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Optical Studies of

Nano-Structures in the Beetle

Cetonia Aurata

Rizwana Shamim

LITH-IFM-A-EX--09/2060--SE

Department of Physics, Chemistry, and Biology Linköping University, SE-581 83 Linköping, Sweden

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Master’s Thesis.

Linköping studies in science and technology. LITH-IFM-A-EX--09/2060--SE

Optical Studies of Nano-Structures in the Beetle Cetonia Aurata Rizwana Shamim

rizwana_shamim@yahoo.com

Supervisor: Hans Arwin

IFM, Linkoping University Examiner: Kenneth Jarrendahl

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Chemistry

Department of Physics, Chemistry and Biology Linköping University

URL för elektronisk version

ISBN

ISRN: LITH-IFM-A-EX--09/2060--SE

_________________________________________________________________

Serietitel och serienummer ISSN

Title of series, numbering ______________________________ Språk Language Svenska/Swedish Engelska/English Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport Titel

Optical Studies of Nano-Structures in the Beetle Cetonia Aurata

Författare Author Rizwana Shamim Nyckelord Keyword Sammanfattning Abstract

The main objective of this thesis is to study the polarization effects of the beetle Cetonia aurata using Mueller-matrix ellipsometry. The outer shell of the beetle consists of complex microstructures which control the polarization of the reflected light. It has metallic appearance which originates from helicoidal structures. When these microstructures are exposed to polarized or unpolarized light, only left-handed circularly polarized light is reflected. Moreover, the exo-skeleton of the beetle absorbs right-handed polarized light. Multichannel Mueller-matrix ellipsometer or dual rotating compensator ellipsometer, called RC2, from J.A.Woollam is used to measure the polarization caused by different parts of beetle’s body. The 16 Mueller matrix elements are measured in the spectral range 400-800 nm at multiple angles of incidence in the range 400-700. An Optical model is developed to help us understand the nature and type of

microstructure which only reflects the green colour circularly polarized light. With the help of multi-parametric modeling, we were able to find optical properties and structural parameters. The parameters are: the number of layers, the numbers of sub-layers, their thicknesses, and the orientation with respect to optical axes. This optical model describes the nanostructures which provide the reflection properties similar to the nanostructure found in the beetle Cetonia aurata. The model is also useful for analysis of the optical response data of different materials with multilayer structures.

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Abstract

The main objective of this thesis is to study the polarization effects of the beetle Cetonia aurata using Mueller-matrix ellipsometry. The outer shell of the beetle consists of complex microstructures which control the polarization of the reflected light. It has metallic appearance which originates from helicoidal structures. When these microstructures are exposed to polarized or unpolarized light, only left-handed circularly polarized light is reflected. Moreover, the exo-skeleton of the beetle absorbs right-handed polarized light.

Multichannel Mueller-matrix ellipsometer or dual rotating compensator ellipsometer, called RC2, from J.A.Woollam is used to measure the polarization caused by different parts of beetle’s body. The 16 Mueller matrix elements are measured in the spectral range 400-800 nm at multiple angles of incidence in the range 400-700.

An Optical model is developed to help us understand the nature and type of microstructure which only reflects the green colour circularly polarized light. With the help of multi-parametric modeling, we were able to find optical properties and structural parameters. The parameters are: the number of layers, the numbers of sub-layers, their thicknesses, and the orientation with respect to optical axes. This optical model describes the nanostructures which provide the reflection properties similar to the nanostructure found in the beetle Cetonia

aurata. The model is also useful for analysis of the optical response data of

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Abbreviations

CCD Charged Coupled device

EMA Effective Media Approximation E-vector Electric field vector

FA Fast Axis

MSE Mean Square error p-direction Parallel direction

r r

PC SC A Polarizer, Compensator (rotating) ellipsometer, Sample, Compensator (rotating), Analyzer RC2 Dual rotator compensator

SA Slow Axis

s-direction Perpendicular direction TA Transmission Axis

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Acknowledgments

All praise and thanks are due to the Almighty Allah, the most gracious, and the most merciful. This master’s thesis has been done at the Laboratory of Applied Optics, Department of Physics, Chemistry and Biology, Linköping University. I am thankful to my family members, teachers, students, and friends. Here I would especially want to thank the persons related to this thesis work:

• My supervisor and advisor Prof. Hans Arwin, for giving me this opportunity, for his guidance, patience and ever helping attitude. He has always encouraged me when I felt that I am cought up in some problem and showed me the wayout, with a nice smile on his face.

• My examiner Prof Kenneth Järrendahl, for reading my thesis and giving good sugesstions for its improvement.

• M.Sc. Roger Magnusson, Ph.D. student at the labarotory of Applied optics for helping me during the experiments and teaching me the efficient way to use the lab equipment and the computer software.

• My husband Rashad.M.Ramzan, Ph.D. student at ISY Linköping University for continuous encouragement and helping me in formating this thesis. My two sons Talha and Irtiza for their ultimate cooperation during course of studies.

• My mother for her unlimited sacrifices, I do not have the proper words to describe.

Rizwana Shamim Linköping.

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Contents

Abstract iii Abbreviations v Acknowledgments vii Contents viii Chapter 1 Introduction 1 1.1 Historic background...2 1.2 Scientific background ...3

1.3 Aim of this thesis ...3

Chapter 2 Theory of Polarized Light 5 2.1 The refractive index N...5

2.2 Optics of anisotropic media ...6

2.3 Polarization of light ...8

2.4 Linear birefringence...9

2.5 Optical activity...10

2.6 Interference colour phenomena ...11

2.7 Stokes parameters ...12

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2.8 The Jones vectors- A mathematical representation of polarized light

...14

2.8.1 Jones matrix of the optical system...16

2.8.2 Basis vectors ...16

2.8.3 Examples of Jones vectors...17

2.8.4 Mathematical representation of polarizers ...17

2.8.5 Jones matrix of the optical device that has been rotated ...20

2.9 Mueller matrix ...21

Chapter 3 Ellipsometry 23 3.1 Principle ...23

3.2 Standard ellipsometry ...24

3.2.1 External reflection ellipsometry ...24

3.2.2 Internal reflection ellipsometry...26

3.2.3 Transmission ellipsometry...26 3.3 Generalized ellipsometry ...27 3.4 Mueller-matrix ellipsometry...28 Chapter 4 Instrument 31 4.1 Polarization analysis ...31 4.2 Spectral analysis ...32

4.2.1 Dual rotating compensator ellipsometer...33

Chapter 5 Models for Cetonia aurata Optical Properties 37 5.1 The cuticle structure of the beetle...37

5.2 Optical model...39

5.2.1 The Cauchy model ...39

5.2.2 The Liquid crystal model...40

Chapter 6 Results and Discussion 41 6.1 Spectroscopic ellipsometry...41

6.2 Data analysis ...41

Chapter 7 Conclusions and Future Prospects 59 References 61 Appendix 65

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Chapter 1

Introduction

There are many colourful creatures in our world and their fascinating colours are produced by nature. Scientists are trying to find the answers to the questions related to these colours especially those which are present in beetles and butterflies. Scientific giants like Newton, Michelson and Rayleigh have started working on these colours and their structure [1].

