Multimode Formalism Research Articles

Modeling of the multimodal radiation from an open-ended waveguide.

The multimodal radiation from the open end of a cylindrical waveguide with arbitrary wall thickness is solved by deriving algebraic solutions of the radiation impedance matrix, without restrictive hypothesis on the frequency range. The basic idea of the method is to turn the original unbounded problem into the problem of a cylindrical waveguide embedded in an infinite waveguide with an annular perfectly matched layer (PML) on its wall. Then, using a multimodal formalism of the guided wave propagation and a complex coordinate stretching PML, algebraic expressions are derived for the continuity and radiation conditions in this coupled system.

Evaluation of multiphoton effects in down-conversion

Multiphoton effects in down-conversion are investigated based on the full-quantum multimode formalism by considering a three-level system as a prototype nonlinear system. We analytically derive the three-photon output wave function for two input photons, where one of the two input photons is down-converted and the other one is not. Using this output wave function, we calculate the down-conversion probability, the purity, and the fidelity to evaluate the entanglement between a down-converted photon pair and a non-down-converted photon. It is shown that the saturation effect occurs by multiphoton input and that it affects both the down-conversion probability and the quantum correlation between the down-converted photon pair and the non-down-converted photon. We also reveal the necessary conditions for multiphoton effects to be strong.

On the use of leaky modes in open waveguides for the sound propagation modeling in street canyons

An urban, U-shaped, street canyon being considered as an open waveguide in which the sound may propagate, one is interested in a multimodal approach to describe the sound propagation within. The key point in such a multimodal formalism is the choice of the basis of local transversal modes on which the acoustic field is decomposed. For a classical waveguide, with a simple and bounded cross-section, a complete orthogonal basis can be analytically obtained. The case of an open waveguide is more difficult, since no such a basis can be exhibited. However, an open resonator, as displays, for example, the U-shaped cross-section of a street, presents resonant modes with complex eigenfrequencies, owing to radiative losses. This work first presents how to numerically obtain these modes. Results of the transverse problem are also compared with solutions obtained by the finite element method with perfectly mathed layers. Then, examples are treated to show how these leaky modes can be used as a basis for the modal decomposition of the sound field in a street canyon.

Effect of bending portions of the air column on the acoustical properties of a wind instrument

The need to keep long wind musical instruments compact imposes the bending of portions of the air column. Although manufacturers and players mention its effects as being significant, the curvature is generally not included in physical models and only a few studies, in only simplified cases, attempted to evaluate its influence. The aim of our study is to quantify the influence of the curvature by modelling the wave propagation in an air column with a multimodal formalism. In a duct with a circular cross-section and a finite curvature, two infinite sets of coupled first-order differential equations are constructed for the components of the pressure and axial velocity, projected on the local transverse modes. From these an impedance matrix is defined, which can be easily calculated, particularly when considering a duct with a piecewise constant curvature. Influence of the curvature on the input impedance, effective length, or playing frequencies is then quantified, displaying notably a dependence to frequency such that, compared to an equivalent straight tube, the shift in resonance frequencies in a tube with bent sections is not always positive, as generally stated. Results are independently corroborated by numerical - finite differences - computations.

Gravitational-wave spectroscopy of massive black holes with the space interferometer LISA

Newly formed black holes are expected to emit characteristic radiation in the form of quasinormal modes, called ringdown waves, with discrete frequencies. LISA should be able to detect the ringdown waves emitted by oscillating supermassive black holes throughout the observable Universe. We develop a multimode formalism, applicable to any interferometric detectors, for detecting ringdown signals, for estimating black-hole parameters from those signals, and for testing the no-hair theorem of general relativity. Focusing on LISA, we use current models of its sensitivity to compute the expected signal-to-noise ratio for ringdown events, the relative parameter estimation accuracy, and the resolvability of different modes. We also discuss the extent to which uncertainties on physical parameters, such as the black-hole spin and the energy emitted in each mode, will affect our ability to do black-hole spectroscopy.

Ray-wave correspondence in bent waveguides

The present paper is concerned with wave propagation at high frequency in bent waveguides. The multimodal formalism proposed in earlier papers by the authors is shown to be suitable for investigating very high frequency problems. Then, following works made by Luna-Acosta et al. (G. Luna-Acosta, J.A. Méndez-Bermúdez, P. S˘eba, K.N. Pichugin, Classical versus quantum structure of the scattering probability matrix: chaotic waveguides, Phys. Rev. E 65 (2002) 046605; J.A. Méndez-Bermúdez, G. Luna-Acosta, P. P˘eba, K.N. Pichugin, Understanding quantum scattering properties in terms of purely classical dynamics: two-dimensional open chaotic billiards, Phys. Rev. E 66 (2002) 046207) for open quantum billiards, the ray-wave correspondence of the scattering matrix ( S matrix) is studied by first constructing a ray- S matrix and then comparing its structure with the structure of the wave- S matrix that is obtained with the exact multimodal formalism, for different geometries of curved waveguides. A great similarity between these two matrices is observed and it is shown that the scattering matrix constructed only by counting rays allows us to predict and understand numbers of the wave scattering properties in waveguides.

Multimodal analysis of acoustic propagation in three-dimensional bends

An exact multimodal formalism is proposed for acoustic propagation in three-dimensional rigid bends of circular cross-section. Two infinite systems of first-order differential equations are constructed for the components of the pressure and axial velocity in the bend, projected on the local transverse modes. These equations are numerically unstable, due to the presence of evanescent modes, and cannot be integrated directly. An impedance matrix is defined, which obeys a Riccati equation, numerically workable. With this nonlinear first-order differential equation, the impedance can be calculated everywhere in the bend, allowing a direct characterization of its acoustical properties or allowing the acoustic field to be integrated. An exact algebraic formulation of the reflection and transmission matrices is carried out to allow bends and more complex duct systems to be characterized. This result is applied to calculate the reflection and transmission of a typical bend, and also to obtain the resonance frequencies of closed tube systems.

Multimode analysis of self locked FM operation in laser diodes

A multimode formalism has been used to estimate the intrinsic modulation index of semiconductor lasers. The calculated value of 1.3 is in agreement with the available experimental evidence. Pure FM operation is inhibited and a small AM component is present in the self locked FM supermode.