Showing papers on "Coupled mode theory published in 2005"
TL;DR: A photonic nanocavity with a high Q factor of 100,000 and a modal volume V of 0.71 cubic wavelengths, is demonstrated and a point-defect cavity in a two-dimensional (2D) photonic crystal (PC) slab is improved where the arrangement of six air holes near the cavity edges is fine-tuned.
Abstract: A photonic nanocavity with a high Q factor of 100,000 and a modal volume V of 0.71 cubic wavelengths, is demonstrated. According to the cavity design rule that we discovered recently, we further improve a point-defect cavity in a two-dimensional (2D) photonic crystal (PC) slab, where the arrangement of six air holes near the cavity edges is fine-tuned. We demonstrate that the measured Q factor for the designed cavity increases by a factor of 20 relative to that for a cavity without displaced air holes, while the calculated modal volume remains almost constant.
504 citations
TL;DR: The deposition of an overlay of higher refractive index than the cladding in a Long Period Fiber Grating permits to improve the sensitivity to ambient refractiveIndex changes in a great manner, and henceforward fast shifts of the resonance wavelength of the attenuations bands in the transmission spectrum are studied.
Abstract: The deposition of an overlay of higher refractive index than the cladding in a Long Period Fiber Grating (LPFG) permits to improve the sensitivity to ambient refractive index changes in a great manner. When the overlay is thick enough, one of the cladding modes is guided by the overlay. This causes important shifts in the effective index values of the cladding modes, and henceforward fast shifts of the resonance wavelength of the attenuations bands in the transmission spectrum. This could be applied for improving the sensitivity of LPFG sensors. The problem is analysed with a numerical method based on LP mode approximation and coupled mode theory, which agrees with so far published experimental results.
357 citations
TL;DR: In this article, an optical circulator formed of a magneto-optical cavity in a 2D photonic crystal was designed to support a pair of counterrotating states at different frequencies.
Abstract: We propose an optical circulator formed of a magneto-optical cavity in a 2D photonic crystal. With spatially engineered magnetic domain structures, the cavity can be designed to support a pair of counterrotating states at different frequencies. By coupling the cavity to three waveguides, and by proper matching of the frequency split of the cavity modes with the coupling strength between the cavity and the waveguide, ideal three-port circulators with complete isolation and transmission can be created. We present a guideline for domain design needed to maximize the modal coupling and the operational bandwidth for any given magneto-optical constant.
292 citations
TL;DR: The numerical results have confirmed the feasibility of this simple, all-fiber approach to processing optical signals with temporal features in the picosecond and subpicosecond ranges.
Abstract: It is demonstrated that a single, uniform long-period fiber grating (LPFG) working in the linear regime inherently behaves as an ultrafast optical temporal differentiator. Specifically, we show that the output temporal waveform in the core mode of a LPFG providing full energy coupling into the cladding mode is proportional to the first derivative of the optical temporal signal (e.g., optical pulse) launched at the input of the LPFG. Moreover, a LPFG providing full energy recoupling back from the cladding mode into the core mode inherently implements second-order temporal differentiation. Our numerical results have confirmed the feasibility of this simple, all-fiber approach to processing optical signals with temporal features in the picosecond and subpicosecond ranges.
136 citations
TL;DR: In this paper, coupled-mode theory was used to examine the nonlinear behavior of photonic-crystal switches with two side-coupled resonators and a judiciously chosen intercavity distance.
Abstract: Using coupled-mode theory we examine the linear and Kerr nonlinear behavior of multiple consecutive photonic-crystal switches. Two types of resonators are considered, those with the cavity inside and those adjacent to the waveguide. We observe gap solitons in both structures and examine a nonlinear mode with energy localized near the boundaries of the finite system. Finally, we propose a device with two side-coupled resonators and a judiciously chosen intercavity distance that demonstrates switching at low powers. In addition to coupled-mode theory, rigorous simulations are performed for this structure.
96 citations
TL;DR: This work investigates light propagation and self-localization in a voltage-controlled array of channel waveguides realized in undoped nematic liquid crystals and reports on discrete diffraction and solitons, as well as all-optical angular steering and the formation of multiband vector breathers.