The optical study of the iridescent outer-shell of the beetle Cetonia Aurata has presented a microstructure which controls both the polarization and wavelength of the reflected light. The beetle’s surface exhibits left-handed circularly-polarized light, the origin of which is a helicoidal layer. Reflectivity spectra collected from the beetle are compared to the theoretical data produced using a multi-layer optical model for modeling chiral anisotropic media such as liquid crystals. There is an agreement between data obtained experimentally and from theory produced using a model that gives details about the upper isotropic layer of the beetle, the inner chiral structure, number of layers present in the endocuticle surface and the refractive indices.

Cetonia Aurata beetles reflect left-handed circularly polarized light. This phenomenon was observed by Michelson in 1911. He observed the production of circularly polarized reflected light from unpolarized incident light from the scarab beetle Plusiotis resplendens [2]. This is different to the circularly polarized light reflected from a plane mirror, which undergoes a 180 phase shift 0

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cuticle maintains its original handedness. This conservation of initial handedness is characteristic of the behavior of circularly polarized light interacting with a helicoidal structure which is composed of anisotropic media whose optic-axis rotates with the same handedness as that of the incident light [3].

Head

Head

Right Wing

Right Wing

Left Wing

Left Wing

Scutellum

Scutellum

Head

Head

Right Wing

Right Wing

Left Wing

Left Wing

Scutellum

Scutellum

Figure 1.1: Photograph of Cetonia Aurata beetle

1.1 Historic background

The Scarab species belong to two families of Scarabaeoidea: Rutelidea and Centoniidae. The family Rutelidea comprises about 200 genera and 4100 species distributed worldwide. Rutelidea are generally called leaf chafers, the most colourful species which often are known as jewel scarab beetles. Ruteline beetles have different shapes and colours. Some are metallic silver and gold. In 1911 Michelson was studying the metallic gloss of the scarab beetle Plusiotis resplendens and discovered the circular polarization of reflected light. Adult rutelines are phytophagous and feed on leaves or flowers of trees and shrubs. Adult leaf chafers emerge out with a soft and pale cuticle, but within hours, their bodies harden and the jewel scarabs show their true metallic-shiny colours [4].

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The family Centoniidae consists of more than 400 genera and 3200 species distributed worldwide. These beetles are commonly known as flower beetles (or fruit chafers or flower chafers). These are mostly colourful species of different sizes. Some of them are metallic green, red, blue or purple, with the majority of the iridescent species seen in the tropics. These are mostly pollen-feeders and are usually found on flowers. Adult flower-chafers prefer to eat nectar, sap and the juice and flesh of soft, ripe fruits. Their main predators are omnivorous birds and mammals [4].

1.2 Scientific background

In 1911 Michelson discovered the circular polarization of reflected light from the metallic gloss of the scarab beetle Plusiotis resplendens from the family of Rutelidae. He explained metallic colouring in insects by grating-like structures and “screw structures”. Beetles have appealing bright colours and some of them have metallic appearance. Scientists have observed that some of the beetles in the zoological museum are more than 200 years old and have their colours and brightness same as they had when they were alive [12]. Their metallic look is from structures in organic materials which is both electrically and thermal insulating.

The investigation of the spatial distribution and wavelength dependencies of the left-handed circular polarization of light reflected from the Scarab cuticle by using polarimetric techniques was first time done in 2005. In the red and green ranges of the spectrum while in the blue some of the ventral areas of Plusiotis resplendens are strongly left-circularly polarizing while the dorsal part is circularly unpolarized in the red and green ranges of the spectrum. It is only weakly left- or right-circularly polarized in the blue in some tiny spots [4].

1.3 Aim of this thesis

In this thesis, we seek to determine the polarization effects in the beetle

Cetonia aurata with Mueller-matrix ellipsometry. To describe the nanostructure which provides the reflection properties, an optical model is developed which is used to analyze the results obtained experimentally. Mueller-matrix spectroscopic ellipsometry is used to measure reflection properties of the green and shiny beetle Cetonia aurata. The reflected left-handed circularly polarized light is modeled with a chiral dielectric layer on a substrate.

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Chapter 2

Theory of Polarized Light

2.1 The refractive index N

When we are studying propagation of light through materials, it is convenient to discuss properties of materials in terms of the refractive index which is a complex quantity, written as:

N n ik= + ( 2.1)

where n is the usual refractive index and k is the extinction coefficient. The refractive index N is very useful as it enters directly into the expression describing propagation of a plane wave. Its real part n gives the phase velocity and the imaginary part k gives the attenuation of the electric field.

From the dispersion relation of a plane wave, it is found that the dielectric function ε is related to N through

2

N

ε = ( 2.2)

The dielectric function ε is a complex number which can be written

(

)

2

n ik

ε = + ( 2.3)

1 i 2

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for isotropic materials.

The relation between real and imaginary parts of Nand ε are then

2 2 1 n k and 2 2nk ε = − ε = ( 2.5)

( ) ( )

(

2 2

)

1 2 1 1 2 n= ε + ε +ε ( 2.6)

( ) ( )

(

2 2 2

)

1 2 1 2 k ε ε ε ε = + + ( 2.7)

ε can be a tensor and have different values in different directions in space. For anisotropic materials, when the light interacts with materials, its optical response varies in different directions. The dielectric functionε is described as a tensor in anisotropic materials.

One of the constitutive relations for anisotropic materials can be written as:

0 ij , , , , i j j x y z D ε ε E i x y z = =

= ( 2.8)

In tensor form equation (2.8) can be written as

xx xy xz 0 yx yy yz zx zy zz x x y y z z D E D E D E ε ε ε ε ε ε ε ε ε ε             =                 ( 2.9)

2.2 Optics of anisotropic media

A plane wave of polarized light propagates through an anisotropic medium along the z-axis of xyz Cartesian coordinate system. The properties of the wave can be uniform over any transverse plane perpendicular to the direction of propagation of the beam. The properties may be different in the beam direction [5].

