Showing papers on "Coupled mode theory published in 1986"
TL;DR: In this paper, an improved coupled-mode equation for parallel dielectric waveguides was derived by using a newly found relationship that connects the propagation constants of the individual guides to the coupling coefficients via an overlap integral that measures the guides' proximity.
Abstract: An improved version of coupled-mode equations for parallel dielectric waveguides has been derived by using a newly found relationship that connects the propagation constants of the individual guides to the coupling coefficients via an overlap integral that measures the guides' proximity. The four parameters of these new coupled equations are simple functions of essentially one single quantity: the asynchronism of the individual guides properly normalized.
254 citations
TL;DR: In this paper, a new theory describing coupled mode propagation in an array of arbitrary optical waveguides is developed, which unambiguously accounts for real and/or imaginary index perturbations and its solutions yield supermode patterns and propagation constants.
Abstract: A new theory describing coupled mode propagation in an array of arbitrary optical waveguides is developed. The formulation unambiguously accounts for real and/or imaginary index perturbations and its solutions yield supermode patterns and propagation constants. Several examples of coupled TE slab waveguides are evaluated and the results are shown to compare very favorably with exact solutions. The calculated propagation constants and mode patterns differ quantitatively and qualitatively from those derived from the prior theory. In particular, the supermode gains derived according to the new theory agree very well with exact solutions and predict different supermode ordering and splitting than those derived by the prior theory.
87 citations
TL;DR: In this paper, a coupled mode formulation for guided wave propagation in an array of N -parallel waveguides is presented and the resulting matrix differential equations are solved for two-and three-waveguide systems.
Abstract: We present a new coupled mode formulation for guided wave propagation in an array of N -parallel waveguides and solve the resulting matrix differential equations. Analytic results for two- and three-waveguide systems are derived and several examples of three waveguide couplers are given. In particular, we show that field amplitudes in the case of asymmetrical excitation of a three-waveguide coupler are not periodic functions along the propagation direction as previously had been supposed.
84 citations
TL;DR: In this paper, the evolution of a general two-level system under arbitrary operators is cast in a three-dimensional form and a formal connection to the theory of rigid body dynamics is made and explicit linearity and transformation properties are rigorously established.
Abstract: The evolution of a general two-level system under arbitrary operators is cast in a three-dimensional form. An earlier geometrical representation is generalized to include contradirectional, parametric, and skew-Hermitian coupling as well as systems with loss or gain. A formal connection to the theory of rigid body dynamics is made and explicit linearity and transformation properties are rigorously established in a coordinate-free form. The connection with mechanics is shown to permit transformations to rotating coordinate systems, a useful technique in analyzing typical guided wave systems.
75 citations
TL;DR: Coupled-mode theory for parallel waveguides is extended to include systems with multimode guides, and the basic set of coupled differential equations are more broadly defined to allow for coupling among all the modes.
Abstract: Coupled-mode theory for parallel waveguides is extended to include systems with multimode guides. The basic set of coupled differential equations is similar to that for single-mode guides, but the matrices are more broadly defined to allow for coupling among all the modes. Cases of anisotropic dielectric waveguides and/or an anisotropic embedding medium are also considered.
50 citations
TL;DR: In this paper, the spectral Galerkin procedure is used to calculate the dispersion properties of multiple conductor microstrip lines and the resulting propagation constants are then used in a coupled-mode theory which demonstrates a frequency-dependent coupling of current in a five-conductor system.
Abstract: The spectral Galerkin procedure is used to calculate the dispersion properties of multiple conductor microstrip lines. The resulting propagation constants are then used in a coupled-mode theory which demonstrates a frequency-dependent coupling of current in a five-conductor system. These results should he useful in the study of crosstalk between parallel microstrip lines used in VLSI interconnections.
38 citations
TL;DR: In this paper, the responses of specially designed directional couplers built with Ti:LiNbO3 in-diffused guides were measured and found to be substantially better predicted by an improved version of the coupledmode theory than by the traditional one.
Abstract: The responses of specially designed directional couplers built with Ti:LiNbO3 in‐diffused guides were measured and found to be substantially better predicted by an improved version of the coupled‐mode theory than by the traditional one.
