Showing papers on "Coupled mode theory published in 2000"

Cladding-mode-resonances in air-silica microstructure optical fibers

Abstract: We present a comprehensive study of mode propagation in a range of different air-silica microstructured fibers. The inscription of both Bragg and long-period gratings (LPGs) into the photosensitive core region of microstructured air-silica fibers has allowed us to generate complex transmission spectra from a range of fibers with various fill fractions and with increasing air-clad hole diameters. The spectral characteristics for typical air-hole geometry's are explained qualitatively and modeled using beam propagation simulations, where the numerical modeling corroborates the experimental measurements. Specifically, the data reveal the propagation of higher order leaky modes in fibers with periodically spaced air-holes, and relatively small air-fill fraction. And as the air-hole diameter increases, spectra show cladding modes defined solely by the inner air-clad region. We describe these measurements and corresponding simulations and discuss their implications for the understanding of such air-hole structures.

Two-dimensional vector-coupled-mode theory for textured planar waveguides

Abstract: We develop a model to treat coupling between guided modes in planar dielectric waveguides that have been textured in two dimensions with a thin surface grating The formulation is based on a general Green's-function technique that self-consistently determines the field in the surface grating due to the polarization there With simplifying approximations, this formalism is cast into a two-dimensional (2D) vector-coupled-mode theory that is more computationally efficient, and that gives considerable insight into the nature of mode coupling in 2D textured structures These models are applied, by way of example, to illustrate some interesting properties of leaky and bound modes that are coupled together by 2D periodic texture In particular we discuss the complex photonic band structure describing the dispersion, lifetimes, and polarization properties of the resonant states associated with the textured waveguide In our analysis we emphasize the fundamental differences between coupling in 2D textured waveguides and infinite 2D photonic crystals We also show that the vector-coupled-mode theory agrees well with the self-consistent formulation

On the application of coupled mode theory for modeling fiber Bragg gratings

Abstract: We remove some ambiguities associated with the coupled mode description of light propagation in fiber Bragg gratings (FBC's). We show, in particular, that different methods employed in the literature lead to physically distinct results. The significant distinctions are discussed both for interferometric systems and intensity-only spectral measurements. Analysis of the reflection spectrum of a suitably designed double-grating structure is shown to result in a novel form of spectral hole, similar to the well-known effect derived from discontinuous phase gratings.

Large magnetooptical Kerr rotation with high reflectivity from photonic bandgap structures with defects

Abstract: We perform a theoretical study of enhancement of magnetooptical rotation on reflection of light from a periodic system with a defect. Using calculations based on a coupled mode approach and the transfer matrix method we demonstrate that an asymmetric placing of a single defect allows arbitrary Kerr rotations with better than 99% reflectivity from very short devices.

Analysis of TM-polarized DFB laser structures with metal surface gratings

Abstract: An analysis of distributed feedback (DFB) laser structures with metallized surface grating structures in TM polarization is presented. The modal properties of these structures are described using coupled-mode theory where the coupling coefficients are derived from rigorously computed on-resonant Floquet-Bloch solutions of the waveguide grating problem. Based on this theory, first- and second-order DFB quantum cascade laser structures operating at a wavelength of 10 /spl mu/m are investigated numerically. We show that, utilizing a metal stripe grating structure, second-order laser structures are feasible showing efficient surface emission, whereas radiation into the substrate is strongly suppressed. The fraction of stimulated emission power being emitted via the surface can be as high as 17.5% whereas a low threshold gain of 20 cm/sup -1/ is maintained.

Corrections to coupled mode theory for deep gratings

Abstract: We generalize the standard coupled mode equations describing interactions between forward and backward propagating waves in a nonlinear optical Bragg grating. Including the lowest order corrections of the grating depth, we obtain a Hamiltonian system that can be regarded as an extension of the usual coupled mode equations for shallow gratings. The results are consistent with existing results based on a Bloch wave expansion. We also obtain exact traveling solitary wave solutions, that can be regarded as a generalized gap soliton, modified by the grating's depth.

