光电子学 chapter 3精品PPT课件

3.1 wave equation in cylindrical
coordinates(柱坐标)
In Chapter 2 we have shown that optical waveguides with a quadratic index profile (See Equation 2.9-1a) can support guided nondiffracting modes. The effect of diffraction spreading is counterbalanced by the lensing effort of the index pro the guide. Commercial(商用的) silica-based optical fiber use a step index pro a “high” index core and a “low” index cladding(覆层). These fibers form the backbone(脊椎, 骨干)of most modern communication systems, and the study of their modes of propagation is the subject at hand.
2b 2a
n(r) n1 n2
Figure 3-1 Structure and index pro a stepindex circular waveguide
Since the unit vector ar and aφ are not constant vectors, the wave equation involving the transverse(横向的)
Chapter 3 Propagation of optical beams in fibers
Introduction
Since the realization of low-loss fibers in 1970s, fibers become the most important medium for optics communication.
The technology of optical communication in fibers can be stated as that of feeding(饲养, 吃, 输送) optical pulses at a maximal rate into one end of a fiber and retrieving(恢复) them at the other end. The main goal of a communication system is to receive the pulses at the output end with minimal loss of energy, minimal spread, and minimal contamination(玷污, 污染) by noise. For example, the silica([化]硅石)glass fiber ,which has the character of low-loss propagation of confined optical modes, has become the most important transmission medium for long distance.
structure are usually approached by solving for Ez and Hz first and then expressing Er , E , Ez , Hr , H and H z in terms of Ez and Hz
Since we are concerned with the propagation along the waveguide, we assume:
,) H(r, )
exp[i(t
z)]
3.1-2
every component of the field vector assume the same zand t-dependence of exp[i(t z)] .
In this chapter, we will study :
1. the subject of optical guided modes in fibers 2. The problem of pulse spreading due to group velocity
dispersion and various strategies of combating it
components are very complicated. The wave equation for
the z component of the field vectors, however, remains
simple
2 k2
EZ HZ
0
3.1-1
The problems of wave propagation in a cylindrical
Since the refractive(折射的) index profiles n(r) of most fibers are cylindrically symmetric (柱对称性的), it is convenient to use the cylindrical coordinate system. The field components are Er , E , Ez , Hr , H and H z , the wave equation 2.4-3 assumes its simple form only for the Cartesian(笛卡儿) components of the field vectors(矢量)。