Question: 3.8. Number of wave guide modes With increasing V parameter (3.18) not only the number of allowed i values for Je(X) increases but also

3.8. Number of wave guide modes With increasing V parameter (3.18) not

3.8. Number of wave guide modes With increasing V parameter (3.18) not only the number of allowed i values for Je(X) increases but also the num- ber of roots Xf < V continues to rise. In order to estimate the number of modes for a given V parameter, begin by assuring yourself that J(x) = (2/nx)/2 cos(x - (l+1/2)/2) is a good approximation for large x. Use this approximation to calculate explicitly the number M of allowed modes and show that it rises with M 4V/n. Calculate the mode number for a step- index fibre with NA = 0.2 and core diameter 2a = 50 um. How does the mode number change if the cladding is replaced with air, i.e. if a pure solid 50 um diameter glass fibre is used?

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