Chiral Optical Fibres and Gratings Gonçalo José da Silva Pimenta Thesis to obtain the Master of Science Degree in Electrical and Computer Engineering Supervisor: Prof. António Luís Campos da Silva Topa. Examination Committee Chairperson: Prof. José Eduardo Charters Ribeiro da Cunha Sanguino. Supervisor: Prof. António Luís Campos da Silva Topa. Member of Committee: Prof. Adolfo da Visitação Tregeira Cartaxo. May 2015
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Chiral Optical Fibres and Gratings
Gonçalo José da Silva Pimenta
Thesis to obtain the Master of Science Degree in
Electrical and Computer Engineering
Supervisor: Prof. António Luís Campos da Silva Topa.
Examination Committee
Chairperson: Prof. José Eduardo Charters Ribeiro da Cunha Sanguino.
Supervisor: Prof. António Luís Campos da Silva Topa.
Member of Committee: Prof. Adolfo da Visitação Tregeira Cartaxo.
May 2015
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Acknowledgements
Acknowledgements
First of all, I would like thank Professor António Topa, for the all the help he gave me along the
development of this thesis. Also my family, specially my sister Claudia Pimenta, which gave me the
will to continue. As well, my friend, António Rodrigues for all the support and ideas. Finally my friends
for all the happiest and funniest moments of my life.
iv
v
Abstract
Abstract
The focal purpose of this thesis is to study chirality specifically in telecommunications area, through
the pure chiral fibres (optical fibres constituted by chiral material) and chiral fibre grating (twisted
optical fibre), analysing also its behaviour and applications. Nevertheless we shall also address this
theme from an economical perspective.
The study begins by giving a brief introduction of the history behind optical fibre and chiral fibres,
followed by an explanation about chirality, using the constitutive relations. While analysing the
constitutive relations of the bi-isotropic medium, we will also study the polarization and its rotation. To
better understand this chiral medium, we will verify how a plane wave behaved when it focus on the
dielectric-chiral medium interface.
Then we shall analyse a pure chiral fibre (optical fibre built with chiral material) and with it study the
semileaky and surface modes.
Afterwards, we will introduce chiral fibre grating, explaining how they are built and their properties.
Through these characteristics, we will be able to divide these fibres in three groups: chiral short period
gratings, chiral intermediate period grating and chiral long period grating, but also sub-divide each one
into two types, double-helix and single-helix.
Finally we shall end by analysing the viability of this new technology, not only as the breakthrough
innovations that bring telecommunication systems, but also from an economical point of view.
Keywords
Chirality; Pure chiral fibre; Chiral fibre gratings; Chiral long period gratings; Double-helix structures;
Single-helix structures.
vi
Resumo
Resumo
O objectivo principal desta dissertação é estudar o meio quiral e as suas eventuais aplicações na
área das telecomunicações, especificamente através das fibras quirais puras (fibras ópticas
constituídas com material quiral) e as redes de fibra quiral (fibra óptica retorcida. Igualmente, iremos
analisar sobre uma perspectiva económica esta nova tecnologia.
O estudo começa como uma breve introdução à história das fibras ópticas seguida de uma explicação
sobre quiralidade, através relações constitutivas. Á medida que vamos analisando as relações
constitutivas do meio bi-isotropico, igualmente iremos analisar a polarização e a sua rotação. Para
melhor compreendermos o meio quiral, iremos simular o comportamento de uma onda plano quando
incide na interface do meio dieléctrico-quiral.
De seguida debruçamo-nos sobre as fibras quirais puras (fibras ópticas construídas com material
quiral) e com isto estudamos os modos semileaky e superficial.
Depois introduzimos as redes de fibras quirais, nomeadamente explicando o modo de construção
assim como as suas propriedades. Seguidamente, procedemos à divisão das referidas fibras em três
grupos: pequeno período pequeno fibras quirais, meio período fibras quirais e grande período fibras
quirais, subdividindo cada um desses grupos em dois tipos duplo-hélice e singular-hélice.
