Showing papers on "Coupled mode theory published in 2003"
TL;DR: A theory of the Fano resonance for optical resonators, based on a temporal coupled-mode formalism, is presented and it is shown that the coupling constants in such a theory are strongly constrained by energy-conservation and time-reversal symmetry considerations.
Abstract: We present a theory of the Fano resonance for optical resonators, based on a temporal coupled-mode formalism. This theory is applicable to the general scheme of a single optical resonance coupled with multiple input and output ports. We show that the coupling constants in such a theory are strongly constrained by energy-conservation and time-reversal symmetry considerations. In particular, for a two-port symmetric structure, Fano-resonant line shape can be derived by using only these symmetry considerations. We validate the analysis by comparing the theoretical predictions with three-dimensional finite-difference time-domain simulations of guided resonance in photonic crystal slabs. Such a theory may prove to be useful for response-function synthesis in filter and sensor applications.
1,223 citations
TL;DR: All-optical switching action in a nonlinear photonic crystal cross-waveguide geometry with instantaneous Kerr nonlinearity is demonstrated, in which the transmission of a signal can be reversibly switched on and off by a control input.
Abstract: We demonstrate all-optical switching action in a nonlinear photonic crystal cross-waveguide geometry with instantaneous Kerr nonlinearity, in which the transmission of a signal can be reversibly switched on and off by a control input. Our geometry accomplishes both spatial and spectral separation between the signal and the control in the nonlinear regime. The device occupies a small footprint of a few micrometers squared and requires only a few milliwatts of power at a 10-Gbit/s switching rate by use of Kerr nonlinearity in AlGaAs below half the electronic bandgap. We also show that the switching dynamics, as revealed by both coupled-mode theory and finite-difference time domain simulations, exhibits collective behavior that can be exploited to generate high-contrast logic levels and all-optical memory.
364 citations
TL;DR: A method for dispersion-tailoring of OmniGuide and other photonic band-gap guided fibers based on weak interactions ("anticrossings") between the core-guided mode and a mode localized in an intentionally introduced defect of the crystal is presented.
Abstract: We present a method for dispersion-tailoring of OmniGuide and other photonic band-gap guided fibers based on weak interactions (“anticrossings”) between the core-guided mode and a mode localized in an intentionally introduced defect of the crystal. Because the core mode can be guided in air and the defect mode in a much higher-index material, we are able to obtain dispersion parameters in excess of 500,000 ps/nm-km. Furthermore, because the dispersion is controlled entirely by geometric parameters and not by material dispersion, it is easily tunable by structural choices and fiber-drawing speed. So, for example, we demonstrate how the large dispersion can be made to coincide with a dispersion slope that matches commercial silica fibers to better than 1%, promising efficient compensation. Other parameters are shown to yield dispersion-free transmission in a hollow OmniGuide fiber that also maintains low losses and negligible nonlinearities, with a nondegenerate TE01 mode immune to polarization-mode dispersion (PMD). We present theoretical calculations for a chalcogenide-based material system that has recently been experimentally drawn.
153 citations
TL;DR: It is shown that an adequate ansatz of the classical coupled-mode theory remarkably well accounts for this new phenomenon, and the fit of experimental transmission data from GaAs-based photonic crystal waveguides leads to an accurate determination of the propagation losses of both fundamental and higher, low-group-velocity modes.
Abstract: Mode coupling phenomena, manifested by transmission “mini-stopbands”, occur in two-dimensional photonic crystal channel waveguides. The huge difference in the group velocities of the coupled modes is a new feature with respect to the classical Bragg reflection occurring, e.g., in distributed feedback lasers. We show that an adequate ansatz of the classical coupled-mode theory remarkably well accounts for this new phenomenon. The fit of experimental transmission data from GaAs-based photonic crystal waveguides then leads to an accurate determination of the propagation losses of both fundamental and higher, low-group-velocity modes.
106 citations
TL;DR: In this article, it is shown that interaction of radiative and guided modes through a photonic crystal, especially under conditions where the latter correspond to extrema of the dispersion characteristics, results in resonance phenomena, which can be used practically for the development of new classes of devices.
Abstract: One- and two-dimensional photonic crystal slabs have numerous applications in integrated optics. Unfortunately, due to their finite height, their in-plane guided modes can suffer outcoupling losses. Although considered as detrimental in the context of the development of photonic integrated circuits, it turns that the coupling of waveguided modes to radiative modes can be usefully exploited for the manipulation of photons in free space. It is shown in this paper that interaction of radiative and guided modes through a photonic crystal, especially under conditions where the latter correspond to extrema of the dispersion characteristics of the photonic crystal, results in resonance phenomena, which can be used practically for the development of new classes of devices, e.g., combining photonic crystal and microoptoelectromechanical systems structures.
