Improved coupled-mode equations for dielectric guides
TL;DR: In this paper, an improved coupled-mode equation for parallel dielectric waveguides was derived by using a newly found relationship that connects the propagation constants of the individual guides to the coupling coefficients via an overlap integral that measures the guides' proximity.
Abstract: An improved version of coupled-mode equations for parallel dielectric waveguides has been derived by using a newly found relationship that connects the propagation constants of the individual guides to the coupling coefficients via an overlap integral that measures the guides' proximity. The four parameters of these new coupled equations are simple functions of essentially one single quantity: the asynchronism of the individual guides properly normalized.
Citations
More filters
TL;DR: In this article, a method of coupling of modes in time was proposed to simplify both the analysis and filter synthesis aspects of these devices, and the response of filters comprised of an arbitrarily large dumber of resonators may be written down by inspection, as a continued fraction.
Abstract: Microring resonators side coupled to signal waveguides provide compact, narrow band, and large free spectral range optical channel dropping filters. Higher order filters with improved passband characteristics and larger out-of-band signal rejection are realized through the coupling of multiple rings. The analysis of these devices is approached by the novel method of coupling of modes in time. The response of filters comprised of an arbitrarily large dumber of resonators may be written down by inspection, as a continued fraction. This approach simplifies both the analysis and filter synthesis aspects of these devices.
1,733 citations
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TL;DR: In this paper, the authors give a brief historic perspective of the coupled mode theory and the development and applications of the theory in microwaves in early years and in optoelectronics and fiber optics in recent years.
Abstract: 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. >
853 citations
TL;DR: In this paper, a review of the recent development of coupled-mode theory for optical waveguides is given, with emphasis on the analysis of coupled optical waveguide, and three typical coupler configurations (uniform, grating-assisted, and tapered) are examined in detail.
Abstract: 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.
691 citations
TL;DR: In this paper, a compact optical channel dropping filter incorporating side-coupled ring resonators as small as 3 /spl mu/m in radius is realized in silicon technology.
Abstract: Compact optical channel dropping filters incorporating side-coupled ring resonators as small as 3 /spl mu/m in radius are realized in silicon technology. Quality factors up to 250, and a free-spectral range (FSR) as large as 24 nm are measured. Such structures can be used as fundamental building blocks in more sophisticated optical signal processing devices.
678 citations
TL;DR: In this article, the authors investigate the properties of high-Q, wide free-spectral-range semiconductor microcavity ring and disk resonators coupled to submicron-width waveguides.
Abstract: We investigate the properties of high-Q, wide free-spectral-range semiconductor microcavity ring and disk resonators coupled to submicron-width waveguides. Key optical design parameters are characterized using finite-difference time-domain (FDTD) solutions of the full-wave Maxwell's equations. We report coupling efficiencies and resonant frequencies that include the effects of waveguide dispersion and bending and scattering losses. For diameters of 5 /spl mu/m, the microcavity resonators can have Q's in the several thousands and a free spectral range of 6 THz (50 nm) in the 1.55 /spl mu/m, wavelength range. Studies of the transmittance characteristics illustrate the transition from single-mode resonances to whispering-gallery-mode resonances as the waveguide width of the microring is increased to form a solid microdisk. We present nanofabrication results and experimentally measured transmission resonances of AlGaAs/GaAs microcavity resonators designed in part with this method.
271 citations
References
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TL;DR: Simple formulas and functions for the fiber parameters are presented as a help for practical design work that considers the propagation constant, mode delay, the cladding field depth, and the power distribution in the fiber cross section.
Abstract: Thin glass fibers imbedded into a glass cladding of slightly lower refractive index represent a promising medium for optical communication. This article presents simple formulas and functions for the fiber parameters as a help for practical design work. It considers the propagation constant, mode delay, the cladding field depth, and the power distribution in the fiber cross section. Plots vs frequency of these parameters are given for 70 modes
1,506 citations
TL;DR: In this paper, a coupled mode formulation for parallel dielectric waveguides is described, and the results apply to any guided modes (TE, TM, or hybrid) in waveguide of arbitrary cross-section, dissimilar index, and non-identical shape.
Abstract: 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.
435 citations
TL;DR: In this paper, the current status of guided-wave optical communication devices is reviewed and the operation and presently demonstrated performance characteristics of waveguides switches, modulators, filters and polarization transforming devices are discussed.
Abstract: We review the current status of guided-wave optical communication devices. The operation and presently demonstrated performance characteristics of waveguides switches, modulators, filters, and polarization transforming devices are discussed. Emphasis is given to recent developments with very high speed modulators and polarization insensitive devices.
294 citations