Finalmente concluímos este estudo com a analise da viabilidade desta nova tecnologia, não só numa
perspectiva dos avanços tecnológicos trazidos por esta, mas igualmente numa perspectiva
económica.
Palavras-chave
Quiralidade; Fibras quirais puras; Redes de fibras quirais; Fibras quirais de longo período; Estrutura
de hélice-duplo; Estrutura de hélice-singular.
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Table of Contents
Table of Contents
Acknowledgements ................................................................................ iii
Abstract ................................................................................................... v
Resumo ................................................................................................. vi
Table of Contents .................................................................................. vii
List of Figures ........................................................................................ ix
List of Tables .......................................................................................... xi
List of Acronyms ................................................................................... xii
List of Symbols ...................................................................................... xiii
List of Software ................................................................................... xviii
List of Figures Figure 1.1. Optical Fibre Attenuation along through the decades. ........................................................... 2
Figure 1.2. Chiral object to the left and enantiomorphism on the right. ................................................... 3
Figure 2.1. As the rotation of the ellipse changes of direction, the vector p(a) also changes. based on [15] ................................................................................................................16
Figure 2.2. Dielectric medium to left and chiral medium to right. based on[16] .....................................18
Figure 3.1. Anatomy of optical fibre. .......................................................................................................24
Figure 3.2. Propagation of light inside an optical fibre. ..........................................................................25
Figure 3.3. Diameters of multi-mode fibre and single-mode fibre. .........................................................26
Figure 3.4. Chiral optical fibre. based on [10] .........................................................................................26
Figure 3.5. a) Surface mode cut. b) Semileaky mode cut. [10] ..............................................................34
Figure 3.6. Dispersion diagram of m=0. [10] ..........................................................................................35
Figure 3.7. Radiation loss of L type mode and R type mode. [10] .........................................................35
Figure 3.8. Cut of surface mode and semileaky mode for m=0. [10] .....................................................36
Figure 3.9. Dispersion diagram of the modes with m=0. [10] .................................................................36
Figure 3.10. Radiation loss of the modes 01L and 02
L .[10] .....................................................................37
Figure 4.1. Design process of FBG.[27] .................................................................................................41
Figure 4.2. Table with a variety of function of FBGs. [26] ......................................................................42
Figure 4.3. Variation of the parameters and g
. (based on [31]) ......................................................43
Figure 4.5. Wavelength shift with strain. [33] .........................................................................................45
Figure 4.6. Wavelength shift with Temperature. [33] .............................................................................46
Figure 4.7. Long period grating.[35] .......................................................................................................47
Figure 4.8. Transmission spectrum of an LPG. [35] ...............................................................................48
Figure 4.9. Schematic of LPG construction with ultra-violet.[35]............................................................49
Figure 4.10. Wavelength as a function of LPG period for coupling between the core mode and cladding mode .[35].......................................................................................................50
Figure 4.11. Shift in 1469nm band of a long period grating. [38] ...........................................................51
Figure 4.12. Shift in transmission spectrum with strain.[39] ...................................................................52
Figure 4.13. The spectra of the mobile liquid level sensor with a 1,546.25-nm resonance ...................53
Figure 4.15. Performance of a double-helix chiral fibre grating giving the ratio of right to left
circularly polarization vs /i
Q P .[24] .......................................................................55
Figure 4.16. Example of a double-helix chiral long period grating.[40] ..................................................56
Figure 4.17. a) Side image and schematic of face image of a double-helix fibre. b) Transmission spectra of a double-helix. [43] .......................................................................................57
Figure 4.18. a) Side image and schematic of face image of a double-helix fibre. b) Transmission spectra of a double-helix. [43] .......................................................................................57
Figure 4.19. Example of a single-helix chiral long period grating. [40] ..................................................58
Figure 4.20. Behaviour of CLPG transmission dips of single-helix covered with alcohol at different heights.[40] .....................................................................................................59
Figure 4.21. CLPG versus temperature, wavelength of transmission dip of single-helix.[40] ................59
x
Figure 4.22. CLPG versus temperature, wavelength of transmission dip of single-helix.[40] ................60
Figure 4.23. a) Side image and schematic of face image of a single-helix fibre. b) Transmission spectra of a single-helix.[43] .........................................................................................60
Figure 4.24. a) Side image and schematic of face image of a single-helix fibre. b Transmission spectra of a double-helix.[43] ........................................................................................61
Figure 4.25. a) Side image and schematic of face image of a single-helix fibre. b) Transmission spectra of a double-helix.[43] ........................................................................................61
Não foi encontrada nenhuma entrada do índice de ilustrações.