We have a crystal which is oriented in a specific direction and light is falling on it. It refracts the light in one way and when oriented in the other direction, it refracts light in another way. The phenomena that a light beam falling normally on the surface of such crystal propagates straightforwardly inside the crystal only along a definite direction and for other directions, the optical beam splits into two beams. Such phenomena are called optical birefringence and this dependence of optical properties on crystalline direction is called anisotropy.

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When a white light beam passes through this crystal and the crystal is placed perpendicular to the axis of the incident beam, two light spots of equal brightness are formed on the screen at the same point as shown in Figure 2.1.

Crystal

Figure 2.1: Light is traveling along optic axis of the crystal and no optical birefringence is seen.

When rotating the crystal about the axis of the incident beam, one light spot on the screen will be at the same place while the other moves to the new position as shown in Figure 2.2.

Extra Ordinary

optical wave

Ordinary

optical wave

Crystal

Figure 2.2: Light is falling normally on the face of the crystal and optical birefringence is seen.

Figure 2.2 shows anisotropic refraction of light where the ordinary wave is

perpendicular to the principal plane and extraordinary wave is in the direction of the principal plane. The phenomenon of optical birefringence can also be applied to produce polarized light [5].

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Optical anisotropy is caused by the anisotropy of the medium. Anisotropic properties are only observed in crystal but not in gases and liquids (except liquid crystals), plastic materials or glasses [6]. Optical anisotropy is sometime seen in isotropic media because of mechanical stress or an external electric field (Kerr’s effect). Same phenomena can be seen in an alternating electric field and in the field of a powerful laser pulse [7].

2.3 Polarization of light

For the study of reflection of light from surfaces, it is necessary to determine the orientation of the fields in the propagating electromagnetic waves which is its polarization state. The state of polarization of the beam is determined by dividing the beam into two components with plane of incidence as its reference. The p-direction is parallel to the plane of incidence and the s-direction is perpendicular to both the direction of propagation and the p-direction. The polarization is described by choosing the plane of propagation when there is no oblique incidence or reflection occurs. For p-component, the electric field lies in the plane and for the s-component, the electric field is perpendicular to the plane. For light with angle of incidenceθo, the p- and s- components are shown in Figure 5. is

E

0

θ

1 N is

H

1

θ

rs

E

rs

H

0 N ts

E

ts

H

ip

E

0

θ

1 N ip

H

1

θ

rp

E

rp

H

0 N tp

E

tp

H

a)

b)

0

θ

θ

0 z x y Λ Λ Λ

Figure 2.3: a) The p-polarized and b) the s-polarized parts of the incident reflected

and transmitted fields when the reflection is from a single surface with refractive index N for the ambient and o N1 for the substrate. The angle of incidence θo is

equal to angle of reflection θ and angle of refraction is r θt

The xyz-coordinates of the electric field of the propagating light wave are related with its polarization coordinates as

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0 0 0 0 cos cos sin sin ix ip rx rp iy ip ry rp iz is rz rs E E E E E E E E E E E E θ θ θ θ = = − = = = = ( 2.10) The electromagnetic plane wave E(r,t) can be written as

ˆ ˆ

p s

E E p E s= + ( 2.11)

The Fresnel equations for reflection and transmission of p-polarized light are

1 0 0 1 1 0 1 cos cos cos cos rp p ip o E N N r E N N θ θ θ θ − = = + ( 2.12a) and 0 0 1 0 1 2 cos cos cos tp p ip o E N t E N N θ θ θ = = + ( 2.13b)

The Fresnel equations for reflection and transmission of s-polarized light are

0 0 1 1 0 0 1 1 cos cos cos cos rs s is E N N r E N N θ θ θ θ − = = + ( 2.13a) and 0 0 0 0 1 1 2 cos cos cos ts s is E N t E N N θ θ θ = = + ( 2.13b)

The degree of polarization is the ratio between the irradiance of the polarized part Ipol and the total irradiance Itot is given as

pol tot I P I = ( 2.14)

2.4 Linear birefringence

In cubic crystals, atoms are arranged in such a manner that the optical properties are the same in all directions. The material is optically isotropic and can be described with a scalar ε. However, crystals belonging to a hexagonal, trigonal or tetragonal system have an asymmetric structure which yields an optical anisotropy. These materials are anisotropic with a dielectric function tensor ε.

In the absence of optical activity, ε will be a symmetric tensor with εijji. If the coordinatesystem coincides with the principal axes of the crystal, the non-diagonal elements are zero and we obtain in an orthogonal xyz coordinate system.

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2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 x x y y z z N N N ε ε ε ε         = =          ( 2.15)

where the short notations εiii

(

i x y z= , ,

)

have been used and Ni is the

refractive index in direction i. Nx, Ny and Nz are the refractive indices in the x-,

y- and z-directions [9]. If ε εx, y and εz all are different, the crystal is called biaxial. If two of them e.g. εxandεy are equal, the crystal is called uniaxial. The z-direction in a uniaxial crystal is called the optic axis and the refractive index in this direction is named the extraordinary indexNe =ne+ike. The refractive indices in the x- and y-directions are the ordinary indexNo =no+iko . For a uniaxial crystal, we thus have the following tensor

2 2 2 0 0 0 0 0 0 o o e N N N ε     =       ( 2.16) Uniaxial crystals are characterized by the equality of the two principle axes which can be taken as

x y o z e o n n n n n n = = = ≠ ( 2.17)

Equation (2.17) is valid for a rotation about the optic axis of the crystal [9].

A measure of birefringence is ∆ =n neno and can be negative or positive depending on whether no or ne is larger.

2.5 Optical activity

In certain materials, the direction of linearly polarized light undergoes a continuous rotation as the light propagates in the material. Any such material that causes the E-field of an incident linear plane wave to rotate is called optically active. If the rotation is clockwise, while looking into the beam (towards the source), the material is called dextrorotatory or d-rotatory. If the rotation is counter-clockwise, it is called levorotatory or l-rotatory.

In an optically active material, the dielectric tensor is nonsymmetrical. An optically active material show circular birefringence by which is meant that circularly polarized light propagates at different speed depending on if it is

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right-handed or left-right-handed polarized. In other words, the material possesses two indices of refraction, nrandnl, for right-handed or left-handed polarization

respectively. Like linear birefringence, we can define circular birefringence asnlnr. If the path length in the material is d, the angle of rotation of linearly polarized light will be

(

l r

)

d n n l π θ = − ( 2.17) where d

θ is called specific rotatory power.

