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Showing papers on "Coupled mode theory published in 2007"


Journal ArticleDOI
TL;DR: Starting from Lagrangian principles, a formalism suitable for describing coupled optical parity-time symmetric systems is developed.
Abstract: Starting from Lagrangian principles we develop a formalism suitable for describing coupled optical parity-time symmetric systems.

1,184 citations


Journal ArticleDOI
TL;DR: While substrate leakage loss has warranted the necessity of substrate undercut structures in the past, it is shown here that the substrate has a very useful role to play for both passive chip-scale device integration as well as active electronic device integration.
Abstract: We report the fabrication and experimental characterization of an ultra-high Q microdisk resonator in a silicon-on-insulator (SOI) platform. We examine the role of the substrate in the performance of such microdisk resonators. While substrate leakage loss has warranted the necessity of substrate undercut structures in the past, we show here that the substrate has a very useful role to play for both passive chip-scale device integration as well as active electronic device integration. Two device architectures for the disk-on-substrate are studied in order to assess the possibility of such an integration of high Q resonators and active components. Using an optimized process for fabrication of such a resonator device, we experimentally demonstrate a Q~3×106, corresponding to a propagation loss ~0.16 dB/cm. This, to our knowledge, is the maximum Q observed for silicon microdisk cavities of this size for disk-on-substrate structures. Critical coupling for a resonance mode with an unloaded Q~0.7×106 is observed. We also report a detailed comparison of the obtained experimental resonance spectrum with the theoretical and simulation analysis. The issue of waveguide-cavity coupling is investigated in detail and the conditions necessary for the existence or lack of critical coupling is elaborated.

240 citations


Journal ArticleDOI
TL;DR: In this article, a coupled-mode-theory treatment of free-space scattering of waves from resonant objects is presented, which can be used for almost any linear wave system, as long as the resonant scatterer has either three-dimensional (3D) spherical or 2D cylindrical symmetry, or else is sufficiently smaller than the incident wave.
Abstract: We present a universal coupled-mode-theory treatment of free-space scattering of waves from resonant objects. The range of applicability of the presented approach is fairly broad: it can be used for almost any linear wave system, as long as the resonant scatterer has either three-dimensional (3D) spherical or 2D cylindrical symmetry, or else is sufficiently smaller than the resonant wavelength of the incident wave. The presented framework, while being intuitive and analytically simple, can nevertheless provide quantitatively very accurate modeling of scattering cross sections, absorption cross sections, and many other quantities of interest. We illustrate this approach by showing how it applies to the particular examples of scattering of light from spherically symmetric resonant objects and atoms, and scattering of neutrons off nuclei.

157 citations


Journal ArticleDOI
TL;DR: The coupling properties of multi-core fibers are analyzed using the multipole method and coupled mode theory in order to gain insights into the performance of image fibers that are commonly used in flexible endoscopes.
Abstract: The coupling properties of multi-core fibers are analyzed using the multipole method and coupled mode theory in order to gain insights into the performance of image fibers that are commonly used in flexible endoscopes. It is explained that coherent fiber bundles with high core density are able to transport images because nonuniformity in the pixel size reduces the inter-core coupling that causes crosstalk. The wavelength, average core size and separation, and degree of core size variation determine the strength of coupling between adjacent cores, such that fibers with a smaller core size and separation at longer wavelengths require more nonuniformity in order for reliable image transmission. Guidelines are given for assessing the performance of image fibers in a particular system.

103 citations


Journal ArticleDOI
TL;DR: The studies illustrate the conditions for continuous-wave and pulsed highly-efficient Raman frequency conversion to be practically realized in monolithic silicon high-Q/V(m) photonic band gap defect cavities.
Abstract: We examine the dynamics of stimulated Raman scattering in designed high-Q/Vm silicon photonic band gap nanocavities through the coupled-mode theory framework towards optically-pumped silicon lasing. The interplay of other χ(3) effects such as two-photon absorption and optical Kerr, related free-carrier dynamics, thermal effects, as well as linear losses such as cavity radiation and linear material absorption are included and investigated numerically. Our results clarify the relative contributions and evolution of the mechanisms, and demonstrate the lasing and shutdown thresholds. Our studies illustrate the conditions for continuous-wave and pulsed highly-efficient Raman frequency conversion for practical realization in monolithic silicon high-Q/Vm photonic band gap defect cavities.