Analysis of core-mode to radiation-mode coupling in fiber Bragg gratings with finite cladding radius

Abstract: Fiber Bragg gratings (FBGs) are often surrounded with dielectric material whose refractive index is higher than that of cladding. The purpose is to prevent cladding modes because coupling to cladding modes may cause undesirable dips on the short wavelength side of the main Bragg band in the core-mode transmission spectrum. In such FBGs, core-mode to radiation-mode coupling can cause a loss band continuum. Until now, however, reported analyses of this core-mode to radiation-mode coupling have been limited to hypothetical FBGs with an infinite cladding radius. This paper presents, to the best of our knowledge, the first analysis of core-mode to radiation-mode coupling in real FBGs with a finite cladding radius. We derive a formula to calculate the core-mode transmission loss caused by the radiation-mode coupling. We show calculated core-mode transmission spectra that exhibit such fringes as have already been observed experimentally but not yet theoretically estimated.

Collinear guided wave to leaky wave acoustooptic interactions in proton-exchanged LiNbO/sub 3/ waveguides

Abstract: The results of a detailed theoretical study on collinear guided wave to leaky wave acoustooptic (AO) interactions in proton-exchanged LiNbO/sub 3/ (PE:LiNbO/sub 3/) planar waveguides are presented. The guided-to-leaky mode conversion for an input optical beam at the wavelength of 632.8 nm by the induced diffraction grating from a collinear surface acoustic wave (SAW) is analyzed using a generalized multimode formulation of the coupled mode theory. Mode conversion efficiency and AO bandwidth have been calculated as functions of acoustic frequency, interaction length, guiding layer thickness, and acoustic drive power density for three cuts of the LiNbO/sub 3/ substrate. High performance configurations that are desirable for application to demultiplexing and switching in optical communication systems are identified, and the corresponding channel capacity and frequency resolution are determined. For example, it was shown that the X-cut configuration features the highest mode conversion efficiency. However, a relatively small AO bandwidth is associated with this configuration. Both high mode conversion efficiency and large AO bandwidth can be accomplished at the guiding layer thickness of 1.0 /spl mu/m. A TM/sub o//spl rarr/TE/sub /spl nu// mode conversion efficiency as high as 42% together with an AO bandwidth of approximately 70 MHz can be achieved in the Z-cut waveguide at the guiding layer thickness of 1.0 /spl mu/m, acoustic drive power density of 50 mW/mm, interaction length of 40 mm, and acoustic frequency of 460 MHz. The corresponding channel capacity and frequency resolution are 745 and 0.09 MHz, respectively. Measured mode conversion efficiencies as high as 90 and 78% obtained at the acoustic frequencies of 107 and 367 MHz using the X-cut substrate and the Y-propagation SAW have verified the theoretical prediction on the mode conversion efficiencies.

Mode coupling in tilted planar waveguide gratings

Abstract: Three different grating tilting formulas for predicting the optimum grating tilt angle for strong mode coupling in planar waveguide gratings are derived. The optimum tilt angles obtained by the ray-optics approach deviate ∼1° for transmissive mode coupling and ∼1.5° for reflective mode coupling from those computed by the coupled-mode approach. The coupled-mode analysis and ray-optics analysis of the tilted planar waveguide gratings show that the transmissive planar waveguide gratings should be tilted more than 84° for strong TE0-to-TEμ mode coupling near 1550 nm.

Coupled-Mode Analysis of Loss in Bent Single-Mode Optical Fibers

Abstract: In this study, we analyzed the loss formation in bent single-mode optical fibers using a semi-analytical method, which is a combination of conformal mapping and coupled-mode theory based on the two-layer step-index optical fiber model. The pure bend loss results were compared to those reported in the existing literature. The advantage of using this method is that it provides insight into the mode field behavior and loss formation in bent fibers and accurately presents the power distribution in the cross section of the fibers.

