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Showing papers on "Coupled mode theory published in 1997"


Journal ArticleDOI
TL;DR: In this paper, an approximate closed-form expression for the loss in a planar phase grating is derived by using coupled-mode theory, which can be used to determine the spectral and angular width of a resonant-grating filter.
Abstract: An approximate closed-form expression for the loss in a planar phase grating is derived by using coupled-mode theory. It is shown that this loss expression can be used to determine the spectral and angular width of a resonant-grating filter. A resonant-grating filter is a free-space optic that takes advantage of grating resonances to create narrow-band reflection peaks. Design characteristics, such as bandwidth, have previously been determined by profiling the resonance in reflectivity with the use of numerically intensive vector-diffraction methods such as rigorous coupled-wave analysis. The coupled-mode approach described here, however, gives the resonant-filter width directly, without the need to profile the resonance. Therefore computation time and hence design time are reduced. In addition, it is shown that the coupled-mode approach provides physical insights into the factors contributing to filter bandwidth.

152 citations


Journal ArticleDOI
TL;DR: In this article, the coupling and detuning coefficients for multilayer interference coatings with coupled-mode theory were derived for Bragg mirror consisting of layers with arbitrary high and low refractive indexes.
Abstract: The analysis of multilayered interference coatings by coupled-mode theory is considered to be an approximation useful for small index, gain, and/or loss modulations. In this paper, we show that an exact analysis of a multilayer coating with coupled-mode theory is possible by redefining the coupling and detuning coefficients. We derive the correct coefficients for the case of a Bragg mirror consisting of layers with arbitrary high and low refractive indexes. A detailed comparison with coupled-mode theories using the standard coupling and detuning coefficients is presented.

94 citations


Journal ArticleDOI
TL;DR: A coupled-mode theory of fiber-optic add-drop filters, which involve directional coupling between two fibers combined with fiber Bragg gratings defined inside the coupling region, and the calculated device parameters satisfy the requirements for dense wavelength-division multiplexing applications.
Abstract: We present a coupled-mode theory of fiber-optic add drop filters, which involve directional coupling between two fibers combined with fiber Bragg gratings defined inside the coupling region. The analysis self-consistently accounts for both the directional and the reflection coupling, and the propagation constants and structure of the supermodes of the combined structure are derived. We present a detailed analysis of a filter design based on identical fibers. The calculated device parameters satisfy the requirements for dense wavelength-division multiplexing applications.

88 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical study of direct TM/sub 01/-TE/sub 11/ mode converters in highly overmoded, bent smooth, circular waveguides is presented for high-power millimeter waves.
Abstract: In this paper, a numerical study of direct TM/sub 01/-TE/sub 11/ mode converters in highly overmoded, bent smooth, circular waveguides is presented for high-power millimeter waves. The various shapes of bent waveguides are elaborately chosen, and their optimized geometrical dimensions have been achieved with a general optimization code employing the coupled mode theory. The mode converters designed can have high conversion efficiencies over 98% and wide bandwidths of 28%.

56 citations


Journal ArticleDOI
TL;DR: In this article, coupledmode equations that describe the switching dynamics of optical pulses in two parallel waveguides are derived, which differ from the conventional ones in having extra coupling terms that arise from the dispersion properties of the coupling coefficient.
Abstract: The coupled-mode equations that describe the switching dynamics of optical pulses in two parallel waveguides are derived. These equations differ from the conventional ones in having extra coupling terms that arise from the dispersion properties of the coupling coefficient. It is shown that the coupling-coefficient dispersion can cause pulse distortion or even pulse breakup and in general produces much more significant effects than the group-velocity dispersion.

54 citations


Journal ArticleDOI
TL;DR: The interaction between two one-dimensional quadraticsolitons has been investigated experimentally in lithium niobate planar waveguides for both parallel- and crossing-launched solitons.
Abstract: The interaction between two one-dimensional quadratic solitons has been investigated experimentally in lithium niobate planar waveguides for both parallel- and crossing-launched solitons.

