Titus Sandu

Applications of electrostatic capacitance and charging

The capacitance of an arbitrarily shaped object is calculated with the same second-kind integral equation method used for computing static and dynamic polarizabilities. The capacitance is simply the dielectric permittivity multiplied by the area of the object and divided by the squared norm of the Neumann-Poincare operator eigenfunction corresponding to the largest eigenvalue. The norm of this eigenfunction varies slowly with shape thus enabling the definition of two scale-invariant shape factors and perturbative calculations of capacitance. The result is extended to a special class of capacitors in which the electrodes are the equipotential surfaces generated by the equilibrium charge on the object. This extension allows analytical expressions of capacitance for confocal spheroidal capacitors and finite cylinders. Moreover, a second order formula for thin constant-thickness capacitors is given with direct applications for capacitance of membranes in living cells and of supercapacitors. For axisymmetric g...

Fluorescence and fluorescence quenching in a two-level system

Usually, fluorescence of a two-level system increases with the coupling strength to an electromagnetic field. However, we show numerically that the fluorescence is quenched in the ultra-strong coupling limit of a two-level system interacting with an electromagnetic field. This behavior is attributed to the onset of multi-photon processes which occur for the ultra-strong coupling between the two-level system and the electromagnetic field.

Capacitance of back-gated nanowires in various dielectric embeddings

The effect of dielectric embedding on the capacitance of back-gated nanowires can be accurately captured as an effective dielectric constant that depends solely on the difference between the nanowire-gate distance and the dielectric thickness. When used for sensing purposes this property provides the maximum sensitivity within a range of two diameters around the center of the nanowire.

Modeling thermal conductivity of graphene-based nanocomposites

We report a general setting in which the thermal conductivity of nanocomposites can be calculated. Interfacial thermal resistance is also considered and no shape assumptions are made. By this method we have found that oblate spheroidal approximation of graphene nanodots in graphene-based nanocomposites is not adequate to model thermal conductivity of these composites.

Simpler description of the quantum dynamics in the ultra-strong coupling regime of the Rabi Hamiltonian

The Rabi Hamiltonian is characterized by: Ω — the frequency of the transition between the atomic levels, ω — the oscillator frequency, and λ — the coupling between these two subsystems. Even though the Rabi Hamiltonian is quite simple its complete solution is rather complicated and simpler Hamiltonian forms are needed for various regimes of parameters. In the ultra-strong coupling regime of the Rabi Hamiltonian there is a quantum transition point given by λ = √Ωω. In an adiabatic regime this point is also a transition from an adiabatic potential with one minimum to an adiabatic potential with two minima. In this short communication we verify the validity of the approximate adiabatic dynamics around quantum transition point.

A heuristic look at plasmon resonances in graphene nanodisks

Plasmon resonances in graphene nanodisks were analyzed by examining plasmon modes resulted from a boundary integral equation method applied to disks of finite thickness. The main resonance modes are identified for both electric field polarizations: parallel and perpendicular to the nanodisk plane. Using physical arguments resulted from our method we show: (a) the scaling of plasmon frequency with the diameter of the nanodisk for parallel polarization, and (b) the disappearance of the plasmon mode induced by fields with perpendicular polarization in the case of infinitesimally thin disks. Numerical calculations performed with our method agree very well with results obtained using commercial programs.

Calculation of dielectrophoretic force acting on biological cells and on micro- and nanoparticles

It is presented a theory that permits to calculate the ac dielectrophoretic force acting on biological cells and other micro- and nanoparticles of arbitrary shape. The theory includes intrinsically all the higher-order terms of dielectrophoretic force without additional computation costs. For sufficiently small electric field gradients the dielectrophoretic force is weighted by the induced cell dipole moment that depends on both shape and electric parameters of the cell. Examples of red blood cells are given.

Charging and capacitance of conductors by the integral equation approach

The integral equations of the first- and second-kind can be used to calculate the capacitance and charging of an arbitrary conductor. In this communication we discuss the relationship between these two formulations and their numerical implementations in terms of a spectral method. Also a relationship between the second-kind integral equation formulation of capacitance and a boundary integral equation method for calculation of surface plasmon resonances in metallic nanoparticles is established and a numerical example is analyzed.

Near-field enhancement of a rod-like nanoantenna: Elctrostatic versus fully retarded results

The near-field enhancement of rod-like nanoantenna is studied in two variants: in the electrostatic approximation and in a fully retarded approach. A boundary integral equation (BIE) method has been used in the electrostatic approximation. The BIE method allows a transparent eigenmode decomposition of both the far-field and near-field, which are valid as long as the size of the nanoantenna is much smaller than every representative light wavelength. Our near-field calculations show that for a rod-like nanoantenna with a length below 100 nm the electrostatic and the fully retarded results are in good agreement with each other.

Extinction spectra and near-field enhancement of metallic nanoparticles

Extinction spectra and near-field enhancement of metallic nanoparticles are calculated with a boundary integral equation (BIE) method. With the BIE method the far-field response and the near-field evanescent coupling are expressed as an eigenmode sum of resonant terms. In particular, the near-field enhancement around nanoparticles is obtained as a sum of resonant terms which acquire the spatial dependence of the eigenfunctions of the BIE operators. Moreover, the presented method permits a direct link between near-field and far field spectral properties. Finally, a numerical example is given.