xi
List of Tables
List of Tables Table 2.1. Polarizations’ conditions. based on [15] ................................................................................15
Table 4.1. Parameters used on the strain equation. [33] .......................................................................45
Table 4.2. Purchase cost of several in-line fibre polarizers. ...................................................................62
Não foi encontrada nenhuma entrada do índice de ilustrações.
xii
List of Acronyms
List of Acronyms CP
CIPG
Circular polarization
Chiral intermediate period grating
CLPG Chiral long period grating
CSPG Chiral short period grating
FBG Fibre Bragg grating
LCP
LP
Left circular polarization
Linear polarization
LPG Long period grating
RCP Right circular polarization
TE Transversal electrical mode
TM Transversal magnetic mode
TEM Transverse electromagnetic modes
xiii
List of Symbols
List of Symbols
a Acceptance Angle
1 Angle of the transmitted wave 1
2 Angle of the transmitted wave 2
Angular Frequency
z Applied strain on the fibre grating longitudinal axis
AT Attenuation band A
BT Attenuation band B
Attenuation on the unlimited chiral medium
, ,n x y z Average refractive index
n Average refractive index
BA Backward propagation mode
B Bragg wavelength
( , , )x y z Cartesians coordinates
2Z Chiral medium impedance
2 2 2, , Cladding parameters
11p , 12
p Components of strain-optic tension
g Confinement factor
eP Contribution of E for polarization
mP Contribution of H for polarization
eM Contributions of the E for magnetization
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mM Contributions of the M for magnetization
1 1 1( , , ) Core parameters
Coupling coefficient
g Coupling coefficient of the gratings
c Critical angles
12R Cross-reflection coefficient
21R Cross-reflection coefficient
12T Cross-transmission coefficient
21T Cross-transmission coefficient
cv Cut-off frequency
, ,r z Cylinder coordinates
Dielectric contrast
1Z Dielectric medium impedance
Dimensionless chirality parameter
Distance
Effective detuning
neff Effective index of refraction
ep Effective strain optic constant
D Electric displacement field
E Electric field
2oE Electric field associated with the left circular polarization
1oE Electric field associated with the right circular polarization
e Electric susceptibility
xv
(u)m
J Electrical current density
fA Forward mode
HE11 Fundamental mode
l Grating length
Grating period
z Gratings phase
g Gyrotropic parameter
oiE Incident electric field
0n Index of refraction of the core without disturbance
E
Left circular polarization electric field
H
Left circular polarization magnetic field intensity
k
Left circular polarization propagation constant
L Length of the LPG
Longitudinal wave number
B Magnetic field
H Magnetic field intensity
m Magnetic susceptibility
M Magnetization
( )T L Minimum transmission value of the attenuation band
, ,n x y z Modulation of the refractive index
w Normalize attenuation
u Normalize propagation
v Normalized frequency
xvi
g Normalized gyrotropic parameter
Normalized impedance
2g Normalized parameter gyrotropic of the cladding
1g Normalized parameter gyrotropic of the core
m Number of azimuthal variation
rE Parallel Reflected electric field
rE
Perpendicular Reflected electric field
iP Pitch
Poisson’s ratio
P Polarization
k Propagation constant
Q Range between each pitch
( )A t Real vector
( )p a Real vector p
orE Reflected electric field
2n Refraction of the cladding
1n Refraction of the core
,cl mn Refractive index of the 'm th cladding mode
c Relative permeability
c Relative permittivity
E Right circular polarization electric “plus” field
H Right circular polarization magnetic field intensity
k Right circular polarization propagation constant
xvii
Rotation of the polarization angle
n z Small amplitude of the index modulation
Temperature
x Thermal expansion coefficient
Thermo-optic
1h Transmitted wave 1
2h Transmitted wave 2
Transversal attenuation
Vacuum permeability
0 vacuum permeability
0 Vacuum permeability of free space
0 vacuum permittivity
ik Wave vector of the incident
rk Wave vector of the reflected
Wavelength
xviii
List of Software
List of Software Matlab
1
Chapter 1
Introduction
1 Introduction
We begin by giving a brief overview of the work, firstly by presenting a summary regarding the history
of chirality and the steps that have been given to reach chiral fibres and afterwards by explaining the
scope of the work. At the end of the chapter, the work structure is provided.
