Showing papers on "Coupled mode theory published in 2001"
TL;DR: In this article, a multiplexer-demultiplexer (MUX-DEMUX) based on photonic crystal (PC) waveguide couplers is proposed.
Abstract: A multiplexer-demultiplexer (MUX-DEMUX) based on PC waveguide couplers is proposed, and its wavelength demultiplexing properties are theoretically investigated. First, a two-channel MUX-DEMUX is designed and characterized, and then, by cascading, two stages of photonic crystal (PC) waveguide couplers with different coupling coefficients are constructed. The device sizes are expected to be drastically reduced from a scale of a few tens of micrometers to a scale of a few hundreds of micrometers in a MUX-DEMUX.
319 citations
TL;DR: In this article, theoretical and numerical analyses of waveguide branches in a photonic crystal are discussed, and numerical simulations of electromagnetic-wave propagation in photonic crystals are performed to identify structures with near-complete transmission.
Abstract: Theoretical and numerical analyses of waveguide branches in a photonic crystal are presented. Conditions for perfect transmission and zero reflection are discussed. Based upon these conditions, numerical simulations of electromagnetic-wave propagation in photonic crystals are performed to identify structures with near-complete transmission.
279 citations
TL;DR: In this paper, the transmission and Faraday rotation characteristics of one-dimensional photonic crystals in cerium-substituted yttrium iron garnet (Ce:YIG) with multiple defects in the optical bandgap were studied theoretically at /spl lambda/ = 1.55 /spl mu/m.
Abstract: The transmission and Faraday rotation characteristics of one-dimensional photonic crystals in cerium-substituted yttrium iron garnet (Ce:YIG) with multiple defects in the optical bandgap are studied theoretically at /spl lambda/ = 1.55 /spl mu/m. It is found that the interdefect spacing can be adjusted to yield a flat top response, with close to 100% transmission and 45/spl deg/ Faraday rotation, for film structures as thin as 30 to 35 /spl mu/m. This is better than a three-fold reduction in thickness compared to the best Ce:YIG films for comparable rotations, and may allow a considerable reduction in size in manufactured optical isolators. Transmission bands as wide as 7 nm are predicted, which constitutes a considerable improvement over previously reported bandwidths for magnetic photonic crystals. Diffraction across the structure corresponds to a longer optical path length than the thickness of the film, calling for the use of guided optics to minimize insertion losses in integrated devices. The basis for the flat-top transmission in ferrite photonic crystals is presented and discussed.
124 citations
TL;DR: In this article, the electromagnetic problem of modeling vertical-cavity surface-emitting lasers with their full three-dimensional characteristics is analyzed, including oxide confinement, mesa mirrors, metal contacts, and noncircular geometries.
Abstract: The electromagnetic problem of modeling vertical-cavity surface-emitting lasers with their full three-dimensional characteristics is analyzed, including oxide confinement, mesa mirrors, metal contacts, and noncircular geometries. The model is based on the mode expansion of the electromagnetic field in the continuous basis of cylindrical TE and TM modes of the cavity medium and on coupled mode theory. The full vectorial treatment of the problem allows a correct analysis of the polarization characteristics of these lasers, which is a topic of great interest both for the device physics and for many applications. A comparison between the fully vectorial treatment and the LP scalar approximation is carried out and polarization resolved results for rectangular and elliptical structures are presented.
80 citations
TL;DR: In this paper, a novel corrugated structure on an optical fiber is proposed and demonstrated to produce tunable long-period index modulation based on photoelastic effect, and the coupledmode theory based on Fourier series expansion is also developed.
