Showing papers on "Coupled mode theory published in 2004"

Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities

Abstract: We develop a general temporal coupled-mode theory for multimode optical resonators. This theory incorporates a formal description of a direct transmission pathway, and is therefore capable of describing Fano interference phenomena in multimode cavities. Using this theory, we prove a general criterion that governs the existence of nonorthogonal modes. The presence of nonorthogonal modes creates interesting transport properties which can not be obtained in normal resonator systems. We validate our theory by comparing its predictions with first-principles finite-difference time-domain simulations and obtaining excellent agreement between the two.

Optical fiber microcoil resonators.

Abstract: The optical microfiber coil resonator with self-coupling turns is suggested and investigated theoretically. This type of a microresonator has a three-dimensional geometry and complements the well-known Fabry-Perot (one-dimensional geometry, standing wave) and ring (two-dimensional geometry, traveling wave) types of microresonators. The coupled wave equations for the light propagation along the adiabatically bent coiled microfiber are derived. The particular cases of a microcoil having two and three turns are considered. The effect of microfiber radius variation on the value of Q-factor of resonances is studied.

Surface modes in air-core photonic band-gap fibers

Abstract: We present a detailed description of the role of surface modes in photonic band-gap fibers (PBGFs). A model is developed that connects the experimental observations of high losses in the middle of the transmission spectrum to the presence of surface modes supported at the core-cladding interface. Furthermore, a new PBGF design is proposed that avoids these surface modes and produces single-mode operation.

Highly efficient photonic crystal-based multichannel drop filters of three-port system with reflection feedback

Abstract: We have derived the general condition to achieve 100% drop efficiency in the resonant tunneling-based channel drop filters of a three-port system with reflection feedback. According to our theoretical modeling based on the coupled mode theory in time, the condition is that the Q-factor due to coupling to a bus port should be twice as large as the Q-factor due to coupling to a drop port and the phase retardation occurring in the round trip between a resonator and a reflector should be a multiple of 2π. The theoretical modeling also shows that the reflection feedback in the three-port channel drop filters brings about relaxed sensitivity to the design parameters, such as the ratio between those two Q-factors and the phase retardation in the reflection path. Based on the theoretical modeling, a five-channel drop filter has been designed in a two-dimensional photonic crystal, in which only a single reflector is placed at the end of the bus waveguide. The performance of the designed filter has been numerically calculated using the finite-difference time domain method. In the designed filter, drop efficiencies larger than 96% in all channels have been achieved.

Coupling of small, low-loss hexapole mode with photonic crystal slab waveguide mode

Abstract: Coupling characteristics between the single-cell hexapole mode and the triangular-lattice photonic crystal slab waveguide mode is studied by the finite-difference time-domain method The single-cell hexapole mode has a high quality factor (Q) of 33Chi106 and a small modal volume of 118(lambda/n)3 Based on the symmetry, three representative types of coupling geometries (shoulder-couple, butt-couple and side-couple structures) are selected and tested The coupling efficiency shows strong dependence on the transverse overlap of the cavity mode and the waveguide mode over the region of the waveguide The shoulder-couple structure shows best coupling characteristics among three tested structures For example, two shouldercouple waveguides and a hexapole cavity result in a high performance resonant-tunneling-filter with Q of 97Chi105 and transmittance of 048 In the side-couple structure, the coupling strength is much weaker than that of the shoulder-couple structure because of the poor spatial overlap between the mode profiles In the direct-couple structure, the energy transfer from the cavity to the waveguide is prohibited because of the symmetry mismatch and no coupling is observed

Polarization conversion in ring resonator phase shifters

Abstract: The effect of the polarization rotation induced by curved waveguides on the spectral behavior of phase shifter ring resonators is investigated both theoretically and experimentally. At resonance the polarization rotation that takes place in curved waveguides is strongly enhanced. The effect can be detrimental, or it can be exploited for new devices. The ring vectorial transfer function is derived, together with the conditions for the total conversion of TE polarization into TM polarization. These conditions are verified experimentally.