Reduced cladding mode losses in tilted gratings that are rotationally symmetric

Abstract: We present a novel method to manipulate mode coupling by using tilted gratings written in standard fiber that is rotated during the writing process. We show theoretically that such gratings exhibit significantly reduced transmission losses in the 15-nm wavelength range below the main core-to-core reflection peak. By combining with existing methods, cladding mode losses can be further reduced.

Bandpass spectra of evanescent couplers with long period gratings

Abstract: The authors propose a novel optical bandpass filter with strong sidelobe extinction but without the reflected light associated with Bragg grating filters. Long period index gratings written in the cores of an evanescent singlemode coupler suppress cross-coupling at the desired transmission wavelength, while strong optical loss in the secondary core rejects out-of-band wavelengths. Transmission spectra are calculated using coupled mode theory.

Second- and higher order resonant gratings with gain or loss-Part II: designing complex-coupled DFB lasers with second-order gratings

Abstract: For part I see, ibid., p. 1421, (2000). This paper deals with the investigation of second-order DFB lasers with a gain grating. It is shown that by proper choice of the duty cycle, one may take advantage of the different radiation losses between the mode with the lowest threshold gain and the second mode to increase the single-mode yield and also obtain a strong complex-coupling with high external efficiency. The impact of the random phase of high-reflection (HR)-coated facet on modal properties in an anti-reflection and HR combination is also investigated.

Generation, acousto-optic interactions, applications

Abstract: 1. Piezoelectric Transducers for Bulk Waves.- 2. Interdigital-Electrode Transducers for Surface Waves.- 3. Elastic Waves and Light Waves.- 4. Signal Processing Components.- 5. Sensors and Instrumentation.- A. Spatial Distribution of Electrical Quantities.- A.1 Simple Transducer.- A.2 Single-Element Charge Distribution.- A.3 General Case. Charge Density. Current Intensity.- B. Coupled Mode Theory.- B.1 Formulation. Coupled Mode Equations.- B.2 Solution.- B.2.1 Propagation in the Same Direction.- B.2.2 Propagation in Opposite Directions.- C. Legendre Functions and Polynomials.- D. Scattering Matrix and Mixed Matrix.- D.1 Quadripole. Scattering Matrix.- D.2 Hexapole. Mixed Matrix. Directionality.- E. Matrix Representation of a Dioptrie System.- F. Linear Systems of Differential Equations.- G. Stationary Phase Method.- References.

Analysis of twisted nematic liquid crystal Fabry-Perot interferometer (TN-FPI) filter based on the coupled mode theory

Abstract: The tuning characteristics of a twisted nematic (TN) liquid crystal (LC) Fabry–Perot interferometer (FPI) wavelength filter, which is a basic component of wavelength division multiplexed transmission systems, is analyzed using coupled mode theory. First, a simplified modeling of the refractive index change in the LC layer is presented. Next, various characteristics of the eigen polarization modes of the LC medium and the cavity are derived analytically. Finally, the qualitative interpretation of the behavior of the FPI's resonance spectrum are given.

High speed integrated acousto-optic switch with high extinction ratio

Abstract: The technology of single phase unidirectional transducer and focused transducer was adopted for the design of acousto-optic switch. The extinction ratio up to 32 dB and switching speed at 300 ns was achieved.

Azimuthal mode discrimination in radially chirped concentric-circle-grating distributed feedback lasers

Abstract: We report a theoretical investigation analyzing the threshold modes of a concentric-circle-grating (CCG) distributed feedback laser with a radially chirped first-order Bragg grating. A numerical coupled-mode analysis of a chirped CCG laser shows improved azimuthal mode discrimination for chirped gratings with linear, quadratic, and square-root radial dependence. Negatively chirped gratings, in which the grating period decreases with radius, result in improved threshold discrimination between the circularly symmetric fundamental mode and higher order modes; positively chirped gratings, in which the grating period increases with radius, result in decreased threshold for higher order modes in general. Also, the intensity for the fundamental mode at the grating center can be reduced by an order of magnitude using linearly chirped gratings.