86 citations


Journal ArticleDOI
TL;DR: This work demonstrates highly efficient evanescent coupling via a silica loop-nanowire, to ultra-small quantum-dot photonic-crystal cavities, that enables the tuning of both the Q-factor and the wavelength of the cavity mode independently.
Abstract: We demonstrate highly efficient evanescent coupling via a silica loop-nanowire, to ultra-small (0.5 (λ/n)3), InAs/InP quantum dot photonic crystal cavities, specifically designed for single photon source applications. This coupling technique enables the tuning of both the Q-factor and the wavelength of the cavity mode independently, which is highly relevant for single photon source applications. First, this allows for the optimization of the extraction efficiency while maintaining a high Purcell factor. Second, the cavity mode can be matched with a spectrally misaligned quantum dot without changing the structure or degrading the Q-factor: a 3 nm resonance shift is reported.

75 citations


Journal ArticleDOI
TL;DR: In this article, a generalized coupled-mode approach of metamaterial coupled-line couplers is presented, which is completely rigorous and applicable to any type of coupler.
Abstract: A generalized coupled-mode approach of metamaterial coupled-line couplers is presented. This approach is an extension of the traditional coupled-mode theory (CMT) to the cases of arbitrary types of conventional or metamaterial couplers with lines represented by the most general composite right/left-handed (CRLH) transmission line models. The proposed approach is completely rigorous and applicable to any type of coupler, symmetric or asymmetric, conventional or metamaterial. The CRLH generalized CMT is thoroughly derived and closed-form results for both the complex propagation constants and scattering parameters are provided. Simplified formulas based on a quasi-TEM approximation (exact in the perfectly TEM limit) are derived for contra-directional couplers, which are the most common types in microwaves. The phenomenology of both symmetric CRLH-CRLH and asymmetric conventional CRLH metamaterial coupled-line couplers is completely explained from the proposed approach. The theoretical predictions and phenomenological explanations are validated by experimental demonstration, accompanied by ideal circuit simulation, for the case of a symmetric conventional coupler, a symmetric CRLH coupler, and an asymmetric conventional CRLH coupler

68 citations


Journal ArticleDOI
TL;DR: The first experimental demonstration of electrically controlled Solc-type optical wavelength filters and TE-TM mode converters based on Ti-diffused periodically poled lithium niobate (Ti:PPLN) waveguides is reported.
Abstract: We report the first experimental demonstration of electrically controlled Solc-type optical wavelength filters and TE-TM mode converters based on Ti-diffused periodically poled lithium niobate (Ti:PPLN) waveguides. A maximum mode conversion efficiency or a peak spectral transmittance of ~99% in the telecom C-L bands was obtained from a 9-mm long, 21.5-21.8-μm multiple-grating Ti:PPLN waveguide device with a switching voltage of as low as 22 V or 0.99 V×d(μm)/L(cm), where d is the electrode separation and L is the electrode length. The spectral range of this device can be tuned by temperature at a rate of ~0.758 nm/°C.

55 citations


Journal ArticleDOI
TL;DR: The results show that the can effectively trap and delay light by using ultra-small cavities, which can potentially increase the packing density of optical buffers and bit-shifters if applied to coupled-cavity waveguides.
Abstract: We systematically studied the spectral and temporal characteristics of wavelength-sized ultrahigh-Q photonic crystal nanocavities based on width-modulated line defects. By employing accurate measurements, we confirmed that the cavity exhibits an ultra-sharp resonance width (1.23 pm), an ultrahigh-Q (1.28×106), and an ultra-long photon lifetime (1.12 ns). We discussed the correlation between the spectral and temporal measurements for various cavities, and obtained extremely good agreement. In addition, we demonstrated photon trapping for the side-coupling configuration by employing ring-down measurement, which sheds light on another interesting aspect of this phenomenon. Finally, we performed pulse propagation experiments for samples with different waveguide-cavity coupling configurations, and achieved a smallest group velocity of about 4.6 km/s for a novel configuration. These results show that we can effectively trap and delay light by using ultra-small cavities, which can potentially increase the packing density of optical buffers and bit-shifters if applied to coupled-cavity waveguides.