Single-atom detection using whispering-gallery modes of microdisk resonators

Abstract: We investigate the possibility of using dielectric microdisk resonators for the optical detection of single atoms trapped and cooled in magnetic microtraps near the surface of a substrate. The bound and evanescent fields of optical whispering-gallery modes are calculated and the coupling to straight waveguides is investigated using finite-difference time domain solutions of Maxwell's equations. Results are compared with semianalytical solutions based on coupled mode theory. We discuss atom detection efficiencies and the feasibility of nondestructive measurements in such a system depending on key parameters such as disk size, disk-waveguide coupling, and scattering losses.

Analytical Approaches to the Description of Optical Microresonator Devices

Abstract: Optical ring resonators are commonly discussed on the basis of a frequency‐domain model, that divides a resonator into coupler elements, ring cavity segments, and the straight port waveguides. We look at the assumptions underlying this model and at its implications, including remarks on reciprocity/symmetry arguments, the general power transfer characteristics, the resonance condition, the spectral distance and width of the resonances, the quantities that describe the resonator performance, and a few remarks about tuning. A survey of bend mode properties and a coupler description in terms of coupled mode theory fills the abstract notions of the model. As an example for devices that rely on a standing wave principle, in contrast to the traveling waves found in the microrings, we consider in less detail microresonators with square or rectangular cavity shapes. Also here a frequency domain coupled mode theory can be applied that opens up simple possibilities to characterize resonant configurations.

Coupled core-surface solitons in photonic crystal fibers.

Abstract: We predict existence and study properties of the coupled core-surface solitons in hollow-core photonic crystal fibers. These solitons exist in the spectral proximity of the avoided crossings of the propagation constants of the modes guided in the air core and at the interface between the core and photonic crystal cladding.

Femtosecond light pulse propagation through metallic nanohole arrays: The role of the dielectric substrate

Abstract: We study theoretically ultrafast light propagation through a periodic array of holes in a silver film deposited on a dielectric substrate using a three-dimensional finite-difference time-domain (FDTD) simulation. We focus on studying the effects of the coherent coupling between resonant surface plasmon polariton (SPP) excitations at the top and bottom interfaces of the metal film on the transmission dynamics. In a free standing film, the SPP excitations at both interfaces are fully in resonance and pronounced temporal oscillations in the energy flow between the bottom and top interfaces give evidence for coupling between the (±1,0) SPP modes via photon tunneling through the holes. Variation of the dielectric constant of the substrate lifts the energetic degeneracy between the two modes and thus decreases the coupling and suppresses the energy oscillations. New SPP-enhanced transmission peaks appear when higher order modes at the substrate/metal interface are brought into resonance with the (±1,0) air/metal resonance and efficient mode coupling is achieved. Both temporal transmission dynamics and near-field mode profiles are reported and their implications for tailoring the optical properties of these two-dimensional plasmonic crystals are discussed.

Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere

Abstract: Coupled mode theory is used to numerically calculate the optimal fiber radius for coupling to a fused-silica microsphere. Also calculated are whispering-gallery mode spectra that take into account some nonideal experimental conditions.

Higher order mode conversion via focused ion beam milled Bragg gratings in Silicon-on-Insulator waveguides.

Abstract: We report the first Bragg gratings fabricated by Focused Ion Beam milling in optical waveguides. We observe striking features in the optical transmission spectra of surface relief gratings in silicon-on-insulator waveguides and achieve good agreement with theoretical results obtained using a novel adaptation of the beam propagation method and coupled mode theory. We demonstrate that leaky Higher Order Modes (HOM), often present in large numbers (although normally not observed) even in nominally single mode rib waveguides, can dramatically affect the Bragg grating optical transmission spectra. We investigate the dependence of the grating spectrum on grating dimensions and etch depth, and show that our results have significant implications for designing narrow spectral width gratings in high index waveguides, either for minimizing HOM effects for conventional WDM filters, or potentially for designing devices to capitalize on very efficient HOM conversion.