44 citations


Journal ArticleDOI
TL;DR: It is shown that, for the same degree of disorder, photon localization is drastically reduced as the array dimensionality increases, and the influence of cavity nonuniformities on the near-field and far-field patterns in arrays of different dimensionalities is analyzed in the framework of coupled-mode theory.
Abstract: Arrays consisting of coupled vertical-cavity surface-emitting lasers represent a model system for photonic lattices. Fluctuations among array elements, caused by wafer nonuniformities or processing defects, can lead to photon-mode localization, thus deteriorating the spatial coherence of such devices. The influence of cavity nonuniformities on the near-field and far-field patterns in arrays of different dimensionalities is analyzed in the framework of coupled-mode theory. It is shown that, for the same degree of disorder, photon localization is drastically reduced as the array dimensionality increases.

42 citations


Journal ArticleDOI
TL;DR: In this article, a study of the important parameters of synchronous and nonsynchronous, weakly and strongly coupled optical directional couplers using the finite element method has been conducted, where accurate propagation constants and field profiles were obtained for the modes of the isolated guides and the supermodes of the coupled system.
Abstract: Results are presented on a study of the important parameters of synchronous and nonsynchronous, weakly and strongly coupled optical directional couplers using the finite element method Accurate propagation constants and field profiles have been obtained for the modes of the isolated guides and the supermodes of the coupled system The power transfer efficiency between nonidentical coupled optical waveguides has been calculated using the coupled mode, the least squares boundary residual and the finite element-based propagation methods To show the advantages of the finite element-based approaches, the power transfer efficiency between coupled waveguides with two-dimensional confinement is presented

21 citations


Journal ArticleDOI
TL;DR: In this article, the synthesis of realistic coupled waveguide filters is considered and variational optimization is combined with the normal-mode analysis of interacting waveguides, where physical effects such as the change in coupling strength with waveguide or material dispersion are considered.
Abstract: The synthesis of realistic coupled waveguide filters is considered. The emphasis is on the synthesis of physical devices, rather than on the approximate coupled-mode representations. For this purpose, variational optimization is combined with the normal-mode analysis of interacting waveguides. Physical effects such as the change in coupling strength with waveguide or material dispersion are naturally taken into account. The beam propagation method (BPM) is used to verify the effectiveness of the designs and thus lends a measure of confidence of the applicability of the method to realistic devices.

15 citations


Journal ArticleDOI
TL;DR: In this article, the acoustooptic interaction of guided optical waves and surface acoustic waves (SAW's) is studied in multilayered structures of dimensions of the order of those seen in multiple-quantum-well (MQW) structures.
Abstract: The acoustooptic interaction of guided optical waves and surface acoustic waves (SAW's) is studied in multilayered structures of dimensions of the order of those seen in multiple-quantum-well (MQW) structures. The guided mode profiles and SAW-induced electric field and strain profiles are used to calculate the diffraction efficiency, using an expression derived from coupled mode theory. Diffraction efficiency is plotted as a function of SAW frequency, and the effects of acoustic power, acoustic aperture, and material structure are considered. For a specific structure, the diffraction efficiency is seen to increase with increasing aluminum content for low concentrations and the opposite is seen for higher concentrations. This is explained in terms of the opposing effects of guided optical mode parameters and material properties. Possibilities for optimization of the diffraction efficiency through tailoring of the refractive index profile of the material structure are suggested.

13 citations


Journal ArticleDOI
TL;DR: In this paper, finite difference equations for second-harmonic generation in two-dimensional planar structures for coupling between TE polarizations at two frequencies as well as for TM polarizations, including the effect of birefringence in the latter case, are given.
Abstract: Finite difference equations are given for second-harmonic generation in two-dimensional planar structures for coupling between TE polarizations at two frequencies as well as for TM polarizations at two frequencies, including the effect of birefringence in the latter case. Attention is given to obtaining accurate expressions for the finite difference operators for points close to interfaces, and it is shown how the equations for nonlinear coupling can be incorporated into the beam-propagation method and the coupled-mode theory. Computational results of second-harmonic generation incorporating both the coupled mode theory and the beam-propagation method are given and discussed.


Journal ArticleDOI
Xiaochun Li1, Minxian Wu1, Yingbai Yan1, Qingsheng He1, Guofan Jin1 
TL;DR: In this article, an analytical expression for the dynamic range metric of a photorefractive crystal in a volume holographic memory is found on the basis of the coupled mode theory for polarized waves inside crystals and the linearized band transport model.

