Download Applications To Optical Fiber and Integrated Optics

Dielectric Rod Waveguides
Project for ELEC 590, UVIC, BC, Canada
Session - September 2002
Directed Study
Prepared by: Deepak Sarkar
Student # 0124480
Dieletric Rod Waveguides
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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
Dielectric Constant/Permitimitty
• 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.
Typical Dielectric Constants
•
•
•
•
•
•
•
•
•
•
•
•
•
Hard Vacuum
1.0
Pure Teflon®
2.1
Type GY Teflon®-Glass 2.2 - 2.3
Type GX Teflon® Glass
2.55
Cyanate Ester/Glass
3.2 - 3.6
Cyanate Ester-Quartz
2.8 - 3.4
Polyimide-Quartz
3.5 - 3.8
Polyimide-Glass
4.0 - 4.6
Epoxy-Glass (FR-4)
4.4 - 5.2
Non-woven Aramid Epoxy
3.8 - 4.1
Woven Aramid Epoxy
3.8 - 4.1
Ceramic-Filled Teflon®
6.0 - 10.2
Water
70.0
Overview Of DRW
The cylindrical dielectric waveguide[1]
usually consists of a high permittivity (d)
central core dielectric of radius ‘a’
surrounded by a lower dielectric cladding
(which is usually air). It is assumed for
simplicity that both mediums are perfect
dielectrics with permeability equal to that of
free space
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
x

z
Direction of propagation
y
Maxwell’s Equations
Assuming a linear, isotropic dielectric material having no
currents and free charges , the equations take the form
B
XE  
t
D
XH 
t
.D  0
.B  0
Where D=E and B=H. The parameter  is the permittivity
(or dielectric constant) and  is the permeability of the medium
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 Ez
and E being continuous at the boundary
• The general solution has both Hz and Ez component
• Let us start with Maxwell’s equations expressed in terms of the
longitudinal(Ez, Hz) and transverse(Et, Ht) field components
^
^
^
^
a z  t E z  j z a z Et  jH t ..................................(1)
a z  t H z  j z a z H t   jEt ...............................(2)
• Solving for Et and Ht in terms of Ez and Hz,
^
^
^
^

2
2
2
0
 jn ( ) a z  t E z  j z a z [a z H z  j z a z H t  n  0 H t
0
- and multiplying through by -j
.....(3)
- using n202=2
- =n20/0
• Expanding using the vector identity
A X B X C = (A.C)B - (A.B)C
^
 jn (  0 /  0 ) a z  t E z  j z  t H z  (n 2  02   z2 ) H t ............(3)
2
^
j 0 0 a z  t H z  j z  t E z  (n 2  02   z2 ) Et ............(4)
where
n   
2
2
0
2
z
• If Ez = 0, TE mode
• If Hz = 0, TM mode
2
t
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
• za
• n0
Cutoff Conditions
V
Mode
0
TE0m, TM0m
J0(ua) = 0
1
HE1m, EH1m
J1(ua) = 0
>= 2
EHm
J(ua) = 0
HEm
Cutoff Conditions
 n12 
ua
 2  1 J ( 1) (ua) 
J (ua)
 1
 n2 
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
Dielectric Rod Resonator [1]
In order for the dielectric resonator to function as a resonant cavity
the dielectric constant of the material must be very large >= 30
Applications To Optical Fiber and Integrated
Optics
An optical fiber is a dielectric waveguide, normally
cylindrical in form, that operates at optical
frequencies.
Core
Cladding
Other Applications
Microwave tuning devices, high frquency low loss tuning [9]
Dielectric resonator antennas, possible candidate for
adaptive antenna arrays [10]
Mounting Radars with Rod Waveguides, dielectric rotor[7]
.Dielectric Rod Leakywave Antennas [8]
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 HEM11 (HE11) 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 HE11 mode can be
maintained within the rod provided the
normalized central core radius or numerical
aperture V < 2.4049. 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
1. Advanced Engineering Electromagnetics, Constantine A Balanis, Chapter 9
2. Optical Fiber Communications, Gerd Keiser, Chapter 2
3. Various Fiber Related Internet Sites including
www.arlonmed.com/everything/material
4. A Technique For Designing Ring and Rod Dielectric Resonators in Cutoff
Waveguides, Smain Amari, Jens Bornemann, and Rudlger Vahldeck
5. Analysis of Disk-on-Rod Surface Wave Element Inside a Corrugated Horn Using the
Mode-Matching Technique, J.C. Chen
6. Propagation in a Circular Waveguide Periodically Loaded with Dielectric Disks, S.
Amari, R Vahldieck, J. Bonemann and P. Leuchtmann
7. Mounting Radars with Rod Waveguides –
http://www.ohmartvega.com/pdf/mounting/rod_waveguides_mounting.pdf.
8. Leakywave antennas, Dr. DeLisio's website, http://wwwee.eng.hawaii.edu/~chiao/leaky.htm
9. http://www.temex-components.com/temex/product/capacit/trimmer/mte.html
10. DIELECTRIC RESONATOR ANTENNA - POSSIBLE CANDIDATE FOR ADAPTIVE ANTENNA ARRAYS
http://www.ee.olemiss.edu/darko/dra-pcfaaa.pdf