36 citations
TL;DR: In this paper, a coupled mode theory is used to examine surface wave propagation in a laterally inhomogeneous acoustic waveguide and the results for radiation losses due to interaction with the irregular boundary of the waveguide are presented in analytical form.
Abstract: Summary. A coupled mode theory is used to examine surface wave propagation in a laterally inhomogeneous acoustic waveguide. The theory is developed from the equations of motion for the pressure and velocity fields. The presence of lateral inhomogeneities in the form of varying layer thickness causes coupling among the discrete modes of the waveguide and radiation to the continuum. Expressions for the coupling coefficients among all mode types including coupling to the continuum spectrum are derived. The coupling coefficients are proportional to the horizontal derivative of the function describing the interface between layers of constant material properties but varying thickness. The coupled mode equations are solved in approximation for the case of a sinusoidal boundary and a sloping boundary. The results for radiation losses due to interaction with the irregular boundary of the waveguide are presented in analytical form, which clearly show the primary physical effects on the wavefield of the interaction. The far field amplitude of the scattered modes, excited by the interaction of some incident signal with a weak boundary irregularity, is modulated by the spatial Fourier transform of the irregularity.
35 citations
TL;DR: In this article, it was shown by explicit calculations on the same model problem that direct orthogonal expansion in local normal modes of the intrinsic mode produces the same expansion coefficients as those obtained by a perturbation analysis of the coupled mode equations.
Abstract: Recent theoretical studies of acoustic wave propagation in a model waveguide consisting of a homogeneous wedge with one reflecting and one penetrable boundary have established the utility of the concept of an intrinsic mode, which generalizes for nonseparable problems the normal mode of separable configurations. In this paper, it is shown by explicit calculations on the same model problem that direct orthogonal expansion (in local normal modes) of the intrinsic mode produces the same expansion coefficients as those obtained by a perturbation analysis of the coupled mode equations. The perturbation method used is that of renormalization, in which the mode coupling operator is iteratively diagonalized up to a certain order in the nonseparability parameter, which, in this case, is the wedge angle α.
26 citations
TL;DR: A recently developed, more accurate coupled-mode formulation for arbitrary parallel waveguides is applied to two single-mode weakly guiding coupled fibers.
Abstract: A recently developed, more accurate coupled-mode formulation for arbitrary parallel waveguides is applied to two single-mode weakly guiding coupled fibers. Propagation constants and coupling coefficients are calculated for both identical and dissimilar fiber pairs.
17 citations
TL;DR: In this article, generalized coupled-mode equations for two or more coupled weakly guiding fibres are presented, when the fibres were not well separated and applied to studying fiber couplers.
Abstract: Generalised coupled-mode equations for two or more coupled weakly guiding fibres are presented, when the fibres are not well separated. These equations are applied to studying fibre couplers. Compared with the results derived from previous coupled-mode equations, our results are in better agreement with those calculated rigorously by a numerical method.
TL;DR: In this paper, the improved coupled-mode theory is extended and applied to multi-waveguide systems consisting of any number of nonparallel guides, such as Y-junction laser arrays and directional couplers.
Abstract: The improved coupled-mode theory is extended and applied to multiwaveguide systems consisting of any number of nonparallel guides, such as Y-junction laser arrays and directional couplers. The impact of the improved analysis on the design of devices containing nonparallel sections is illustrated by an example of Ti-indiffused LiNbO3 directional couplers. It is shown that the overall performance of the device may be significantly affected by the nonparallel sections.
TL;DR: A method is presented for determining the eigenvalues and eigenvectors (characteristic mode shapes) for coupled waveguide arrays in which the interguide coupling is uniform but where the dephasing varies periodically from guide to guide.
Abstract: A method is presented for determining the eigenvalues and eigenvectors (characteristic mode shapes) for coupled waveguide arrays in which the interguide coupling is uniform but where the dephasing varies periodically from guide to guide It is demonstrated that if the dephasing alternates from guide to guide, a quadratic equation must be solved for the eigenvalues, whatever the number of guides For dephasing functions of larger period, the eigenvalue equation is of correspondingly higher order The effect of such functions is to insert additional band gaps into the eigenvalue distribution and to couple together spatial harmonics Numerical examples illustrating the method are presented where relevant
01 Jan 1986
TL;DR: Coupled Mode T h e o r y (COM) as discussed by the authors has been a well-known model in the field of autonomous vehicles and has been widely used for vehicular applications.
