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## 2.3 LINEAR LIGHTWAVE PROPAGATION IN AN OPTICAL FIBER

### 2.3.1 Electromagnetic Preliminaries

Any treatment of light guiding in a fiber must begin with the Maxwell equations and describe their solution to some degree of mathematical detail. Many excellent treatments of dielectric waveguides exist [14 19], and the reader would benefit by consulting one or more of these. We draw heavily on Buck s treatment [19].

The Maxwell equations in MKS units can be written as

where D= E and B= H, where ? and are the permittivity and permeability, respectfully, of the medium. In a source-less medium, J=0 and ? free =0. Using standard manipulations, the wave equations for propagating E and H fields can be derived from the Maxwell equations as

The formulas in Eq. (2.2) are each three-wave equations, one for each vector component of E and H. Assuming time harmonic fields, we may generally write (for a wave propagating in the z direction)

where ?= ?/ ?= ?n/c is the propagation constant, or the phase shift per length, of a sinusoidal wave measured along the z axis, and is the wave velocity.

The explicit form of the time dependence can be used to simplify the form of the Maxwell equations [17] to

Defining , we can derive the wave equation in phasor form [19] as the vector Helmholtz equations:

The wave number k has...

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##### Topics of Interest

2.4 WORKING DEFINITIONS OF CUTOFF WAVELENGTH 2.4.1 Introduction The cutoff wavelength of a single-mode optical fiber is the wavelength above which only a single bound mode, the fundamental LP...

2.1 Plane-Wave Solution for Uniform Dielectrics If a dielectric is uniform (and possibly complex) ?( r) = ? then (2.17), (2.18) have a simple solution. The propagating electromagnetic wave is...

The study of electromagnetic wave propagation is based on the ideas of the great nineteenth-century theoretical physicist, James Clerk Maxwell. He was able to describe time-varying electromagnetic...

2.3 Properties of the Harmonic Modes of Maxwell s Equations At the beginning of Section 2 we have demonstrated that Maxwell s equations can be rewritten in terms of either only electric or only...

1.2. Reminders and Prerequisites [1] 1.2.1. Maxwell equations The undulatory nature of light is expressed in terms of an electromagnetic field whose electrical E(r, t) and magnetic H(r, t)...

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