The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

The authors give a brief historic perspective of the coupled mode theory. The development and applications of the theory in microwaves in early years and in optoelectronics and fiber optics in recent years are described. They then consider lossless coupling of two modes in time. Two coupled resonance circuits, or two coupled microwave or optical resonators, are the physical examples. The start-up of a parametric oscillator is another example. Then they look at the formal derivation of coupled mode theory and consider the more general case when the modes are not energy-orthogonal and the energies are not necessarily positive. A more detailed account of the nonorthogonal coupled mode theory developed in the last five years for optical waveguides is given. >

Coupled-mode theory

We present a review of the use of diode lasers in atomic physics with an extensive list of references. We discuss the relevant characteristics of diode lasers and explain how to purchase and use them. We also review the various techniques that have been used to control and narrow the spectral outputs of diode lasers. Finally we present a number of examples illustrating the use of diode lasers in atomic physics experiments.

Using diode lasers for atomic physics

The coupled-mode theory (CMT) for optical waveguides is reviewed, with emphasis on the analysis of coupled optical waveguides. A brief account of the recent development of the CMT for coupled optical waveguides is given. Issues raised in the debates of the 1980’s on the merits and shortcomings of the conventional as well as the improved coupled-mode formulations are discussed. The conventional coupled-mode formulations are set up in a simple, intuitive way. The rigorous CMT is established on the basis of a linear superposition of the modes for individual waveguides. The cross-power terms appear logically as a result of modal nonorthogonality. The cross power is necessary for the self-consistency of the CMT for dissimilar waveguides. The nonorthogonal CMT, though more complicated, yields more-accurate results than the conventional orthogonal CMT for most practical applications. It also leads to the prediction of cross talk in directional couplers. The conventional orthogonal CMT is, however, reliably accurate for describing the power coupling between two weakly coupled, nearly identical waveguides. For dissimilar waveguides, a self-consistent orthogonal CMT can be derived by a redefinition of the coupling coefficients, and it predicts the coupling length and therefore the power exchange between the waveguides accurately if the two waveguides are far apart. Three typical coupler configurations—the uniform, the grating-assisted, and the tapered—are examined in detail. The accuracy, scope of validity, limitations, and extensions of the coupled-mode formulations are discussed in conjunction with each configuration. To verify the arguments in the discussions, comparisons with the exact analytical solutions and the rigorous numerical simulations are made.

Coupled-mode theory for optical waveguides: an overview

Nonlinear Optical Crystals: A Complete Survey

A new coupled mode formulation for parallel dielectric waveguides is described. The results apply to any guided modes (TE, TM, or hybrid) in waveguides of arbitrary cross-section, dissimilar index, and nonidentical shape. Additional index perturbations not included within the waveguides are encompassed by the theory. Propagation constants and mode patterns for the coupled modes computed according to this theory are shown to agree very well with numerical solutions for the system modes when the latter can be determined. Moreover, the new results are more accurate than those obtained from prior coupled mode formulations. It is shown that even for Iossless guides the coupling coefficients from waveguide "b" to "a" and from "a" to "b," described by k ab and k ba respectively, are not related by their complex conjugates if the guides are not identical.

Coupled mode theory of parallel waveguides

Strongly pumped fiber lasers are analyzed, based on a rate equation model. Examples include Nd/sup 3+/-doped and Yb/sup 3+/-doped fiber lasers, with distributed Bragg reflector mirrors at either end. Approximate analytical and quasi-analytical expressions are shown to be in excellent agreement with the exact numerical solution of the rate equations, and both agree well with recently published experimental data.

Strongly pumped fiber lasers

Signal amplification is analyzed in strongly pumped fiber amplifiers both for three-level and four-level transitions, including scattering loss and excited state absorption. Simple analytic expressions are derived for the signal amplification and pump attenuation, along the fiber length, when either the signal and the pump are injected at the same fiber end (forward pumping) or when they are injected at the two opposite ends (backward pumping). Numerical examples for rare-earth doped fibers show excellent agreement between the analytical solution and the exact numerical solutions of the rate-equations for practical operating conditions.

Signal amplification in strongly pumped fiber amplifiers

Modal properties of periodically segmented waveguides (PSWs) are analyzed by using the beam-propagation method and coupled-mode theory. The modal effective indices in a PSW are shown to be equal to those of a continuous waveguide with an averaged Delta n. As a result, guided modes spread out, particularly those that are not strongly guided. The radiation loss is shown to oscillate with most of the waveguide parameters. In practical terms, this loss can be made negligible even for long periods. The results can be applied to the design of waveguide devices such as two-dimensional mode tapers and frequency-selective couplers. >

Modes of periodically segmented waveguides

Backreflection of the residual pump power into the cavity, and optimization of the fiber length, may significantly improve the efficiency of a strongly pumped fiber laser. A rate equation model is introduced and studied. Examples for Yb/sup 3+/-doped fiber lasers, with DBR mirrors at either end, show that employing such a geometry results in higher efficiency with shorter optimal fiber length. Approximate analytical and quasi-analytical expressions are shown to be in excellent agreement with the exact numerical solution of the rate equations.

Amos A. Hardy

Papers

Coupled mode theory of parallel waveguides

Strongly pumped fiber lasers

Signal amplification in strongly pumped fiber amplifiers

Modes of periodically segmented waveguides

Optimization of strongly pumped fiber lasers