Transverse electric mode, waveguide

TE modes. Transverse-electric modes, sometimes called H modes. These modes have = 0 at all points within the waveguide, which means that the electric field vector is always perpendicular (i.e., transverse) to the waveguide axis. These modes are always possible in waveguides with uniform dielectrics. 

The effective index represents the dimensionless in-plane component of the propagation vector of the mode (the propagation vectors are in units of A being the vacuum wavelength). The optical modes can be characterized as transversal electric (TE the electric field is polarized in-plane) and transversal magnetic (TM the magnetic field is polarized in-plane). For unsymmetric slab waveguides, a minimum thickness (cutoff) exists for each mode to appear [48]. 

Although waveguide modes are not plane waves, the ratio of their transverse electric and magnetic field magnitudes is constant throughout the cross section of the waveguide, just as for plane waves. This ratio is called the modal wave impedance and has the following values for TE and TM modes ... 

This structure provides good coupling between the TEM (transmission line) mode on a coaxial cable and the TEio mode in the waveguide because the antenna probe excites a strong transverse electric field in the center of the waveguide, directed between the broad walls. The distance between the probe and the short circuit back wall is chosen to be approximately X/4, which allows the TEm mode launched in this direction to reflect off the short circuit and arrive in phase with the mode launched toward the right. 

The exponentially decaying field outside the slab is called the evanescent field. Since the electric field y lies in the waveguide plane the modes are called transverse electric or TE. A corresponding set of transverse magnetic or TM modes also exist. These satisfy a wave equation for Hy similar to Eq. [7]. The dispersion relationship for TM modes is... 

There are two exceptional cases when the V, In n terms do not appear in the vector wave equations for the transverse fields. These occur for modes with e j = 0 everywhere on a planar waveguide and on a circularly symmetric fiber, and are called TE modes. In these two special cases, it is indeed true that the transverse electric field ey satisfies the scalar wave equation. Section 33-1, everywhere. 

Table 13-1 Boond-mode flelds of weakly guiding waveguides. The form of the transverse electric field depends on the shape of the waveguide cross-section. Vector operators are defined in Table 30-1, page S92, and parameters are defined inside the back cover.

The higher-order modes of waveguides with noncircular cross-sections are constructed from each pair of solutions Pj (x, y) and Pg (x, y) of Eq. (13-8) and their corresponding scalar propagation constants and p. The transverse electric fields of these modes are polarized along the same optical axes as the fundamental modes of Section 13-5. There are two pairs of higher-order modes. Each pair has fields given by Eq. (13-10), with p and P(X) y) replaced by Pg and Pj(x,y) for one pair, and by p and Pj,(x,y) for the other pair. The polarization corrections Sp, Sp, SPy and SPy are obtained from Eq. (13-11) with the appropriate field substituted for e,. 

Modes of weakly guiding waveguides obey the fundamental properties of modes delineated in Chapter 11, and mainly because of the approximate TEM nature of the modal fields, these properties have the simpler forms of TaHe 13—2. The expressions in the first column are in terms of the transverse electric field e, and apply to all weakly guiding waveguides. Those in the second column are for waveguides which are sufficiently noncircular that e, can be replaced by either of the two fields for noncircular waveguides in Table 13-1, while the third column is for circular fibers only, when e, is replaced by any one of the four linear combinations Ct, for circular cross-sections in Table 13-1. We emphasize that Table 13-2 applies to all modes. 

The scalar propagation constants P+ and for the fundamental modes of the composite waveguide are given by Eq. (18-35) in terms of the fundamental mode propagation constant for either fiber in isolation and C of Eq. (18-42). We explained in Section 13-5 that polarization corrections are required to correctly distinguish between the propagation constants of each pair of fundamental modes associated with P+ or P-. To determine each correction, we substitute the approximate transverse electric field of Eq. (18-36) into Eq. (13-12), where I now denotes the interface of both fibers. Thus, in the notation of Section 18-12, and with the help of Eqs. (18-36) and (18-33), we obtain 5 by setting... 

Fig. 18-6 (a) The transition of an / = 1 mode of the two-fiber waveguide to the superposition of two even HE21 modes, where arrows denote the direction of the transverse electric field, (b) Plots of the normalized parameter 2A A of Eq. (18-53) as a function of the fiber parameter- for various values of djp. The mode is cut of at K = 2.4 and the vertical dashed line corresponds to F = 3.8. 

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