In a similar manner, circular dichroism is defined as klkr, where kland krare the extinction coefficient of the medium for left-handed and right-handed circularly polarized light, respectively.

When light propagates through a linear medium, its polarization properties are usually described either by Stokes vector [10] formalism or by the polarization matrix that was introduced by Wiener [11] and Wolf [7].

2.6 Interference colour phenomena

Two basic structure models have been identified to explain many of the interference colour phenomena seen:

• The observed colour phenomena can be caused by a multilayer structure with alternating high and low refraction indices. These structures do not change the orientation of polarized light.

• The observed colour phenomena are explained by a twisted multilayer chitin rich structure. The chitin molecules are predominantly arranged helical (Bouligand) and behave similar to liquid crystals. These structures reflect circularly polarized light.

These models can explain narrowband and broadband (metallic) reflection. The `twisted` Bouligand structures are used to explain why the golden beetles can have an optically active surface, which reflect and change the plane of polarized light. Most insects with metallic appearance exhibit both specular metallic reflection and diffusive reflection. For beetles this can be a multilayer structure combined with irregular surface textures that breaks the flatness of the reflector [12].

Circularly polarized light is rare in nature. The wavelength- and species-dependent circular polarization patterns are of a rather complex nature.

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The direction of rotation of the electric field vector (E-vector) of circularly polarized reflected light depends on the sense of rotation of the helix of the molecules. In living organisms, the capability to produce a given helical molecule is restricted to one sense of rotation, which has been fixed at very early stage in evolution, thus, perhaps apart from some mutants; this sense is the same for all living organisms. Since the exoskeletons of all beetles reflecting circularly polarized light consists of the same substance, the sense of rotation of the E-vector of reflected light is the same, left-handed, for all of them [13].

In the literature, only sporadic photographs taken from a few scarab species (e.g. Cetonia aurata, Plusiotis woodi) through left- and right-circular polarizer are available [4].

2.7 Stokes parameters

In 1852, George Gabriel Stokes discovered that the polarization state of electromagnetic radiation (including visible light) could be represented in terms of observables and his work made foundation of the modern representation of polarized light. He defined four quantities which are functions of observables of the electromagnetic wave and are known as Stokes parameters. These values are description of incoherent and partially polarized light in terms of irradiance I, degree of polarization P and shape parameters of the polarization ellipse.

Monochromatic and quasi-monochromatic light may be represented by a 4D column vector with real-valued elements with dimension of irradiance.

      =             = s S S S S S S 0 3 2 1 0 ( 2.18)

and 3D column vector

          = 3 2 1 S S S s

For unpolarized light

1 2 3 0

S =S =S = ( 2.19)

For a completely polarized beam of light

2 2 2 2

0 1 2 3

S =S +S +S

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2 2 2 2 0 1 2 3

S S〉 +S +S

The physical meanings of the Stokes vector elements are:

0

S represents the irradiance of the light wave, S1 represents the difference between the intensities of the x-and y- components i.e. the preference to either x- or y-polarization, S2 represents the difference between the intensities of the light

waves in the +45 and −45directions of linear polarization and S3represents the

difference between the intensities of the right-circular state and left-circular state of polarization. A beam of light can be either neutral or partial or totally polarized. All these states are described by the Stokes vectors [10].

The monochromatic and quasi-monochromatic light may be represented by a 4D column vector which is not a real vector but a Stokes column matrix with real-valued elements having dimension of irradiance.

The degree of polarization P is given by

2 2 2 1 2 3 0 0 pol tot I S S S s P I S S + + = = = ( 2.20) where 0≤ P≤1

Thus P=0 indicates that the light is unpolarized, P=1 that the light is completely polarized and 0〈 〈P1 that the light is partially polarized.

2.7.1 Examples of Stokes vectors

Unpolarized light with irradiance I0has the Stokes vector

            = 0 0 0 1 0 I S ( 2.21)

For normalized Stokes parameters I0 =1

The total polarization of elliptically polarized light in the general case will be

2 2 0 0 2 2 0 0 0 0 0 0 2 cos 2 sin x y x y x y yx x y yx E E E E S E E E E δ δ  +      =         ( 2.22)

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where the amplitudes E0x and E0yand the phase difference δyxy −δx are constants. For linear polarized light with E0y =0 and is normalized with 02 1

x E = in the x-direction             = 0 0 1 1 S ( 2.23)

S is often written horizontally as transpose to save space

[

1 1 0 0

]

t

S = ( 2.24)

The examples of Stokes vectors are given in Table 3.1

Stokes vectors Polarization

[

1 0 0 0

]

t unpolarized

[

1 1 0 0

]

t Linear in the x-direction

[

1 −1 0 0

]

t Linear in the y-direction

[

1 0 1 0

]

t Linear in the+45º -direction

[

1 0 −1 0

]

t Linear in the-45º -direction

[

1 0 0 1

]

t Right-handed circular

[

1 0 0 −1

]

t Left-handed circular

Table3.1: Examples of normalized Stokes vectors with their polarization where t indicates transpose

2.8 The Jones vectors- A mathematical representation of

polarized light

In 1941, another representation of polarized light was proposed by the American physicist R. Clark Jones. This technique was being applicable to coherent waves which are polarized. Jones vectors are vectors in an abstract mathematical space and have complex-valued elements.

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Two waves with identical wavelength and irradiance, but different directions of their electric fields, can behave quite differently. Polarization of wave can accommodate the dependence on the direction of the electric fields. We describe the plane wave by its propagation direction and space and time dependencies of

) , ( tr

E . If z-axis is the direction of propagation, then E( tr, ) can be written as

(

ˆ ˆ

)

( ) ( , ) x y i qz t E z t = ℜ E x E y e+ −ω  ( 2.25) or in complex form y E x E E = xˆ+ yˆ ( 2.26)

where the complex-valued field amplitudes i x

x x

E = E eδ and i y

y

E = Ey eδ represents the propagations of the fields or the complex-valued field amplitudes along the x-axis and the y-axis and are representing sinusoidal linear oscillations along two perpendicular directions [9].