Journal ArticleDOI
TL;DR: In this paper, a perturbative iteration method of the integral equation of the wave equation was used to investigate light wave diffraction from multiple superposed volume gratings using the perturbation iteration method.
Abstract: Light wave diffraction from multiple superposed volume gratings is inestigated using a perturbative iteration method of the integral equation of Maxwell's wave equation. The host material and index gratings are anisotropic and non-coplanar multiple volume gratings are considered. In this method, the paraxial approximation and lack of backward scattering in conventional coupled mode theory are not assumed. Systematic analysis of anisotropic wave diffraction due to multiple noncoplanar volume index gratings is performed in increasing level of diffraction orders corresponding to successive iterations.

Journal ArticleDOI
TL;DR: In this paper, the power transfer characteristics of a grating-assisted three-waveguide coupler were analyzed by using the nonorthogonal coupled-mode theory based on the isolated waveguide modes.
Abstract: The power transfer characteristics in a grating-assisted three-waveguide coupler are analyzed by using the nonorthogonal coupled-mode theory based on the isolated waveguide modes. The coupler consists of three asynchronous, parallel, planar waveguides in which the upper and lower surfaces of the intermediate waveguide are corrugated with different periods. When two phase-matching conditions and an additional constraint on the coupling constants are satisfied, the guided modes in the two outer waveguides couple selectively at a certain wavelength by means of the corrugated intermediate waveguide. It is shown that the wavelength selectivity in the power transfer between the two outer waveguides becomes noticeably sharper than that of the grating-assisted two-waveguide coupler and that the sidelobes in the wavelength response are almost completely suppressed.

Journal ArticleDOI
TL;DR: In this paper, the influence of transverse structures on the coherent coupling of laser modes was demonstrated and an improved model was proposed to describe the gain-induced coupling of two non-orthogonal modes of a solid-state laser.
Abstract: We demonstrate the influence of transverse structures on the coherent coupling of laser modes. From the Maxwell-Bloch equations in the approximation of a finite mode expansion we derive Adler equations for the relative phases. We use an improved model to describe the gain-induced coupling of two non-orthogonal modes of a solid-state laser. Experimental results for some time-dependent experiments are presented and compared with theoretical predictions of our model.

Journal ArticleDOI
TL;DR: An accurate method to analyze integrated optics waveguides with a grating with a novel approach to produce symmetric diffracted beams is proposed, which results in symmetrical diffracted beam profiles.
Abstract: An accurate method to analyze integrated optics waveguides with a grating is used to design diffractive gratings. A novel approach to produce symmetric diffracted beams is proposed. In this approach, we vary the grating duty cycle along the propagation direction. We demonstrate that this method results in symmetrical diffracted beam profiles.

Journal ArticleDOI
TL;DR: In this article, the analysis of the X-junction waveguide switches with a large branching angle ranging from 2° to 12° was carried out using the beam propagation method, and it was shown that, for an X-intersecting waveguide with a branching angle more than 2°, the eigenmodes interference remains and prevails even up to 12 degrees.
Abstract: This is a study on the analysis of the X-junction waveguide switches with a large branching angle ranging from 2° to 12°. The characteristics of the modeled are simulated by using the beam propagation method. We will show that, for an X-intersecting waveguide with a branching angle more than 2°, the eigenmodes interference remains and prevails even up to 12°. This produces a high unbiased crosstalk. In the analysis of the modulation efficiency of the switch, it is revealed that a large positive refractive index change will produce higher modulation efficiency than a negative refractive index change because of optical field re-distribution. In designing an X-intersecting waveguide switch using the coupled mode theory, a -40 dB crosstalk can be achieved for device smaller than 2 µ m. The interference X-intersecting waveguide switches will be more suitable for large scale switching arrays.

Journal ArticleDOI
TL;DR: In this article, it was shown that the nonlinear coupled-mode equations for multiple-core couplers can be solved analytically under a resonant condition, and that power swapping among three cores placed in the shape of an isosceles triangle is aperiodic at high power.
Abstract: Nonlinear coupled-mode equations governing the modal coupling of a two-mode coupled system (such as twin core couplers) are integrable; power swapping in such a system follows a periodical manner and can be expressed analytically. When three or more modes (for systems such as multiple-core couplers) are involved, the nonlinear coupled-mode equations are no longer integrable and chaotic power swapping is expected. A numerical approach is required, in general, to solve such nonlinear coupled systems involving the coupling of three or more modes. We find, however, that for certain structural configurations, such as triple-core couplers with the cores arranged in the shape of an isosceles triangle, the nonlinear coupled-mode equations for multiple-core couplers can be solved analytically under a resonant condition. The analytical solution indicates that power swapping among, for example, the three cores placed in the shape of an isosceles triangle can be aperiodic at high power, although power may fl...