Abstract: A novel corrugated structure on an optical fiber is proposed and demonstrated to produce tunable long-period index modulation based on photoelastic effect. The corrugated structure is a periodic variation made by chemical etching on the cladding radius of an optical fiber. By imposing this corrugated structure upon a built-in fiber Bragg grating (FBG), a superstructure grating with tunable reflectance is formed. In addition, couplings between the fundamental core mode and cladding modes take place under such a corrugated structure when the phase-matching condition is satisfied. Thus, the device can also act effectively as a long-period fiber grating (LPFG) with tunable coupling strength. We also develop the coupled-mode theory based on Fourier series expansion to describe such a corrugated sampled Bragg grating. The phase-matching condition for various sampling orders can be derived, and the calculated spectra are compared with those based on the fundamental matrix method. Optical measurements demonstrate some unique characteristics of these devices, and good qualitative agreements between simulation and measurement verify the viewpoint that long periodic index modulation is indeed induced by such a corrugated structure through the photoelastic effect when a tensile force is applied.
46 citations
TL;DR: In this paper, a method based on time-frequency representations is presented for identifying the non-linear modal parameters of a multi-degree-of-freedom nonlinear lightly damped mechanical system.
38 citations
TL;DR: In this paper, a heuristic formalism is developed for efficiently determining the specular reflectivity spectrum of two-dimensional textured planar waveguides, based on a Green's function approach where the electric fields are assumed to vary little over the thickness of the textured part of the waveguide.
Abstract: A heuristic formalism is developed for efficiently determining the specular reflectivity spectrum of two-dimensionally textured planar waveguides. The formalism is based on a Green’s function approach wherein the electric fields are assumed to vary little over the thickness of the textured part of the waveguide. Its accuracy, when the thickness of the textured region is much smaller than the wavelength of relevant radiation, is verified by comparison with a much less efficient, exact finite difference solution of Maxwell’s equations. In addition to its numerical efficiency, the formalism provides an intuitive explanation of Fano-like features evident in the specular reflectivity spectrum when the incident radiation is phase matched to excite leaky electromagnetic modes attached to the waveguide. By associating various Fourier components of the scattered field with bare slab modes, the dispersion, unique polarization properties, and lifetimes of these Fano-like features are explained in terms of photonic eigenmodes that reveal the renormalization of the slab modes due to interaction with the two-dimensional grating. An application of the formalism, in the analysis of polarization-insensitive notch filters, is also discussed.
37 citations
Patent•
27 Jul 2001
TL;DR: In this article, a waveguide structure consisting of concatenated grating sections, each having different physical characteristics as compared with adjacent grating segments, is proposed for filtering optical radiation.
Abstract: A grating, suitable for filtering optical radiation, comprises a plurality of concatenated grating sections each having different physical characteristics as compared with adjacent grating sections. At least one of the sections comprises a waveguide structure formed by a thin strip (100) of a material having a relatively high free charge carrier density surrounded by material having a relatively low free charge carrier density. The strip has finite width (W) and thickness (t) with dimensions such that optical radiation having a wavelength in a predetermined range couples to the strip and propagates along the length of the strip as a plasmon-polariton wave. Various grating architectures may be implemented, e.g. chirped, interleaved, uniform, etc. A method of producing such gratings derives normalized phase constants and attenuation constants and then uses, for example, TMM or Coupled Mode Theory to derive therefrom the optical response of the grating.
35 citations
TL;DR: In this article, a linear grating fabricated on top of the waveguide reproduces a photonic-bandgap structure was used for second-harmonic generation in planar waveguide geometry.
Abstract: Second-harmonic generation (SHG) is investigated in a planar waveguide geometry under conditions for which the use of a linear grating fabricated on top of the waveguide reproduces a photonic-bandgap structure. The fundamental mode of the guide, which coincides with the fundamental pump frequency, is tuned at the photonic band-edge resonance in order to enhance field-localization effects. However, the linear grating alone is not able to produce both field confinement and phase matching of the second-harmonic-generation process. Phase matching is obtained with the additional modulation of the nonlinear susceptibility χ(2), as in conventional quasi-phase-matching schemes. The conversion efficiency achieved with both linear and nonlinear gratings is orders of magnitude greater than that of a quasi-phase-matched device of the same length.