The mathematical description of light propagation was presented by Clark Jones in early 1940s by introducing matrix formalism. Jones vector is written in the column vector as:

( ) ( ) x y E t E E t   =     ( 2.27)

where Ex

( )

t and Ey

( )

t are the instantaneous scalar components of E

By including z dependence we obtain

( )

, (( )) x y i qz t x i qz t y E e E z t E e ω δ ω δ − + − +     =     ( 2.28)

which can be written as:

( )

, cos

(

(

)

)

cos x x y y E qz t E z t E qz t ω δ ω δ  − +  =   − +     ( 2.29)

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2.8.1 Jones matrix of the optical system

When a monochromatic plane wave is passing through a non-depolarizing and frequency conserving optical system S, it will come out as a modified wave. The relationship between incoming Ei and outgoing Eowaves is given by

11 12 21 22 ox ix iy oy ix iy E j E j E E j E j E ′ ′ = + = + ( 2.30)

this can be written as

11 12 21 22 ox ix oy iy E j j E E j j E ′ ′      =            ( 2.31)

whereEix and Eiyrepresent the electric fields in the xyz-coordinate system at the

input and Eox′ and Eoy represent the electric fields in the x´y´z´-coordinate

system at the output and

11 12 21 22 j j J j j   =     ( 2.32)

is the Jones matrix of the optical system.

2.8.2 Basis vectors

For Jones vectors, basis vectors are same as the unit vectors and

in coordinate systems. The Cartesian basis vectors are

      = 0 1 ˆ x E ˆ 0 1 y E =      ( 2.33) so we can write y y x x xy E E E E E = ˆ + ˆ ( 2.34)

we can write Cartesian basis vectors as Eˆx′ and Eˆy′ which are rotated with

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      = r q E E E ( 2.35)

The circular basis vectors in the xy-system are given by

      − = − = i E i E El x y 1 2 1 ˆ 2 ˆ 2 1 and       = + = i E i E Er x y 1 2 1 ˆ 2 ˆ 2 1 ( 2.36)

2.8.3 Examples of Jones vectors

Jones vectors for linearly polarized waves for which the electric vector oscillates along a direction inclined an angel α to the x -axis is given by

      = α α sin cos E ( 2.37)

Jones vectors for the left- and right-circularly polarized waves are given by

      − = i Exy 1 2 1 and       = i Exy 1 2 1 ( 2.38) The factor 2

1 is included for normalization.

2.8.4 Mathematical representation of polarizers

There are four types of polarizer. 2.8.4.1 Linear polarizer

The linear polarizer removes all or most of the E-vibrations in a given direction while transmitting those vibrations which are in the perpendicular direction. Unpolarized light traveling in the +z-direction passes through a plane polarizer whose transmission axis TA is vertical. The unpolarized light is represented by perpendicular (x and y) vibrations. The light transmitted include components only along the TA direction and is linear polarized in the vertical or y-direction. The horizontal component is removed by absorption. Jones vector for the linear polarizer is

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      = 1 0 0 0 J ( 2.39) X Y TA Linear Polarizer Z

Figure 2.4: Operation of a linear polarizer

2.8.4.2 Elliptical polarizer

Jones vector for the elliptical polarizer is

      = + − α α α α α α δ δ 2 2 sin cos sin cos sin cos i i e e J ( 2.40)

This is the Jones matrix for any type of elliptical polarizer including a linear polarizer and a circular polarizer. For a linear horizontal polarizer α =00

      = 0 0 0 1 J ( 2.41)

For right circularly polarized light α =450and δ =900

( 2.41) 1 1 1 2 i J i −   =    

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2.8.4.3 Phase Retarder

The phase retarder introduces a phase difference between the E-vibrations. When light corresponding to these vibrations travels with different speeds through retarding plates, there will be a phase difference of ∆Φbetween the emerging waves.

Y

X

FA

Retardation

Plate

Z

SA

Figure 2.5: Operation of a phase retarder

Figure 2.5 shows the effect of a retarding plate on unpolarized light whose vertical component travels through the plate faster than the vertical component. When the net phase difference∆Φ=900 , the retardation plate is called a

quarter-wave plate, when∆Φ=1800, it is called a half-wave plate.

The Jones matrix for a retarder is given by         = Φ Φ + 2 2 0 0 i i e e J ( 2.43)

and for a homogenous right circular retarder

          Φ Φ − Φ Φ = 2 cos 2 sin 2 sin 2 cos J ( 2.44)

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2.8.4.4 Rotator

The rotator has the effect of rotating the direction of linearly polarized light incident on it by some particular angle. Vertically linear polarized light is incident on a rotator as shown in Figure 2.6. The effect of rotator element is to transmit linearly polarized light whose direction of vibration has rotated counterclockwise by an angleθ.

The requirement for a rotator of angleβ is that an E-vector oscillating linearly at angleθbe converted to one that oscillates linearly at angle

(

θ +β

)

. The Jones matrix for a rotator through angle +β is given by [14]

      − = β β β β cos sin sin cos J ( 2.45)

X

Rotator

Z

Y

θ

Figure 2.6: Operation of a rotator

2.8.5 Jones matrix of the optical device that has been

rotated

In an ellipsometer, we have a cascade of optical devices which are rotated individually, so we need a fixed reference laboratory frame, called the laboratory frame. We can call this laboratory frame as uv coordinate system. Consider an optical device which is rotated an angle α where α is an angle between the x-axis of the input coordinate system of the device and u-axis of the fixed coordinate system. A light wave with Jones vectors uv

i

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incident on the optical device. The Jones vector in the input coordinate system xy is

( )

xy uv i i E =R α E ( 2.46)

where R

( )

α is the rotation matrix given by

( )

cos sin sin cos R α α α α α   =     ( 2.47)

For the optical device with Jones matrixJxy, the output Jones vector in the

x´y´-system will be

( )

x y xy uv

o i

E ′′ =J R α E ( 2.48)

This is the electric field vector after transmission through the optical device. If the xy and x´y´ coordinate systems are parallel then the output Jones vector in the uv coordinate system is

( )

uv x y

o o

E =R −α E ′ ′ ( 2.49)

and we can write

( )

( )

uv xy uv

o i

E =R −α J R α E ( 2.50)

Finally we can write that, in a fixed uv coordinate system, the Jones matrix

uv

J of a rotated optical device is given by

( )

( )

uv xy

J =R −α J R α ( 2.51)

2.9 Mueller matrix

In 1943 Hans Mueller, a professor of physics at the Massachusetts Institute of Technology, devised a matrix method for dealing with the Stokes vectors. Stokes vectors are applicable to both unpolarized and partially polarized light. The Jones method is valid only for totally polarized light.

For light which is partially polarized or unpolarized, the depolarization of light caused by an optical device can be studied by Mueller matrices.

