Quantum Modelling of Electro-Optic Modulators

Many components that are employed in quantum information and communication systems are well known photonic devices encountered in standard optical fiber communication systems, such as optical beamsplitters, waveguide couplers and junctions, electro-optic modulators and optical fiber links. The use of these photonic devices is becoming increasingly important especially in the context of their possible integration either in a specifically designed system or in an already deployed end-to-end fiber link. Whereas the behavior of these devices is well known under the classical regime, in some cases their operation under quantum conditions is less well understood. This paper reviews the salient features of the quantum scattering theory describing both the operation of the electro-optic phase and amplitude modulators in discrete and continuous-mode formalisms. This subject is timely and of importance in light of the increasing utilization of these devices in a variety of systems, including quantum key distribution and single-photon wavepacket measurement and conformation. In addition, the paper includes a tutorial development of the use of these models in selected but yet important applications, such as single and multi-tone modulation of photons, two-photon interference with phase-modulated light or the description of amplitude modulation as a quantum operation.Comment: 29 pages, 10 figures, Laser and Photonics Reviews (in press

The Hamiltonian Structure of Soliton Equations and Deformed W-Algebras

The Poisson bracket algebra corresponding to the second Hamiltonian structure of a large class of generalized KdV and mKdV integrable hierarchies is carefully analysed. These algebras are known to have conformal properties, and their relation to $\cal W$-algebras has been previously investigated in some particular cases. The class of equations that is considered includes practically all the generalizations of the Drinfel'd-Sokolov hierarchies constructed in the literature. In particular, it has been recently shown that it includes matrix generalizations of the Gelfand-Dickey and the constrained KP hierarchies. Therefore, our results provide a unified description of the relation between the Hamiltonian structure of soliton equations and $\cal W$-algebras, and it comprises almost all the results formerly obtained by other authors. The main result of this paper is an explicit general equation showing that the second Poisson bracket algebra is a deformation of the Dirac bracket algebra corresponding to the $\cal W$-algebras obtained through Hamiltonian reduction.Comment: 41 pages, plain TeX, no figures. New introduction and references added. Version to be published in Annals of Physics (N.Y.

Modelocking of a Frequency Shifted Feedback Laser triggered by Amplitude Modulation

We report an experimental technique to trigger modelocking (ML) emission in Frequency-Shifted Feedback (FSF) lasers. These lasers feature an intracavity modulator driven by a radio-frequency tone, which shifts the light spectrum every cavity roundtrip. The technique consists of the drive of the modulator with a second tone at the cavity free spectral range (FSR) frequency. So, in addition to the frequency shift, a weak amplitude modulation (AM) appears synchronous with the cavity roundtrip time. The approach is successful as FSF cavities support chirped modes evenly spaced by the FSR, whose AM coupling produces convenient seed pulses for the ML onset. This results in ML emission at arbitrary frequency shifts and initiation thresholds lower than in standard, spontaneous FSF laser ML. Simulations indicate that the role of AM is to trigger the formation of ML pulses, but the primary mechanism of pulse buildup is Kerr effect. The technique opens a new practical route to initiate ML emission in FSF laser

Dyonic Integrable Models

A class of non abelian affine Toda models arising from the axial gauged two-loop WZW model is presented. Their zero curvature representation is constructed in terms of a graded Kac-Moody algebra. It is shown that the discrete multivacua structure of the potential together with non abelian nature of the zero grade subalgebra allows soliton solutions with non trivial electric and topological charges. The dressing transformation is employed to explicitly construct one and two soliton solutions and their bound states in terms of the tau functions. A discussion of the classical spectra of such solutions and the time delays are given in detail.Comment: Latex 30 pages, corrected some typo