95 citations
TL;DR: A novel geometry for a Mach-Zehnder interferometer in which one arm of the interferometers consists of serially coupled microresonators and the other a simple ridge waveguide is proposed.
Abstract: We propose a novel geometry for a Mach-Zehnder interferometer in which one arm of the interferometer consists of serially coupled microresonators and the other a simple ridge waveguide. The device was fabricated in an optical polymer and its spectral characteristics were measured at telecommunications wavelengths. The serially coupled rings are modeled using a simple transfer matrix approach. Good agreement is found between the measurement and the theory.
81 citations
TL;DR: In this article, a novel scheme based on evanescent guided-wave coupling for optically interfacing between conventional fiber-optic and planar photonic crystal devices such as waveguides and resonant cavities is described.
Abstract: We describe a novel scheme based on evanescent guided-wave coupling for optically interfacing between conventional fiber-optic and planar photonic crystal devices such as waveguides and resonant cavities. By considering the band structure of bulk photonic crystal slabs, we analyze the k space properties of a linear defect waveguide and establish a set of design rules to ensure efficient evanescent coupling with optical fiber tapers. These rules are used to design a waveguide in a square-lattice photonic crystal. The coupling efficiency is calculated with a coupled-mode theory incorporating the finite-difference time-domain-calculated uncoupled modes of the fiber taper and photonic crystal waveguide. On the basis of this coupled-mode theory, 95% power transfer from the fiber taper to the photonic crystal waveguide is possible over a coupling length of 80 lattice periods and with a bandwidth of 1.5% of the center wavelength. The integration of this waveguide with a photonic crystal defect resonant cavity is also presented, thus showing the usefulness of the combined fiber taper and photonic crystal waveguide system for efficient, optical fiber-based probing of optical elements based on planar photonic crystal technologies.
81 citations
TL;DR: Vertical resonators with a top mirror constituted of 1D photonic crystal membrane on top of a Bragg stack are investigated and allow the fabrication of compact vertical-cavity surfaceemitting lasers, which can be designed, in addition, for in-plane emission.
Abstract: Vertical resonators with a top mirror constituted of 1D photonic crystal membrane on top of a Bragg stack are investigated in this paper. These structures allow the fabrication of compact vertical-cavity surfaceemitting lasers, which can be designed, in addition, for in-plane emission. With this hybrid approach, fabrication problems related to both classical VCSEL and Photonic Crystal lasers may be significantly relaxed, given that a full Bragg stack is replaced by a single photonic crystal membrane and that the Photonic Crystal is not formed in the active gain layer.
62 citations
TL;DR: A monotonic increase in the Raman gain is found as the waveguide cross section decreases for the range of dimensions considered, and mode coupling between the Stokes modes is insignificant, and thus polarization multiplexing is possible.
Abstract: Coupled-mode theory is used to calculate Raman gain and spontaneous efficiency in silicon waveguides with cross-sectional areas ranging from 0.16 to 16 μm2 . We find a monotonic increase in the Raman gain as the waveguide cross section decreases for the range of dimensions considered. It is also found that mode coupling between the Stokes modes is insignificant, and thus polarization multiplexing is possible. The results also demonstrate that for submicrometer waveguide dimensions the Einstein relation between spontaneous efficiency and stimulated gain no longer holds.
55 citations
TL;DR: Using finite-difference time-domain calculations, out-of-plane coupling between a square-lattice planar photonic crystal and a conventional waveguide located above the photonic Crystal is investigated and it is shown that single Photonic crystal modes can be selectively excited.
Abstract: Using finite-difference time-domain calculations, we investigate out-of-plane coupling between a square-lattice
planar photonic crystal and a conventional waveguide located above the photonic crystal. We couple a waveguide
oriented in the GX direction to a photonic crystal mode in the second band and show that anticrossing takes place. In this way, a self-collimated beam is launched in the planar photonic crystal, with full power transfer. Furthermore, we investigate the coupling between a waveguide oriented in the GM direction and a photonic crystal and show that single photonic crystal modes can be selectively excited.
48 citations
TL;DR: Although the symmetric defect waveguide becomes multimode for increased coupling it does not support antisymmetric modes, and theoretical predictions are confirmed in excellent agreement with experimental observations in polymer waveguide arrays.
