diagonalize the Coulomb and Ampere interaction energy terms of the Hamiltonian in the Coulomb gauge. We expand the radiation fields in terms of the transverse plane wave modes of free space. Few static longitudinal and transverse modes are needed to calculate each element of the impulse response matrix for dielectric objects with sizes of the order up to $\min\limits_{\omega}\{c_0/[\omega \sqrt{|{\chi}(\omega)|}]\}$ where ${\chi}(\omega)$ is the susceptibility of the dielectric.

Butterfly-shaped ultra slim piezoelectric ultrasonic linear motor

In this paper, we use nonequilibrium molecular dynamics modeling to investigate the thermal properties of monolayer hexagonal boron nitride nanoribbons under uniaxial strain along their longitudinal axis. Our simulations predict that hexagonal boron nitride shows an anomalous thermal response to the applied uniaxial strain. Contrary to three dimensional materials, under uniaxial stretching, the thermal conductivity of boron nitride nanoribbons first increases rather than decreasing until it reaches its peak value and then starts decreasing. Under compressive strain, the thermal conductivity of monolayer boron nitride ribbons monolithically reduces rather than increasing. We use phonon spectrum and dispersion curves to investigate the mechanism responsible for the unexpected behavior. Our molecular dynamics modeling and density functional theory results show that application of longitudinal tensile strain leads to the reduction of the group velocities of longitudinal and transverse acoustic modes. Such a phonon softening mechanism acts to reduce the thermal conductivity of the nanoribbons. On the other hand, a significant increase in the group velocity (stiffening) of the flexural acoustic modes is observed, which counteracts the phonon softening effects of the longitudinal and transverse modes. The total thermal conductivity of the ribbons is a result of competition between these two mechanisms. At low tensile strain, the stiffening mechanism overcomes the softening mechanism which leads to an increase in the thermal conductivity. At higher tensile strain, the softening mechanism supersedes the stiffening and the thermal conductivity slightly reduces. Our simulations show that the decrease in the thermal conductivity under compressive strain is attributed to the formation of buckling defects which reduces the phonon mean free path.

Tapered lasers are extensively employed in high power single-mode lasing, yet still suffering from the potential formation of higher-order transverse modes in the tapered region, which severely degrades the laser beam quality. Herein, we propose a novel supersymmetric segmented tapered laser to achieve stable fundamental transverse mode operation. Our design features a three-segmented tapered waveguide along the light propagation direction, with sub-waveguides of varying widths flanking each main waveguide segment. The main waveguides measure 8 μm, 12 μm, and 16 μm in width. Specifically, the 8 μm main waveguide has a corresponding subsidiary waveguide of 2.67 μm; the 12 μm main waveguide has two subsidiary waveguides measuring 4.82 μm and 6.63 μm; and the 16 μm main waveguide has two subsidiary waveguides measuring 7.13 μm and 3.68 μm. Based on coupled-mode theory, we systematically analyzed the coupling coefficients under different inter-waveguide spacings, leading to an optimized spacing of 1.2 μm through comprehensive theoretical simulations and fabrication compatibility constraints. Furthermore, phase-shifted gratings were integrated between tapered waveguide segments to enable precise longitudinal mode selection. This synergistic design could successfully realize robust single-mode operation, offering a scalable framework for on-chip integrated high-power, high-beam-quality tapered lasers.

Previous works on photorefractive self-organizing laser cavities were about lasers that oscillate, prior the self-organization process occurs, on a set of axial modes sharing the same transverse structure. We have now demonstrated that the insertion of a photorefractive crystal can also create a dynamic spatial filter. In a well-designed extended cavity broad-area laser diode, such a filter can affect the transverse modal structure to force a laser, initially oscillating on several transverse modes, to oscillate on a single transverse and longitudinal mode. A large increase of the single-mode operating range of the laser has been observed.