Abstract: We investigate light propagation and self-localization in a voltage-controlled array of channel waveguides realized in undoped nematic liquid crystals. We report on discrete diffraction and solitons, as well as all-optical angular steering and the formation of multiband vector breathers. The results and are in excellent agreement with both coupled mode theory and full numerical simulations.
80 citations
TL;DR: An analytical solution to the add and drop spectra arising from such interactions in the limit of linear dispersion is derived, which can accurately predict the cold cavity quality factor (Q) when the interaction is weak.
Abstract: We derive a coupled mode theory for the interaction of an optical cavity with a waveguide that includes waveguide dispersion. The theory can be applied to photonic crystal cavity waveguide structures. We derive an analytical solution to the add and drop spectra arising from such interactions in the limit of linear dispersion. In this limit, the spectra can accurately predict the cold cavity quality factor (Q) when the interaction is weak. We numerically solve the coupled mode equations for the case of a cavity interacting with the band edge of a periodic waveguide, where linear dispersion is no longer a good approximation. In this regime, the density of states can distort the add and drop spectra. This distortion can lead to more than an order of magnitude overestimation of the cavity Q.
79 citations
TL;DR: A novel grating which only produces reflection with mode conversion in a two-mode waveguide is experimentally demonstrated which can improve the performance of optical devices that currently use tilted Bragg gratings to provide the mode conversion.
Abstract: We experimentally demonstrate a novel grating which only produces reflection with mode conversion in a two-mode waveguide. That characteristic can improve the performance of optical devices that currently use tilted Bragg gratings to provide the mode conversion. Tilted Bragg gratings produce also reflections without mode conversion which increases noise and crosstalk of the optical device.
75 citations
TL;DR: In this article, the authors theoretically and experimentally investigate the characteristics of a multichannel add/drop filter which utilizes in-plane hetero photonic crystals (IP-HPCs).
Abstract: We theoretically and experimentally investigate the characteristics of a multichannel add/drop filter which utilizes in-plane hetero photonic crystals (IP-HPCs). The structure consists of an in-plane array of photonic crystals with different lattice-constants. Finite-difference time-domain calculations reveal that optimal performance in terms of wavelength resolution and efficiency can be kept almost constant at different wavelengths even though slab thickness is not changed. The multichannel add/drop device fabricated consists of seven photonic crystals, with a lattice parameter difference of 1.25 nm between neighboring regions. This device demonstrated wavelength spacing /spl sim/5nm with almost constant Q factor and efficiency. It is also shown that the boundary between different PCs (the heterointerface), plays an important role not only in improving add/drop efficiency but also in performing directional filtering.
63 citations
TL;DR: Wide wavelength tuning through optical injection of carriers of a photonic resonance observed in reflectivity at 1543 nm in an InP-based two-dimensional photonic crystal slab is reported on.
Abstract: We report on wide wavelength tuning through optical injection of carriers of a photonic resonance observed in reflectivity at 1543 nm in an InP-based two-dimensional photonic crystal slab. An 8-nm blueshift, which represents 20 times the resonance linewidth, is observed when a 4?kW/cm2 intense optical pump is incident on the sample. An analytical model that we developed, based on a coupled-mode nonlinear approach, allows us to describe this phenomenon in detail.
60 citations
TL;DR: In this article, a spatially three-dimensional (3-D), fully vectorial coupled mode theory model for the interaction between several straight or bent dielectric optical waveguides, each supporting multiple modes, is described.
TL;DR: A detailed theoretical analysis of the ring resonator in the linear regime is presented, and its linear temporal dynamics are investigated to develop a dynamic optical memory cell where a data modulated train of optical pulses can be stored.
Abstract: A recently proposed concept suggests that a matched periodic modulation of both the refractive index and the gain/loss of the media breaks the coupling symmetry of the two co-propagating modes and allows only a unidirectional coupling from the i-th mode to j-the mode but not the opposite. This concept has been used to design a ring resonator coupled through a complex grating composed of both real (index) and imaginary (loss/gain) parts according to Euler relation: Δn=n0 exp(-jkx)=n0 (cos(kx)−j sin(kx)). Such asymmetrical coupling allows light to be coupled into the ring without letting it out. We present a detailed theoretical analysis of the ring resonator in the linear regime, and we investigate its linear temporal dynamics. Three possible states of the complex grating leads to the possibility of developing a dynamic optical memory cell where, for example, a data modulated train of optical pulses can be stored. This data can be accessed without destroying it, and can also be erased thus permitting the storage of a new bit. Finally, the ring can be used for pulse retiming.