Abstract: The formation of localized states or modes at defects in waveguide arrays is investigated both, theoretically and experimentally. If the effective index or the coupling of the defect guide to its neighbors is varied the number and character of respective modes bound to the defect can be altered. Waveguide arrays may be considered as tailor-made or metamaterials with new and unexpected properties as e.g. guiding staggered modes bound to defects with reduced index. Although the symmetric defect waveguide becomes multimode for increased coupling it does not support antisymmetric modes. All theoretical predictions are confirmed in excellent agreement with experimental observations in polymer waveguide arrays.
TL;DR: A numerical and analytical study of mode field patterns and mode coupling in planar waveguide-coupled square microcavities, using two-dimensional (2D) finite-difference time-domain (FDTD) method and k-space representation suggests that k- space modes that nearly match the waveguide propagation mode have a relatively high coupling efficiency.
Abstract: We report a numerical and analytical study of mode field patterns and mode coupling in planar waveguide-coupled square microcavities, using two-dimensional (2-D) finite-difference time-domain (FDTD) method and k-space representation. Simulated mode field patterns can be identified by k-space modes. We observe that different mode number parities permit distinctly different mode field patterns and spectral characteristics. Simulation results suggest that k-space modes that nearly match the waveguide propagation mode have a relatively high coupling efficiency. Such preferential mode coupling can be modified by the mode number parity.
TL;DR: In this article, an experimental and theoretical study of whispering-gallery-mode propagation of sub-picosecond terahertz pulses in a dielectric cylinder coupled by means of a Dielectric slab waveguide was performed.
Abstract: We report an experimental and theoretical study of whispering-gallery-mode propagation of subpicosecond terahertz pulses in a dielectric cylinder coupled by means of a dielectric slab waveguide. We observed repetitive cavity pulses from this structure for which the output pulse shapes were determined by the multi-whispering-gallery-mode coupling into the cylinder. A coupled-mode theory derived for this cylindrical system and coupling structure gives reasonably good agreement with the experiment in both the frequency and time domains.
TL;DR: A rigorous analysis methodology of fundamental to higher order mode converters in step index few mode optical fibers is presented and a modal decomposition algorithm is demonstrated to characterize the modal content excited in the fiber.
Abstract: We present a rigorous analysis methodology of fundamental to higher order mode converters in step index few mode optical fibers. We demonstrate experimental conversion from a fundamental LP01 mode to the higher order LP11 mode utilizing a multiple mechanical bend mode converter.We perform a quantitative analysis of the measured light intensity, and demonstrate a modal decomposition algorithm to characterize the modal content excited in the fiber. Theoretical modelling of the current mode converter is then performed and compared with experimental findings.
TL;DR: This paper developed coupled mode and perturbation theory formulations for treating generic perturbations of a waveguide cross section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates that are accurate beyond the first order and rapidly converges to an exact result when used in a coupled mode theory framework even for the high-index-contrast discontinuous dielectric profiles.
Abstract: Perturbation theory formulation of Maxwell's equations gives a theoretically elegant and computationally efficient way of describing small imperfections and weak interactions in electromagnetic systems. It is generally appreciated that due to the discontinuous field boundary conditions in the systems employing high dielectric contrast profiles standard perturbation formulations fails when applied to the problem of shifted material boundaries. In this paper we developed coupled mode and perturbation theory formulations for treating generic perturbations of a waveguide cross section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates. We show that our formulation is accurate beyond the first order and rapidly converges to an exact result when used in a coupled mode theory framework even for the high-index-contrast discontinuous dielectric profiles. Among others, our formulation allows for an efficient numerical evaluation of such quantities as deterministic PMD and change in the GV and GVD of a mode due to generic profile distortion in a waveguide of arbitrary cross section. To our knowledge, this is the first time perturbation and coupled mode theories are developed to deal with arbitrary profile variations in high-index-contrast waveguides.
TL;DR: A new type of optical amplifier is proposed that is formed by addition of gain in the periodic cladding of a transverse Bragg resonance waveguide using the coupled-wave formalism and, for comparison, the gain enhancement compared with those of conventional semiconductor optical amplifiers.
Abstract: We propose and analyze a new type of optical amplifier that is formed by addition of gain in the periodic cladding of a transverse Bragg resonance waveguide [Opt. Lett. 27, 936 (2002)]. Using the coupled-wave formalism, we calculate the mode profiles, the exponential gain constant, and, for comparison, the gain enhancement compared with those of conventional semiconductor optical amplifiers. In contrast with coupled-mode theory, in one-dimensional structures (e.g., the distributed-feedback laser) the exponential gain constant in the longitudinal direction is involved in both longitudinal and transverse confinement, and its solution has to be achieved self-consistently, together with the quantized guiding channel width.