52 citations


Journal ArticleDOI
TL;DR: A third-order Chebyshev bandpass filter based on compound phase-shifted PC waveguide gratings suitable for dense wavelength-division-multiplexed (DWDM) optical communication systems with a channel spacing of 100-GHz is proposed.
Abstract: In this paper, a bandpass transmission filter realized in phase-shifted waveguide gratings based on photonic crystals (PCs) is proposed. Phase-shift regions each composed of one period of photonic crystal (PC) waveguide are incorporated into PC waveguide gratings. The magnitudes of the phase-shifts are modified by involving small changes in the size of the border rods in the phase-shift regions. Using standard coupled-mode theory and finite-difference time-domain (FDTD) method, we show that by properly choosing the magnitudes of phase-shifts and the lengths of waveguide gratings, a flat-top and sharp roll-off response with a narrow bandwidth is theoretically and numerically achieved by the designed filter. A further analysis shows that the center frequency of the transmission band can be changed by altering the magnitude of the phase-shift and the response performance exhibits relaxed sensitivity to the phase-shift variation. As a specific application, we theoretically demonstrate a third-order Chebyshev bandpass filter based on compound phase-shifted PC waveguide gratings. The filter performance is suitable for dense wavelength-division-multiplexed (DWDM) optical communication systems with a channel spacing of 100-GHz.

51 citations


Journal ArticleDOI
TL;DR: In this article, a planar surface plasmon-polariton (SPP) refractive index sensor with a long period grating (LPG) is presented and comprehensively investigated.
Abstract: A theoretical model of a new integrated planar surface plasmon-polariton (SPP) refractive index sensor with a long period grating (LPG) is presented and comprehensively investigated. The main principle of operation of this device is based on high-efficiency energy transfer between a p-polarized guided mode propagating in a waveguide layer of the structure and copropagating SPP supported by a metal layer separated from the waveguide layer by a buffer. The high-efficiency energy transfer is realized by means of a properly designed LPG imprinted in the waveguide and buffer layers. This device is compact and free from any moving parts and can be easily integrated into any planar scheme. Our simulations are based on the coupled-mode theory and done at the well-developed and commercialized telecom wavelengths in the 1500 nm window.

Journal ArticleDOI
TL;DR: In this paper, a theoretical model of a planar surface plasmon-polariton (SPP) refractive index sensor is presented and comprehensively investigated based on a Bragg grating imprinted in the waveguide layer.

Journal ArticleDOI
TL;DR: In this article, a new representation of the coupling coefficient of resonators using coupled mode theory was obtained by the authors using an overlap integral of the electric field and the magnetic field.
Abstract: A new representation of the coupling coefficient of resonators has been obtained by the authors using the coupled mode theory. In this expression, the coupling coefficient is given by an overlap integral of the electric field and the magnetic field. This expression is extremely useful for explanation of the physical meaning of coupling. In the present paper, various microstrip resonators are discussed and their coupling mechanisms are explained by the above theory resulting in a clear interpretation that includes phenomena hitherto not adequately explained. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 90(9): 11– 18, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20342

