Normalized Scattering Junctions

The Three-Multiply Normalized Scattering Junction. Figure 10.10 illustrates a three-multiply normalized scattering junction [Smith, 1986b], The one-multiply junction of Fig. 10.8 is normalized by a transformer. Since the impedance discontinuity is created locally by the transformer, all wave variables in the delay elements to the left and right of the overall junction are at the same wave impedance. Thus, using transformers, all waveguides can be normalized to the same impedance, e.gRi= 1. ... 

Passive Four-Multiply Normalized Junctions. Unlike the structurally lossless cases, the (four-multiply) normalized scattering junction has two parameters, st = kt and a = /l - kf, and these can get out of synch in the presence of quantization. 

It is interesting to define 0 = sin-1 (lq), always possible for passive junctions since -1 < ki < 1, and note that the normalized scattering junction is equivalent to a 2D rotation ... 

Figure 10.10 A three-multiply normalized scattering junction.

Figure 17. Reflectivity (O) and Raman scattering intensities (9) for an Al-AlOx-4-pyridine-COOH-Ag tunneling junction prepared on a diffraction grating substrate, as a function of the angle between the incident laser beam and the normal to the grating surface (45). At the same angles that absorption by surface plasmons causes reflectivity dips, the Raman signal shows peaks.

We start with the case of a symmetric single barrier junction, when the scattering barrier is situated in the middle of the normal region, i.e. I = L/2 in Eq. (3). Then = 0 and the second cosine term in the spectral equation Eq. (3) is equal to one... 

While it appears that scattering of normalized waves at a two-port junction requires four multiplies and two additions, it is possible to convert this to three multiplies and three additions using a two-multiply transformer to power-normalize an ordinary one-multiply junction. 

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