Abstract: Coupled Mode t h e o r y has been a p p l i e d t o SAW devices i n o rde r t o s tudy d i s p e r s i o n character i s t i c s o f r e f l e c t i v e g r a t i n g s and t r a n s ducers. I n t h i s work t h e MASON equ iva len t c i r c u i t i s mod i f i e d by elements rep resen t ing impedance and v e l o c i t y d i s c o n t i n u i t y and evanescent mode gener a t i o n by meta l e lec t rodes on o r by grooves i n t o t h e surface. Coupled mode a n a l y s i s (COM) i s a p p l i e d s imu l ta neously t o t h e p h y s i c a l g r a t i n g and t h e equ i v a l e n t c i r c u i t model. The r e s u l t s o f t h e two procedures a r e then s e t equal and thus t h e va lues o f t h e elements o f t h e MASON c i r c u i t a r e c a l c u l a t e d by means o f t h e a n a l y t i c equat ions g i v e n i n t h i s paper.
TL;DR: In this paper, a generalization of the method for conical diffraction mounting based on the rigorous differential formalism of Chandezon et al. is presented for the case of planar corrugated waveguides.
Abstract: A generalization of the method for conical diffraction mounting based on the rigorous differential formalism of Chandezon et al. is presented for the case of planar corrugated waveguides. The coupled mode equations are derived from the phenomenological theory. A detailed comparison between the numerical results and the results of mode matching approach is given. It is shown that the Brewster's law analogy depends on the corrugation depth.
TL;DR: In this paper, it is pointed out that within the propagation distance the range-dependent variation of the waveguide may be accummulative (1) or nonaccummulative (2).
Abstract: In the present paper, it is pointed out that there are two catagories of adiabatic approximation: within the propagation distance the range-dependent variation of the waveguide may be accummulative (1) or nonaccummulative (2). The well-known criterion given by Milder is applicable for the first catagory. The criterion for the second category has been derived by the present authors. Two example are discussed, (1) a shallow water waveguide with slight surface roughness and (2) a shallow water waveguide with range-dependent sediment properties.
Journal Article•
DOI•
01 Oct 1986TL;DR: In this article, the spectral components of the index perturbation can no longer be taken to be independent of each other, and it is shown that the reflection bandwidth of the weak perturbations is narrowed by this particular configuration, but an effective limit on narrowing is imposed by relatively strong side lobes of the reflectance of the strong pertyrbation.
Abstract: Wave propagation through a slab dielectric waveguide with two periodic perturbations of the permittivity of very different amplitude but similar pitch is considered. The pitch of the weaker perturbation is chosen so that it lies in that part of the dispersion characteristic of the guide that is strongly distorted by the presence of the stronger perturbation. Coupled mode theory is used to analyse this situation, in which the spectral components of the index perturbation can no longer be taken to be independent of each other. Hence it is shown that the reflection bandwidth of the weak perturbation is narrowed by this particular configuration. The bandwidth decreases as the two pitches approach one another, but an effective limit on narrowing is imposed by the relatively strong side lobes of the reflectance of the strong pertyrbation.
09 Jun 1986
TL;DR: The first insights into the operation of diode laser arrays were obtained through coupled-mode theory calculations, which assume weak coupling between neighboring channels that operate almost independently of one another as mentioned in this paper.
Abstract: The first insights into the operation of diode laser arrays were obtained through coupled-mode theory calculations, which assume weak coupling between neighboring channels that operate almost independently of one another. These calculations produced (for n-coupled waveguides) a set of n eigenmodes designated in the literature as "supermodes",1 which have since dominated the thinking concerning array operation. In particular, gain-guided arrays have been described using coupled-mode theory with complex coupling coefficients,2 a picture reinforced largely by the fact that such arrays generally exhibit a two-lobed far-field emission pattern which is suggestive of the highest-order supermode of an index-guided array.