Journal ArticleDOI
TL;DR: In this article, a coupled mode space approach within the nonequilibrium Green's function formalism is presented, which allows performing simulations of realistic carbon nanotube field effect transistors (CNT-FETs) with no spatial symmetry.
Abstract: A coupled mode space approach within the nonequilibrium Green's function formalism is presented, which allows performing simulations of realistic carbon nanotube field-effect transistors (CNT-FETs) with no spatial symmetry. Computing time is significantly reduced with respect to the real space approach, since only few modes are needed in order to obtain accurate results. The advantage of the method increases with increasing nanotube diameter, and is a factor of 20 in computing time for a (25,0) nanotube. As a consequence, computationally demanding simulations like those required by a statistical investigation, or by a device performance study based on the exploration of the design space, become more affordable. As a further test of the method, we have applied the coupled mode space approach to double-gate CNT-FETs devices and devices with discrete distribution of doping atoms. In the latter case, nonballistic transport due to elastic scattering with ionized impurities in doped source and drain extensions occurs. We show that even in the case of very rough potential, the coupled mode space approach is accurate with very few modes, enabling atomistic simulations of statistical properties with reduced computational resources.

Journal ArticleDOI
TL;DR: In this paper, an extended transmission line theory for C/D-CRLH metamaterials is developed and the fundamental C-cRLH properties are described comparatively in terms of dispersion/attenuation diagrams and Bloch/characteristic impedances with subsequent transmission characteristics.
Abstract: Broadband conventional- and dual-composite right/left-handed (C/D-CRLH) transmission line metamaterials are presented. The extended transmission line theory for these structures is developed and the fundamental C-CRLH and D-CRLH properties are described comparatively in terms of dispersion/attenuation diagrams and Bloch/characteristic impedances with subsequent transmission characteristics. A D-CRLHstructure, implemented in microstrip technology, is demonstrated experimentally for the first time and shown to have potential for unique applications. As an illustration of such applications, a novel double-band coupled-line coupler constituted of one C-CRLH and one D-CRLH transmission line is demonstrated and explained by generalized coupled-mode theory.

Journal ArticleDOI
TL;DR: In this paper, a theoretical model of etched fiber Bragg grating (FBG) backward cladding-mode resonances for ambient refractive index sensing is presented, based on the classical coupling-mode theory while considering interactions among multiple modes and developed on a three-layer step-index fiber geometry.
Abstract: The theoretical model of etched fiber Bragg grating (FBG) backward cladding-mode resonances for ambient refractive index sensing is presented. The dependent behaviors of the mode resonances have been analyzed in the etching process and the ambient refractive index changed. The analysis is based on the classical coupling-mode theory while considering interactions among multiple modes and developed on a three-layer step-index fiber geometry. Experimental data match the theoretical model wonderfully. This model not only describes the relationship between the FBG backward cladding-mode resonances and the ambient index but also is valuable for the design of a flexible highly sensitive ambient index sensor.

Journal ArticleDOI
TL;DR: In this article, the wavelength dependence of differential group delay (DGD) and polarization dependent loss (PDL) for Bragg gratings written in birefringent fibers was studied.

Journal ArticleDOI
TL;DR: A light-stopping process that uses dynamic loss tuning in coupled-resonator delay lines and demonstrates that increasing the loss of selected resonators traps light in a zero group velocity mode concentrated in the low-loss portions of the delay line.
Abstract: We introduce a light-stopping process that uses dynamic loss tuning in coupled-resonator delay lines. We demonstrate via numerical simulations that increasing the loss of selected resonators traps light in a zero group velocity mode concentrated in the low-loss portions of the delay line. The large dynamic range achievable for loss modulation should increase the light-stopping bandwidth relative to previous approaches based on refractive index tuning.

Journal ArticleDOI
TL;DR: Based on two-dimensional photonic crystals with a triangular lattice, a channel drop filter with a wavelength-selective reflection microcavity is designed that shows complete power transfer between the bus and drop waveguides via the system.
Abstract: Based on two-dimensional photonic crystals with a triangular lattice, a channel drop filter with a wavelength-selective reflection microcavity is designed. In the structure, two microcavities are used. One is used for a resonant tunneling-based channel drop operation. The other is used to realize wavelength-selective reflection feedback in the bus waveguide. The phase term, which is derived by means of coupled-mode theory to achieve close to 100% drop efficiency, is satisfied by modifying the sizes of the border air holes next to the bus waveguide section between the two cavities. Using the finite-difference time-domain method, the simulation results show complete power transfer between the bus and drop waveguides via the system.