Proceedings ArticleDOI
14 Nov 1997
TL;DR: In this paper, a theoretical analysis of Bragg gratings, in isolation and in an array, is presented, with a view to reduce the sensor's bandwidth Effect of inclusion of second derivatives and cladding modes in the coupled mode theory used here is explained for a typical 4% Ge doped single mode fiber, FWHM of a grating is found to be 17 nm as against 37 nm, when no such modification is done
Abstract: Optical fibers are used in smart structures mainly as sensor elements and communication links Fiber Bragg grating (FBG) based sensors have become the most popular ones among all the fiber sensors For distributed measurement, the sensing network is required to cover as much area as possible Also, the sensors are required to be placed as closely as possible to achieve a better surface-scanning These together necessitate the need for a number of sensors to be incorporated in one fiber line, something restricted in practice by the individual sensor response and the source bandwidth In this paper, a theoretical analysis of Bragg gratings, in isolation and in an array is presented An existing theory of FBG has been revisited with a view to reduce the sensor's bandwidth Effect of inclusion of second derivatives and cladding modes in the coupled mode theory used here is explained For a typical 4% Ge doped single mode fiber, FWHM of a grating is found to be 17 nm as against 37 nm, when no such modification is done Uniform grating array is preferred over the non-uniform type, from the fabrication and signal processing point of view But for an array consisting of a large number of uniform gratings, addressing each sensor element becomes the problem An array of non- uniform cluster of uniform gratings can be a good remedy for this The number of gratings in one cluster is a trade-off between the measurement and signal-processing ease

Journal ArticleDOI
TL;DR: In this article, a modified scalar coupled mode approach that takes into account the non-orthogonality of the fields and also the perturbation correction terms to the effective indices of individual waveguides was proposed.
Abstract: Analytical expressions for power exchange in two waveguide directional couplers have been obtained using the modified scalar coupled mode approach that takes into account the non-orthogonality of the fields and also the perturbation correction terms to the effective indices of individual waveguides which were ignored in the old Coupled Mode Theory. Our results show considerable difference when compared with old Coupled Mode Theory, specially for non-identical waveguides. However, they are consistent with results obtained by the exact modal analysis.

Journal ArticleDOI
TL;DR: In this article, the existence of an ideal six-port directional coupler has been proved under the following conditions: the coupling coefficients of the system are equalized using substrate anisotropy and the lines are matched to their characteristic impedances.
Abstract: The coupled-mode formulation has been applied to simplify the analysis of a symmetrical three-line microstrip coupler (TMC) on an anisotropic substrate. The existence of an ideal six-port directional coupler has been proved under the following conditions: the coupling coefficients of the system are equalized using substrate anisotropy and the lines are matched to their characteristic impedances. The singular behaviour of the normal-mode parameters that occur at the critical equalization point of k1 = kc has been examined. The numerical and simulation results confirm the developed analysis.

Proceedings ArticleDOI
02 Dec 1997
TL;DR: In this article, an efficient and simple method of analyzing a mode converter consisted of optical fiber directional coupler, by using FFT beam propagation method (FFT-BPM) and coupled mode theory (CMT), based on effective index method that approximates an optical fiber into a two-dimensional structure of a 3-layer and 5-layer slab waveguide.
Abstract: We demonstrate an efficient and simple method of analyzing a mode converter consisted of optical fiber directional coupler, by using FFT beam propagation method (FFT-BPM) and coupled mode theory (CMT), based on effective index method that approximates an optical fiber into a two-dimensional structure of a 3-layer and 5-layer slab waveguide.

Proceedings ArticleDOI
03 Oct 1997
TL;DR: In this paper, the effect of tiled-poling-induced birefringence on the polarization conversion in single mode waveguides was analyzed and a polarization-independent electro-optic modulator with continuous-electrode structure was designed by using formulae deduced from coupled mode theory.
Abstract: An analysis is made of the effect of tiled-poling-induced birefringence on the polarization conversion in single mode waveguides. A polarization-independent electro-optic modulator with continuous-electrode structure for high speed modulation is designed by using formulae deduced from coupled mode theory. This device uses a Mach-Zehnder structure where both arms are constructed using tilted poling. The same device can be operated in two different modes. One is common-mode which has the advantage of polarization preserving, while the other is differential- mode which features a low driving voltage. An estimation of the influence of misalignment of the poling electrodes on the extinction ratio shows a large fabrication tolerance.

