Field representation for optical defect resonances in multilayer microcavities using quasi-normal modes

Quasi-normal modes are used to characterize transmission resonances in 1D optical defect cavities and the related field approximations. We specialize to resonances inside the bandgap of the periodic multilayer mirrors that enclose the defect cavities. Using a template with the most relevant QNMs a variational principle permits to represent the field and the spectral transmission close to resonances

Effects of delayed Kerr nonlinearity and ionozation on the filamentary ultrashort laser pulses in air

We present a systematic study of filamentary ultrashort laser pulses in air, through numerical solutions of the nonlinear Schrödinger equation for various contributions of the delayed Kerr nonlinearity. The results show that a relatively larger contribution of the delayed Kerr nonlinearity will lead to a longer stable filament. This is explained from the transfer of the nonlinear contributions from the frontier part to the back of the pulse and the counterbalanced action of the negative plasma induced nonlinearity by the delayed Kerr nonlinearity in the trailing part of the pulses. Furthermore, effect of ionization on the stability of the filament is investigated. Two formulas are used to generate the data of the ionization, i.e., the Perelemov, Popov, and Terent'ev (PPT) and the Ammosov, Delone, and Krainov formula. It is found that simulation with higher ionization rate (PPT) could generate a more stable and longer filament

Variational coupled mode theory and perturbation analysis for 1D photonic crystal structures using quasi-normal modes

Quasi-normal modes are used to directly characterize defect resonances in composite 1D Photonic Crystal structures. Variational coupled mode theory using QNMs enables quantification of the eigenfrequency splitting in composite structures. Also, variational perturbation analysis of complex eigenfrequencies is addressed

Field representations for optical defect microcavities in 1D grating structures using quasi-normal modes

Quasi-Normal Modes are used to characterize transmission resonances in 1D optical defect cavities and the related field approximations. Using a mirror field and the relevant QNM, a variational principle permits to represent the field and the spectral transmission close to resonances

Quantum suppression of shot noise in atom-size metallic contacts

The transmission of conductance modes in atom-size gold contacts is investigated by simultaneously measuring conductance and shot noise. The results give unambiguous evidence that the current in the smallest gold contacts is mostly carried by nearly fully transmitted modes. In particular, for a single-atom contact the contribution of additional modes is only a few percent. In contrast, the trivalent metal aluminum does not show this property.Comment: Fig. 2 replaced, small errors correcte

Norm discontinuity and spectral properties of Ornstein-Uhlenbeck semigroups

Let $E$ be a real Banach space. We study the Ornstein-Uhlenbeck semigroup $P(t)$ associated with the Ornstein-Uhlenbeck operator $$Lf(x) = \frac12 {\rm Tr} Q D^2 f(x) + .$$ Here $Q$ is a positive symmetric operator from $E^*$ to $E$ and $A$ is the generator of a $C_0$-semigroup $S(t)$ on $E$. Under the assumption that $P$ admits an invariant measure $\mu$ we prove that if $S$ is eventually compact and the spectrum of its generator is nonempty, then \n P(t)-P(s)\n_{L^1(E,\mu)} = 2 for all $t,s\ge 0$ with $t\not=s$. This result is new even when $E = \R^n$. We also study the behaviour of $P$ in the space $BUC(E)$. We show that if $A\not=0$ there exists $t_0>0$ such that \n P(t)-P(s)\n_{BUC(E)} = 2 for all $0\le t,s\le t_0$ with $t\not=s$. Moreover, under a nondegeneracy assumption or a strong Feller assumption, the following dichotomy holds: either \n P(t)- P(s)\n_{BUC(E)} = 2 for all $t,s\ge 0$, \ $t\not=s$, or $S$ is the direct sum of a nilpotent semigroup and a finite-dimensional periodic semigroup. Finally we investigate the spectrum of $L$ in the spaces $L^1(E,\mu)$ and $BUC(E)$.Comment: 14 pages; to appear in J. Evolution Equation

Coupling constants and transition potentials for hadronic decay modes of a meson

Within the independent-harmonic-oscillator model for quarks inside a hadron, a rigorous method is presented for the calculation of coupling constants and transition potentials for hadronic decay, as needed in a multi-channel description of mesons.Comment: 19 pages, 4 figure