Scan and paint: theory and practice of a sound field visualization method

Sound visualization techniques have played a key role in the development of acoustics throughout history. The development of measurement apparatus and techniques for displaying sound and vibration phenomena has provided excellent tools for building understanding about specific problems. Traditional methods, such as step-by-step measurements or simultaneous multichannel systems, have a strong tradeoff between time requirements, flexibility, and cost. However, if the sound field can be assumed time stationary, scanning methods allow us to assess variations across space with a single transducer, as long as the position of the sensor is known. The proposed technique, Scan and Paint, is based on the acquisition of sound pressure and particle velocity by manually moving a P-U probe (pressure-particle velocity sensors) across a sound field whilst filming the event with a camera. The sensor position is extracted by applying automatic color tracking to each frame of the recorded video. It is then possible to visualize sound variations across the space in terms of sound pressure, particle velocity, or acoustic intensity. In this paper, not only the theoretical foundations of the method, but also its practical applications are explored such as scanning transfer path analysis, source radiation characterization, operational deflection shapes, virtual phased arrays, material characterization, and acoustic intensity vector field mapping

Tau-Functions generating the Conservation Laws for Generalized Integrable Hierarchies of KdV and Affine-Toda type

For a class of generalized integrable hierarchies associated with affine (twisted or untwisted) Kac-Moody algebras, an explicit representation of their local conserved densities by means of a single scalar tau-function is deduced. This tau-function acts as a partition function for the conserved densities, which fits its potential interpretation as the effective action of some quantum system. The class consists of multi-component generalizations of the Drinfel'd-Sokolov and the two-dimensional affine Toda lattice hierarchies. The relationship between the former and the approach of Feigin, Frenkel and Enriquez to soliton equations of KdV and mKdV type is also discussed. These results considerably simplify the calculation of the conserved charges carried by the soliton solutions to the equations of the hierarchy, which is important to establish their interpretation as particles. By way of illustration, we calculate the charges carried by a set of constrained KP solitons recently constructed.Comment: 47 pages, plain TeX with AMS fonts, no figure

Multicharged Dyonic Integrable Models

We introduce and study new integrable models of A_n^{(1)}-Non-Abelian Toda type which admit U(1)\otimes U(1) charged topological solitons. They correspond to the symmetry breaking SU(n+1) \to SU(2)\otimes SU(2)\otimes U(1)^{n-2} and are conjectured to describe charged dyonic domain walls of N=1 SU(n+1) SUSY gauge theory in large n limit. It is shown that this family of relativistic IMs corresponds to the first negative grade q={-1} member of a dyonic hierarchy of generalized cKP type. The explicit relation between the 1-soliton solutions (and the conserved charges as well) of the IMs of grades q=-1 and q=2 is found. The properties of the IMs corresponding to more general symmetry breaking SU(n+1) \to SU(2)^{\otimes p}\otimes U(1)^{n-p} as well as IM with global SU(2) symmetries are discussed.Comment: 48pages, latex, v2. typos in eqns. (1.7) and (3.20) corrected, small improvements in subsection 2.2, new reference added;v3. improvements in text of Sect. 1,2 and 6; new Sect 7 and new refs. added; version to appear in Nucl. Phys.

Phase sensitive low-coherence interferometry using microwave

We report on a low-coherence interferometer based on Microwave Photonics (MWP) which allows, for the first time to the best of our knowledge, stable determination of the interferogram’s phase. The interferometer is built on suppressed carrier, double-sideband modulation, dispersive propagation in a chirped fiber Bragg grating, demodulation by electrooptical frequency down-conversion, and suitable signal processing techniques to account for modulation impairments. Taking as a reference a direct normalization of the link’s microwave response, the system retrieves high-resolution interferograms, both in amplitude and phase and free from distortion induced by higher-order dispersion, in an optical path difference of 16.3 mm, surpassing previously reported values based on MWP implementations. We present representative applications targeted to the characterization of C-band sources and components, such as direct analysis of interferograms with 5.5 fs temporal resolution, Fourier-transform spectroscopy with 14 GHz spectral resolution, and optical low-coherence reflectrometry of the impulse response’s amplitude of fiber Bragg gratings with 0.55 m spatial resolution