Journal ArticleDOI
TL;DR: In this paper, the authors performed a simulation of fiber Bragg grating sensor with different grating lengths and showed that the grating length represents as one of the critical parameters in contributing to a high performance fiber bragg sensor.
Abstract: In this paper we perform a simulation of fiber Bragg grating sensor with different grating lengths. It is shown that the grating length represents as one of the critical parameters in contributing to a high performance fiber Bragg grating sensor. The simulated fiber gratings with different lengths were analyzed and designed by calculating reflection and transmission spectra, and the bandwidth. Such simulations are based on solving coupled mode equations that describe the interaction of guided modes. The coupled mode equations are solved by the Transfer Matrix Method (a fundamental matrix method).

Journal ArticleDOI
TL;DR: In this paper, the continuous wave (CW) nonlinear transmission characteristics of chalcogenide-fiber Bragg gratings (c-FBGs) were derived analytically to govern nonlinear wave propagation by counting until seventh-order nonlinearity.
Abstract: We study the continuous wave (CW) nonlinear transmission characteristics of chalcogenide-fiber Bragg gratings (c-FBGs). The set of Cubic quintic septic nonlinear coupled mode equations (CQSNLCMEs) is derived analytically to govern nonlinear wave propagation in c-FBGs by counting until seventh-order nonlinearity in chalcogenide glass. Double-optical bistability is observed in the CW nonlinear transmission characteristics of π phase-shifted c-FBG. Based on unstable state principle in the hysteresis, all-optical transistor operation is shown as a prominent application of optical bistability in such device.

Journal ArticleDOI
TL;DR: The spectral characteristics of non-uniform symmetrically ring shaped coatings deposited on long-period fiber gratings (LPFGs) have been theoretically and experimentally investigated and provides a valid technological platform for the development of advanced photonic devices for sensing and telecommunication applications.
Abstract: In this work, the spectral characteristics of non-uniform symmetrically ring shaped coatings deposited on long-period fiber gratings (LPFGs) have been theoretically and experimentally investigated. To optimize the structure performances, the device was designed with a simulation tool based on vectorial analysis of modes in a multilayer cylindrical waveguide and coupled mode theory. Electrostatic self-assembling technique was selected to deposit with fine control uniform azimuthally symmetric coatings on the cladding of the LPFG. UV laser micromachining operating at 193nm was used to selectively remove the coating with high spatial resolution and with azimuthal symmetry. By locally and selectively removing portions of the overlay surrounding the LPFG from the middle of the grating, strong modifications of its spectral characteristics were observed. Phase-shift effects and multiple interference fringes have been observed for all the attenuation bands, strongly depending on the length of the uncoated region and the overlay features (thickness and optical properties). This provides a valid technological platform for the development of advanced photonic devices for sensing and telecommunication applications.

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed the transmission of light through coupled-resonator optical waveguides in the form of evanescently coupled Fabry-Perot resonator arrays and developed a transfer matrix method to calculate the amplitude and phase responses of the arrays.
Abstract: We analyze the transmission of light through coupled-resonator optical waveguides in the form of evanescently coupled Fabry-Perot resonator arrays. We develop a transfer matrix method to calculate the amplitude and phase responses of the arrays. We also discuss the inclusion of optical gain in the system to compensate for losses in these structures. Owing to the compact length along the propagation direction in evanescently coupled arrays, large slowing factors of the order of 10^2-10^3 can be achieved even with a weak index contrast of ∼0.1%. The large slowing factor, coupled with weak index contrast, makes this structure a promising candidate for artificial slow light system.

Journal ArticleDOI
TL;DR: Four new types of dual microring resonators coupled via 3x3 couplers are proposed and a model for these four types is developed and analytical expressions for characterizing their transmissions are derived.
Abstract: New types of dual microring resonators coupled via 3×3 couplers are proposed. By employing the transfer matrix method, a model for these four types is developed and analytical expressions for characterizing their transmissions are derived. The first two types show a coupled-resonator-induced-transparency-like transmission spectrum at the through port. The third type holds the same transmission spectrum, while the last type simultaneously realizes a first-order and a second-order filters at two drop ports. The effects of coupling coefficients on their transmission spectra are investigated in more detail. Moreover, the effects of loss are also discussed. These proposed types can be found applications in fields such as sensors and filters.

