Drawbacks in Metallic Waveguides. α f. Skin effect. Surface roughness Mono-mode operation Narrow band in metallic rectangular waveguide

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2 Drawbacks in Metallic Waveguides Skin effect α f Surface roughness Mono-mode operation 1 Narrow band in metallic rectangular waveguide 2 α f α 3 f 2 to f 5 2

3 Types of Dielectric Waveguide ε r2 (a) Circular dielectric rod guide (variants: elliptical dielectric rod guide) (b) Rectangular dielectric rod guide Ground Plane (c) Image guide Ground Plane (d) Insulated image guide (variants: strip guide an un-grounded insulated image guide) Ground Plane (e) Grounded rib waveguide (variants: un-grounded ridge guide) ε r0 ε r2 (f) Embedded stripline (variants: optical fibre a fully embedded circular dielectric rod, and trapped image guide) ε r0 ε r1 Guided Wave Multiple reflections (g) 2D Photonic Crystal Structure (Periodic discontinuities cause matchedmultiple-reflections, which form a photonic bandgap or virtual cut-off. It can be developed into 2D or 3D wave guiding structures. Variants: circular photonic crystal fibre, etc.) (h) Dielectric slab guide: one of the dimensions at the cross-section is extended to infinite. (This physically unrealisable guide is only used for the field and wave analysis, e.g. a rectangular dielectric rod guide can be mathematically approximated by the combination of two slab guides perpendicular to each other.)

4 Ray trace in a rectangular dielectric rod waveguide. ( ε 2 > ε 1 ) C C D C A B A B ε 1 ε 2 A B y z x D C A B z The zigzagging wave is bounced off from each of the four walls sequentially within the rectangular dielectric rod guide under internal reflection y A z B C D A B C x

5 Propagation modes in dielectric waveguide y x x (1) The E 11 mode in a rectangular dielectric rod waveguide is the combination of the TM 10 and TE 01 modes in dielectric slab guides. ε ε r1 r 2 2b 2a E x 2b ε r 2 E x ε ε ε r1 r 2 r 1 2a TM 10 Mode TE 01 Mode (2) The y E 11 mode can be treated as the combination of the TE 10 and TM 01 modes. There are two dominant modes in dielectric waveguide: E x and E y modes E y ε 2b r 2 Ey ε ε ε r1 r 2 r 1 2a TE 10 Mode TM 01 Mode

6 Selection of dielectric materials Name Dielectric Constant ε Dissipation Factor tanδ Coefficient of Thermal Expansion ( x10-6 K -1 ) Rigidity PEEK (Polyetheretherketone) 3.2 to 50 Hz 10 khz 1 MHz 47/108 Good PTFE (Polytetrafluoroethylene) MHz MHz Poor Rexolite (Cross-link Polystyrene) 1 MHz 1 MHz V. Good PP (Polypropylene) MHz MHz Fair HDPE (High Density Polyethylene) MHz MHz V. Poor TPX (Polymethylpentene) 1 MHz 1 khz 117 V. Good

7 Measurement of different dielectric materials 1 Comparing Different Dielectric Materials 0-2 S21 (db) Frequency (GHz) PP PTFE HDPE Rexolite PEEK TPX

8 Measurement of different dielectric materials S 21 (db) PP HDPE -3 Rexolite TPX Frequency (GHz)

9 Tapered transition Dielectric-filled Rectangular Waveguide Rectangular Waveguide Taper Section Port 2 b=1270µm E y z a=2540µm Port 1 x

10 Different types of taper (a) H-Plane Asymmetric Taper. (b) H-Plane Symmetric Taper. (c) E-Plane Asymmetric Taper. (d) E-Plane Symmetric Taper. (e) Pyramidal Taper. (Tapered in both H- and E-planes)

11 Simulation result of different tapers 0 No Taper (a) (b) (c) (d) (e) S11 (db) (a) (b) (c) -50 (d) (e) H-plane asymmetric H-plane symmetric E-plane asymmetric E-plane symmetric Pyramidal Frequency (GHz)

12 Field analysis in different tapers Ray Trace Taper Length (TL) α = 3.2 η1 η2 E ε r a E η 1 α ε r η 2 = 3.2 (a) Asymmetric H-plane taper. (b) Symmetric H-plane taper. E-field E ε r = 3.2 b ε r = 3.2 λ1 λ 2 (c) E-plane asymmetric taper. λ1 λ 2 (d) E-plane symmetric taper.

13 Standard wheel

14 Measurement of different off-set shorts 1 75 GHz 110 GHz Short 0.4 Short Imaginary mm 3.632mm 4.561mm 5.100mm Imaginary mm 3.632mm 4.561mm 5.100mm mm mm Real Real Measured in an un-calibrated system

15 Measurement of different off-set shorts GHz 96 GHz Short 0.4 Short Imaginary mm 3.632mm 4.561mm 5.100mm Imaginary mm 3.632mm 4.561mm 5.100mm mm mm Real Real

16 Calibration using 4 standards

17 Uncertainty profile

18 Expected size of errors in S11 at 75 GHz Transmission medium Random errors due to connection repeatability Systematic errors due to connection misalignment Combined standard uncertainty Dielectric Waveguide Rectangular Metallic Waveguide

19 Conclusions Lower loss Better connectivity (even with small air gap) Good repeatability It can be used on integrated waveguides and photonic band-gap structures