An analysis of the transverse and longitudinal mode structure of broad area quantum dot lasers emitting at 1060 nm is presented. In particular, temperature is shown to play an important role in the stabilisation of the transverse mode structure of the devices. In addition, the investigation of the interaction between these transverse modes, through the measurement of the spatial intensity correlation, shows that the laser retains some modal properties in the unstable regime. Finally, measurements of spectral correlations between longitudinal mode groups display a strong dependency on their respective transverse mode structures indicating the importance of spatial overlap.

The authors have realized a film bulk acoustic wave resonator (FBAR) using a thin LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> film deposited by a chemical vapor deposition (CVD) for the first time. As a result, a 2.9GHz FBAR, which is higher than 2.1GHz of the BAW using a LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> single crystal thin plate, with an impedance ratio of 40dB at a resonant (fr) and an antiresonant (fa) frequencies was realized. The LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> film has a mixture of the polarity. As a result of a scanning non-linear dielectric microscope (SNDM) measurement, -c domains and +c domains occupy 82% and 18%, respectively. A quality factor is small because it is considered that the film has the mixed polarity, the thickness is not flat and the structure of electrode is not optimum. A transverse mode was not excited on the fabricated FABR According to a calculation, the transverse wave mode is observed when the thickness of electrodes is thin. On the other hand, the transverse wave mode isn't observed when the thickness of electrodes is thick. The main responses of longitudinal mode wave are not different by the thicknesses of electrodes. Therefore it is found that the transverse wave mode can be suppressed by selecting the thickness of electrodes. Further, the effect that LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> film is twinned crystalline epitaxial one is evaluated by calculation. The transverse wave mode is excited even if the film is twinned epitaxial one. It is important to deposit another oriented LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> film with larger coupling factor to realize a wider band resonator.

We analyze the dependence of the effective action and the entanglement entropy in the Maxwell theory on the gauge fixing parameter a in d dimensions. For a generic value of a the corresponding vector operator is nonminimal. The operator can be diagonalized in terms of the transverse and longitudinal modes. Using this factorization we obtain an expression for the heat kernel coefficients of the nonminimal operator in terms of the coefficients of two minimal Beltrami-Laplace operators acting on 0- and 1-forms. This expression agrees with an earlier result by Gilkey et al. Working in a regularization scheme with the dimensionful UV regulators we introduce three different regulators: for transverse, longitudinal and ghost modes, respectively. We then show that the effective action and the entanglement entropy do not depend on the gauge fixing parameter a provided the certain (a-dependent) relations are imposed on the regulators. Comparing the entanglement entropy with the black hole entropy expressed in terms of the induced Newton’s constant we conclude that their difference, the so-called Kabat’s contact term, does not depend on the gauge fixing parameter a. We consider this as an indication of gauge invariance of the contact term.

In this paper, we demonstrate a scheme to tailor both longitudinal and transverse modes inside a laser cavity and constitute an eye-safe single longitudinal mode Er:Y3Al5O12 (Er:YAG) vector laser. A q-plate is employed as a spin-orbital conversion element to modulate the transverse mode and obtain cylindrical vector beams. An optical isolator is employed as a non-reciprocal element for the ring cavity to enforce unidirectional operation and achieve single longitudinal oscillation. The characteristics of power, transverse intensity, and polarization spectrum of the output beams are observed. The observed typical single longitudinal mode and highly matched special polarizations prove the successful tailoring of both longitudinal and transverse modes.

In Phys. Rev. E 70, 047102 (2004), Torgerson and Lamoreaux investigated for the first time the real-frequency spectrum of the finite temperature correction to the Casimir force, for metallic plates of finite conductivity. The very interesting result of this study is that the large correction from the TE mode is dominated by low frequencies, for which the dielectric description of the metal is invalid, and the authors correctly point out that a more realistic description is provided by low-frequency metallic boundary conditions. However, their subsequent analysis uses an incorrect form of metallic boundary conditions for TE modes. After correcting this error, we find that their main conclusion was nevertheless qualitatively correct: contrary to the result of the dielectric model, the thermal TE mode correction leads to an increase in the TE mode force of attraction between the plates. The correction found by us, however, has a magnitude about 20 times larger than that quoted by Torgerson and Lamoreaux.