3.5. FUNDAMENTAL HE ₁₁ MODE

It has been clarified in the previous sections that the fundamental mode of the optical fiber is the HE ₁₁ mode. Therefore it is indispensible to understand the propagation characteristics of the HE ₁₁ mode in order to grasp the signal transmission properties of single-mode fibers. Here the dispersion characteristics and electromagnetic field distributions of the HE ₁₁ mode are investigated in detail. In order to rewrite Eqs. (3.40) and (3.41b) to easily understand expressions, we use the recurrence formulae of J ? = J ₀ ? J ₁ /u and K ? = ? K ₀ ? K ₁ /w. Noticing that ? ? 1 in practical fibers and also that the dispersion equation in the form

can be adopted for the HE ₁₁ mode, Eqs. (3.40) and (3.41b) are reduced to

Since the maximum value of ( uw/v) ² J ₀ /uJ ₁ is about 0.7, s can be well approximated by s ?1. Equation (3.91) is a slightly more rigorous dispersion equation than the simple LP mode approximation of Eq. (3.71).

Setting n = 1 in Eqs. (3.44) and (3.45), and using the transformation relations in the forms

the electromagnetic field distributions of HE ₁₁ mode in the Cartesian coordinate become the following.

1. Core region (0 ? r ? a) :

   
   
   
   
   
   
   
   
   
   
   
   

2. Cladding region (r ? a) :

   
   
   
   
   
   
   
   
   
   
   
   

There are two independent polarization modes in Eqs. (3.94)...