Transverse electric field mode

Transverse electric field mode indicates that the electric field of the laser beam is perpendicular to its direction of propagation. TEMqo imphes a Gaussian beam profile. 

The refractive indices (RI) for transverse electric field (TE) mode were measured using the m-line method at the wavelengths of 632.8 and 830 nm. Wavelength dispersion of RI, was fitted to a one-oscillator Sellmeier-dispersion formula,... 

Since extrinsic silicon photoconductor material has high resistivity at cryogenic temperatures it can be used to form the substrate of an accumulation mode CCD as shown in Fig. 6.11. With an accumulation mode MIS structure the gates are biased so that majority carriers are stored and transferred down the insulator semiconductor interface. Local potential wells are formed under the gates however the dynamics of the charge transfer process will be very different from those for an inversion mode device since with an accumulation mode device the transverse electric fields will extend all the way to the back contact instead of being confined to the depletion region of an inversion mode structure. 

Based on the same operation principle, fringing field switching (FFS) [14] also utilizes the transverse electric field to switch the LC directors. The basic structure of FFS is similar to IPS except for the mueh smaller eleetrode gap (f 0-1 pm). In the IPS mode, the gap ( ) between... 

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 transverse electric fields in heterogeneous POPs can be approximately expressed as a superposition of the transverse guided mode fields of the ideal optical fiber without any inhomogeneities ... 

As the name suggests, the in-plane switching (IPS) mode is a method that applies an in-plane transverse electric field that is generated by comb-shaped electrodes placed on the substrate, and the liquid crystal layer is switched in the in-plane direction [67]. The modeling of the IPS mode requires an at least two-dimensional model, for example, with respect to the arrangement of the various comb-shaped electrodes to obtain the two-dimensional distribution of the liquid crystal alignment and the transverse electric field described above. There is no alternative to a simulation to get a realistic model, which is totally different from the case of the TN display described above. 

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. 

The fundamental and HEi , modes of a fiber of circular cross-section are formed from the scalar wave equation solution with no azimuthal variation. Hence in Eq. (13-8) depends only on the radial position r. There is no perferred axis of symmetry in the circular cross-section. Thus, in this exceptional case, the transverse electric field can be directed so that it is everywhere parallel to one of an arbitrary pair of orthogonal directions. If we denote this pair of directions by x- and y-axes, as in Fig. 12-3, then there are two fundamental or HEi , modes, one with its transverse electric field parallel to the x-direction, and the other parallel to the y-direction. The symmetry also requires that the scalar propagation constants of each pair of modes are equal. 

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 two fundamental, or HEj j, modes and all other pairs of HEi modes were discussed in Section 13-4. Each mode of a particular pair has a transverse electric field whose direction, or polarization, is parallel to one of an arbitrary pair of orthogonal directions in the fiber cross-section [1], Thus, these modes are uniformly polarized. For convenience we take one mode to be x-polarized and the other y-polarized in Fig. 14-1. There is only one solution of the scalar wave equation for these modes, corresponding to 1 = 0 in Eq. (14-4). The transverse fields, given by Eq. (13-9) and repeated in Table 14-1, ignore all polarization properties of the fiber. For future reference, we give the transformation of the components of these fields from cartesian to polar... 

The transverse fields of the fundamental modes in Table 14-1 contain no polarization effects due to the fiber. These effects are included in higher-order corrections through the expansions in Section 32-1. The second-order transverse electric field corrections satisfy the equation in Table 32-1, page 627. If we set f = R, substitute e or e,3 from Table 14-1 fore, and take = 51//A from Table 14-2, it is readily verified that the... 

The finite propagation constant corrections SPi discussed above are responsible for interference effects between pairs of modes with the same scalar propagation constant. For example, suppose the odd HE21 and TEqi modes are excited with equal power and all other modes have zero power. If we erroneously ignore all polarization effects, then bPj = 5p = 0, and the total transverse electric field of the fiber follows from Table 14-1 as... 

It follows from the above discussion that propagation of the two fundamental modes on the eUiptical fiber is similar to plane-wave propagation in an anisotropic medium discussed in Section (11 -23) [1 ]. In particular, the total transverse electric field E, of the two modes is elliptically polarized and its direction changes with distance z along the fiber. On the other hand there is no... 

If the unperturbed fiber is noncircular, the transverse electric field of each mode is polarized parallel to one of the optical axes, Xq or as discussed in Sections 13-5 and 13-8. The directions of the optical axes on the perturbed fiber, which determine the polarization of the perturbed mode fields, are found either by inspection or by the formal methods of Section 32-5. 

The polarization of the transverse electric field as the fiber changes from elliptical to circular cross-section is shown qualitatively in Fig. 18-3 (a) for the four / = 1 modes. Here we examine the transition region between the two extremes, as discussed in Section 13-9. The transition is described quantitatively by the parameter A of Table 13-1, page 288. Substituting from Eq. (18-28) and Table 14-6, page 319, the absolute value of A is given by [9]... 

The four fundamental modes of the two identical fibers are composed of pairs of symmetric and antisymmetric modes corresponding, respectively, to T+ and T of Eq. (18-33). By symmetry the transverse electric fields are polarized parallel to either the x- or y-axes, as shown in Fig. 18-5. If subscripts x,y denote polarization and +, — denote symmetry, then... 

Fig. 18-5 Orientation of the transverse electric field for the four fundamental modes of a pair of identical fibers.

We assume that only x-polarized modes are involved. Hence the magnitude E of the total transverse electric field is given everywhere by... 

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. 

The direction of the fundamental-mode transverse electric field within the core of an arbitrary step-profile fiber is shown schematically in Fig. 12-6. When the nonuniformity of Fig. 18-1 (c) is included, the symmetry of the circular fiber is broken. However, since the nonuniformity is infinitesimal, it is clear that the two fundamentalmode patterns are oriented as shown in Fig. 18-8. The propagation constants associated with Figs. 18-8(a) and 18-8(b) are, and by, respectively. If we substitute Eq. (18-64) into Eq. (18-63) and recall the normalization definition in Table 11-1, page 230, we obtain... 

Consider a single-mode, elliptical fiber whose refractive-index profile rotates along its length, as shown in Fig. 19-2. We recall from Section 13-5 that in the weak-guidance approximation one fundamental mode of the cylindrically symmetric, elliptical fiber is plane polarized with its transverse electric field parallel to the x-axis in Fig. 19-2(a) and has propagation constant The other fundamental mode s field is parallel to the y-axis... 

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