When light, either propagating through the medium or is reflected from some interface, its polarization state is changed. There can be a change in amplitude or

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phase or direction of the orthogonal electric field vectors [15]. The depolarizing optical system is represented by a 4x4 Mueller matrix and the state of polarization of the light waves is represented by Stokes vectors.

It is analogous to Jones matrix definition to write as

o i

S =MS ( 2.52)

where Soand Siare the Stokes vectors of the outgoing and incoming beams of

light. The matrix Miis called the Mueller matrix of the optical system. The out

-going Stokes vector is having a linear combination with incoming Stokes vector as 0 11 0 12 1 13 2 14 3 1 21 0 22 1 23 2 24 3 2 31 0 32 1 33 2 34 3 3 41 0 42 1 43 2 44 3 o i i i i o i i i i o i i i i o i i i i S m S m S m S m S S m S m S m S m S S m S m S m S m S S m S m S m S m S = + + + = + + + = + + + = + + + ( 2.53)

In matrix form equations (2.53) can be written as

0 11 12 13 14 0 1 21 22 23 24 1 2 31 32 33 34 2 3 41 42 43 44 3 o i o i o i o i S m m m m S S m m m m S S m m m m S S m m m m S               =                            ( 2.54) The combined effect of several optical elements in a cascade is given by

1... 2 1

o N N i

S =M M M M S ( 2.55)

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Chapter 3

Ellipsometry

3.1 Principle

Ellipsometry is the art of measuring and analyzing the elliptical polarization of light [15]. It is used for thin films, surface and interface characterization. Alexandre Rothen in 1944 suggested the name ellipsometry and he is one of the pioneers in this field. Ellipsometry is a measurement technique which is sensitive to surface layers and is very useful for thin film metrology. It gives the full complex-valued optical response function of a sample. It has applications in different fields, from semiconductor physics to microelectronics and biology. It plays a vital role from basic research to industrial applications [16].

Ellipsometry is based on measuring phase differences and the ratios of electric field amplitudes. With ellipsometry, we are able to find the thickness of layers which are thinner than the wavelength of the incoming light and multi- layered structures with different layers can also be studied. Spectroscopic ellipsometry is such a technique which has many applications in research and industry.

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In a reflection-based ellipsometric measurement, the change in polarization of a light beam reflected from a sample is measured. The phase and amplitude changes are different for the p-and s-polarized complex-valued electric field components. These differences are measured by an ellipsometer. The change in polarization depends on the surface and thin film properties.

3.2 Standard ellipsometry

Standard ellipsometry is here described in external reflection, internal reflection and transmission configurations.

3.2.1 External reflection ellipsometry

When a polarized monochromatic plane wave is incident on a surface at oblique incidence, the polarization changes on reflection. In Figure 3.1, a linearly polarized light is incident on an optically isotropic sample and is reflected. There is no coupling between parallel (p) and perpendicular (s) polarizations for an isotropic sample. After reflection, light become elliptically polarized. The incident light can be either linearly polarized or can have any state of polarization. Epi and Esi are incident electric field components. Epr

andEsrare reflected electric field components. The reflectance ratioρ is measured with an ellipsometer and is found to be the ratio between two reflection coefficients for an isotropic sample. ρ can then be written as

Plane of

incidence

o

θ

s-plane

p-plane

E

E

s-plane

p-plane

Figure 3.1: Principle of reflection ellipsometry. The incoming light is linearly polarized and has known polarization

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p s

r r

ρ= (3.1)

where rp and rs are the complex-valued reflection coefficients for light polarized

in the p-and s-direction, respectively. Generallyρ is defined in terms of the ratio between the states of polarization of the reflected and incident beams as

r i χ ρ χ = ( 3.2)

where χrand χi are the complex-number representation of the states of polarization of the reflected and incident beam, respectively. χis defined by

p s

E E

χ= ( 3.3)

where Epand Esare the complex-valued representation of the electric fields in

the p-and s-directions, respectively. With pi i si E E χ = and pr r sr E E χ = ,equation (3.2) becomes: pr si sr pi E E E E ρ = (3.4)

The reflection coefficients are pr p pi E r = E and sr s si E r = E , so pr si p sr pi s E E r E E r ρ= = (3.5)

In terms of ellipsometric angles ψ and ∆, we get

( ) tan p s i p i s r e e r δ δ ρ== ψ ∆ (3.6) where tan p s r r

ψ = is the amplitude ratio and phase difference ∆ =δp −δs.

The quantities ψ and ∆ are functions of the optical constants of the medium, the thin film and the substrate, the wavelength of the light, the angle of incidence and thickness of an optical film deposited on the substrate. A general observation is that ψ =450 at both normal and glancing incidences for all

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3.2.2 Internal reflection ellipsometry

In internal reflection ellipsometry, light is incident at an interface and is reflected. Incidence is from a medium with higher refractive index than that of the reflected medium. Consider a two-phase model where a glass prism is ambient and air is the substrate. For internal reflection configuration, in the three-phase model, there will be a thin film on the prism as shown in Figure (3.2). The ambient medium must be transparent so that the light penetrates down to the interface, reflects and propagate back to the external ambient. The layer on the prism must be transparent or semi-transparent. N0 must be greater than

1

N andN2. For total internal reflection, θoc

3.2.3 Transmission ellipsometry

In ellipsometry, if there is transmission instead of reflection, then ellipsometric ratios for the complex transmission coefficients tp and ts are

tan t p i t t s t e t ρ = = ψ ∆ (3.7)

The ellipsometric parametersρt , ψt and ∆tare the transmission ratio, amplitude ratio and phase difference in transmission ellipsometry.

o

θ

1

N

o

N

θ

c 1

N

o

θ

o

N

2

N

c

θ

Figure 3.2: Internal reflection ellipsometry in the two-phase model (left) and three-phase model (right). The angle of incidence θois larger then the

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3.3 Generalized ellipsometry

In standard ellipsometry, the sample is isotropic and has a diagonal Jones matrix. For a general anisotropic sample, we need a non-diagonal Jones matrix.

pp sp r ps ss r r R r r   =     (3.8)

First index is for incident polarization and second index for reflected polarization. In generalized ellipsometry, we require at least three values of ρ

measured at three different incident polarization in order to get three pairs of

(

ψ,∆

)

. Three complex-valued generalized ellipsometric parameters are defined as tan tan tan pp ps sp i pp pp pp ss i ps ps ps pp i sp sp sp ss r e r r e r r e r ρ ψ ρ ψ ρ ψ ∆ ∆ ∆ = = = = = = (3.9)

In generalized ellipsometry, we have to find six parameters

, , , ,

pp ps sp pp ps

ψ ψ ψ ∆ ∆ and ∆sp. By using equation (3.9), the reflection Jones matrix in equation (3.8) can be written as:

1 pp sp r ss ps pp R =rρ ρρ ρ    (3.10)

The objective of generalized ellipsometry is now to determine the unknown values ofρ ρpp, ps andρsp.