26 citations
TL;DR: In this paper, the authors derived near-threshold coupled-mode equations that include the effects of radiation for TE fields in circular grating surface-emitting distributed feedback (DFB) lasers with second-order gratings.
Abstract: We derive near-threshold coupled-mode equations that include the effects of radiation for TE fields in circular-grating surface-emitting distributed feedback (DFB) lasers with second-order gratings. The analysis uses an exact description of the periodic grating that is valid for any grating shape and depth. For low-order azimuthal modes, approximate equations are found that are the same as those for a linear DFB laser, though the boundary conditions differ. We solve the coupled-mode equations for a weakly guiding laser numerically for low- and higher-order radial and azimuthal modes and compare these numerical results to previous experimental observations and to the results found for linear gratings. For sufficiently strong coupling, radiative losses have a significant impact on the mode structure of the laser, breaking the radial (longitudinal) mode symmetry otherwise seen for the lowest order azimuthal modes and improving mode selectivity.
23 citations
TL;DR: Theoretical analysis of a recently experimentally demonstrated erbium-doped twin-core (ErTCF) fiber saturable-absorber-based narrow-band tracking filter is presented in this article.
Abstract: Theoretical analysis of a recently experimentally demonstrated erbium-doped twin-core (ErTCF) fibre saturable-absorber-based narrow-band tracking filter is presented. Basic qualitative characteristics of the filter are deduced from an analogy with an ideally inhomogeneously broadened saturable absorber while the effect of wide band saturation of absorption due to spatial overlap of individual spectral components of the radiation is studied in detail using a numerical model based on coupled mode theory, resolved in space and frequency. The effect of the input power, twin-core fibre length and laser operating wavelength on the spectral characteristics of the filter is investigated.
TL;DR: In this paper, a model of one-dimensional waveguiding photonic bandgap (PBG) structures, based on leaky mode propagation (LMP) method, is proposed for the first time.
Abstract: A model of one-dimensional (1-D) waveguiding photonic bandgap (PBG) structures, based on leaky mode propagation (LMP) method, is proposed for the first time. A complete analysis of the propagation characteristics, including the determination of modal propagation constants, electromagnetic field harmonics and total field distribution, transmission and reflection coefficients, total forward and backward power flow in the structure, guided and radiated power, and total losses, has been carried out for a finite extension configuration. The numerical results have been compared with those obtained by using other methods, showing a very good agreement together with some significant advantages in terms of very low computational time, absence of any a priori theoretical assumptions and approximations, capability of simulating the actual behavior of the device as a reflector, and fast determination of the bandgap position.
TL;DR: In this paper, a novel scheme is presented that can be used to efficiently pump optical waveguide amplifiers based on the coupling between two adjacent waveguides, where pump light is gradually coupled from a nonabsorbing pump waveguide into the amplifier waveguide.
Abstract: A novel scheme is presented that can be used to efficiently pump optical waveguide amplifiers. It is based on the coupling between two adjacent waveguides, where pump light is gradually coupled from a nonabsorbing pump waveguide into the amplifier waveguide. The coupling between the waveguides in such a configuration is calculated using an improved coupled mode theory (CMT). The proposed distributed coupling scheme can enhance the optical gain in systems that exhibit a reduced pumping efficiency at high pump power. A numerical example is given for a sensitized neodymium-doped polymer waveguide amplifier, in which the optical gain increases from 0.005 dB to 1.6 dB by changing from conventional butt-coupling to distributed coupling.
TL;DR: In this paper, the analytic behavior of an asymmetric triple mode evolution coupler based on window filter functions is analyzed by the coupled mode theory, and its performance verified by the method of lines.
TL;DR: In this article, the authors apply the full vectorial model recently published in Bava et al. which is based on the mode expansion of the vectorial electromagnetic field in the continuous basis of cylindrical TE and TM modes of a reference medium.
