María C. Nistal

Quantization of coupled 1D vector modes in integrated photonic waveguides

A quantum mechanical analysis of the guided light in integrated photonics waveguides is presented. The analysis is made starting from one-dimensional (1D) guided vector modes by taking into account the modal orthonormalization property on a cross section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time symmetry in order to quantize the 1D vector modes and to derive the quantum momentum operator and the Heisenberg equations. The results provide a quantum-consistent formulation of the linear and nonlinear quantum light propagations as a function of forward and backward creation and annihilation operators in integrated photonics. As an illustration, an application to an integrated nonlinear directional coupler is given, that is, both the nonlinear momentum and the Heisenberg equations of the nonlinear coupler are derived.

Geometric phases in multidirectional electromagnetic coupling theory

Abstract Geometric phases are determined for N coupled electromagnetic wave amplitudes evolving in their projective Hilbert space. Multidirectional coupling systems subject to SU (N) dynamical symmetry are proposed and Aharonov-Anandan phases are evaluated in a spinorial representation, for both closed and partial circuits described by the SU(2) group. Following closely Bhandaris idea, this kind of systems enlarges the general framework of topological phases for electromagnetic waves.

Quantization of coupled modes propagation in integrated optical waveguides

Abstract A quantum mechanical analysis of the propagation of coupled modes in integrated optical waveguides is given. The modal orthonormalization property on a cross-section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time symmetry are taken into account to derive the quantum momentum operator and Heisenbergs equations giving a quantum-consistent formulation of the coupled mode propagation as a function of forward and backward creation and annihilation operators.

Optical field-strength generalized polarization of multimode single photon states in integrated directional couplers

A quantum analysis of the generalized polarization properties of multimode single photon states is presented. It is based on the optical field-strength probability distributions in such a way that generalized polarization is understood as a significant confinement of the probability distribution along certain regions of the multidimensional optical field-strength space. The analysis is addressed to multimode integrated waveguiding devices, such as N × N integrated directional couplers, whose modes fulfil a spatial modal orthogonality relationship. For that purpose a definition of the quantum generalized polarization degree in a N-dimensional space, based on the concept of distance to an unpolarized N-dimensional Gaussian distribution, is proposed. The generalized polarization degree of pure and mixture multimode single photon states and also of some multi-photon states such as coherent and chaotic ones, is evaluated and analyzed.

SPATIAL PROPAGATION OF QUANTUM LIGHT IN NONLINEAR WAVEGUIDING DEVICES: THEORY AND APPLICATIONS

We present the main theoretical results on spatial propagation of quantum light in nonlinear waveguiding devices together with a few applications. We show that the quantization of the classical momentum provides a consistent quantum mechanical formulation of both the linear and the nonlinear quantum light propagation in waveguiding devices. The momentum operator allows us to derive the correct spatial Heisenbergs equations for the forward and backward absorption and emission operators and consequently to analyze the spatial propagation in the multimode optical-field strength space. For that purpose we use the Feynmans path integral method in order to derive the quantum spatial optical propagators of different nonlinear waveguiding devices and accordingly to calculate the spatial propagation of the optical-field strength probability amplitude of quantum states in these nonlinear devices. Likewise, we present a preliminary and heuristic formulation of quantum dissipation in order to take into account the losses under spatial quantum propagation in lossy nonlinear waveguiding devices. It must be stressed that these optical-field strength probabilities have the advantage of being measured by homodyne techniques and therefore their theoretical analysis is of a remarkable interest in the optical characterization of quantum states obtained under linear and nonlinear propagation in waveguiding devices.

Optical field-strength polarization of two-mode single-photon states

We present a quantum analysis of two-mode single-photon states based on the probability distributions of the optical field strength (or position quadrature) in order to describe their quantum polarization characteristics, where polarization is understood as a significative confinement of the optical field-strength values on determined regions of the two-mode optical field-strength plane. We will show that the mentioned probability distributions along with the values of quantum Stokes parameters allow us to characterize the polarization of a two-mode single-photon state, in an analogous way to the classical case, and to distinguish conceptually between mixture and partially polarized quantum states; in this way, we propose a simple definition of the quantum polarization degree based on the recent concept of distance measure to an unpolarized distribution, which gives rise to a depolarization degree equivalent to an overlapping between the probability distribution of the quantum state and a non-polarized two-mode Gaussian distribution. The work is particularly intended to university physics teachers and graduate students as well as to physicists and specialists concerned with the issue of optical polarization.

Optical field-strength generalized polarization of non-stationary quantum states in waveguiding photonic devices

A quantum analysis of the generalized polarization properties of multimode non-stationary states based on their optical field-strength probability distributions is presented. The quantum generalized polarization is understood as a significant confinement of the probability distribution along certain regions of a multidimensional optical field-strength space. The analysis is addressed to quantum states generated in multimode linear and nonlinear waveguiding (integrated) photonic devices, such as multimode waveguiding directional couplers and waveguiding parametric amplifiers, whose modes fulfill a spatial modal orthogonality. In particular, the generalized polarization degree of coherent, squeezed and Schrödinger’s cat states is analyzed.

Glass processing by ion exchange to fabricate integrated optical planar components: applications

Ion-Exchanged Glass Integrated Optics has received a considerably attention during the laser years because of their well-known advantages. On the other hand, ion- exchanged waveguide components are finding important applications in the implementation of analogue processing devices, optical sensing devices and some kind of circuit for optical communications. Many of these develop devices are based on channel guides, however planar components with optical confinement in only one dimension have been also recognized to be among the basic components of glass integrated optics. In this paper we show the specific advantages of using these kinds of integrated optical elements. Thus, conventional photolithographic techniques can be used with a great accuracy but within the high requirements needed for channeled devices. Likewise, as it will be shown, the components can be realized by simple selective ion-exchange processes in a few steps, and with a high transmission of guided light, in a monomode regime, through the various boundaries shaping the planar components. Finally, their planar configuration facilitates considerably the use of glass integrated devices with other materials and thus a high-performance hybrid optical devices can be achieved. In short, we show various approaches to the design and fabrication of planar components and presents several passive components implementing simple functions such as: beam-splitting, focusing, and so on, which are important for optical sensing and processing applications.

Designing of monomode step-index channel guides with quasi-exact modal solutions by the effective index method

Abstract A type of monomode step-index channel guide is presented, such that modal propagation can be solved by the effective index method, in a quasi-exact form. With these results both the designing and fabrication of integrated optical devices based on channel guides, such as directional couplers, can be greatly simplified and improved.

Geometric Phases in Chiral Waveguiding Structures

Abstract Geometric phases, generated by directional coupling processes in chiral waveguiding structures, are determined. Aharonov-Anandan phases are acquired by N coupled wave amplitudes in cyclic evolution on their Hilbert projective space. Geometric phases generated by closed and partial cycles and unitary and non-unitary transformations are evaluated; in particular, a N-dimensional pure Faraday rotation is shown, generalizing the topological phase recently presented in magneto-optic Faraday rotation. An Aharonov-Bohm type of experiment is proposed.