Modelling of guided-wave Bragg gratings and grating sensors using the collocation method

Abstract: We have used the collocation method to model the characteristics of guided-wave Bragg gratings. The collocation method being a total field method, takes into account all modes, guided as well as radiation. We have first studied the effect of the grating structural parameters such as the grating profile and the duty cycle of periodic variation and have shown that these can have significant effect on the Bragg wavelength and the reflection spectrum. We have then obtained the response characteristics of gratings for their use in strain, temperature and pressure sensing. Our results compare very well with available experimental results. Comparisons with the coupled mode theory have also been included.

Micro-opto-electro-mechanical (MOEM) vibration sensor

Abstract: The combination of Integrated Optics with micro-mechanical structures on silicon offers immense potential for smart structure applications. One such application is sensing and mapping of vibration and vibrational modes. In the present proposal, a cantilever formed by bulk micro machining of . Silicon and optical waveguides formed by sol-gel process is considered. Among the various configurations possible, an optical directional coupler located close to foot of the cantilever is analyzed in detail. Analytical and simulation result using optical coupled mode theory to obtain the power transfer that is dependent on cantilever vibrations are presented.

Coupled mode theory for resonant excitation of waveguiding structures

Abstract: Resonant coupling of light beams via high-index media or gratings to planar waveguiding structures are of interest for both applications and from a theoretical point of view. Coupled Mode theory (CMT) can give an accurate description of the coupling process in terms of relatively simple expressions involving often a large number of coupling parameters. In this paper it is shown, using time reversal and energy conservation how these parameters are interrelated. The evaluation of the remaining independent parameters is shown to be possible using a few reflection and transmission coefficients for incoming plane waves, including in the calculations, if present, the effect of the grating. Further, it is proved that under certain condition a grating coupler may show exactly 100% reflection. Analytical expressions for the reflected and transmitted beams and the amplitude distribution of the excited mode are given for the case of incoming Gaussian beams. A few applications of the theory and considerations on its applicability are presented.

Effect of wavelength shift on PLC-type WDM directional coupler by UV irradiation

Abstract: The UV light of KrF excimer laser, which is used for making fiber gratings, is irradiated on PLC-type WDM directional couplers. After the irradiation, the shift of transmission wavelengths is observed as a function of UV exposure dose. The amount of the effective refractive index change of rectangular silica waveguides is calculated by the coupled mode theory and the measured data.

Crosstalks of two-waveguide and three-waveguide directional couplers

Abstract: Crosstalks of two-waveguide and three-waveguide directional couplers are analyzed mathematically based on the relationship between the coupled mode and the normal mode. Numerical techniques such as the finite-difference method and the beam propagation method are employed to confirm the validity of the derived expressions. The calculation results show that two-waveguide directional coupler is superior to any type of three-waveguide couplers from the practical viewpoint of the crosstalk and the coupling length.

Optimisation of digital optical switches

Abstract: A generally applicable procedure is given for shaping of 1 × 2 digital optical switches in order to reduce the cross-talk (CT) or, equivalently, the required device length. The method is based on coupled mode theory and assumes that the two coupled mode equations may be decoupled in good approximation. Doing so it follows that the cross talk may be expressed in terms of a Fourier component of a function, which depends on the shape of the device. Based on this a procedure for optimising the Y-junction may be formulated. Calculations, using the beam propagation method and coupled mode theory, on a thus obtained structure are presented and show that a length reduction by a factor of ∼2 can be obtained at a CT level of −38 dB.