TL;DR: In this paper, a method for the design of waveguide-coupled microring resonators based on an improved coupled mode theory (CMT) approach is described, and the effects of variations in the refractive index, waveguide width, bus-to-ring gap spacing and ring radius are investigated.
Abstract: A method for the design of waveguide-coupled microring resonators is described based on an improved coupled mode theory (CMT) approach. Characteristic parameters including coupling efficiency and Q factor are theoretically analyzed. The effects of variations in the refractive index, waveguide width, bus-to-ring gap spacing, and ring radius are investigated. The accuracy of this model is evaluated by comparing its predicted calculation results to those of the numerical beam propagation method (BPM) and finite difference time domain (FDTD) simulations obtained using commercial software. The predictions of the model agree well with the simulation results.
TL;DR: In this article, a passive optical add-drop filter incorporating microdisk resonators, in complementary metal-oxide-semiconductor compatible silicon-on-insulator technology, is presented.
Abstract: We present a passive novel optical add-drop filter incorporating microdisk resonators, in complementary metal-oxide-semiconductor compatible silicon-on-insulator technology, which enables a simple layout of complex optical networks-on-chip. The measured properties of the fabricated devices are in agreement with theory, established using the time-domain coupled mode theory and finite-difference time-domain simulations.
TL;DR: New and basic equations for the coupling coefficient are derived and compared with those of waveguides and should be useful for understanding the physical background of coupling and designing a new coupling scheme.
Abstract: Coupling between resonators are analyzed theoretically on basis of the coupled mode theory. New and basic equations for the coupling coefficient are derived and compared with those of waveguides. They should be useful for understanding the physical background of coupling and designing a new coupling scheme.
TL;DR: In this article, a gain element is placed in the resonator closest to the excitation waveguide, provided the structure is over-coupled, but the resonance farthest from the waveguide is under-cooperative sufficiently to avoid lasing at the split modes.
Abstract: We predict transparent superluminal pulse propagation in co-resonant coupled optical resonators, when a gain element is placed in the resonator closest to the excitation waveguide, provided the structure is over-coupled, but the resonator farthest from the excitation waveguide is under-coupled sufficiently to avoid lasing at the split modes. The effective steady-state absorptive and dispersive response of coupled resonators is derived, and the coupled-mode approximation is used to determine the conditions for transparent superluminal pulse propagation in these systems.
TL;DR: The existence of localized or defect modes in a periodic array of symmetric and lossless micro-ring resonators is demonstrated for both finite and infinite structures using the transfer matrix method, for two types of array.
Abstract: The existence of localized or defect modes in a periodic array of symmetric and lossless micro-ring resonators is demonstrated for both finite and infinite structures using the transfer matrix method, for two types of array: one consisting of a cascade of coupled resonators coupled to an input and an output waveguide, and another consisting of uncoupled resonators periodically coupled between two bus waveguides. The defect can be introduced either by removing one ring, or by making one ring bigger or smaller. The 1-D periodic dielectric waveguide structures consisting of micro-ring resonators can exhibit photonic bandgaps, and when point defects are introduced defect states can form within the bandgaps, giving rise to donor and acceptor modes similar to other photonic crystals. The results based on the transfer matrix model agree with the finite-difference time-domain method, and are compared with those of a quarter-wave mirror stack.
TL;DR: In this paper, it was shown that perfect and fractional revivals are possible in finite waveguide arrays with engineered parameters, and potential applications of waveguide lattices utilizing operations such as multi-couplers and multi-beam splitters.
TL;DR: In this paper, the switching operation of a nonlinear dual-core photonic crystal fiber (PCF) coupler, based on a highly nonlinear As2Se3 chalcogenide glass, is numerically studied for the first time.
14 Oct 2005
TL;DR: In this article, the authors restrict their model to two dimensional settings and treat the circular microcavities as traveling wave resonators in the framework of a pure frequency domain description.
