scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals.

18 Dec 2002-Physical Review E (American Physical Society)-Vol. 66, Iss: 6, pp 066608-066608
TL;DR: It is shown how one can thereby compute semianalytical reflection and transmission through crystal tapers of almost any length, using only a single pair of modes in the unit cells of uniform gratings, which becomes more accurate as the taper becomes more gradual, with no significant increase in the computation time or memory.
Abstract: We prove that an adiabatic theorem generally holds for slow tapers in photonic crystals and other strongly grated waveguides with arbitrary index modulation, exactly as in conventional waveguides. This provides a guaranteed pathway to efficient and broad-bandwidth couplers with, e.g., uniform waveguides. We show that adiabatic transmission can only occur, however, if the operating mode is propagating (nonevanescent) and guided at every point in the taper. Moreover, we demonstrate how straightforward taper designs in photonic crystals can violate these conditions, but that adiabaticity is restored by simple design principles involving only the independent band structures of the intermediate gratings. For these and other analyses, we develop a generalization of the standard coupled-mode theory to handle arbitrary nonuniform gratings via an instantaneous Bloch-mode basis, yielding a continuous set of differential equations for the basis coefficients. We show how one can thereby compute semianalytical reflection and transmission through crystal tapers of almost any length, using only a single pair of modes in the unit cells of uniform gratings. Unlike other numerical methods, our technique becomes more accurate as the taper becomes more gradual, with no significant increase in the computation time or memory. We also include numerical examples comparing to a well-established scattering-matrix method in two dimensions.

Content maybe subject to copyright    Report

Citations
More filters
Journal ArticleDOI
TL;DR: This work fabricate, characterize, and analyze a MM absorber with a slightly lower predicted A(omega) of 96%.
Abstract: We present the design for an absorbing metamaterial (MM) with near unity absorbance A(omega). Our structure consists of two MM resonators that couple separately to electric and magnetic fields so as to absorb all incident radiation within a single unit cell layer. We fabricate, characterize, and analyze a MM absorber with a slightly lower predicted A(omega) of 96%. Unlike conventional absorbers, our MM consists solely of metallic elements. The substrate can therefore be optimized for other parameters of interest. We experimentally demonstrate a peak A(omega) greater than 88% at 11.5 GHz.

5,550 citations

Journal ArticleDOI
TL;DR: The physical principles behind the phenomenon of slow light in photonic crystal waveguides, as well as their practical limitations, are discussed and put into context in this paper, including the nature of slow-light propagation, its bandwidth limitation, the scaling of linear and nonlinear interactions with the slowdown factor, issues such as losses, coupling into and the tuning of slow modes.
Abstract: The physical principles behind the phenomenon of slow light in photonic crystal waveguides, as well as their practical limitations, are discussed and put into context This includes the nature of slow light propagation, its bandwidth limitation, the scaling of linear and nonlinear interactions with the slowdown factor as well as issues such as losses, coupling into and the tuning of slow modes Applications in all-optical signal processing appear to be the most promising outcome of the phenomena discussed

627 citations

Journal ArticleDOI
TL;DR: In this article, a waveguide with vanishing second-and third-order dispersion is presented, which can be explained by the strong interaction of the modes with the bulk photonic crystal waveguide.
Abstract: Modes of photonic crystal (PC) line-defect waveguides can have small group velocity away from the Brillouin zone edge. This property can be explained by the strong interaction of the modes with the bulk PC. An anticrossing of “index guided” and “gap guided” modes should be taken into account. To control dispersion, the anticrossing point can be shifted by the change of the PC waveguide parameters. An example of a waveguide is presented with vanishing second- and third-order dispersion.

269 citations

Journal ArticleDOI
TL;DR: It is estimated that gratings can be designed to exhibit tunable delays in the picosecond range using current fabrication technology and it is shown that exact calculations of the figures of merit for a realistic, three-dimensional grating structure are well predicted by a simple quadratic-band model.
Abstract: We propose the use of slow-light, band-edge waveguides for compact, integrated, tunable optical time delays. We show that slow group velocities at the photonic band edge give rise to large changes in time delay for small changes in refractive index, thereby shrinking device size. Figures of merit are introduced to quantify the sensitivity, as well as the accompanying signal degradation due to dispersion. It is shown that exact calculations of the figures of merit for a realistic, three-dimensional grating structure are well predicted by a simple quadratic-band model, simplifying device design. We present adiabatic taper designs that attain <0.1% reflection in short lengths of 10 to 20 times the grating period. We show further that cascading two gratings compensates for signal dispersion and gives rise to a constant tunable time delay across bandwidths greater than 100 GHz. Given typical loss values for silicon-on-insulator waveguides, we estimate that gratings can be designed to exhibit tunable delays in the picosecond range using current fabrication technology.

242 citations

Journal ArticleDOI
TL;DR: In this article, different types of dispersion engineered photonic crystal waveguides have been developed for slow light applications, and the group index bandwidth product (GBP) and the loss per delay in terms of dB ns −1 were compared.
Abstract: We review the different types of dispersion engineered photonic crystal waveguides that have been developed for slow light applications. We introduce the group index bandwidth product (GBP) and the loss per delay in terms of dB ns −1 as two key figures of merit to describe such structures and compare the different experimental realizations based on these figures. A key outcome of the comparison is that slow light based on photonic crystals performs as well or better than slow light based on coupled ring resonators.

231 citations


Cites background from "Adiabatic theorem and continuous co..."

  • ...A second approach is to reduce the coupling loss via an adiabatic taper [34]....

    [...]

References
More filters
Book
03 Jul 1995
TL;DR: In this paper, the authors developed the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory, and investigated the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions.
Abstract: Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications. Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers.Extensively revised and expanded Features improved graphics throughout Includes new chapters on photonic-crystal fibers and combined index-and band-gap-guiding Provides an introduction to coupled-mode theory as a powerful tool for device design Covers many new topics, including omnidirectional reflection, anomalous refraction and diffraction, computational photonics, and much more.

8,188 citations