Comparison of a new modal transfer matrix method with coupled-mode theory for simulation of long-period grating fiber sensors

Abstract: The modal transfer matrix method (MTMM) is a new general- purpose technique developed by the authors as an alternative to coupled mode theory (CMT) to study complex optical waveguide systems. It is applied here to overcome the numerical accuracy limitation of the beam propagation method (BPM) when simulating long-period gratings (LPG). Simulation of a LPG optical fiber sensor with a broad-wavelength source using the MTMM is compared with analytical results based on CMT. A simple grating parameter study shows that both methods are in agreement, indicating that the MTMM is a promising method of analysis. In addition, the results reveal the potential effect of combined variation in grating amplitude, spatial wavelength, and length on sensor performance. By discretizing the waveguide into small elements, the MTMM reduces the problem domain size and makes use of proven electromagnetic numerical simulation methods. An appropriate numerical method, in this case the BPM, is selected to compute each element's modal transfer matrix. The elements are then combined to predict the output from the overall waveguide system.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Analysis of High Power Millimeter Wave Waveguide Mode Converters with Input Mode Mixture

Abstract: Based on the coupled mode theory, this paper presents the study on the influence of input mode mixture in circular oversized waveguide mode converters. Three kinds of commonly used waveguide mode converters, including the waveguide mode converters with varying wall radius or small axis perturbations, and the waveguide mode converters with bent structures, are taken as the examples. The results show that the spurious input modes do not simply superimpose onto the output modes, and in some cases they may deteriorate the conversion efficiency for the main output mode. Methods for transforming such spurious input mode mixture simultaneously into the main output mode are also presented in this paper.

Application of the coupled mode theory to the problem of coupling between bent and straight waveguides.

Abstract: The coupling between high finesse (up to 140) cylindrical microresonators and straight waveguides is analysed using the Coupled Mode Theory and numerically calculated 2D fields of the unperturbed bend and straight waveguides. The calculated coupling constants are in good agreement with bouth experiments and other numerical methods. Extension of our approach to more advanced geometries, like coupling between bends, is straightforward.

Characterization of semiconductor Bragg gratings

Abstract: Bragg grating-based optical systems are important for both telecommunications and sensor applications. A new approach presented here which is rigorous yet computationally efficient, incorporates the finite element, the least squares boundary residual and the transfer matrix methods. The simulated results obtained show that the coupled mode theory (CMT) could be adequate for the characterization of Bragg grating devices in fiber, since the perturbed refractive index change is small. However, for Bragg grating devices in semiconductors, the use of CMT is shown to generate less accurate results than expected. Simulated results for various types of grating devices, such as uniform, chirped, apodized, super-structures and sampled grating devices are presented.

Ray optical determination of strong backward coupling coefficients of waveguide grating devices

Abstract: For calculation of strong backward coupling coefficients of waveguide gratings with arbitrary shapes, a rigorous method based on the ray-optics approach is proposed. Calculation accuracy depends on only on the limit of the rigorous coupled-wave theory used in the method.

Geometrical coupling effects in microchip laser array

Abstract: Summary form only given. We present an optical analysis of an hexagonal array of Nd:YAG microchip lasers using a coupled mode theory. Each microchip laser is designed with a stable plano-spherical microcavity. The supermode theory is used to calculate the near and the far field of a conventional hexagonal cell of lasers and the results are extend to an infinite hexagonal array.

Design and simulation of an integrated adiabatic transition for OADM devices

Abstract: The increasing diffusion of WDM communication systems requires low cost and efficient optical add-drop devices to add or drop channels at predefined wavelengths with reduced insertion loss and cross-interference. Many fiber based devices have already been proposed, however their integration allows an increase in the compactness and mechanical stability. We designed an integrated OADM that is composed of an asymmetric adiabatic transition followed by an asymmetric grating that converts the supermodes of the combined structure. In this paper we focus our attention mainly on the design of the transition that, besides having low insertion losses, should also be tolerant to the variation of the fabrication parameters and in particular of the grating position. Assuming typical glass on silica waveguides, the transition geometry has been determined using the coupled mode theory. Then the result have been verified and optimized with BPM simulations.