The relation between the incident and reflected light in terms of reflection Jones matrix, is given by

r r i E =R E (3.11) We can write it as pr pp pi sp si sr ps pi ss si E r E r E E r E r E = + = + (3.12) By using p s E E

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pp i sp r ps i ss r r r r χ χ χ + = + (3.13)

Combining equations (3.2), (3.9) and (3.13) we have

1 1 pp sp i pp ps i ρ ρ χ ρ ρ ρ χ − + = + (3.14)

Hence ρ is representing a transformation of the incident polarization stateχi. For a givenχi, ellipsometer gives value ofρ. In practice i=1, 2,3 so we can find the values ofρ ρpp, psandρsp.

3.4 Mueller-matrix ellipsometry

From a Stokes vector of reflected light, we can describe a sample with a Mueller matrixMr. A Stokes meter is used to determine the Stokes vector of the

reflected light. Mueller matrix ellipsometry is used for non-depolarizing samples. The reflection Mueller matrix elements are:

(

2 2 2 2

)

11 1 2 pp ss sp ps m = r + r + r + r (3.15)

(

2 2 2 2

)

12 1 2 pp ss sp ps m = rrr + r (3.16) 13 pp sp ss ps m = ℜr r ∗+r r ∗ (3.17) 14 pp sp ss ps m == ℑr r ∗+r r ∗ (3.18)

(

2 2 2 2

)

21 1 2 pp ss sp ps m = rr + rr (3.19)

(

2 2 2 2

)

22 1 2 pp ss sp ps m = r + rrr (3.20) 23 pp sp ss ps m == ℜr r∗ −r r∗  (3.21) 24 pp sp ss ps m == ℑr r∗ −r r∗  (3.22) 31 pp ps ss sp m = ℜr r+r r   (3.23)

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32 pp ps ss sp m = ℜr r∗ −r r∗  (3.24) 33 pp ss ps sp m = ℜr r∗+r r∗  (3.25) 34 pp ss ps sp m = ℑr r∗ −r r∗  (3.26) 41 pp ps ss sp m = −ℑr r∗ +r r∗  (3.27) 42 pp ps ss sp m = −ℑr r∗ −r r∗  (3.28) 43 pp ss ps sp m = −ℑr r∗+r r∗  (3.29) 44 pp ss ps sp m = ℜr r∗ −r r∗  (3.30) 31 pp ps ss sp m = ℜr r∗ +r r∗  (3.31) For isotropic samples rsp =rps =0,rpp =rpandrss =rsand are described fully with

equation tan i

e

ρ = ψ ∆. The Mueller matrix for isotropic sample is

(

) (

)

(

) (

)

2 2 2 2 2 2 2 2 1 1 0 0 2 2 1 1 0 0 2 2 0 0 0 0 p s p s r p s p s p s p s p s p s r r r r r r r r M r r r r r r r r ∗ ∗ ∗ ∗  +       +  =     ℜ −ℑ            ℑ ℜ     (3.32) If tan i p s r e r

ρ = ψ + = is used, equation (3.32) is written as

2 2

1 cos 2 0 0

cos 2 1 0 0

0 0 sin 2 cos sin 2 sin

2

0 0 sin 2 sin sin 2 cos

p s r r r M ψ ψ ψ ψ ψ ψ −     + =  ∆ ∆     (3.33) With short notations of

cos 2 , sin 2 cos , sin 2 sin

N = ψ C= ψ ∆ S = ψ ∆ (3.34)

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2 2 1 0 0 1 0 0 0 0 2 0 0 p s r N r r N M C S S C −     + =       (3.35) For a non-depolarizing sample, N S, and C are related by

2 2 2 1

N +S +C = (3.36)

The complex ratio ρ is now written as

tan 1 i C iS e N ρ = ψ ∆ = + + (3.37)

In terms of Mueller matrix elements, it can be expressed as

(

)

(

)

(

)

33 44 34 43 12 21 1 1 2 2 tan 1 1 2 i m m i m m e m m ρ= ψ ∆ = − + + − − + (3.38)

For the description of an isotropic sample three parameters N S and C, are

needed in Mueller matrix ellipsometry, while for a non-depolarizing sample, from equation (3.37) we need two independent parameters ψ and ∆. For ideal instrumentm33 =m44,m12 =m21 and m34 = −m43.

The most recent development in the field of ellipsometry is the Mueller matrix ellipsometer. The new generation of ellipsometers has the ability to measure the Mueller matrix along with the ellipsometer angles ∆ and ψ. We can now determine every optical property of any sample, anisotropic as well as isotropic, depolarizing as well as non-depolarizing.

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Chapter 4

Instrument

In this chapter we briefly discuss the method and instrumentation used during the polarization analysis of light reflected from Cetonia aurata. Initially a simple polarizer is used to determine the polarization of the sample beetle. In a second stage, an ellipsometer system with dual rotating compensators is used to determine the Mueller matrix of the reflected polarized light.

4.1 Polarization analysis

Light reflected from Cetonia aurata is left-handed circularly polarized and the beetle appears black if we are viewing it through right-handed circular polarizer. Figure 4.1 is showing that we have a light source, a linear polarizer and a quarter-wave retarder. These two combined together form a circular polarizer.

When we will look at Cetonia Aurata with a left-circular polarizer, it will appear as having green gloss over its body surface but with a right-circular polarizer, the colour disappear and beetle look black as shown in Figure 4.2 The exoskeleton of the beetle is composed of such materials having the property of transmitting right-handed polarized light and reflecting left-handed polarized light.

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4.2 Spectral analysis

The 16 Mueller matrix elements are measured with a dual rotating compensator ellipsometer in the spectral range 300-900 nm at multiple angles of incidence in the range 40-70º with a data acquisition of 20 s/angle.

Figure 4.1: A simple desktop polarization system

Figure 4.2: The color of beetle Cetonia aurata under right and left handed circular polarizer is black and green, respectively

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4.2.1 Dual rotating compensator ellipsometer

This ellipsometer system has dual rotating compensators. The setup is denoted

r r

PC SC A or Polarizer, Compensator (rotating), Sample, Compensator (rotating),

Analyzer. The ellipsometer is manufactured by a company named J.A.Woollam Co., Inc. The name of the instrument is RC2® and is shown in Figure 4.3.

