Since the discovery of photosensitivity in optical fibers there has been great interest in the fabrication of Bragg gratings within the core of a fiber. The ability to inscribe intracore Bragg gratings in these photosensitive fibers has revolutionized the field of telecommunications and optical fiber based sensor technology. Over the last few years, the number of researchers investigating fundamental, as well as application aspects of these gratings has increased dramatically. This article reviews the technology of Bragg gratings in optical fibers. It introduces the phenomenon of photosensitivity in optical fibers, examines the properties of Bragg gratings, and presents some of the important developments in devices and applications. The most common fabrication techniques (interferometric, phase mask, and point by point) are examined in detail with reference to the advantages and the disadvantages in utilizing them for inscribing Bragg gratings. Reflectivity, bandwidth, temperature, and strain sensitivity of the Bragg reflectors are examined and novel and special Bragg grating structures such as chirped gratings, blazed gratings, phase-shifted gratings, and superimposed multiple gratings are discussed. A formalism for calculating the spectral response of Bragg grating structures is described. Finally, devices and applications for telecommunication and fiber-optic sensors are described, and the impact of this technology on the future of the above areas is discussed.

Fiber Bragg gratings

Whispering gallery mode (WGM) optical microresonators have attracted intense interests in the past decades. The combination of high quality factors (Q) and small mode volumes of modes in WGM resonators significantly enhances the light-matter interactions, making them excellent cavities for achieving low threshold and narrow linewidth lasers. In this Review, the progress in WGM microcavity lasers is summarized, and the laser performance considering resonator geometries and materials as well as lasing mechanisms is discussed. Label-free detection using WGM resonators has emerged as highly sensitive detection schemes. However, the resolution is mainly limited by the cavity Q factor which determines the mode linewidth. Microcavity lasers, due to their narrow laser spectral width, could greatly improve the detection resolution. Some recent developments in sensing using microcavity lasers are discussed.

Whispering gallery microcavity lasers

The investigation of nonlinear wave phenomena has been one of the main direc tions of research in optics for the last few decades. Soliton concepts applied to the description of intense electromagnetic beams and ultrashort pulse propagation in various media have contributed much to this field. The notion of solitons has proved to be very useful in describing wave processes in hydrodynamics, plasma physics and condensed matter physics. Moreover, it is also of great importance in optics for ultrafast information transmission and storage, radiation propagation in resonant media, etc. In 1973, Hasegawa and Tappert made a significant contribution to optical soliton physics when they predicted the existence of an envelope soliton in the regime of short pulses in optical fibres. In 1980, Mollenauer et al. conducted ex periments to elucidate this phenomenon. Since then the theory of optical solitons as well as their experimental investigation has progressed rapidly. The effects of inhomogeneities of the medium and energy pumping on optical solitons, the interaction between optical solitons and their generation in fibres, etc. have all been investigated and reported. Logical devices using optical solitons have been developed; new types of optical solitons in media with Kerr-type nonlinearity and in resonant media have been described.

Optical Solitons

The theoretically determined slope efficiency and threshold pump power for continuous wave (CW) operation of a Tm-doped silica fiber laser are presented. The associated rate equations are solved using standard techniques and, in conjunction with the published and our measured spectroscopic parameters as input, the model was used to examine the fiber laser output for a variety of fiber and pump configurations. After good agreement was achieved between the model calculations and the published experimental measurements, the model was used to examine the relative performance of the fiber laser when the pump wavelength was varied over the /sup 3/F/sub 4/, /sup 3/H/sub 5/, and /sup 3/H/sub 4/ absorption bands of Tm/sup 3+/. The calculated maximum slope efficiencies were determined to be /spl sim/40, /spl sim/57, and /spl sim/84%, respectively, for each of the /sup 3/F/sub 4/, /sup 3/H/sub 5/, and /sup 3/H/sub 4/ absorption band pump schemes and the threshold pump power over the range of pump schemes was determined to vary by only 28%. The model was further used to analyze the fiber laser output when the fiber length, Tm/sup 3+/ concentration and /sup 3/H/sub 4/ energy level lifetime were varied and the consequences on the operation of the fiber laser with these variations are discussed.

Theoretical modeling of Tm-doped silica fiber lasers

A selective classified bibliography of symbolic computation in some areas of chemistry is provided together with some examples of computer algebra algorithms and techniques to facilitate future joint work of chemists and computer scientists. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Symbolic calculation in chemistry: Selected examples

Experiments with erbium-doped fiber lasers demonstrate cw, sinusoidal, and self-pulsing operation. The obtained regimes depend on three control parameters: ion-pair concentration, photon lifetime, and pumping rate. We present a theoretical model which describes the active medium as a mixture of isolated ions and ion pairs. Starting with the adapted laser rate equations we show that the description of the dynamical behavior of this system can be reduced to only four first-order coupled equations. A linear stability analysis demonstrates the existence of self-pulsing for a finite range of pumping rates. At both ends of this range Hopf bifurcations occur: one located near the first laser threshold and the other at a higher pumping ratio, whose position is closely related to the pair concentration

Effects of ion pairs on the dynamics of erbium-doped fiber lasers.

We demonstrate experimentally the influence of ion-pair concentration on the dynamical behaviour of erbium-doped fibre lasers. At low pair densities, the laser has a CW output, while at higher densities it exhibits a self-pulsing behaviour. For intermediate pair concentrations, the output intensity evolves continuously from an infinite train of pulses to a CW steady state as the pumping ratio is increased.

Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers

We present experimental evidence of antiphase dynamics in self-pulsing erbium-doped fiber lasers operating simultaneously at 1.536- and 1.55-microm wavelengths. Autonomous chaos is also observed for several ranges of pumping rates. The fractal dimension of the chaotic attractor, calculated from experimental data by use of the Procaccia method, is found to depend on the pumping ratio but always remains smaller than 4.1, regardless of the chaotic regime considered.

Antiphase dynamics and chaos in self-pulsing erbium-doped fiber lasers.

The output intensity of an erbium-doped fibre laser was studied. Experiments were performed with three pumping wavelengths: 514.5 nm, 810 nm and 980 nm. The laser output intensity exhibits three different dynamical behaviours: steady-state, sinusoidal variation or self-pulsing. In particular, in a bad (high-loss) cavity configuration, when the pumping ratio is increased above the lasing threshold the output intensity changes continuously from a steady-state to an infinite train of pulses. We also show that, depending on the cavity configuration, the transient oscillations display different forms.

Self-pulsing in Er3+-doped fibre laser

We present experimental evidence of quasiperiodic route to chaos in erbium-doped fiber laser operating simultaneously at 1.550 /spl mu/m and 1.536 /spl mu/m. Starting from a CW state for high pumping rates the system becomes T-periodic, 2T-periodic, 3T-periodic and chaotic for decreasing pumping ratios. The low-frequency spectra shows two fundamental frequencies. The nT-periodic regimes correspond to a frequency locking of the low frequency on a subharmonic of the high frequency. An adapted model based on the rate equations is numerically investigated and leads to a good qualitative agreement with the experimental data. >

Pierre-Luc François

Papers

Effects of ion pairs on the dynamics of erbium-doped fiber lasers.

Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers

Antiphase dynamics and chaos in self-pulsing erbium-doped fiber lasers.

Self-pulsing in Er3+-doped fibre laser

Quasi-periodic route to chaos in erbium-doped fiber laser