Fiber-optic multiple-wavelength filter based on one-dimensional photonic bandgap structures with defects

Abstract: In this paper, a theoretical analysis is given of an optical fiber multiple-wavelength tunable filter based on a one-dimensional (1-D) photonic bandgap (PBG) structure with four defects. To understand the positioning of the modes in the bandgap, a previous analysis of structures with one and two defects is performed. By adequate parameterization, it will be possible to control the central wavelengths of the various filters of the device. Parameters responsible for this effect are the contrast of refractive indexes of high- and low-index layers, the optical thickness of the defects, and the number of layers stacked among the defects related to those stacked at the extremes. In addition to this, the finesse of the filters can be controlled by the adequate addition of layers among defects. As a result, a simple 1-D PBG structure with defects will permit designing almost any multiple-wavelength filter, with immediate application in the treatment of wavelength-division-multiplexed (WDM) signals. The possibility of the tunability of this device can be introduced if materials are included whose refractive index changes with some parameter, such as temperature, voltage, or strain. As an example, liquid crystals change their refractive index with an applied voltage, leading to a shift of the central wavelengths of the filters.

Finite-Difference Time-Domain Analysis of Wavelength-Selective Characteristics in Weighted Acoustooptic Switches for Wavelength-Division-Multiplexed Photonic Routing

Abstract: Waveguide-type acoustooptic (AO) switches can switch optical waves wavelength-selectively for wavelength-division-multiplexed (WDM) signals. The switches can be expected to be used in WDM photonic networks. In this paper, finite-difference time-domain (FDTD) analysis is presented for wavelength-selective switching with a collinear weighted AO device consisting of an optical directional coupler, input/output Y-branches and a tapered surface acoustic wave (SAW) waveguide. The FDTD simulated results are compared with the result from the coupled mode theory. It is shown that a sidelobe level as low as -20 dB in the filtering characteristics is realized by using weighted AO interaction. It is also shown that the sidelobe structure is affected by the characterisitcs of the input Y-branch.

Three-mirror resonator with aspheric feedback mirror for laser spatial mode selection and mode shaping

Abstract: The spatial-mode characteristics are studied for a three-mirror resonator consisting of a diffractive aspheric third mirror aligned collinearly with a standing-wave two-mirror resonator. Simulations predict that enhanced spatial-mode selection and mode shaping can be achieved by this three-mirror cavity. A three-mirror Nd:YVO/sub 4/ solid-state laser with an optimized aspheric third mirror has been designed and implemented to oscillate in a designed fundamental Gaussian mode. The modal discrimination was measured to be 1.43 and the propagation factor M/sup 2/ was 1.02.

Photonic bandgap structures in planar nonlinear waveguides: application to squeezed-light generation

Abstract: Quadrature-amplitude and phase squeezing are theoretically investigated in a planar waveguide geometry where the use of a linear grating fabricated on top of the waveguide reproduces a photonic bandgap structure. The introduction of a nonlinear grating, obtained with a modulation of the nonlinear susceptibility χ(2), provides an additional degree of freedom that allows, together with the linear grating, tuning of the fundamental field in a selected resonance of the transmission spectrum and, at the same time, control of the phase-matching condition between the fundamental and second-harmonic fields. The results show that quadrature-amplitude squeezing is achieved for the fundamental field, increasing the second-harmonic input intensity. The second-harmonic field is tuned in the passband of the photonic bandgap. The low nonlinear conversion efficiency, given by a suitable selection of the mismatch, gives rise to the possibility of having a fundamental field of quite the same intensity, but less noisy than at the entry.