TL;DR: An add-drop filter consisting of two adjacent waveguides carved into a two-dimensional photonic crystal that is etched through a standard guiding structure based on distributed energy transfer via the frequency-selective intermediate conversion of the fundamental guided mode to a high-order low-group-velocity mode.
Abstract: We propose an add-drop filter consisting of two adjacent waveguides carved into a two-dimensional photonic crystal that is etched through a standard guiding structure. This filter is based on distributed energy transfer via the frequency-selective intermediate conversion of the fundamental guided mode to a high-order low-group-velocity mode. This geometry circumvents the fabrication sensitivity on the single-hole scale of previous cavity-based designs. Combining distributed energy transfer and reduced group velocity preserves compactness. The design is analytically optimized with a coupled-mode approach.
TL;DR: In this article, the problem of grating coupling of a focused incident beam under non-normal incidence into a slab waveguide is given a complete three-dimensional (3D) solution, where the diffracted field is expressed as the Fourier integral of a regular part and of a singular part resulting from the existence of the coupled guided mode.
Abstract: The problem of grating coupling of a focused incident beam under non-normal incidence into a slab waveguide is given a complete three-dimensional (3D) solution. The diffracted field is expressed as the Fourier integral of a regular part and of a singular part resulting from the existence of the coupled guided mode. A suitable expression of the field in the neighborhood of the pole and a rigorous definition of the modal field lead to a generalized coupled mode equation relating the incident field and the two-dimensional (2D) modal field propagating in the plane of the slab waveguide. The phenomenological parameters involved in the coupled wave equation: the propagation constant, the radiation coefficient as well as the modal field shape are derived from the exact treatment of plane wave diffraction in the same structure. The solution of the complete coupling problem is given in the particular case of a Gaussian incident beam, and of a high index step-index waveguide.
TL;DR: A new approach to design a wavelength-insensitive optical power splitter is presented, where a coupled-mode theory is cast in operatorial form, and the resulting graphical tool is applied to different structures, giving a clear interpretation of previous results in literature as well as hints on how to find improved solutions.
Abstract: A new approach to design a wavelength-insensitive optical power splitter is presented. First, a coupled-mode theory is cast in operatorial form. This allows us to solve the equivalent of coupled differential equations as simple limits. The operators are then represented on a generalized Poincare sphere, and the resulting graphical tool is applied to different structures, giving a clear interpretation of previous results in literature as well as hints on how to find improved solutions.
TL;DR: In this paper, a fast effective index method for the analysis of fiber Bragg gratings based on the use of V-I transmission matrices was proposed, which combines the exactitude of traditional effective index methods and the speed of coupled-mode methods.
Abstract: We propose the use of V-I matrices well known in microwave engineering to the analysis of photonic devices, especially those based on multilayer dielectrics. As an application we present a novel fast effective index method for the analysis of fiber Bragg gratings based on the use of V-I transmission matrices. It combines the exactitude of traditional effective index methods and the speed of coupled-mode methods.
TL;DR: In this paper, a consistent derivation of a system of vector coupled-mode (VCM) equations for parallel dielectric waveguides is presented and compared with earlier versions of the improved coupledmode theory (ICMT).
Abstract: A consistent derivation of a system of vector coupled-mode (VCM) equations for parallel dielectric waveguides is presented and compared with earlier versions of the improved coupled-mode theory (ICMT). As a validity test, it is shown that the effectively scalar transverse electric and transverse magnetic (TM) coupled-mode (CM) equations are direct limits of our full VCM formulation. In particular, our formulation does not lead to the fundamental error found with earlier coupled-mode theories (CMTs) in a case of TM fields. Functional equations of our VCMT are consistent with Maxwell's equations and lead to higher precision. They can be applied to complicated arrays of strongly coupled parallel dielectric waveguides with true vectorial behavior.
TL;DR: In this paper, the contra-directional coupling between two photonic crystal (PC) waveguides was studied using the finite-difference time-domain (FDTD) method.
Abstract: The contra-directional coupling between two photonic crystal (PC) waveguides is studied, using the finite-difference time-domain (FDTD) method. A design of contra-directional coupler is presented and its transmission properties are investigated. The device can be used as an add/drop filter. It is also shown that the coupled mode theory is suitable to study the photonic crystal waveguide coupler.
TL;DR: In this paper, the reflection properties of coplanar waveguides periodically loaded with shunt connected capacitances and periodically perturbed by varying the slot width are investigated, and the effects of the relative position of reactive elements with regard to the perturbation geometry are analyzed.
