Power exchange in tapered optical couplers

The power exchange between nonparallel optical waveguides or tapered couplers is analyzed by the coupled-mode theory based on local modes of the individual waveguides (local waveguide modes). A self-consistent nonorthogonal coupled-mode formulation is presented and transformed into an orthogonal form which is equivalent to the coupled-mode equations for the local modes of the coupled waveguides (local array modes). The coupled-mode equations are then solved numerically and the effect of the taper on the power exchange between the two guides is studied     

Optimization of power transfer in multiple-waveguide couplers

The eigenvalue equations for a slab multiple-waveguide symmetric coupler were solved for the case in which the coupler has more than three guides. It is shown that equal mode spacing in such an N-guide coupler can be obtained by adjusting the widths and the separations of the guides. The optimum widths and separations were calculated by solving the resulting nonlinear simultaneous equations using the Newton-Raphson method. Maximum power-transfer efficiency from one outermost guide to the other outermost guide was found     

Transmission Modes of Closed Elliptic-Groove Waveguides for Millimeter Waves

In this paper, a new type of horizontal-flat and vertical-flat closed elliptic-groove guides is firstly presented. The field components and characteristic equations for some main transmission modes of the closed elliptic-groove guides are derived by with the help of the mode-matching method and Mathieu function. The variations of the cut-off wavelengths along with eccentricities, widths and lengths of the parallel plates for a number of lower order transmission modes of the closed elliptic-groove guides are also analysed in detail. The calculated results in good agreement with ones in the relevant references are of very important values in theoretical researches and actual applications of closed elliptic-groove guides for millimeter and submillimeter waves.     

Relation between normal-mode and coupled-mode analyses of parallel waveguides

The analysis of parallel waveguides can be performed either by expressing the coupling of energy between individual, primary guides (coupled-mode approach) or by directly analyzing a structure consisting of all the guides and their surrounding media (normal-mode approach). A comparison of these two approaches, as well as the derivation of relations enabling the conversion of data, when possible, from one approach to the other, are presented in this paper. Finally, the results are used to investigate the dependence of the coupling coefficient on the spacing between the guides. Although the derivations are performed for 2-D (slab) configurations, the results pertain to 3-D guides as well, by applying an effective refractive-index method. It is also shown that normal-mode analysis predicts incomplete transfer of energy for strongly coupled guides, even for perfectly symmetric configurations.     

Ti扩散LiNbO_3单模波导参数的测量

对Ti扩散LiNbO_3波导分别采用双曲正割和抛物线分布来近似其折射率的高斯分布,在两个波长下由相应的两种近似本征值方程分别推得了单模波导参数的计算公式,并在4880(?)和6328(?)激光波长下利用棱镜耦合器测量了单模波导参数,对测量结果给出必要的理论分析。     

The wave-equation FD-TD method for the efficient eigenvalueanalysis and S-matrix computation of waveguide structures

A modified finite-difference-time-domain (FDTD) formulation based on the direct discretization of the vector wave-equation is applied to the efficient analysis of hybrid-mode waveguiding structures. For both 3-D and 2-D waveguide eigenvalue problems, the formulation requires only one grid, and just the solution of three coupled equations is necessary. Numerical examples concerning the resonant frequencies for an inhomogeneously filled waveguide resonator as well as the fundamental- and higher-order-mode propagation factors for insulated image guides, shielded coupled dielectric guides, and lateral open dielectric ridge guides demonstrate the efficiency of the method. The theory is verified by comparison with results obtained by other methods     

Analysis of dispersion characteristics of groove guides with mode-matching method

Groove guide is widely recognized as one of the most promising millimeter wave transmission structures. In this paper, the mode-matching method is used to analyse the dispersion characteristics of single and asymmetrical double groove guides, and the unified formulae of Nth-order approximation dispersion equations are presented. Based on this analysis, a general program for calculating the dispersion characteristrics of single and asymmetrical double groove guides has been completed. Some comparisons between the results obtained by present method and published data show that very good agreement has been seen. The effectiveness and the reliability of the given formulae and program are thus verified.     

Limitations on power-transfer efficiency in three-guide optical couplers

The eigenvalue equations for a slab three-guide coupler were solved and the power-transfer efficiency was calculated when the coupler is used as 1) a power divider and 2) to transfer power from one outside guide to another. In the first case, two modes take part in the power transfer, and unless the guides are very tightly coupled, periodic beats with high power transfer are obtained at multiples of the coupling length as in a two-guide coupler. In the second case, three modes take part in the power transfer, and periodic beats and high power-transfer efficiency can only be obtained if the propagation velocities of the three modes are related to each other in a simple way. This condition will occur only if the guides of a three-guide coupler made up of identical guides are much more loosely coupled than guides generally used in a two-guide coupler.     