Modeling of grating assisted standing wave, microresonators for filter applications in integrated optics

Abstract: A wide, multimode segment of a dielectric optical waveguide, enclosed by Bragg reflectors and evanescently coupled to adjacent port waveguides, can constitute the cavity in an integrated optical microresonator. It turns out that the device can be described adequately in terms of an approximate coupled mode theory model which involves only a few guided modes as basis fields. By reasoning along the coupled mode model, we motivate a simple design strategy for the resonator device. Rigorous two dimensional mode expansion simulations are applied to verify the predictions of the approximate model. The results exemplify the specific spectral response of the standing wave resonators. As refinements we discuss the single resonance of a device with nonsymmetrically detuned Bragg reflectors, and the cascading of two Fabry-Perot cavities, where the coupling across an intermediate shorter grating region establishes a power transfer characteristic that is suitable for an add-drop filter.

Experimental and numerical investigation of two-dimensional photonic crystals for application in integrated optics

Abstract: Two-dimensional (2D) photonic crystals (PhCs) at near-infrared wavelengths are promising candidates for novel integrated optics applications. The main focus being on 'all PhC' monolithically integrated optical circuits. Because of well established fabrication technologies particular emphasis is on 'quasi' 2D PhCs where a 2D lattice of air holes is etched through a planar step-index waveguide providing the optical confinement in the third dimension. This approach has been successfully demonstrated both in GaAs and InP-based systems. We have studied vertical low-index-contrast structures both in GaAs and InP. These structures suffer inherently from radiation losses that are strongly affected by the air hole depth and shape. A semi-analytical 'e"-model' enables out-of-plane scattering to be described by an effective imaginary dielectric constant in the air-holes which can be used in 2D finite difference time domain (FDTD) calculations. The model, once validated by 3D FDTD, allows us to deduce from optical simple slab transmission measurements the structural parameters (e.g. size, depth and form of the hole). The experimental transmission spectra are obtained with the so-called 'internal light source technique' (ILS), which allows for quantitative normalised transmission measurements, thus eliminating the uncertainties due to the in-out coupling arising in alternative characterisation techniques, i.e. end-fire. The ILS technique proved to be a versatile method without stringent limits for assessing the fabrication parameters (air-filling factor and loss) but also proved to be suitable for testing building blocks. In this thesis different building blocks were fabricated in the GaAs system and analysed using diverse modeling techniques (e.g. plane wave expansion, FDTD and coupled mode theory). The first building block was used to study contra-directional coupling of the fundamental mode with higher-order modes in channel waveguides. It is an extension of the work on waveguides with symmetric periodic corrugation to the case of multi periodicity. We showed that by breaking the translational symmetry in these structures referred to as hybrid waveguides, the number of mini-stopbands is increased and not, as one could have expected, decreased. A second building block analysed to guide light around the corner, are cavity resonant bends (CRBs). As our analysis showd that CRBs work best with non-degenerate cavity modes, different low-symmetry order cavities were studied with differ coupling coefficients between cavity and waveguides. Unfortunately, the resulting peak transmission and overall performance was below our expectations. An important building block in integrated optics are directional couplers. They have a potential for applications such as 3dB-intensity splitting or channel add-drop filtering. To reduce the coupling length, transmission measurements of a series of coupler structures of different lengths were taken. In the case of two W3 waveguides separated by a single row, the coupling length proved to be very dependent on the hole diameter in the single row. For this case the experimentally determined coupling length, which has been validated by both PWE and FDTD simulations, was of the order of 350 periods which corresponds to an absolute length of about 80 μm, a value that is small for conventional optics, but rather large for the domain of PhC optics where due to the unusually high propagation losses the integrated circuit has to be kept small. This value could, however, be reduced by a factor of at least three when reducing the ratio between the barrier hole and the nominal hole radius to 0.5. Finally we studied the waveguides needed to connect the different building blocks. The standard solution are channel waveguides, line-defects obtained by omitting a number of rows of holes. An alternative approach are coupled cavity waveguides (CCWs). They not only offer the potential for waveguiding but may also be used for non-linear optics by exploiting the special dispersion properties of CCWs (e.g. low group-velocity). A tight-binding model has been set-up that describes the interaction between the neighbouring cavities and that allows one to deduce the dispersion properties of the chain from the single cavity field distribution.

