Dielectric Rod Waveguides Project for ELEC 590, UVIC, BC, Canada Session - September 2002 Directed Study Prepared by: Deepak Sarkar Student #

Dieletric Rod Waveguides Objective Overview Of Dielectric Rod Waveguides Cutoff Conditions and Wave Numbers Spectrum Analysis Advantages of Dieletric Rod Waveguides Applications in Microwave Filters and Transformers Applications in Optical Fiber and Integrated Optics Other Applications Summary Conclusion References Appendix

Objective! Objectives of this directed study - Find out the existing work and recent developments in Dielectric Rod Waveguides Determine the advantages, mode spectrum, cutoff conditions and wave numbers Identify applications to microwave filters & transformers, optical fibers and integrated optics.

What Is Dielectric Considering electrical properties, there are three kinds of material. Conductor, conducts electricity with little or no resistance Semi-Conductor, conducts electricity half heartedly Insulator or Dielectric, inhibits flow of electricity A dielectric material is used as the insulation material in cable products. Typical dielectric materials are polyolefins (PE or PP) and teflons. PVC is normally not referred to as a dielectric material

property of a material that determines the relative speed an electrical signal will travel in that material. Signal speed is roughly inversely proportional to the square root of the dielectric constant. Dielectric Constant/Permitimitty

Typical Dielectric Constants Hard Vacuum 1.0 Pure Teflon® 2.1 Type GY Teflon®-Glass Type GX Teflon® Glass 2.55 Cyanate Ester/Glass Cyanate Ester-Quartz Polyimide-Quartz Polyimide-Glass Epoxy-Glass (FR-4) Non-woven Aramid Epoxy Woven Aramid Epoxy Ceramic-Filled Teflon® Water 70.0

Overview Of DRW

Overview (cont.). Such a structure can support an infinite number of modes. However, for a given set of permittivities and radius ‘a’ only a finite number of unattenuated waveguide modes exist with their fields localized in the central dielectric core.

Overview - Geometry r  z y x Direction of propagation

Circular Dielectric Waveguides E and H fields at the interface requires a linear combination of the TE(Transverse Electric) and TM(Transverse Magnetic) modes In general neither TE nor TM mode can alone satisfy both E z and E  being continuous at the boundary The general solution has both H z and E z component

Let us start with Maxwell’s equations expressed in terms of the longitudinal(E z, H z ) and transverse(E t, H t ) field components Solving for E t and H t in terms of E z and H z, - and multiplying through by -j  - using n 2  0 2 =  2  -  =n 2  0 /  0

Expanding using the vector identity A X B X C = (A.C)B - (A.B)C where If E z = 0, TE mode If H z = 0, TM mode

Mode Spectrum Algorithm First, we chose a frequency and we start from  z /  0 =1 Then we find pa and qa from Equation (20) Then we find J and K for pa and qa Then we plug in J and K in Equation (19) and evaluate if it is zero If zero, that is the solution; we save it and proceed with next frequency If NOT zero, we save the solution and decrement the value of  z /  0 and repeat from pa and qa until Equation (19) = 0 Once we got the solutions for all frequencies, we plot them to determine modes Eigen value method would be used in the actual evaluation process.

Balanis Vs. Presentation (Notation)  0 d   0  d  z     d P q  0  z pa qa  z a n  0

Cutoff Conditions V Mode Cutoff Conditions 0TE 0m, TM 0m J 0 (ua) = 0 1HE 1m, EH 1m J 1 (ua) = 0 >= 2EH m J (ua) = 0 HE m

Cutoff Conditions

Advantages Of DRW The material is inexpensive and easy to maintain in the lower frequency range (up to say 20 GHz) easy to manufacture due to rotational symmetry easy to connect to circular waveguide equipment through conical section which fits into a standard conical waveguide horn

Advantages of DRW -In the qusi-optic range (several hundred GHz) implementation as filters, transformers and gratings Future applications might include incorporating gratings directly into the optical fiber

Applications to Microwave Filters and Transformers

Applications To Optical Fiber and Integrated Optics Core Cladding

Other Applications

Summary Dielectric Rod Waveguides are simple cylindrical symmetric structures made of high permittivity dielectric material capable of carrying high frequency electromagnetic wave with low loss capability. Fields within and outside the waveguide are complicated in nature due to the angular variations which give rise to hybrid modes apart from usual TE or TM modes out of which HEM 11 (HE 11 ) is the dominant mode.

Summary(cont.) Applications go beyond fiber and integrated optics to Dielectric Rod Resonators, Filters, Antennas, and various interfaces and transformers among various microwave and millimeter wave components. Its cost effective high frequency low noise low maintenance aspects and versatility might lead to enormous future research possibilities integrating electromagnetics and optics.

Conclusion A single dominant HE 11 mode can be maintained within the rod provided the normalized central core radius or numerical aperture V < This can be accomplished by making the radius ‘a’ of the central core small and/or choosing, between the central core and the cladding, a small dielectric constant  r.

References