Abstract: In this thesis, we restrict ourself to two dimensional settings. While for specic congurations one could regard the present two dimensional model as an approximate description of realistic devices in terms of effective indices, in other cases simulations in three spatial dimensions are certainly necessary, e.g. for vertically coupled resonators. Therefore our model is formulated such that an extension to three dimensions is straightforward. We treat the circular microcavities as traveling wave resonators in the framework of a pure frequency domain description.
TL;DR: In this article, coupled mode theory (CMT) is applied to study the implication of the variation of the size of the rods, and the relation between the size nonuniformities and the coupler's insertion loss and extinction ratio is analyzed.
Abstract: Photonic crystals (PCs) are a promising technology for the realization of high-density optical integrated circuits. PC-based couplers have been proposed as a compact means of achieving wavelength multiplexing and demultiplexing. However, the performance of such devices can be limited by fabrication imperfections such as rod size nonuniformities. In this paper, coupled mode theory (CMT) is applied in order to study the implication of the variation of the size of the rods. CMT can provide a useful insight in the effect of size variations, and unlike other numerical methods such as the finite difference time domain, it does not require excessive computational time. Using CMT, the relation between the size nonuniformities and the coupler's insertion loss and extinction ratio is analyzed. It is shown that even a small size variation of the order of 2%-3% can degrade the performance of the device.
TL;DR: Two systems of coupled-mode equations for spatial gap solitons in one-dimensional and quasi-one-dimensional photonic lattices induced by two interfering optical beams in a nonlinear photorefractive crystal are derived.
Abstract: We derive two systems of coupled-mode equations for spatial gap solitons in one-dimensional s1Dd and quasi-one-dimensional sQ1Dd photonic lattices induced by two interfering optical beams in a nonlinear photorefractive crystal. The models differ from the ordinary coupled-mode system se.g., for the fiber Bragg gratingd by saturable nonlinearity and, if expanded to cubic terms, by the presence of four-wave-mixing terms. In the 1D system, solutions for stationary gap solitons are obtained in an implicit analytical form. For the Q1D model and for tilted s“moving” d solitons in both models, solutions are found in a numerical form. The existence of stable tilted solitons in the full underlying model of the photonic lattice in the photorefractive medium is also shown. The stability of gap solitons is systematically investigated in direct simulations, revealing a nontrivial border of instability against oscillatory perturbations. In the Q1D model, two disjointed stability regions are found. The stability border of tilted solitons does not depend on the tilt. Interactions between stable tilted solitons are investigated too. The collisions are, chiefly, elastic, but they may be inelastic close to the instability border.
TL;DR: Analytical expressions for the new (higher) modulational thresholds and the size of the "band gap" as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory and favorably compared with results obtained from the full system equations.
Abstract: We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean-field models for singly and doubly degenerate optical parametric oscillators. Analytical expressions for the new (higher) modulational thresholds and the size of the "band gap" as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory. Then, by means of a nonlinear analysis, we derive amplitude equations for the unstable modes and find the stationary solutions above threshold. The form of the unstable mode is different in the lower and upper parts of the band gap. In each part there is bistability between two spatially shifted patterns. In large systems stable wall defects between the two solutions are formed and we provide analytical expressions for their shape. The analytical results are favorably compared with results obtained from the full system equations. Inhibition of pattern formation can be used to spatially control signal generation in the transverse plane.
TL;DR: In this article, the authors introduce a model for two coupled waves propagating in a hollow-core fiber: a linear dispersionless core mode and a dispersive nonlinear surface mode.
Abstract: We introduce a model for two coupled waves propagating in a hollow-core fiber: a linear dispersionless core mode and a dispersive nonlinear surface mode. The linear coupling between them may open a bandgap through the mechanism of avoidance of crossing between dispersion curves. The third-order dispersion of the surface mode is necessary for the existence of the gap. Numerical investigation reveals that the entire bandgap is filled with solitons, and they are stable in direct simulations. The gap-soliton (GS) family includes stable pulses moving relative to the given reference frame up to limit values of the corresponding boost delta, beyond which they do not exist. The limit values are asymmetric for delta > or < 0. Recently observed solitons in hollow-core photonic crystal fibers may belong to this GS family.
