Transverse resonance condition

Waveguiding occurs only when the various parameters (the refractive indexes of the substrate, waveguide and cover layer and the waveguide s thickness) are such that the transverse-resonance condition can be met. Waveguide behavior is presented in more detail in [9]. 

If 2a is large compared to the wavelength of the light, then there will be a large number of angles 6 that satisfy the transverse resonance condition. As the thick-... 

Given co, the values of Pj are determined from an eigenvalue equation. This equation is a consistency condition, or transverse resonance condition, resulting from the requirements that the field solutions of the source-free Maxwell equations (i) are bounded everywhere, (ii) go to zero sufficiently fast at infinity and (iii) satisfy all boundary conditions at the core-cladding interface. The formulation of the eigenvalue equation is discussed in Section 11-13, and specific examples are given in the following chapter. 

Here 2tt Aft = trm is imposed to eliminate the effect by the zero-order interaction of the RF field, otherwise a term containing Ix will remain and it will distort the longitudinal magnetization, transverse magnetization, as well as the BSPS of the 13C . For the on-resonance condition, 5 = 0, all the higher-order average Hamiltonians vanish since [7f(/ ), = 0 for arbitrary l and... 

The qualitative and quantitative analysis of obtained spectra has been carried out using the phenomenological equations for the resonance conditions of long cylinder. The influence of demagnetizing factors tends to the following equations for the longitudinal orientation of the magnetization it s eq. 2 and for the transversal it is ... 

We now consider only waves that reproduce themselves after two reflections (resonance condition), called eigenmodes (or simply modes) of the waveguide. These modes have the same transversal held distribution and polarization along the waveguide, which is a direct result of the resonance condition [4]. Figure 3 represents the resonance condition graphically. If we now consider the resonance condition with the help of Fig. 3, i.e., the phase difference needs to be a multiple of 2ti, we get... 

In cylindrical resonant cavities there exist Electric (E) and Magnetic (B) fields orthogonal to each other. Eigenvalue solutions of the wave equation subjected to proper boundary conditions are called the modes of resonance and are labeled as either transverse electric (TEfom) or transverse magnetic (TM/mn). The subscripts l,m,n define the patterns of the fields along the circumference and the axis of the cylinder. Formally, these l,m,n values are the number of full-period variations of A... 

Note that Eqs. (4.127)-(4.130) describe only the longitudinal (with respect to the easy axis) relaxation of the magnetic moment. We remark that under condition 0) L, that is, far from the ferromagnetic resonance range, the transversal components of hi = p(e) are of minor importance. 

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