Proceedings ArticleDOI
06 May 2007
TL;DR: In this article, coupled-optical-microcavity geometries incorporating non-adjacent cavity coupling and "negative" ("inductive") coupling are proposed to enable new compact, quasi-elliptic microring filters.
Abstract: Coupled-optical-microcavity geometries incorporating non-adjacent-cavity coupling and "negative" ("inductive") coupling are proposed. These enable new compact, quasi-elliptic microring filters, and can circumvent Kramers-Kronig causality constraints to support square- amplitude and linear-phase response over >80% of the passband.

Journal ArticleDOI
TL;DR: In this article, an exact and compact analytical formalism has been developed to calculate the Q factor for circular Bragg resonators, where electromagnetic fields, energy, and power flow have been expressed analytically relying on the transfer matrix coefficients.
Abstract: An exact and compact analytical formalism has been developed to calculate the Q factor for circular Bragg resonators. The electromagnetic fields, energy, and power flow have been expressed analytically relying on the transfer matrix coefficients. The Q factor has been derived for both TM and TE polarizations. The proposed formalism is then compared with two numerical methods.

Journal ArticleDOI
TL;DR: In this paper, a modal theory of sub-millimeter-wave and far-infrared power detectors is presented. The theory is based on the contraction of the coherence tensor of the light with another coherent tensor that incorporates all of the physics of the detector and applies equally to quasi-monochromatic and pulsed systems.
Abstract: We present a comprehensive, spatiotemporal, modal theory of submillimeter-wave and far-infrared power detectors. The theory is based on the contraction of the coherence tensor of the light with another coherence tensor that incorporates all of the physics of the detector. The theory is extremely general and applies to detectors of any bandwidth, with light in any state of polarization and spatiotemporal coherence. The theory applies equally to quasi-monochromatic and pulsed systems. We show that the tensor associated with the detector is a measureable quantity and outline a procedure for its experimental determination. We derive expressions for the statistical properties of a detector's output, including the correlations between the outputs of different detectors, say, in an array or interferometer. The theory provides a clear conceptual understanding of how any general detector couples to the modes of an optical system and thereby provides a powerful and flexible way of modeling the behavior of detectors and instruments.

Journal ArticleDOI
TL;DR: In this article, a comprehensive coupled-mode theory, including resonant vertical emission effects, for the analysis of nonperiodic circular Bragg laser was derived, yielding the threshold gain level and the resonance frequency.
Abstract: We derive a comprehensive coupled-mode theory, including resonant vertical emission effects, for the analysis of nonperiodic circular Bragg lasers. We derive the governing characteristic equation for such lasers, yielding the threshold gain level and the resonance frequency. By reducing the threshold gain and maximizing the ratio of "useful signal" to the power leakage, we find optimum conditions for vertically emitting circular Bragg microdisk lasers which indicate that low-threshold operation is possible

Journal ArticleDOI
TL;DR: In this paper, the dispersion relations of the modes traveling along these devices explain the numerically observed formation of single and multiple copies of the input beam, which can be employed as filters and demultiplexers.
Abstract: Light propagation in multimode photonic crystal (PC) waveguides and in arrays of single-mode PC waveguides is analyzed. The dispersion relations of the modes traveling along these devices explain the numerically observed formation of single and multiple copies of the input beam. As the analogous devices constructed in a standard planar geometry, the proposed PC devices can be employed as filters and demultiplexers. The use of PC structures, where the light is truly confined by the stopband, adds the valuable benefit of a dramatic reduction of the overall geometrical dimensions

Journal ArticleDOI
TL;DR: In this paper, a method for describing and quantifying the vibratory behaviour of interacting structural/fluid systems based upon reference to the relative energy associated with each of the sub-systems is described.