TL;DR: The dependence of the resonator characteristics on the reflector design and parameters is studied in detail and high quality factors and small modal volumes are found for a wide variety of design parameters.
Abstract: We study comprehensively using numerical simulations a new class of resonators, based on a circular photonic crystal reflector. The dependence of the resonator characteristics on the reflector design and parameters is studied in detail. The numerical results are compared to analytic results based on coupled mode theory. High quality factors and small modal volumes are found for a wide variety of design parameters.
TL;DR: Polarization-resolved measurements of power transmission, reflection and group delay clearly reveal the PC waveguide filtering properties.
Abstract: An experimental study of light propagation near a small band gap for a lattice-of-holes InP photonic crystal waveguide is reported. Polarization-resolved measurements of power transmission, reflection and group delay clearly reveal the PC waveguide filtering properties. Group delay enhancement was observed close to the band-edges together with very large dispersion. The test devices were fabricated with a novel technique that allows incorporation of deeply-etched photonic crystals within an InP photonic integrated circuit.
TL;DR: In this paper, a two-dimensional (2D) method describing the whispering gallery mode in a microgear resonator is presented, which analytically describes the field within the disk and outside the grating using a finite-difference scheme in polar coordinates.
Abstract: In this paper, a two-dimensional (2-D) method describing the whispering gallery mode in a microgear resonator is presented. The microgear is a microdisk surrounded by a circular grating. The method, which is based on the Floquet-Bloch formalism, analytically describes the field within the disk and outside the grating. On the other hand, the field within the grating is calculated using a finite-difference scheme in polar coordinates. Matching the boundary conditions, it is possible to work in a forced oscillation regime or in a free oscillation regime (laser mode). The resonant wavelength and quality factor can then be deduced. Compared to the coupled mode theory and to 2-D finite-difference time-domain computations, the method is faster and more accurate. Moreover, a polarization effect of the microgear is demonstrated. The TE polarization experiences a Q-factor improvement contrary to TM polarization. Finally, microgear structures prove to be more efficient than micro flowers.
TL;DR: Small random nonuniformities in two-core photonic crystal fibers can lead to essentially independent core propagation by drastically reducing the efficiency of coupling.
Abstract: Random nonuniformities in the photonic crystal lattice are shown to reduce the coupling length and the coupling efficiency of two-core photonic crystal fibers. These coupling properties are extremely sensitive to imperfections when the air holes are large; variations in the lattice of less than 1% are sufficient to cause essentially independent core propagation due to a drastic reduction in the efficiency of the core coupling. The observed sensitivity of two-core fibers to lattice imperfections is explained through a comparison with coupled mode theory.
TL;DR: By means of coupled mode theory and transfer matrix technique, a method is presented in this article for analyzing the bending coupling between straight and bent rectangular waveguides, or between two bent rectangular Waveguides.
Abstract: By means of the coupled mode theory and transfer matrix technique, a method is presented for analyzing the bending coupling between straight and bent rectangular waveguides, or between two bent rectangular waveguides. Calculations show that an effective coupling region exists around the central coupling point, in which the bending coupling appears, beyond which the bending coupling is very weak, and the propagation power in each waveguide becomes constant. When the bending radius becomes larger or the central coupling gap becomes smaller, this effective coupling region becomes wider, in which the coupling behavior becomes stronger.
TL;DR: It is found that modes polarized perpendicular to the metal surface can resonantly excite surface plasmons, extinguishing the mode in the waveguide core, while modes polarized parallel to metal surface only suffer mode attenuation due to the presence of the metal.
Abstract: We demonstrate that metallic electrodes symmetrically placed about a single mode dielectric waveguide can effectively polarize the mode by excitation of surface plasmons The transmission through the metal electrode waveguide structure is examined as a function of mode polarization and electrode spacing It is found that modes polarized perpendicular to the metal surface can resonantly excite surface plasmons, extinguishing the mode in the waveguide core, while modes polarized parallel to metal surface only suffer mode attenuation due to the presence of the metal The phase matching conditions for excitation of surface plasmons are examined and the polarization and insertion loss of the transmitted mode is experimentally verified