The Surrounding Environment and Contact Sensitivity Issue: An Innovative Design

The environmental sensitivity of pure dielectric waveguides is further illustrated in this part. We first consider a case of practical interest: the impact of the user touching the waveguide, which is actually a very aggressive perturbation regarding the propagation conditions. To mitigate this effect, an innovative plastic waveguide design is proposed (Magic Wheel). Comparison measurements with respect to a simpler tubular design are provided in section 2.7.

2.5.1. Contact Sensitivity Issue

Figure 2-36: Semi-infinite water slab surrounding a 2 mm diameter Teflon waveguide. (a) side view with symmetry conditions enforced and E-field computed at 120 GHz (logarithmic scale). (b) impact on transmission parameters in blue. Undisturbed propagation is provided for comparison in dash

black.

To illustrate the sensitivity to external perturbations, i.e. the presence of materials different from air around the waveguide, a numerical simulation is carried out in which a semi-infinite slab is introduced around a slightly overmoded dielectric rod (with confinement greater than 80%). This slab is uniformly filled of water (𝜀𝑟 = 80) as a fair approximation of a human finger.

Nevertheless, the slab thickness is only a 2.23 mm in this example because of computational limitations. A real finger (1.5 – 2 cm width) is thus likely to create an even more aggressive perturbation. Symmetry conditions are also enforced to simplify the model, as shown in Figure 2-36 (a).

Expected attenuation is almost negligible in the undisturbed configuration because of a very limited propagation distance (Figure 2-36 (b)). This result is to be compared to a noticeable insertion loss observed in the presence of the slab. From Figure 2-36 (a), it is clear

-25 -20 -15 -10 -5 0

80 90 100 110 120 130 140

Transmission parameters (dB)

Frequency (GHz)

Contact Undisturbed (b)

(a)

y

Overmoded Single mode

Water slab 2.23 mm Plastic waveguide

that the finger slab introduces significant return losses as well. By locally breaking the condition 𝜀_{𝑟_𝑐𝑜𝑟𝑒} > 𝜀_{𝑟_𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔}, the wave guiding condition is actually no longer satisfied in the core rod, which causes energy radiation in the slab and reflected waves. Furthermore, the slab has a very long electrical-length due to water high dielectric permittivity, which potentially causes longitudinal resonances like in a 2D-cavity. This phenomenon is likely to be responsible for the considerable attenuation observed in Figure 2-36 (b) at 85 GHz. This hypothesis is further consolidated in Appendix A. Finally, with this possibility in mind, it is worth noting that finite 3D-pertubations (like a water drop instead of a slab) could induce much more frequency-dependent behaviors as the radial dimension may also resonate.

Another illustration is given in [Fukuda, 2011] where the long plastic waveguide is

“floating” above the table thanks to little paper or plastic trestles (see section 2.1.2.2).

To put in a nutshell, these examples illustrate the lack of reliability of pure dielectric waveguides from an applicative point of view. Moreover, it is worth noting that an overmoded waveguide has been considered in Figure 2-36 to benefit from a higher Poynting confinement such that maximal robustness should be expected. Consequently, external contact is likely to be even more detrimental while operating in the single mode regime, a trend that seems confirmed by the basic results obtained at lower frequencies in Figure 2-36 (b).

Figure 2-37: Semi-infinite water slab surrounding a foam-coated 2 mm-diameter Teflon waveguide.

(a) isometric view of the simulation model with E-field computed at 120 GHz for a 2 mm-thick foam (not represented since it is made of pure air) and (b) impact of the foam thickness on transmission

parameters at different frequencies.

In the context of an energy-efficient system, the external contact sensitivity cannot be mitigated relying on important link budget margins. On the contrary, link budget margins should be minimized advocating for a reliable by design plastic waveguide. A high-complexity plastic waveguide assembly embedding a protective tube has been proposed in [Nickel, 2014].

Nevertheless, this complex design is likely to suffer from high manufacturing costs. At the opposite, a very straightforward and efficient design modification is possible by introducing foam materials around the core waveguide (see section 2.1.2.2). The foam is essentially composed of air and ensures that propagation condition 𝜀_{𝑟_𝑐𝑜𝑟𝑒} > 𝜀_{𝑟_𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔} is always satisfied. The precedent simulation model can be simulated for various foam thicknesses. For

Transmission parameters (dB)

the sack of simplicity we assume that 𝜀_{𝑟_𝑓𝑜𝑎𝑚} = 𝜀_{𝑟_𝑎𝑖𝑟} = 1. Therefore, the slab is progressively moved further when the (air) foam thickness is increased (Figure 2-37 (a)). Besides, detailed results are provided in Appendix A.

From the results of Figure 2-37 (b), the thicker the cladding is made, the better robustness is enforced, especially in the low-confinement region However, this solution suffers from multiple disadvantages:

 Enlarged footprint,

 Poor mechanical reliability – Hard foams like PU foams may not also offer the desired flexibility,

 Porous foams incompatibility – only foams containing dry air cavities should be preferred since porous foams are subject to humidity contamination. Otherwise, an external moisture barrier film should be added.

 Additional manufacturing process – the foam may be added after the extrusion process of the core rod or co-extruded with the core during the same process. In any case, at least a small cost penalty is expected.

While still having some practical limitations with foams, the idea of maintaining propagation condition thanks to a low complexity design modification is interesting and is further investigated in the following section.

2.5.2. Magic Wheel: An Innovative Design Proposal

Figure 2-38: Description of the Magic Wheel waveguide as presented in [Voineau, 2018].

Initially proposed as an alternative to foam coated waveguides, the Magic Wheel waveguide was first introduced in [Voineau, 2018] as an attempt to provide both mechanical reliability and contact insensitivity. At the expense of a higher complexity cross-sectional shape, the design embeds a thin shell that defines four enclosed spaces, which collectively behave as a cladding (Figure 2-38). Consequently, the waveguide core is protected from detrimental external contacts similarly as a foam coating. However, the whole design can be made of the very same dielectric material and extruded all at the same time while still ensuring higher mechanical robustness.

Circular shell

X-shape core

Air cavities (x4)

Note that the core cross-section featuring two orthogonal branches is carefully designed so that:

 The shell is mechanically supported thus offering good rigidity and limiting shield deformation in the case of external contact.

 Two linearly polarized orthogonal modes are available in the structure – one in each branch of the cross – with very similar propagation properties and obvious polarization maintaining.

 The shell does not participate in the propagation. In other words, the shell should be designed thinner compared to the core branches to make sure that only a negligible part of the energy is effectively carried by the shell region, while most of it travels inside the core and cladding regions.

This design also features two favorable properties: single-mode operation capability and improved Poynting confinement in this regime with respect to lower complexity waveguides.

Careful modal analysis is conducted using Ansys HFSS simulation tool. Simulation results are reported along with measurements in section 2.7.3.