Assessment of coupled-mode theory for tapered optical coupler

The accuracy and the scope of validity of different coupled-mode formulations for a tapered optical waveguide coupler are assessed by comparison with the beam propagation method (BPM). It is demonstrated that the coupled-mode theory (CMT) based on local modes is valid only for small tilt angles, whereas an improved formulation that takes into account the wavefront-tilt effect yields highly accurate results for relatively large tilt angles. The radiation loss at the input and the output junctions can also be estimated by a simple mode-matching method combined with the improved CMT. The coherent coupling between two junctions,which is neglected in the coupled-mode formulations, is observed in the BPM simulations.<>     

A variational coupled-mode theory for periodic waveguides

A simple variational theorem for the dispersion relations and propagation constants of periodic waveguides is derived. The trial fields used in the variational formula incorporate all the Floquet components correct to first order. This yields a propagation constant in which errors enter only to fourth order in the trial field. The analysis yields a new coupled mode formulation which is shown to yield excellent agreement with exact analytic solutions (in l-D), and numerical simulations (in 2-D), for high-index contrast structures     

Improved coupled-mode theory for reciprocal anisotropic waveguides

An improved coupled-mode theory for a reciprocal anisotropic multiwaveguide system is derived. The general reciprocal anisotropic medium is described by a symmetric permittivity tensor that can have nonzero off-diagonal elements. The derivation is based on the generalized reciprocity relation. The coupled-mode equations are applicable to both lossy (gain) and lossless systems. For the special case of lossless systems, it is shown that the matrices in the coupled-mode equation are Hermitian, so that energy conservation is observed exactly. For the special case of a single anisotropic waveguide, the results also reduce to the previously derived solutions by D. Marcuse (1975). The improved coupled-mode theory in an anisotropic multiwaveguide system is illustrated with numerical examples     

Improved coupled-mode theory for nonlinear directional couplers

An improved coupled-mode equation for nonlinear directional couplers (NLDC) with Kerr-like nonlinear media is proposed. The method is based on the generalized reciprocity relation in which two sets of field solutions satisfying Maxwell's equations are for the NLDC and for the isolated nonlinear waveguide. That leads to a reasonable result that all the coefficients in the coupled-mode equations, including the coupling coefficient, become power dependent. For the NLDC with a self-focusing or self-defocusing nonlinear material, the authors examine how the coupling coefficient, the coupling length, and the guided power depend on the input power in the range of coupling stronger than in previous reports. It is found that the critical power at which the coupling length becomes infinity does not increase as much with the two guides for the case of self-focusing media     

Improved coupled-mode theory for anisotropic waveguide modulators

An improved coupled-mode theory for the propagation of modulated light waves in anisotropic dielectric waveguides is presented. Starting from Maxwell's equations, a partial differential equation is derived to describe mode-coupling between two normal modes which may propagate in anisotropic waveguide systems under modulation. The theory is applied to the analysis of typical waveguide modulators; examples for LiNbO₃ phase modulator, Mach-Zehnder, and directional coupler modulator are presented. The theory is applicable to both bulk and waveguide modulators/switches from DC to the high-frequency band. The only limitation is that the modulating wave has to propagate collinearly to the light waves     

An exact formulation of coupled-mode theory for coupled-cavitylasers

Coupled-mode rate equations for coupled-cavity lasers are derived using a novel approach. The method, based on the Mittag-Leffler theorem, is exact. The coupling coefficients are compared to those derived by several different approximations     

Section-wise-exact coupled-mode theory of waveguidequasi-phase-matched second-harmonic generation

We derive exact mathematical expressions for both the amplitude and phase evolution of optical waves due to linear and nonlinear interactions in a waveguide device and propose a section-wise-exact coupled-mode theory analysis for quasi-phase-matched second-harmonic generation in the waveguide. Section-wise-exact coupled-mode theory is readily applicable to nonuniform quasi-phase-matched gratings and can be useful as a quantitative method in their analysis and design. Using the method, several numerical results are presented for second-harmonic generation in periodically poled LiNbO₃ channel waveguides. In addition, we introduce a split-step method which takes propagation losses into account and which can include linear and two-photon absorption and waveguide losses     

Vector coupled-mode theory of dielectric waveguides

A consistent derivation of a system of vector coupled-mode (VCM) equations for parallel dielectric waveguides is presented and compared with earlier versions of the improved coupled-mode theory (ICMT). As a validity test, it is shown that the effectively scalar transverse electric and transverse magnetic (TM) coupled-mode (CM) equations are direct limits of our full VCM formulation. In particular, our formulation does not lead to the fundamental error found with earlier coupled-mode theories (CMTs) in a case of TM fields. Functional equations of our VCMT are consistent with Maxwell's equations and lead to higher precision. They can be applied to complicated arrays of strongly coupled parallel dielectric waveguides with true vectorial behavior.     