2
1.1 Overview
Communication has always been an essential part of our lives since the very beginning. We are
constantly using a variety of different communications such as voice, image and data communications.
Considering the phenomenon of globalisation allied with the constant growth of our species, more and
better services of communications are required, i.e. higher data and larger bandwidth and so, light-
wave technology has been developed. This type of technology such as optical fibre has proven to be,
by far a much more capable system than transmission lines through electrons and copper wires, thus
making optical fibre transmission system the backbone of the communication.
The modern impetus for telecommunications concerning carrier waves, at optical frequencies, owes its
origin to the laser, on 16th of May of 1960, by Theodore Maiman. Although, it was known that glass
can be spun into thin threads, which are flexible and also have the possibility to guide light,
unfortunately these fibres had a loss of 1000 dB/km, making it impossible to transmit information. A
profusion of material had been studied and the most appropriated was glass with a chemical
composition given by SiO2 known as fused silica. However it was not enough. Light was attenuated by
at least one third after a distance no longer than 1 meter. [1]
In 1966, K.C. Kao and G.A. Hockhan of Standard Telecommunications Laboratories in London
published a paper that predicted the possibility of producing a fibre with attenuation lower than or
equal to 20 dB/km.[2] Later on, in 1970, was invented the single-mode fibre with an attenuation of 16
dB/km with a wavelength of 633 nm, by Robert Maurer, Donald Keck and Peter Schultz.[3] Afterwards,
Kapron and other workers, improved the attenuation to 4 dB/km, by continuing to perfect the thin
layers of fused silica deposited on the inside surface of glass tube and adding Germanium oxide in a
precisely controlled concentration ( necessary for wave-guiding ). Then in 1976, the attenuation
reached 1 dB/km working with infrared light, in Japan. Finally, when fibres acquire an attenuation of
0.2 dB/km, a number very close to the limit of capacity of fused silica, it became commercial.[4]
Figure 1.1. Optical Fibre Attenuation along through the decades.
3
Chirality is quite common singularity in our world, including on a biological sphere. By observing the
nature we can verify this phenomenon on a molar scale in, for example, snails, flowers and vines, but
also on a molecular scale such as grape sugar and fruit sugar.
By definition, a chiral object is a body that lacks bilateral symmetry, which means that it cannot be
superimposed on its mirror image neither by translations, nor rotation. In other words, handedness.
Chiral media affects directly optics (optical activity), a property caused by asymmetrical molecular
structure that enables a substance to rotate the plane of incident polarized light, where the amount of
rotation in the plane of polarization is proportional to the thickness of the medium traversed as well to
light wave[5]. With the information above we can conclude that chiral objects belong on the bi-isotropic
(BI) media, in other words, when a linear polarized light rotates as it goes through the medium, it
impacts the behaviour of the electromagnetic wave by making it connect selectively either with left or
right circularly polarized component.
Figure 1.2. Chiral object to the left and enantiomorphism on the right.