Abstract: The consequences of material anisotropies in vertical-cavity surface-emitting lasers (VCSELs) are analyzed in detail. To this aim we apply the full vectorial model recently published in Bava et al. [Phys. Rev. A 63, 023816 (2001)] which is based on the mode expansion of the vectorial electromagnetic field in the continuous basis of cylindrical TE and TM modes of a reference medium and on coupled mode theory. The self-consistency between backward and forward waves leads to an eigenvalue problem: the complex eigenvalues determine both the required gain and the lasing frequency of the cavity modes, while the eigenvectors allow the reconstruction of the fields. The capability of the fully vectorial treatment to experience the tensorial nature of the dielectrical permittivity is exploited to analyze in detail the consequences of the elasto-optic effect in VCSELs with reference to modal frequencies, gains and profiles.
04 Jul 2001
TL;DR: In this article, an extended model for the interaction between core and cladding modes in chirped grating is developed and used to study mode dynamics and spectral equalisation, and the model can be used to analyze the spectral equalization.
Abstract: An extended model for the interaction between core and cladding modes in chirped grating is developed and used to study mode dynamics and spectral equalisation.
TL;DR: The transfer-matrix approach is found to account well for the features of the transmission spectra of the corrugated long-period gratings, and the conventional coupled-mode theory is inadequate for the modeling of such a structure.
Abstract: A transfer-matrix method is developed for modeling a corrugated long-period fiber grating. Cladding-mode resonance in such a corrugated structure can be controlled by the applied tensile stress based on the photoelastic effect. A first-order vectorial perturbation expansion is used to derive the mode fields of the two basic regions under the strain-induced index perturbation. Because the etched cladding radius is much smaller than the unetched radius, the effect of the corrugated structure on cladding modes cannot be treated as a small perturbation. Thus the conventional coupled-mode theory is inadequate for the modeling of such a structure. Based on a self-consistent mode-matching technique, mode coupling within the corrugated structure can be described by a set of transfer matrices. We apply the formulation to the calculation of the transmission spectra of a corrugated long-period grating and compare the calculated with the experimental results. The transfer-matrix approach is found to account well for the features of the transmission spectra of the corrugated long-period gratings.
TL;DR: In this article, an optical coupling between a spherical microresonator and a plane dielectric substrate is investigated for a small sphere whose diameter is only a few ten times as large as the optical wavelength.
Abstract: Optical coupling between a spherical microresonator and a plane dielectric substrate is investigated for a small sphere whose diameter is only a few ten times as large as the optical wavelength. A unique characteristic of small microresonators, relaxation of the phase-matching requirement that is due to the small size, is demonstrated on the basis of experimental results and model numerical calculations. The difference between the frequency and the propagation constant as parameters to describe the resonances of microresonators is clarified. Based on the numerical results, intrinsic restriction on a distance between the resonator and the coupler is also suggested.
TL;DR: In this paper, the second harmonic generation of TM polarisation in a planar waveguide with a non-linear anisotropic substrate using coupled mode theory under the non-depleted pump approximation was analyzed.
Abstract: In this paper we analyse the second harmonic generation of TM polarisation in a planar waveguide with a non-linear anisotropic substrate using the coupled mode theory under the non-depleted pump approximation. It is an extention of our previous paper in which we treated TE polarisation. Moreover, both guided waves and Cerenkov radiation are now taken into account simultaneously. It is shown both analytically and numerically that the Cerenkov efficiency peak follows the L3/2 dependence on the interaction length L also for TM polarisation. In an anisotropic KTP/Si3N4/SiO2 waveguide, higher maximum attainable second harmonic generation (SHG) efficiency was calculated for the TM polarisation than for the optimum TE case.
TL;DR: In this paper, an overview of the nonlinear symmetric guided-wave optical coupling systems is given that introduces a generalization of the analysis for nonlinear asymmetric coupling, which is applicable for both symmetric and asymmetric guided wave coupling structures.