Novel optical slow wave structure and surface electromagnetic wave coupler with conducting interfaces

Abstract: Recently, a group of novel devices based on conducting interfaces has been proposed. These conducting interfaces can be implemented, for example, by using the inversion layer of MOS structures, trapped charges, or depletion layer charges. It has been shown that these structures can support surface electromagnetic waves. In this paper, the coupling of surface electromagnetic waves supported by conducting interfaces is first analysed. Next, by direct solution of Maxwell's equations and applying appropriate boundary conditions; exact analytical formulation of the dispersion equation has also been derived. Results driven by a coupled mode theory approach are justified by solving the exact transcendental dispersion equation derived from the second approach. A new type of optical modulator is proposed by demonstrating that the coupling length of this structure can be programmed by applying a transverse voltage. The possibility of optical slow wave propagation in dielectric slab waveguides in the presence of conducting interfaces is also explored.

Comparison of coupled mode theory and FDTD simulations of coupling between bent and straight optical waveguides

Abstract: Analysis of integrated optical cylindrical microresonators involves the coupling between a straight waveguide and a bent waveguide Our (2D) variant of coupled mode theory is based on analytically represented mode profiles With the bend modes expressed in Cartesian coordinates, coupled mode equations can be derived in a classical way and solved by numerical integration Proper manipulation of the propagation matrix leads to stable results even in parameter domains of compact and/or radiative structures, which seemed unsuitable for a perturbational approach due to oscillations of the matrix elements along the propagation Comparisons with FDTD calculations show convincing agreement

Photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers.

Abstract: For nearly 20 years, progress in the field of photonic crystals has greatly benefited from analogies to semiconductor physics and devices. Here we implement the concept of photonic crystal heterojunction and heterostructures, analogues to the concept of the semiconductor heterostructure, and demonstrate devices based on this concept operating in the optical range of frequency spectrum. In particular, we examine the effect of confinement of the photonic envelope wavefunction in a two-dimensional photonic heterostructure quantum well implemented with quasi-periodic array of vertical-cavity surface emitting lasers (VCSELs) as a model system.

Green's-function method for the analysis of propagation in holey fibers

Abstract: A Green's-function method is employed to provide a rigorous analysis to the propagation and coupling phenomena in holey fibers. The analysis is carried out for an arbitrary grid of circular air holes of the fiber guide, while the electromagnetic field is taken to be a vector quantity. Application of the Green's-function concept leads to a coupled system of equations incorporating as unknowns the field expansion coefficients to cylindrical wave functions within the air holes. The propagation constants of the guided waves are computed accurately by determining the singular points of the corresponding system's matrix. Field distribution and dispersion properties of guided modes as well as coupling phenomena between parallel-running holey fibers are investigated, and numerical results are presented.

Novel ring waveguide device in a 2D photonic crystal slab: Transmittance simulated by finit-difference time-domain analysis

Abstract: We propose a novel ring waveguide device in a two-dimensional (2D) photonic crystal (PhC) slab with a hexagonal lattice of air holes in a semiconductor (Si/GaAs). The device consists of a single line-defect ring waveguide and other parts. We simulated the propagation of a 1 ps pulse in the device. We analyzed the device using the 2D finite-difference time-domain (FDTD) method. The 1 ps pulse is transmitted well through sharp 60 degree bends in the ring waveguide. We designed and examined four-port directional couplers (DC) as input/output (I/O) components for the ring device. Coupling between the I/O waveguides and the ring waveguide in the device can be achieved by the four-port DC. We adopted a defect pattern formed with a straight waveguide and a waveguide with bends as the DC structure. This pattern realizes the coupling length based on the coupled mode theory. Our DC with the new multistep-like waveguides improved both the directivity and coupling factor across most of the frequency band where there are practical guided-wave modes in the photonic band gap (PBG). The propagation loss of a 1 ps pulse in the ring waveguide is low, so the transmission property of the ring device depends mainly on the I/O parts. In this study, we confirmed that the ring device would be sufficient for such applications as delay lines.

