Virtual dielectric waveguide mode description of a high-gain free-electron laser I: Theory

A set of mode-coupled excitation equations for the slowly-growing amplitudes of dielectric waveguide eigenmodes is derived as a description of the electromagnetic signal field of a high-gain free-electron laser, or FEL, including the effects of longitudinal space-charge. This approach of describing the field basis set has notable advantages for FEL analysis in providing an efficient characterization of eigenmodes, and in allowing a clear connection to free-space propagation of the input (seeding) and output radiation. The formulation describes the entire evolution of the radiation wave through the linear gain regime, prior to the onset of saturation, with arbitrary initial conditions. By virtue of the flexibility in the expansion basis, this technique can be used to find the direct coupling and amplification of a particular mode. A simple transformation converts the derived coupled differential excitation equations into a set of coupled algebraic equations and yields a matrix determinant equation for the FEL eigenmodes. A quadratic index medium is used as a model dielectric waveguide to obtain an expression for the predicted spot size of the dominant system eigenmode, in the approximation that it is a single gaussian mode.Comment: 14 page

Classical simulation of Quantum Entanglement using Optical Transverse Modes in Multimode Waveguides

We discuss mode-entangled states based on the optical transverse modes of the optical field propagating in multi-mode waveguides, which are classical analogs of the quantum entangled states. The analogs are discussed in detail, including the violation of the Bell inequality and the correlation properties of optical pulses' group delays. The research on these analogs may be important, for it not only provides useful insights into fundamental features of quantum entanglement, but also yields new insights into quantum computation and quantum communication.Comment: RevTeX v4, 17 pages and 4 figure

Model for reflection and transmission matrices of nanowire end facets

Nanowires show a large potential for various electrooptical devices, such as light emitting diodes, solar cells and nanowire lasers. We present a direct method developed to calculate the modal reflection and transmission matrix at the end facets of a waveguide of arbitrary cross section, resulting in a generalized version of the Fresnel equations. The reflection can be conveniently computed using Fast Fourier Transforms. We demonstrate that the reflection is qualitatively described by two main parameters, the modal field confinement and the average Fresnel reflection of the plane waves constituting the waveguide mode.Comment: 11 pages,14 figure

On the attenuation coefficient of monomode periodic waveguides

It is widely accepted that, on ensemble average, the transmission T of guided modes decays exponentially with the waveguide length L due to small imperfections, leading to the important figure of merit defined as the attenuation-rate coefficient alpha = -/L. In this letter, we evidence that the exponential-damping law is not valid in general for periodic monomode waveguides, especially as the group velocity decreases. This result that contradicts common beliefs and experimental practices aiming at measuring alpha is supported by a theoretical study of light transport in the limit of very small imperfections, and by numerical results obtained for two waveguide geometries that offer contrasted damping behaviours

Theory of disorder-induced multiple coherent scattering in photonic crystal waveguides

We introduce a theoretical formalism to describe disorder-induced extrinsic scattering in slow-light photonic crystal waveguides. This work details and extends the optical scattering theory used in a recent \emph{Physical Review Letter} [M. Patterson \emph{et al.}, \emph{Phys. Rev. Lett.} \textbf{102}, 103901 (2009)] to describe coherent scattering phenomena and successfully explain complex experimental measurements. Our presented theory, that combines Green function and coupled mode methods, allows one to self-consistently account for arbitrary multiple scattering for the propagating electric field and recover experimental features such as resonances near the band edge. The technique is fully three-dimensional and can calculate the effects of disorder on the propagating field over thousands of unit cells. As an application of this theory, we explore various sample lengths and disordered instances, and demonstrate the profound effect of multiple scattering in the waveguide transmission. The spectra yield rich features associated with disorder-induced localization and multiple scattering, which are shown to be exasperated in the slow light propagation regime

Scarring in a driven system with wave chaos

We consider acoustic wave propagation in a model of a deep ocean acoustic waveguide with a periodic range-dependence. Formally, the wave field is described by the Schrodinger equation with a time-dependent Hamiltonian. Using methods borrowed from the quantum chaos theory it is shown that in the driven system under consideration there exists a "scarring" effect similar to that observed in autonomous quantum systems.Comment: 5 pages, 7 figure

Effect of an atom on a quantum guided field in a weakly driven fiber-Bragg-grating cavity

We study the interaction of an atom with a quantum guided field in a weakly driven fiber-Bragg-grating (FBG) cavity. We present an effective Hamiltonian and derive the density-matrix equations for the combined atom-cavity system. We calculate the mean photon number, the second-order photon correlation function, and the atomic excited-state population. We show that, due to the confinement of the guided cavity field in the fiber cross-section plane and in the space between the FBG mirrors, the presence of the atom in the FBG cavity can significantly affect the mean photon number and the photon statistics even though the cavity finesse is moderate, the cavity is long, and the probe field is weak.Comment: Accepted for Phys. Rev.

Grating-coupled excitation of multiple surface plasmon-polariton waves

The excitation of multiple surface-plasmon-polariton (SPP) waves of different linear polarization states and phase speeds by a surface-relief grating formed by a metal and a rugate filter, both of finite thickness, was studied theoretically, using rigorous coupled-wave-analysis. The incident plane wave can be either p or s polarized. The excitation of SPP waves is indicated by the presence of those peaks in the plots of absorbance vs. the incidence angle that are independent of the thickness of the rugate filter. The absorbance peaks representing the excitation of s-polarized SPP waves are narrower than those representing p-polarized SPP waves. Two incident plane waves propagating in different directions may excite the same SPP wave. A line source could excite several SPP waves simultaneously

Atom trapping and guiding with a subwavelength-diameter optical fiber

We suggest using an evanescent wave around a thin fiber to trap atoms. We show that the gradient force of a red-detuned evanescent-wave field in the fundamental mode of a silica fiber can balance the centrifugal force when the fiber diameter is about two times smaller than the wavelength of the light and the component of the angular momentum of the atoms along the fiber axis is in an appropriate range. As an example, the system should be realizable for Cesium atoms at a temperature of less than 0.29 mK using a silica fiber with a radius of 0.2 $\mu$m and a 1.3-$\mu$m-wavelength light with a power of about 27 mW.Comment: 5 pages, 5 figure