Using W3 Waveguides

The first example of splitter/combiner is made of three W3 waveguide sections connected by a wedge based on the hole-displacing design, see Fig. 3.26a. First consider the system as a splitter:

a wave is launched into port B and the outgoing power is collected by two detectors placed just in front of ports A and C. Fig. 3.26b compares the transmission of a splitter with the one of a bend (the corresponding structures are displayed in the right panels). Notice that the transmission of the splitter is multiplied by two, that is the sum of the two exit ports⁵. As done for the bend spectra of Fig. 3.16 and Fig. 3.17, the calculated curves are slightly stretched to fit better with the experimental data. Concerning the splitter, the agreement between experiment and FDTD simulations is not as good as for the bend, specially around a/λ ∼ 0.29. However, the overall behavior is matched. The dip in the center of the spectrum is due once more to the mini-stop band in the W3 waveguide. The transmission level of the splitter is quite good, considering that the loss parameter is²⁰⁰= 0.1, and it is maximum in the same frequency domain found for the single bend.

Transmission is always mediated by a cavity resonance, which occurs at the wedge, where three waveguide sections are connected to each others. The basic splitter design is obtained by simply connecting the waveguides at 120^◦ degrees. This yields a cavity with a three-fold symmetry axis.

According to the theorem of scattering matrix theory, it is impossible to make a reflectionless Y splitter with three-fold symmetry [Manolatou, C., et al. (1999)]. Therefore, to improve transmis-sion, the hole-displacing bend design is applied to the splitter: holes are moved from the outer corners and are gathered between two branches, so to form a wedge with two functions: breaking the three-fold symmetry and smoothing the splitter. The rule readsp=n(n+ 1)/2, like for bends.

Fig. 3.27a shows transmission spectra for three designs, corresponding top= 3 (black),p= 6 (red)

5In the simulations, the power through one port is exactly equal to the power though the other one, because the splitter is symmetric. This is not perfectly true in the experiment, where small asymmetries could take place.

(a) (b)

Figure 3.26 (a) Combiner/splitter with W3 waveguide sections. (b) Exper-imental spectra (black curves) and calculated spectra (gray curves) for a bend and a splitter respectively (right panels).

The transmission for the splitter has been multiplied by a fac-tor of 2. The gray areas refer to the mini-stop band region.

The simulations were performed choosing ²= 10.5, f = 35%, and ²⁰⁰ = 0.1. The calculated spectra were slightly stretched to fit the experiments, yielding an effective dielectric constant

²=10.4 instead of 10.5. The experimental data are courtesy of Moosburger, J., University of W¨urzburg, Germany and Olivier, S., EPP, France.

and p= 10 (blue). The values are multiplied by two to account for both exit ports. The designs with 6 or 10 holes displaced are better than the one with p = 3, even though the improvement is not exceptional. For a deeper insight, modal transmission has also been considered: like for bends, the smallest mode-mixing is found arounda/λ'0.24.

More interesting, in view of the demonstrator, is the combiner configuration: the incident power is launched from port A or port C and is collected at port B and also at port Cor port A, re-spectively. The reason why only one entry port is selected for each simulation is that the cross-talk would not be detectable otherwise. Moreover, since the system is symmetric with respect to a plane containing the axis of the waveguide corresponding to portB, it is enough to choose one entry port

0.20 0.22 0.24 0.26 0.28 0.30 0.32

0.20 0.22 0.24 0.26 0.28 0.30 0.32

a/λ

Figure 3.27 (a) Splitter transmission for the system of Fig. 3.26a; i.e.

B→A orB→C. The transmission has been multiplied by a factor of 2. (b) Combiner transmission for the system of Fig. 3.26a for three, six and ten holes displaced at the junction.

A→Btransmission (top) andA→Ctransmission (bottom).

Parameters: ²= 10.5, f = 35%, and²⁰⁰= 0.1.

only, precisely port A. The top panel of Fig. 3.27b shows the transmission spectra for the same designs studied in Fig. 3.27a, but, this time, used as combiners. As to the transmission through port B, the maximum value ('70%) is smaller than for the splitter ('80%), but in the present case, this power is channelled into a single port. In an ideal combiner, one expects that the power is totally transmitted into portB; when it does not happen, it means that there is some cross-talk between the channels and/or back reflection. The cross-talk of the above mentioned designs is shown in the bottom panel of Fig. 3.27b. The cross-talk is rather hight, being of the same order of magnitude of transmission. Nevertheless, the best design is obtained for p= 6, which exhibit a cross-talk of '0.5 in correspondence of the maximum transmission. It must be given for granted that the transmission is not single-mode.

While the W3 splitters have shown satisfactory performances, which can be easily improved by employing the slit-taper designs, the combiners that have been considered so far exhibit a cross-talk

that is too much large to make the device suitable for any application. That is why it is worth to try other designs, which involve larger waveguides, like W5 or W7. For example, combiners made of two W3 waveguides going into one W5 or W7 waveguide have been studied. In both cases, the cross-talk is much reduced with respect to the original W3 designs, even though, the system with W3 → W7 has been found to have a smaller cross-talk than the one with W3→ W5.