Time-dependent dyadic Green's functions for rectangular andcircular waveguides

Closed-form expressions for the time-dependent dyadic Green's functions of electric and magnetic types for rectangular and circular waveguides are derived from the dyadic Maxwell equations in the time domain. These functions can be used to obtain the time-dependent electric and magnetic fields propagating in those guides due to any arbitrary time-dependent current distribution inside the guide. Stationary vector wave functions are introduced that separate the space-dependent parts from the time-dependent parts of the Green's functions. Comparison of the results for the rectangular and circular guides reveals that the time-dependent parts are identical. Thus the results can be easily extended to some other cylindrical pipes such as elliptical waveguides and also to coaxial cables     

New Waveguide Structures for Millimeter-Wave and Optical Integrated Circuits

Some new dielectric waveguide structures suitable for millimeter-wave and optical integrated circuits are presented. A method of analyzing wave propagation in these guides is developed by assuming simple field distribution and approximating the various regions of the guides in terms of effective dielectric constants. The mathematical formulation utilized results in simple eigenvalue equations from which the dispersion characteristics of the waveguides are readily obtained. Experimental results are described and the agreement between theory and experiment is shown to be quite good.     

Tapered, both in dimension and in index, velocity coupler: theoryand experiment

The authors consider a tapered velocity coupler (TVC) that meets the adiabatic invariance condition with sufficiently strong coupling between the fundamental modes of individual guides in the middle region of the coupler while permitting individual excitation at the input end and sorting of the modes at the output end. This approach helps reduce the device length considerably by permitting much higher taper angle. A TVC consisting of one tapered and another straight, graded index waveguide is modeled using the normal modes of the entire, composite TVC structure. The analytical results are in excellent agreement with experimental results for a TVC fabricated in Ti:LiNbO₃. It is shown that the representation of the local normal modes as the superposition of the modes of the uncoupled guides leads to erroneous results     

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     

Coupling characteristics between five-layer slab wave-guides including left-handed materials

To obtain the coupling characteristics between slab wave-guides including left-handed material, we modify the coupled wave equations by using Maxwell＇s equations. First, we obtain new-coupled wave equations and new-coupling coefficient. Second, the coupling between two identical five-layer slab wave-guides where their cores are left-handed material, but their claddings are right-handed materials is studied. The coupling coefficient for even TE mode which is more complex than that of the riglt-handed material slab wave guides, is obtained.     

Coupling Between an Abruptly Terminated Optical Fiber and a Dielectric Planar Waveguide

The coupling between an optical fiber and a dielectric planar waveguide is analyzed when both guides are terminated abruptly and are facing each other. Mixed spectrum eigenwave representations of fields are employed inside the waveguides while Fourier integrals are utilized to describe the field in the space between the two guides. A coupled system of integral equations is derived by satisfying the boundary conditions on the terminal planes of both waveguides. A weak guidance approximation is assumed to facilitate the analysis. Numerical results are presented for several coupling geometries. Misalignment losses and coupling optimization phenomena are investigated.     

A Broad-Band Directional Coupler for Both Dielectric and Image Guides (Short Papers)

A four-port directional coupler is presented for use in dielectric and image guides. Simple design equations are derived and the subsequent results are in good agreement with theory. Broad-band performance has been achieved over the entire conventiortal waveguide bandwidth (26-40 GHz).     

Analytical model of a superluminescent diode

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Analytical model of a superluminescent diode

Using a set of traveling wave rate equations ,a superluminescent diode with a low facet reflectivity is studied .Analytical expressions of the distribu-tions of carrier density ,forward-and backward-propagation photon densities,and gain are obtained at different facet reflectivities.It is shown that the high nonuni-form carrier distribution is evident in the case of low facet reflectivity.The results can serve as useful guides in understanding emission mechanism of superlumi-nescent diodes.     

Analysis of optical fiber directional coupling based on theHE11 modes. II. The nonidentical-core case

For pt.I see ibid., vol.8, no.6, p.823-31 (1990). The analysis of the directional coupling between two single-mode optical fiber cores based on the exact HE₁₁ modes is extended to the cases involving nonidentical fibers. The coupled-mode theory in the vectorial form is used, and analytical expressions for the coupling coefficients and the butt coupling coefficient appearing in the conventional and the coupled-mode equations are presented. The accuracy of the conventional and new theories as applied to the two-core system is examined by comparing the coupled-mode predictions with the exact numerical values for different core-radius ratios, waveguiding strengths, polarization states, and core separations. It is shown that the errors in the coupled-mode theories increase as the two cores become more dissimilar. As long as the dissimilarity between the cores is kept small, the coupled-mode calculations using the HE₁₁ modes in predicting the coupling strength can be of satisfactory accuracy even when the individual guides are not weakly guiding ones. It is found that the new theory may give relatively large errors in the touching-core case with distinctly different core radii     

Non-radiative phenomenon in couple dielectric guide

The solutions of electromagnetic field equations for non-radiative coupled dielectric guides are derived using mode matching technique. Dispersion curves are plotted for various dielectric materials and dimensional parameters. The non-radiative phenomenon in the coupled dielectric guide has been discussed in detail. The hybrid directional couplers in the above configuration have been theoretically designed by computing the normalized propagation constants. The superiority of such directional couplers is discussed.     

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