Variational coupled-mode theory of optical couplers

A scalar coupled-mode theory is developed from the variational principle. The formulation is variational in the sense that the mode parameters are adjustable and can be optimized subject to the coupling between the guides. The theory is applied to slab and fiber couplers. In comparison with the conventional scalar coupled-mode theory in which only the amplitudes of the modes in the individual guides are adjustable, the variational scalar coupled-mode theory predicts more accurate propagation constants and field patterns of the normal modes of the couplers     

Nonorthogonal coupled-mode theory of grating-assisted codirectionalcouplers

Grating-assisted codirectional couplers are analyzed by a nonorthogonal coupled-mode theory. The coupled-mode equations are solved exactly, and the effects of all the space harmonics generated by the periodic gratings are included in the analysis. More rigorous relations among the grating period, the grating height, and the coupling length are established. The power exchange between the guides is investigated as a function of the propagation distance and the wavelength. A comparison with previous approximate solutions is made and discussed     

Self-consistent field theory and calculation for gyromonotron

A self consistent field large signal theory of gyromonotron is studied in this paper. The RF field profile function satisfies a wave equation. The field is determined by cavity geometry and AC electron beam current. The RF field not only satisfies the boundary conditions at the ends of the cavity but also obeys conservation of energy for steady state interaction between electron beam and field. The parameters of a particular gyrotron are calculated numerically using present theory. Effect of some factors on gyrotron characteristic is discussed. Comparison is made between the results of the self consistent field calculations with and without conservation of energy.     

Self-consistent theory of mode competition for gyrotrons

The equations for a fully self-consistent theory of mode competition in gyrotrons are derived and some possible methods of solution are discussed. The importance of including interaction in the resonator output taper is discussed in connection with the validity of linearizing the equations in the amplitude of the parasitic mode.     

Improved coupled-mode theory of anisotropic optical waveguides

A coupled-mode equation for anisotropic waveguide systems of arbitrary cross section and general dielectric distribution is derived. Numerical results comparing the exact calculations to those of the method of Hardy et al. (Opt. Lett., vol.11, 742-4, 1986) show that the same accuracy can be obtained not only for TE, but also for TM mode coupling in the case of anisotropic waveguides, and the improved coupled-mode theory is applicable to the situation when moderately strong coupling occurs under the condition where the edge-to-edge separation of two coupled guides D₂ is about 0.1 μm     

FBG的衍射光学特性和耦合模理论分析

从衍射光学的角度出发研究了光纤布喇格光栅（ Ｆ Ｂ Ｇ） 的光学特性,进而采用理想模展开的耦合模理论对光纤布喇格光栅的模场分布进行了详细分析,推导出反射率、布喇格反射波长及反射主峰带宽等特性参数的表达式。计算结果表明,理论与实验结果吻合较好,从而验证了理论结果的正确性     

Reformulation of the coupled-mode theory of multiwaveguide systems

We show that by proper reformulation the coupled-mode theory of Hardy and Streifer can be reconciled with that of Haus et al based on a variational principle. The new formulation has the merit of leading to simpler coupled-mode equations while giving marginally more accurate results.     

A variational coupled-mode theory including radiation loss forgrating-assisted couplers

We calculate higher order effects such as frequency shifts and radiation loss in grating waveguides and grating couplers. The approach follows a vector variational principle which incorporates the Floquet components correct to first order. It is unnecessary to bring radiation modes into the formalism. This yields a simple coupled-mode formulation which includes attenuation due to radiation loss, and is correct to third order in the index contrast of the grating. Numerous examples are given which show excellent agreement with rigorous numerical simulations     

Analysis of groove NRD waveguide bend using the coupled-mode theory

In this paper, the propagation characteristics of the dominant mode in GNRD guide bend are analysed employing the coupled-mode theory. The curves of bending loss vs. The groove depth or width, radius of curvature and frequency are given, which caused by the mode conversion of the operatingLSM ₁₁ ^x mode to the parasiticLSE ₁₁ ^x mode. It is found that the groove depth has a great influence upon the bending loss than the other parameters. According to the theoretical results, appropriate sizes of groove and radius of curvature should be chosen in designing a GNRD bend structure.     

A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation

Two sets of coupled-mode equations for multiwaveguide systems are derived using a generalized reciprocity relation; one set for a lossless system and the other for a general lossy or lossless system. The second set of equations also reduces to those of the first set in the lossless case under the condition that the transverse field components are chosen to be real. Analytical relations between the coupling coefficients are shown and applied to the coupling of mode equations. It is shown analytically that our results satisfy exactly both the reciprocity theorem and power conservation. New orthogonal relations between the supermodes are derived in matrix form with the overlap integrals taken into account.     

Nonlinear property analysis of long-period fiber gratings usingdiscretized coupled-mode theory

We present generalized mathematical expressions for coupled-mode equations for nonlinear pulse propagation in fiber gratings using discretized coupled-mode theory and quantitatively analyze the nonlinear properties of long-period fiber gratings, considering multimode coupling between the core mode and several cladding modes. The calculations yield nonlinear responses for the case of long-period fiber gratings, including pulse shaping and all-optical switching in the self- and cross-phase modulation regimes. In addition, we briefly discuss the group delay properties of long-period fiber gratings and present several numerical examples of nonlinear pulse compression, which is related to strong dispersion and soliton-like behavior in fiber gratings