Transverse magnetic mode, waveguide

TM modes. Transverse-magnetic modes, sometimes called E modes. These modes have = 0 at all points within the waveguide, which means that the magnetic field vector is perpendicular to the waveguide axis. Like TE modes, they are always possible in waveguides with uniform dielectrics. 

Fig. 4 (a) Schematic of MIM stracture with gap d. Transverse magnetic field is shown in red, which has a hyperbolic cosine dependence in the gap and exponential decay into the metal, (b) Effective refractive index of waveguide mode within MIM gap, which increases as the gap is made smaller. Calculations for two free-space wavelengths are shown using the relative permittivity of gold and the difference is used to estimate the group index ( g), which also increases as the gap is made smaller. Therefore, the light slows down as the gap is made smaller... 

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]. 

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... 

Another useful but less versatile single mode resonant applicator is shown in Figure 26. It consists of a circular waveguide operating in the transverse magnetic or TMq.]q mode and is shortened at both ends. This fixes the overall dimensions which restrictions the operation to a given narrow frequency band for a given ceramic. 

For a Gaussian beam, the fields of the radiating electric and magnetic multipoles satisfy the same boundary conditions (vanishing faster than 1/p as p oo) so that the fields in the plane(s) defined by the transverse E (H) field and the optical axis are symmetric. It is difficult to generate a balanced hybrid mode in conventional smooth-walled metallic waveguide instead, one may use a component called a scalar horn. 

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 ... 

We showed how to determine the radiation modes of weakly guiding waveguides in Sections 25-9 and 25-10, starting with the transverse electric field e, which is constructed from solutions of the scalar wave equation. However, unlike bound modes, the corresponding magnetic field h, of Eq. (25-23b) does not satisfy the scalar wave equation. This means that the orthogonality and normalization of the radiation modes differ in form from that of the bound modes in Table 13-2, page 292, as we now show. 

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