R-matrix-Floquet theory of multiphoton processes:VIII. A linear equations method

A new linear equations method for calculating the R-matrix, which arises in the R-matrix-Floquet theory of multiphoton processes, is introduced. This method replaces the diagonalization of the Floquet Hamiltonian matrix by the solution of a set of linear simultaneous equations which are solved, in the present work, by the conjugate gradient method. This approach uses considerably less computer memory and can be readily ported onto parallel computers. It will thus enable much larger problems of current interest to be treated. This new method is tested by applying it to three-photon ionization of helium at frequencies where double resonances with a bound state and autoionizing states are important. Finally, an alternative linear equations method, which avoids the explicit calculation of the R-matrix by incorporating the boundary conditions directly, is described in an appendix.

Scattering theory of cooling and heating in optomechanical systems

We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is taken into account. The theory is applied to describe the scheme of a Fabry-Perot resonator with one of its mirrors moving. The friction force, as well as the diffusion, acting on the moving mirror is derived. In the limit of a small reflection coefficient, the same model provides for the description of the mechanical effect of light on an atom moving in front of a mirror.

Scattering theory of multilevel atoms interacting with arbitrary radiation fields

We present a generic transfer matrix approach for the description of the interaction of atoms possessing multiple ground state and excited state sublevels with light fields. This model allows us to treat multi-level atoms as classical scatterers in light fields modified by, in principle, arbitrarily complex optical components such as mirrors, resonators, dispersive or dichroic elements, or filters. We verify our formalism for two prototypical sub-Doppler cooling mechanisms and show that it agrees with the standard literature.

Computational techniques for a simple theory of conditional preferences

A simple logic of conditional preferences is defined, with a language that allows the compact representation of certain kinds of conditional preference statements, a semantics and a proof theory. CP-nets and TCP-nets can be mapped into this logic, and the semantics and proof theory generalise those of CP-nets and TCP-nets. The system can also express preferences of a lexicographic kind. The paper derives various sufficient conditions for a set of conditional preferences to be consistent, along with algorithmic techniques for checking such conditions and hence confirming consistency. These techniques can also be used for totally ordering outcomes in a way that is consistent with the set of preferences, and they are further developed to give an approach to the problem of constrained optimisation for conditional preferences.

Design technique for mm-wave IC realization of the load network of switched-mode class-EF power amplifier

Analysis and synthesis of the new Class-EF power amplifier (PA) are presented in this paper. The proposed circuit offers means to alleviate some of the major issues faced by existing Class-EF and Class-EF PAs, such as (1) substantial power losses due to parasitic resistance of the large inductor in the Class-EF load network, (2) unpredictable behaviour of practical lumped inductors and capacitors at harmonic frequencies, and (3) deviation from ideal Class-EF operation mode due to detrimental effects of device output inductance at high frequencies. The transmission-line load network of the Class-EF PA topology elaborated in this paper simultaneously satisfies the Class-EF optimum impedance requirements at fundamental frequency, second, and third harmonics as well as simultaneously providing matching to the circuit optimum load resistance for any prescribed system load resistance. Furthermore, an elegant solution using an open and short-circuit stub arrangement is suggested to overcome the problem encountered in the mm-wave IC realizations of the Class-EF PA load network due to lossy quarter-wave line. © 2010 IEICE Institute of Electronics Informati.