Optical activity was first observed, in 1811, by Arago while watching the effects of crystals of quartz on
light polarized by reflection. He verified that linear polarized light suffered a rotation on its polarized
plane when passed through the quartz crystal. [6]. Later on, in 1812 Biot proved that the optical
activity was dependent on the thickness of the crystal plate and the light wavelength. [6]
Three years later (1815), Biot also discovered that this optical activity was not restricted to crystalline
solids but appeared as well in other environments such as oil of turpentine and aqueous solution of
tartaric acid [7].
In 1822, Fresnel discovered that on entering an optically active medium, light is split into two beams of
opposite circular polarization which travel with different phase velocities [8].
4
In 1840, Pasteurs studied the relationship between the crystals structures and optical activity
concluding reaching the conclusion that chirality was the cause of such phenomenon[9]. Later on, in
1848, he prompted that the optical activity of a tartaric solution is related to the form that the crystal of
the tartrate takes: crystal of opposite handedness dissolve to give solutions with opposite rotatory
power [8].
In 1920, Lindman demonstrated that polarize rotation also occurs in micro-waves[10]. In order to
demonstrate the experience, he used an artificial chiral medium composed of copper helices involved
in cotton balls. Thanks to this the experience the name of “optical activity” was forever changed to
“electromagnetic activity”.[10]
Winkler successfully reproduced Lindman’s results over a wider frequency, in 1965, and also verified
that a chiral arrangement of a set of irregular tetrahedral did not rotate the plane of polarization [11].
In 1975, Kong reunited in a unique study several information and references about the general bi-
anisotropic media, from which the B.I media degenerates [12].
Afterwards, in 1990 Pelet and Engheta created the concept of chirowaveguide. Through this
discovery, many studies have been possible about this structure and its eventual uses in several
areas such as telecommunication systems [13].
In 2004, Pendry proposed to obtain negative refraction with chiral objects. In this experiment she
indicates that by introducing a single chiral resonance that will lead to negative refraction of one
polarisation. With this technology we are able to improve and simplify designs and also offers
prospects of extension of negative refraction into new frequency domains.[14]
1.2 Motivation and Objectives
The main objective of this thesis is to analyse the chiral medium, specifically in telecommunications
area, through the pure chiral fibres (optical fibres constituted by chiral material) and chiral fibre grating
(twisted optical fibre). Besides others aspects, on this thesis we addressed the behaviour of those
fibres, as also theirs applications and its economic viability.
We begin by introducing the definition of the chiral medium, and in order to clarify this definition we
studied the constitutive relations of this medium using the Kong model. Afterwards, we analysed the
properties of the wave propagating, through the chiral medium and for that, due to the difficulty to
study this wave in this medium, we consider as if it were two waves (“plus” and “minus”), independent
of each other in a isotropic medium. Then we were able to verify its polarization and rotation. With all
this, we are able to study the behaviour of a plane wave focusing on the boundary between a dielectric
and a chiral medium, where one is reflected on dielectric medium and two waves, split from the
original wave, are refracted on the chiral medium, and with it we present the Fresnel equation.
After we explain the chiral medium and its polarization, we analyse how optical fibre constituted by
5
chiral material (pure chiral fibres) works. Furthermore we calculated the modal equation, which
represents the modes in the fibre with chiral cladding and achiral core and also a fibre with chiral
cladding and core. With this equation we are able to represent the mode cuts, dispersion diagrams
and finally the radiation loss.
Later on, we present the chiral fibres that are constructed nowadays. These fibres, on the contrary of
chiral fibres explained in chapter 3, are normal glass fibres that contains either a concentric and
birefringence or no-centric core, and are twisted at a high speed as they are passed through a
miniature oven. This chiral fibres or chiral fibre gratings can be divided in three groups, chiral short
period gratings, chiral intermediated period grating and chiral long period grating and in each group
can be sub-divided into two types: double-helix and single-helix. Depending on the type, there are
different advantages on polarization or sensor of temperature or liquid level.