In this ellipsometer, the light is a white light source-a xenon bulb and the full spectral range is transmitted through the system. The light is polarized with a polarizer and then passes through a compensator attached to a focusing probe and then fall on the sample. After reflection from the sample it will go through the other compensator which also is attached to a focusing probe and then reaches the analyzer. After passing through the analyzer, it reaches the detector.

The compensator is an optical element that changes the phase of the incident wave, delaying one of the two orthogonal light constituents by optical anisotropy

Focusing Probes

Focusing Probes

Camera

Camera

Spectrometer

Spectrometer

Optical Fiber

Optical Fiber

Rotating

Rotating

Compensator

Compensator

Focusing Probes

Focusing Probes

Camera

Camera

Spectrometer

Spectrometer

Optical Fiber

Optical Fiber

Rotating

Rotating

Compensator

Compensator

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(n0ne). Each of the two orthogonal electric fields experiences a different index which produces different phase velocities in the two directions.

In ellipsometry, compensators which are quarter-wave plates are used to enhance measurement accuracy. With this ellipsometer, the polarization states of the incident and outgoing lights are determined and then we are able to get the full Mueller matrix. That is the reason for the use of two compensators and hence the equipment got the name RC2.

In RC2 the full spectral range is transmitted and reflected by the sample. After the analyzer the beam is diffracted at a grating and is collected by the detector. In the ellipsometer with the configurationPC1r(3 )ω SC2r(5 )ω A, the 3:5 ratios for

the rotation speeds of the two compensators are chosen [17]. The ratio can be 1:5 [18]. This frequency ratio of 3:5 gives all 15 elements of normalized Mueller matrix. It gives a highest order harmonic frequency of 32ω, in the waveform of the detected irradiance. For ratio of 1:5, the frequency is 24ω.The wavelength-dependent phase retardance values for the first and second compensator areδ1

andδ2.

In the dual compensator, the Stoke’s vector Soutof the light which is incident

on the detector, can be written in terms of Mueller matrix product as

2 2 2 2 1 1 1 1 ( ) ( ) ( ) ( ). ( ) ( ) ( ) ( ) ( ) out A C S C P in S M A C M C M C M C P M P S δ δ = ℜ ℜ − ℜ × ℜ − ℜ ℜ − ℜ (4.1)

where Sinis the Stoke’s vector of the light incident on the polarizer.

1 2

1 2

, ( ), ( ),

P C C S

M M δ M δ M and MA are the Mueller matrices of the polarizer, the first

Figure 4.4: Compensator element is introducing a phase shift between the two electric field components of light

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compensator, the second compensator, the sample and the analyzer. ℜ( )x in equation 4.1 is the Mueller rotation transformation matrix for rotation by the angle x. The angles `

1

C and ` 2

C are the angles of fast axes of the first and second

compensator. For angles `

1 1 s1

C =CC and `

2 2 s2

C =CC ,C11tand C22tare the angular rotation of the elements and Cs1 and Cs2 are absolute angular phases. Cs1

and Cs2are wavelength dependent for a multi-channel system.

The expression for irradiance at the detector is proportional to first element of the Stoke’s vector and is obtained by the multiplication of the matrices in

equation 4.1

(

)

(

)

2 2 2 2 ` 0 1 2 2 2 2 2 ` 2 3 ` 2 2 4

{ [cos cos(2 ) sin cos 4 2 ] 2

2 2

[cos sin(2 ) sin sin 4 2 ]

2 2 [sin sin(2 2 )] } I I K A C A K A C A K C A K δ δ δ δ δ     = + + −         + + −     − − (4.2) where,

(

)

(

)

2 1 2 1 ` 1 1 2 2 1 2 1 ` 1 3 ` 1 1 4

[cos cos(2 ) sin cos 4 2 ]

2 2

[cos sin(2 ) sin sin 4 2 ]

2 2 [sin sin(2 2 )] j j j j j K m P C P m P C P m C P m δ δ δ δ δ     = +   +   −         +   +   −     + − (4.3)

In equation 4.2, mjk(j=1, , 4;" k=1, , 4)" are the elements of the sample

Mueller matrix. It is assumed that Mueller matrix is normalized, i.e. m11=1 and the absolute irradiance is proportional toI0. For the ratio of 5:3, `

1 5( 1 s1)

C = CC

and `

2 3( 2 s2)

C = CC , the equation 4.2 become

(

)

(

)

16 0 2 2 2 2 1 1 [ ncos 2 n nsin 2 n ] n I I α nC φ β nC φ =   = + − + −

 (4.4) 2 2

(α βn, n)are non-zero Fourier coefficients and φ2n are the phase-terms. From 24

non-zero Fourier coefficients of frequencies ranging from 2C to 32C, the eight coefficient of

{

(α β2n, 2n),n=9,12,14,15

}

vanish, the remaining 16 coefficients can

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be used to determine the 15 normalized Mueller matrix elements [18]. Thus the Mueller matrix elementsmjk are the Fourier components of the modulated

intensity [17].

We have a rapid-scanning multi-channel Mueller matrix ellipsometer with a capability of collecting the 15 elements of the normalized Mueller matrix from 245-1700 nm in a minimum acquisition time of 0.2 s. In this system, the rotating motors are operating at 5ω =12.5 Hzand 3ω=7.5 Hzin order to get 36 detectors readings with the integration time of

36

π

ω which is about 5.56 ms.

We have a system in which both quarter-waveplates are rotating with a constant ratio of speeds. In hardware, such system is good for a simple and fast acquisition of data [17].

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Chapter 5

Models for Cetonia aurata Optical

Properties

This chapter is about the optical study of the exoskeleton of beetle Cetonia aurata. The light reflected from the metallic-shiny regions of the cuticle of Cetonia aurata belonging to Scarabaeoidea family is left-handed circularly polarized. The circularly polarized gloss is all over its body and is retained after its death. Some optical models are used to study the complex nature of the cuticle structure.

5.1 The cuticle structure of the beetle

Cetonia aurata has a green gloss over its body which reflects polarized or unpolarized incident light into circularly polarized light. The exoskeleton of the beetle has the property of absorbing right-handed polarized light. The helical structure of the molecules causes this property [20].

The optical study of the iridescent outer-skeleton of the beetle Cetonia aurata has shown a nanostructure which controls the polarization and wavelength distribution of the irradiance of the reflected light. The origin of this effect is the helicoidal layer. Ellipsometry spectra are collected from different areas of the

References

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