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Mode coupling equations first approximation

In the remainder of this article, we shall discuss the proper mode-mode coupling,theory. This discussion naturally falls into two parts. The twofold nature of the theory has already been seen in the previous pages. First, it was necessary to make approximations to obtain Eq. (40), the mode-mode coupling equation. Second, it was necessary to make approximations to solve Eq. [Pg.271]

To solve Eq. (29-2) we need to know . An expression could be obtained by expanding over the complete set of Pj for the bound and radiation modes of the first fiber, and this would, of course, lead to the infinite set of coupled mode equations derived in Section 33-11. The disadvantage of this description is that each mode of the first fiber by itself is a poor approximation to the field within the second fiber. Consequently large numbers of modes are required for accuracy, and. the set of coupled equations is then intractable. [Pg.569]

In Chapter 19 we introduced local modes to describe the fields of waveguides with large nonuniformities that vary slowly along their length. As an individual local mode is only an approximation to the exact fields, it couples power with other local modes as it propagates. Our purpose here is to derive the set of coupled equations which determines the ampUtude of each mode [10]. First, however, we require the relationships satisfied by the fields of such waveguides. [Pg.616]

We present a brief introduction to coupled transport processes described macroscopically by hydrodynamic equations, the Navier-Stokes equations [4]. These are difficult, highly non-linear coupled partial differential equations they are frequently approximated. One such approximation consists of the Lorenz equations [5,6], which are obtained from the Navier-Stokes equations by Fourier transform of the spatial variables in those equations, retention of first order Fourier modes and restriction to small deviations from a bifurcation of an homogeneous motionless stationary state (a conductive state) to an inhomogeneous convective state in Rayleigh-Benard convection (see the next paragraph). The Lorenz equations have been applied successfully in various fields ranging from meteorology to laser physics. [Pg.83]

The coupled local-mode equations can be solved approximately when only a small fraction of the total power of the perturbed waveguide is transferred between modes. We show that the first-order solution is identical to the induced-current solution of Chapter 22. For convenience we assume that only the Ith forward-propagating local mode is excited at z = 0. To lowest order we ignore coupling to all other modes. The solution of Eq. (28-2) is then... [Pg.556]


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