Finally, we approached the chiral fibres from an economical point of view, specifically its acquisition
cost, so that we could determine its monetary viability in comparison with the nowadays technology.
1.3 Structure
This thesis is composed by six chapters.
Chapter 1 – On this chapter, we present a brief history of telecommunications, explaining the
evolution of optical fibres until today. Then we introduce the meaning of chirality, presenting its
history and also some experiences conduct with chiral materials. Finally we describe the
construction of the thesis and its main objectives.
Chapter 2 – On this chapter we introduce the chiral medium with the constitutive relations
using the Kong model. Next we verify the wavefields, and calculate its polarization and
rotation. Later on, we study the behaviour of a wave that has origin on a dielectric medium and
focus on a chiral medium. Finally, we calculated the reflection and transmission coefficients.
Chapter 3 – This chapter serves to introduce the pure chiral fibres (optical fibre constructed
with chiral material). We study its modes by calculating the modal equation. This equation
permits us to produce mode cuts, dispersion diagram and radiation loss.
Chapter 4 – On this chapter we explain a different type of chiral fibre, chiral fibre grating. We
first explain fibre Bragg grating and long period grating, in order to better understand this new
type of chiral fibre. Later on we present that this fibre can be divided in three groups, chiral
short period grating, chiral intermediate period grating and chiral long period grating, also each
group can be sub-divided in two types, double-helix and single-helix. Afterwards, we explain
the advantages of these fibres against actual polarizers and sensors of temperature and liquid
6
level. Finally we make an economical comparison between the chiral fibre gratings and the
nowadays devices.
Chapter 5 – On the final chapter we present our conclusions originated by the after mentioned
analysis and eventual future paths to follow.
Annex A – We present the others models that represent the constitutive relations of the chiral.
1.4 Contributions
The principal contributions of this thesis are:
A. Usage of chiral fibres to nowadays applications.
B. Comparison of pure chiral fibres and chiral fibre gratings.
C. Economical perspective.
7
Chapter 2
Chiral Medium
2 Chiral Medium
On this chapter we focus our study on chirality and its origins bi-isotropic materials. To better
comprehend this phenomenon we begin to explain the constitutive relations through the Kong model.
Afterwards we study the polarization of the chiral medium and its rotation. Finally we illustrate the laws
of reflection and refraction, with the Fresnel equations, among a dielectric and chiral medium.
8
2.1 Introduction
As we explained before, chirality has the power to produce a non-superimposable mirror image of
itself, in other words, chiral means “handedness”, which begets optical activity, having an interaction
with an electromagnetic wave rotating the plane of polarization of the wave to right or left depending
on the handedness of the chiral object. Chiral objects fall into the group of bi-isotropic material, which
have the optical ability to rotate the polarization of the light in either transmission or refraction.
However not all bi-isotropic materials are chiral.
In this chapter, we shall confine our study to reciprocal chiral medium.
2.2 Constitutive Relations
A constitutive equation or constitutive relation is explained on the laws of physic as a relationship
between two physical quantities, restricted to a material or substance, and its response of that material
to external stimulation, usually as applied fields or forces.
Its analytical formulation on a medium material is:[10]
0
D E P (2.2.1)
0(H M)B (2.2.2)
where D is electric displacement field, E electric field, B the magnetic field, H magnetic field intensity,
P the polarization and finally M the magnetization. Also 0 vacuum permittivity and 0
vacuum
permeability. Not forgetting that in general P and M have contributions from E and H fields being:
e m
P P P (2.2.3)
e m
M M M (2.2.4)
being eP and m
P the contribution of the E and H field for polarization and eM and m
M the
contributions of the E and H field for magnetization. In other words, with E and H dependent on D and
also B.
In isotropic and linear medium, eP can be written as:
0(t) (t,t') (t')dt'
t
e eP E (2.2.5)
being e the electric susceptibility. Considering that the medium is time invariant we obtain:
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