Erbium-doped fiber amplifiers are modeled using the propagation and rate equations of a homogeneous two-level laser medium. Numerical methods are used to analyze the effects of optical modes and erbium confinement on amplifier performance, and to calculate both the gain and amplified spontaneous emission (ASE) spectra. Fibers with confined erbium doping are completely characterized from easily measured parameters: the ratio of the linear ion density to fluorescence lifetime, and the absorption of gain spectra. Analytical techniques then allow accurate evaluation of gain, saturation, and noise in low-gain amplifiers (G >

Modeling erbium-doped fiber amplifiers

We find that the parametric four-photon gain for light pulses decreases for fibers longer than a characteristic length. This length is related to the common experimental observation that stimulated parametric emission is usually prominent only in short fibers while in long fibers stimulated Raman scattering dominates. Despite the fact that the actual process involves an intensity dependent bandwidth and broadening of the pump linewidth from self-phase modulation, it is possible to develop a simple expression for the characteristic length which requires only the initial pump linewidth and the low-power parametric bandwidth. This bandwidth can often be estimated from the pump wavelength and the measured frequency shift between the pump and the generated waves. Expressions for gain and amplification are derived from coupled wave equations and in the Appendixes it is shown that these are of the same form as the planewave equations, but modified by coupling coefficients called overlap integrals.

Parametric amplification and frequency conversion in optical fibers

The site isolation of lanthanide cations (Er3+, Tb3+, and Eu3+) has been achieved through the self-assembly of three convergent polyether dendrons, each with a carboxylate anion focal point, around the central trivalent cation. Evidence for the self-assembly of the dendritic complexes can be obtained by a variety of spectroscopic and other analytical means both in solution and in the solid state. The luminescence properties of these new dendrimers measured both in solution and in the bulk show a dependence of luminescence activity on the size of the dendritic shell. The observed enhancement in luminescence properties can be attributed both to a large antenna effect, involving the nonconjugated phenyl benzyl ether dendrimer framework, and to a shell effect that results from the effective site isolation of each lanthanide cation within a dendritic sphere, preventing their mutual interaction and decreasing their rate of self-quenching. The site isolation afforded by self-assembly and the antenna effect provi...

Self-Assembled Lanthanide-Cored Dendrimer Complexes: Enhancement of the Luminescence Properties of Lanthanide Ions through Site-Isolation and Antenna Effects

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

This book, published in 2007, provides comprehensive coverage of the theory and practice of OPAs and related devices, including fiber optical parametric oscillators (OPOs). After introducing the field, the theory and techniques behind all types of fiber OPAs are covered starting from first principles - topics include the scalar and vector OPA theory; the nonlinear Schrodinger equation; OPO theory; and quantum noise figure of fiber OPAs. Challenges of making fiber OPAs practical for a number of applications are discussed, and a survey of the state-of-the-art in feasibility demonstrations and performance evaluations is provided. The capabilities and limitations of OPAs; the potential applications for OPAs and OPOs, and prospects for future developments in the field are discussed. Theoretical tools developed in this text can also be applied to other areas of nonlinear optics. This is a valuable resource for researchers, advanced practitioners, and graduate students in optoelectronics.

Fiber Optical Parametric Amplifiers, Oscillators and Related Devices: The nonlinear Schrödinger equation

When pulse pairs copropagate in a fiber, each pulse chirps the other through cross-phase modulation (XPM). In particular, XPM causes spectral broadening of signal pulses during Raman or parametric optical pulse amplification. We have studied XPM experimentally in the fiber Raman amplification soliton laser. We show that experimentally observed spectra can be explained by a simple model that concentrates on the phase change as a function of pulse walk-off.

Cross-phase modulation in optical fibers

We describe phase-matched stimulated four-photon mixing in single-mode fibers in the minimum-chromatic-dispersion region. Phase matching is achieved by using the refractive-index slope change and the guiding properties of the fundamental mode. Experimental results on large-shift (1600-cm−1) single-idler generation in single-mode fibers with 1.319-μm Nd:YAG laser pumping are presented.

Phase matching in the minimum-chromatic-dispersion region of single-mode fibers for stimulated four-photon mixing.

Continued improvements in the performance of a multi-kilometer, low-erbium-concentration fiber amplifier made by the modified chemical vapor deposition (MCVD) seed fiber method are discussed. Transparency for a -20-dBm signal at 1.55 mu m and fiber length of 11.8 km was achieved with 20 mW of 1.48- mu m copropagating pump power. The wavelength dependence of the gain for this signal level is reported, and the distribution in small signal gain along a 22-km length using an optical domain reflectometer (OTDR) was measured. Simulations are presented to show the effect of erbium concentration, input signal level, and pump power required for transparency of a 50-km span. >

Performance of a distributed erbium-doped dispersion-shifted fiber amplifier

We show that the chirp from cross-phase modulation (XPM) dominates the operation of fiber Raman lasers (FRL's). Thus a FRL in the anomalous group-velocity regime is best described as a XPM-chirped Raman amplifier followed by a linear fiber compressor. While the output of such a laser is generally a narrow pulse with a broad pedestal, we show both experimentally and by computer simulation that negligible background is achievable.

Amplifier/compressor fiber Raman lasers.

To date erbium amplifiers have been based on fiber doped with 10 to 1000 ppm erbium oxide, providing several tens of dB gain in lengths of 100 m or less.[1–4] However, communications systems which use such high gain, "lumped" amplifiers subject the signal to large excursions in amplitude, which can cause significant interchannel interference in a wavelength division multiplexed system. Of equal importance, the amplified spontaneous emission (ASE) is significantly smaller when distributed amplification is used, and a larger signal to noise is obtained when the signal is sustained at a high level throughout the system.[5] We show here that fibers can indeed be made with the controlled, very low Er doping (10–100 ppb Er averaged over the core), required for such distributed amplification. Some of our fibers allowed for just enough gain per unit length (0.2–0.3 dB/Km) to cancel fiber loss, without at the same time introducing significant impurities or other defects.

H.-T. Shang

Papers

Cross-phase modulation in optical fibers

Phase matching in the minimum-chromatic-dispersion region of single-mode fibers for stimulated four-photon mixing.

Performance of a distributed erbium-doped dispersion-shifted fiber amplifier

Amplifier/compressor fiber Raman lasers.

A Distributed Erbium Doped Fiber Amplifier