Abstract: We present an overview and generalized analysis through a number of general cases of coupled-wave equations for nonlinear optical guided-wave coupled systems. They are applicable for both symmetric and asymmetric guided-wave coupling structures. An overview of the nonlinear symmetric guided-wave optical coupling systems is given that introduces a generalization of the analysis for nonlinear asymmetric coupling. General cases including those for nonlinear guided modes and power nonorthogonality are considered, and full, power-conserved and nonorthogonal coupled-mode equations (in terms of parameters directly related to the light-wave power contained in the waveguides) are proposed and analytically described. A numerical case study of the nonlinear asymmetric coupling system, which consists of a slab-planar optical waveguide and an optical fiber is described.
17 Oct 2001
TL;DR: In this article, an improved coupled mode approach is presented for the analysis of plane-wave interaction with a spatially periodic permittivity dielectric layer, which consists of two parts, in the first part the eigenvalues and eigenvectors of coupled mode system of equations are corrected to reduce the inherent errors arising by neglecting second-order derivatives.
Abstract: An improved coupled mode approach is presented for the analysis of plane-wave interaction with a spatially periodic permittivity dielectric layer. The method consists of two parts, in the first part the eigenvalues and eigenvectors of coupled mode system of equations are corrected to reduce the inherent errors, which arise by neglecting second-order derivatives. In the second part, a scattering matrix representation of cascaded systems is used to model the effect of boundaries. The problem under consideration is a 2-D planar grating structure illuminated by a TE polarized incident wave, but the method can be applied to other grating structures such as couplers, or any other structure for which the coupled mode approximation is used, similarly. Comparisons with results obtained using alternative methods are given to verify the accuracy of proposed method.
04 Jul 2001
TL;DR: In this article, a Fourier transform-based analytical coupled-mode theory for high refractive index contrast Bragg gratings is presented, which is useful for designing gratings and photonic crystal structures.
Abstract: We present a Fourier transform-based analytical coupled-mode theory for high refractive index contrast Bragg gratings. The theory is useful for designing gratings and photonic crystal structures. It also predicts photon localisation for only infinite crystalline structures.
Journal Article•
TL;DR: In this article, a Fourier transform formalism is proposed to describe photon behavior near the bandgap region of photonic crystal structures using optical reciprocal-space, which is a modified Debye-Waller approximation in conjunction with the use of a resonant refractive index provides an analytic solution to the coupledmode equations describing photon propagation in a periodic high dielectric contrast structure.
Abstract: We propose an approach to the problem of describing photon behaviour near the bandgap region of photonic crystal structures using a Fourier transform formalism defined in optical reciprocal-space. A modified Debye-Waller approximation in conjunction with the use of a resonant refractive index provides an analytic solution to the coupled-mode equations describing photon propagation in a periodic high dielectric contrast structure. Overall, this represents a new technique for solving the inverse scattering problem. We use this method to consider photon behaviour at the Brillouin zone edges of a one-dimensional photonic crystal structure: our results showing agreement with conventional theory for the standard assumption of an infinitely long grating structure. However, when a photon is located in the bandgap region of a finite (five periods used as an example) high refractive index contrast grating structure, we find that photon velocity becomes superluminal as the photon wave becomes evanescent. This is in agreement with the basic precepts of the uncertainty principle. Additionally, as the bandgap strength increases, the probability of transmission through the dielectric barrier reduces exponentially, with an associated reduction in tunnelling time.
04 Jul 2001
TL;DR: In this article, the performance of a coupler/bragg grating interferometric OADM at 40Gb/s was investigated and it was shown that employing such filters with typically degraded spectral responses can result in at least 0.15 dB higher Eye-Opening Penalty compared to fully optimized OADMs.
Abstract: The performance of a coupler/Bragg grating interferometric OADM is studied theoretically at 40Gb/s. Employment of such filters with typically degraded spectral responses can result in at least 0.15 dB higher Eye-Opening Penalty compared to fully optimized OADMs.