Abstract: In this work, we study the reflection properties of coplanar waveguides (CPW) periodically loaded with shunt connected capacitances and periodically perturbed by varying the slot width. These structures are of interest because the low pass frequency response with spurious frequency bands, inherent to the presence of capacitors, can be improved. This is achieved through the attenuation of frequency parasitics that is obtained by the introduction of slot width modulation. Both sinusoidal and square wave patterns are considered and the effects of the relative position of reactive elements with regard to the perturbation geometry is analysed. According to coupled mode theory, the central frequencies of the rejected bands in periodic transmission media are given by the spectrum of the perturbation function. However, it is demonstrated that, due to the presence of capacitors, multiple spurious bands can be simultaneously suppressed even in the case of a singly tuned (sinusoidal) perturbation geometry. This resu...
TL;DR: In this article, the effect of a microwave field on a train of short optical pulses co-propagating in a traveling-wave modulator structure was analyzed using a coupledmode expansion formalism.
Abstract: In this paper, we present a semiclassical wave equation analysis using a coupled-mode expansion formalism to study the effect of a microwave field on a train of short optical pulses co-propagating in a traveling-wave modulator structure. This device can continuously shift the central frequency of light pulses. We demonstrate the effect of the applied field on the light spectrum, the dependence on the relation between microwave wavelength and pulse length, and the effect of changing the interaction length or the power of the applied microwave field. The results of the calculation of these effects are presented.
TL;DR: An analytical expression for differential group delay of spun and twisted fibers is derived, which should provide valuable guidance for optimization of such parameters to produce low polarization mode dispersion fiber.
Abstract: We derive an analytical expression for differential group delay of spun and twisted fibers, which should provide valuable guidance for optimization of such parameters to produce low polarization mode dispersion fiber.
TL;DR: In this paper, the dynamic switching characteristics in waveguide-type collinear acoustooptic (AO) devices are investigated for applications to wavelength-selective matrix switches and routers in WDM photonic networks.
Abstract: Dynamic switching characteristics in waveguide-type collinear acoustooptic (AO) devices are investigated for applications to wavelength-selective matrix switches and routers in wavelength-division-multiplexing (WDM) photonic networks. The device has the feature of simultaneous controllability for multiple wavelengths over a range of more than 100 nm. Experimental studies on optical filtering have been investigated. In order to find the optimum high-effciency design of a compact integrated optical wave separator, the dynamic characteristics of photonic switching of optical signals by AO interaction are studied numerically using the finite-difference-time-domain (FDTD) method. The analytical model consists of slab-type symmetric directionally coupled waveguides formed on a LiNbO3 substrate. Wavelength-selective switching was numerically simulated and compared with the analysis using the coupled mode theory. A segmented FDTD method for simulating long optical devices with waveguides longer than 1 mm is also discussed.
TL;DR: In this paper, a curved waveguide coupler based on coupled mode theory (CMT) was designed for a 4-channel WDM system and the 3D beam propagation method (BPM) was used to verify the correctness of the design.
TL;DR: In this paper, the authors derived an analytical expression for the conversion efficiency of second-harmonic generation in a one-dimensional photonic crystal, obtained in the undepleted pump limit for the continuous-wave case.
Abstract: Using the multiple-scale approach, we derive an analytical expression for the conversion efficiency of second-harmonic generation (SHG) in a one-dimensional photonic crystal. The results, obtained in the undepleted pump limit for the continuous-wave case, allow us to describe the role played by the feedback and the dispersion introduced by the periodic structure and hence to optimize the SHG process. Numerical simulations are then used to explore the pulsed pump case, proving that the obtained results retain their validity up to a pump field bandwidth of less than approximately 12% of the stack transmission bandwidth. Shorter pulses experience both a reduced conversion efficiency and shape distortions.
Journal Article•
TL;DR: In this article, the coupling coefficient between two adjacent waveguides with conducting interfaces is calculated analytically, and it is shown that the presence of interface charges, their density being controlled via a transverse voltage, leads to the control of the coupling.
01 Jan 2003
TL;DR: In this article, the authors describe how optical energy couples between modes within and between optical waveguides, and describe how simple mechanisms can lead to significant energy exchange among the various modes of a structure.
Abstract: Mutual coupling between optical modes is essential in the design of integrated optic devices. In this chapter we will describe how optical energy couples between modes within and between optical waveguides. Up to now, we have treated the waveguide as an ideal optical wire, which conveys light from one point to another in the form of a “mode”. We have implicitly assumed that these modes, once formed, are unchanging except perhaps through attenuation due to absorption. In reality, simple mechanisms can lead to significant energy exchange among the various modes of a structure. Coupled mode theory describes this energy exchange, and serves as the primary tool for designing optical couplers, switches, and filters.