01 Jan 1997
TL;DR: In this paper, the authors derived a simple analytic formula for the power loss per coupling length that depends only on values obtained from the o-p diagram, which is derived from the leaky space harmonics.
Abstract: Floquet-Bloch theory is used to determine the radiation loss of a grating-assisted directional coupler. Results from both the Floquet-Bloch theory and the analytic formula are compared with results obtained using coupled mode theory. 1. IN'k'RODUCTLON Since grating-assisted directional couplers (GALE) are important elements in many optical applications, a number of methods have been developed in the literature to calculate their radiation loss. Radiation losses have been computed by Marcuse (l) using coupled mode theory (CMT). In this paper, we use the Flcquet-Bloch theory (2) to numerically calculate radiation loss and we derive a simple analytic formula for the power loss per coupling length that depends only on values obtained from the o-p diagram. Also, an analytic formula for the radiation loss is derived. 2. RESULTS AND CONCLUSION Consider the grating-assisted directional coupler discussed by Marcuse (I). Figure 1 shows the power distribution in subwaveguide A, subwaveguide B, and the total guided optical power as a function of the propagation distance at the resonant condition (A = 16.45 p). At the input of the GADC, light is excited in subwaveguide A, and at the coupling length (= 1.12") most of the power (86%) is transferred to subwaveguide E, while 6.5% of the power remains in subwaveguide B. Note that the total guided light has decreased by 7.5% (0.337 dB) at pLC (1.12 mm). The Floquet-Bloch theory accounts for the radiation loss by the leaky space harmonics which represent the leaky mode radiation in the forward direction of the superstrate and the backward direction of the substrate. Since modes A and B generally have different attenuation constants (aA and as), the radiation loss of the superposition of the hyo modes can be obtained by evaluating the total'power difference between the input and the output ends of the GADC. This work was supported by the National Science Council of the Republic of China under Grant NSC90-2215-E-214-009.

Proceedings ArticleDOI
12 Apr 1997
TL;DR: Spectral characteristics of multiple periodic gratings in planar dielectric waveguides are investigated using a coupled-mode theory and it is shown that extremely narrow spectral widths, smaller than 0.1 nm, can be achieved from two or more cascaded gratings.
Abstract: Spectral characteristics of multiple periodic gratings in planar dielectric waveguides are investigated using a coupled-mode theory. Gratings are modeled as periodic perturbations in the refractive index profile about the core-cladding boundary of the waveguide. Power coupling between the forward and backward traveling fundamental modes are calculated for cascaded gratings with arbitrary lengths and separations but equal periods. It is shown that extremely narrow spectral widths, smaller than 0.1 nm, can be achieved from two or more cascaded gratings. Variations of power reflection coefficient with wavelength are examined for several cases. Applications of these gratings are also addressed.

Proceedings ArticleDOI
12 Apr 1997
TL;DR: In this paper, a spectral filter made of single-mode and dual-mode fibers was proposed for applications as narrowband demultiplexers and as wideband mode converters with spectral widths on the order of fraction of 1 nm to few 10 nm.
Abstract: Spectral filters made of single-mode identical or dissimilar core parallel fibers provide 3-dB spectral widths on the order of 1 to 10 nm. A spectral filter made of single-mode and dual-mode fibers and operating based on coupling of power between LP/sub 01/ and LP/sub 11/ modes is proposed for applications as narrowband demultiplexers and as wideband mode converters with spectral widths on the order of fraction of 1 nm to few 10 nm, respectively. With appropriate choice of parameters, filters can be designed such that the LP/sub 01/ mode of the single-mode fiber is phase matched with the LP/sub 11/ mode of the dual-mode fiber at a desired wavelength, thus significant exchange of power between these two modes can occur. The coupled-mode theory of parallel dielectric waveguides is used to analyse the proposed filter. Design data and transmission characteristics for maximum power coupling at 1.33 /spl mu/m and 1.55 /spl mu/m are presented.