TL;DR: In this paper, a class of soliton-like solutions for the electromagnetic wave propagating in an infinite one-dimensional periodic structure with an intensity-dependent refractive index was found. But the amplitude of the solitary wave is dependent on the incident frequency and the pulse width.
Abstract: On the basis of coupled\|mode theory we find a class of solitary solutions for the electromagnetic wave propagating in an infinite one\|dimensional periodic structure with an intensity\|dependent refractive index. We show that the amplitude of the solitary wave is dependent of the incident frequency and the pulse width. In the Bragg resonance limit, the solitary wave can be simplified to a soliton\|like solution which was named as “gap soliton” or “slow Bragg soliton”.
Journal Article•
TL;DR: In this article, a compact optical element integrating a hollow waveguide and a photonic band-gap structure is created by combining a diffraction grating and a mirror, which offers much promise for various applications in nonlinear and ultrafast optics.
Abstract: A compact optical element integrating a hollow waveguide and a photonic band-gap structure is created by combining a diffraction grating and a mirror. This element offers much promise for various applications in nonlinear and ultrafast optics. The main features of experimental transmission spectra of such waveguide structures are qualitatively interpreted in terms of the coupled-mode theory. Localization of light near the surface of a metal-coated grating in lowest order TM modes in the created waveguide enhances effects related to the photonic band-gap structure.
TL;DR: In this paper, a four-layered leaky waveguide configuration in Z-cut LiNbO 3, where the pump and signal waves are guided modes and the idler is radiated into the substrate has been studied using coupled mode approach.
Abstract: Parametric amplification of signal wave in a four-layered leaky waveguide configuration in Z-cut LiNbO 3 , where the pump and signal waves are guided modes and the idler is radiated into the substrate has been studied using coupled mode approach. It is shown that in this configuration, the signal gain can be greatly enhanced as compared to the case of a three-layered QPM Cerenkov-idler configuration. The studies show that by appropriately choosing the waveguide parameters, one can have a trade-off between signal gain bandwidth and the peak signal gain achieved. These studies should find application in designing optical parametric amplifiers and oscillators.
09 Jun 2001
TL;DR: In this article, the first use of the bidirectional Beam Propagation Method to simulate nonlinear problems is presented. And the reection response of a nonlinear grating is calculated.
Abstract: We demonstrate the first use of the bidirectional Beam Propagation Method to simulate nonlinear problems. Specifically, the reection response of a nonlinear grating is calculated. Additionally, nonlinear gratings used for switching or amplification are simulated.
29 Oct 2001
TL;DR: In this paper, the effects of compression induced birefringence on reflection spectra of fiber Bragg gratings (FBG) are investigated experimentally together with the theoretical analysis.
Abstract: In this paper, the effects of compression induced birefringence on reflection spectra of fiber Bragg gratings (FBG) is investigated experimentally together with the theoretical analysis. The coupled mode theory has been employed, by considering the LPx and LPy modes, to obtain accurate results for optical responses of FBG with compression-induced birefringence. The effects of polarization states of the incident light and compression conditions have also been investigated. Good agreements between experimental results and numerical simulations have been obtained.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: In this article, the insertion loss for a filter composed of a TCS-RDT and two split-electrode interdigital transducers (IDTs) was investigated.
Abstract: Computed results of all the coefficients of coupled-mode equations are presented for a transduction center-shift-reversal-of-directivity transducer (TCS-RDT) and an electrode-width-controlled-reversal-of-directivity transducer (EWC-RDT) on a 50°Y-25°X La3Ga5-SiO14 substrate. To the best of our knowledge, an EWC-RDT is being reported for the first time. The aluminum electrode thickness and width dependences of the coefficients are investigated in detail. Numerical results show that we can choose pairs of width and height of the electrodes for a distance of λ/8 with λ being the surface acoustic wave (SAW) wavelength at the center frequency between the reflection center and the transduction one. Our results of the insertion loss for a filter composed of a TCS-RDT and two split-electrode interdigital transducers (IDTs) agree well with those of the earlier experiments.