Wavelength shifting in photonic bandgap microcavities with isotropic media

Abstract: By coupled mode theory in the time domain and a finite-difference time-domain code, we investigate wavelength shifting and frequency conversion via four-wave mixing inside a photonic crystal wire in an isotropic Kerr material. The three-dimensional time-resolved analysis yields ultrafast and all-optically tunable frequency conversion of a signal/channel about the pump frequency.

Spectral anomalies due to coupling-induced frequency shifts in dielectric coupled-resonator filters

Abstract: Coupling-induced frequency shift is identified as a source of spectral response degradation in higher-order coupled-resonator add/drop filters that must be compensated in design. The theoretical basis and experimental verification are presented, and generic solutions proposed.

Polarization effects in short- and long-period fibre gratings: a generalized approach

Abstract: Short- and long-period fibre gratings with linear birefringence and/or rotational effects are studied by using a generalized coupled mode theory which, in a truncated form, is a very good approximation as long as the periodic perturbation is small. This generalized theory made possible the study of the contra-directional and co-directional couplings in an isotropic optical fibre with an isotropic periodic perturbation, in an anisotropic optical fibre with a periodic perturbation and in a fibre with an anisotropic periodic perturbation. That is to say, of short- and long-period fibre gratings with linear birefringence and rotational effects, also in the most general case in which the periodic perturbation is optically anisotropic.

Fiber-optic nanorefractometer based on one-dimensional photonic-bandgap structures with two defects

Abstract: A theoretical analysis of a fiber-optic photonic-bandgap (PBG)-based nanorefractometer is presented. Changes up to 11.2 dB in the optical output power in an index of refraction range of 1.7 with a sensitivity of 1.5/spl middot/10/sup -4/ have been demonstrated. The design is based on a one-dimensional PBG structure with two defects, which originates two defect states inside the bandgap. These states correspond to two localized modes in the defects. By selecting adequate parameters, the frequency of one of the localized modes can be fixed at the same time that its peak amplitude varies with the refractive index of the defect associated to the other localized mode. The refractive index of the defect associated to the localized mode that has been fixed in frequency remains constant. This enables a detection scheme based on a simple photodetector instead of an optical spectrum analyzer, as usual. The thickness of the defect whose refractive index varies determines the variation range of the transmitted power amplitude peak of the localized mode fixed at a concrete frequency. In addition, an analysis of the nonlinear dependence on the refractive index of the peak-transmitted power of the localized mode fixed at a concrete frequency is presented.

Analytical study of whispering gallery mode in 2D microgear cavity

Abstract: We present a two dimensional analytical method for studying the effect of gratings on microdisk dielectric resonators. Our model based on a Coupled Mode Theory (CMT) needs the normalization of the Whispering Gallery Mode (WGM). In the past, few normalizations have been proposed, all of them assume the mode to be bound which is not true as WGMs are leaky modes. In this paper, we propose a new normalization with no approximation. Then we apply the CMT in order to compute the resonance wavelength of the perturbated structure. This theory has been checked against 2D FDTD and shows accurate results with very little computation time.

Controlled transmission in the forbidden photonic bandgap via transient nonlinear states.

Abstract: Using three-dimensional time-domain numerical simulations of the nonlinear dispersive Maxwell equations for a defect microcavity in a photonic crystal wire, we show that the transmission through the bandgap can be all-optically modulated via the generation of transient states associated with the nonlinear splitting of the defect mode. Analytical results based on time-domain coupled-mode theory are derived as well.

Efficient coupling into and out of high-Q resonators.

Abstract: The temporal-coupled-mode theory is directly applied to the design of devices that feature a resonator with a high quality factor. For the temporal-coupled-mode theory we calculate the decay rate of the resonator to determine the transmission properties of the device. The analysis using the decay rates requires little computational effort, and therefore the optimum device properties can be determined quickly. Two examples, a wavelength filter and a resonator crossing, are presented to illustrate the use of the analysis.