Refracting leaky modes

The fundamental modes of all waveguides considered in this text are cut off when F = 0. At cutoff the phase velocity of the mode is equal to that of a z-directed plane wave in an unbounded medium of refractive index n, but the modal fields are not TEM waves except in special cases. In general, a significant fraction of a mode s power can propagate within the core at cutoff, i.e. r]j of Eq. (11-24) is nonzero, and the group velocity differs from the phase velocity. Below cutoff, these modes propagate with loss and are the leaky modes of Chapter 24. 

Shaded regions denote the core and dotted regions denote evanescent fields in the cladding. A tunneling leaky mode is depicted in (a) and (bX a refracting leaky mode in (c) and a bound mode in (d). The table classifies modes according to the value of... 

We derive expressions in Section 36-13 for the number of leaky modes which can propagate on an arbitrary multimode fiber with 1. The numbers of tunneling leaky modes M, and refracting leaky modes M n on a... 

The second set of curves, in Fig. 24-3(b), give U and — IP for the HEi modes (/ = 0) with w = 2, 3 and 4, including the fundamental mode (m = 1) for comparison. Below cutoff each mode becomes a refracting leaky mode there is no tunneling leaky-mode region as in Fig. 24-3(a). These curves exhibit a feature that is peculiar to the HE, modes immediately below cutoff, there is no leaky mode solution of the eigenvalue equation [19], as indicated by the breaks in the curves for U . This discontinuity is associated with the discontinuity in for these modes, which changes from = oo... 

The fraction of leaky-mode power propagating within the fiber core is given by Eq. (24-19). Using this definition and taking the real part of the quotient of Hankel functions, we plot i/ as a function of V in Fig. 24-5 for the modes of Fig. 24-3(a). The solid curves denote bound modes and the dashed curves denote tunneling leaky modes. All refracting leaky modes have / = 1 since = p and = y4 . 

If we substitute for T from Eq. (7-19b) and for Zp from Table 2-1, page 40, and note that p = n in the weak-guidance approximation, it is readily verified that the mode and ray attenuation coefficients are identical [7]. A similar, analytical comparison can be made for refracting leaky modes and rays on the step-profile planar waveguide [8]. 

It is clear from the spacing of the cutoff values of Fin Fig. 12-2 that this result holds for all values of F. Tunneling leaky modes do not propagate on planar waveguides, and the number, of refracting leaky modes is the difference between the total number of modes and the number of bound modes... 

The number of tunneling and refracting leaky modes, M, , is therefore... 

The fully leaky guided mode technique makes use of a thin 3 pm) HAN sample between glass plates with a refractive index lower than both the principal indices of the nematic. A p or 5 polarized He-Ne laser beam, with the electric vector in the plane of incidence or orthogonal to it, respectively, incident in an appropriate range of incident angles / (see... 

---