Subwellenlängen-Strukturen für die Polarisationsmanipulation [Elektronische Ressource] / Zahra Ghadyani. Betreuer: Norbert Lindlein

Subwellenlangen Strukturen fur die
Polarisationsmanipulation
Den Naturwissenschaftlichen Fakult aten der
Friedrich-Alexander-Universit at Erlangen-Nurn berg
zur Erlangung des Doktorgrades
vorgelegt von
Zahra Ghadyani
aus Karaj, IranAls Dissertation genehmigt von den Naturwissenschaftlichen Fakult aten der
Friedrich-Alexander-Universit at Erlangen-Nurn berg
Tag der mundlic hen Prufung: 18.11.2011
Vorsitzender der Promotionskommission: Prof. Dr. Rainer Fink
Erstberichterstatter: Prof. Dr. Norbert Lindlein
Zweitberich Prof. Dr. Hartmut BarteltAllen die dabei warenContents
1 Abstract 8
2 Zusammenfassung 9
3 Publications 11
4 Introduction 12
5 Theoretical Background 14
5.1 Polarized light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.1.1 Jones matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5.1.2 Stokes Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.2 Subwavelength structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.3 E ective medium theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.4 Rigorous electromagnetic calculation . . . . . . . . . . . . . . . . . . . . 22
5.4.1 Homogeneous regions . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.4.2 Modulated region . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.4.3 Numerical errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.5 Spatially homogeneous polarization . . . . . . . . . . . . . . . . . . . . . 29
5.6 Cylindrical vector beam . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.6.1 Generation methods . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.6.2 Properties and applications . . . . . . . . . . . . . . . . . . . . . 37
6 Characterization 39
6.1 Structural parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.1.1 Film Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.1.2 Ellipsometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.1.3 Linewidth and period . . . . . . . . . . . . . . . . . . . . . . . . . 42
6.1.4 Cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.2 Polarization properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.2.1 Stokes parameters measurement . . . . . . . . . . . . . . . . . . . 46
6.2.2 Extinction ratio of a polarizer . . . . . . . . . . . . . . . . . . . . 49
6.2.3 Phase shift of a phase retarder . . . . . . . . . . . . . . . . . . . . 53
7 Metal subwavelength structures 56
7.1 Principle and conventions . . . . . . . . . . . . . . . . . . . . . . . . . . 56
7.2 EMT calculation for metal subwavelength structures . . . . . . . . . . . . 57
7.3 Simulation and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4Contents
7.3.1 Numerical parameters . . . . . . . . . . . . . . . . . . . . . . . . 59
7.3.2 Grating material . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7.3.3 Analysis of structural parameters . . . . . . . . . . . . . . . . . . 61
7.3.4 Tolerances to other . . . . . . . . . . . . . . . . . . . 63
7.3.5 Inverse polarizer . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.4 Fabrication of metal subwavelength structures . . . . . . . . . . . . . . . 67
7.4.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.4.2 Pattern generation . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.4.3 P transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7.5 Polarization array for shearing interferometry . . . . . . . . . . . . . . . 73
7.5.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.5.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.5.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.6 Concentric ring metal grating (CRMG) . . . . . . . . . . . . . . . . . . 78
7.6.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.6.2 Designed pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.6.3 Fabrication results . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.6.4 Characterization of the element . . . . . . . . . . . . . . . . . . . 81
7.6.5 C of propagating mode . . . . . . . . . . . . . . . 83
7.6.6 C of mode with vortext . . . . . . . . 84
7.6.7 Discussion on concentric ring metal nanowire grating . . . . . . . 86
8 Dielectric subwavelength structures 87
8.1 De nitions and conventions . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.2 EMT calculation for dielectric subwavelength structures . . . . . . . . . . 88
8.3 Simulation and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.4 Fabrication of dielectric subwavelength structures . . . . . . . . . . . . . 90
8.4.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 92
8.4.2 Pattern generation . . . . . . . . . . . . . . . . . . . . . . . . . . 93
8.4.3 P transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
8.4.4 Line Broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.5 Design of structural parameters . . . . . . . . . . . . . . . . . . . . . . . 95
8.5.1 Grating height . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.5.2 Period and duty cycle . . . . . . . . . . . . . . . . . . . . . . . . 97
8.6 Continuous pattern SVQW . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8.6.1 Single SVQW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8.6.2 Multi SVQW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
8.6.3 Correction of the structural parameters . . . . . . . . . . . . . . . 104
8.7 Concentric ring segmentation (CRS) . . . . . . . . . . . . . . . . . . . . 106
8.7.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.7.2 Fabrication results . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8.7.3 Characterization of the sample . . . . . . . . . . . . . . . . . . . . 108
8.7.4 of the propagating mode . . . . . . . . . . . . . 110
8.7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5Contents
9 Summary 113
10 Acknowledgements 125
11 Resume 127
6Nomenclature
CRMG Concentric Ring Metal Grating
CRS Concentric Ring Segmentation
CV Cylindrical Vector
EBL Electron Beam Lithography
EMT E ective Medium Theory
FIB Focused Ion Beam
HDP high density plasma
HG Hermit Gauss
IBE Ion Beam Etching
LCD Liquid Crystal Device
LG Laguerre-Gauss
PECVD Plasma Enhanced Chemical Vapor Deposition
PMMA Polymethylmethacrylate
RIE Reactive Ion-beam Etching
SEM Scanning Electron Microscope
SLM Spatial Light Modulators
SOP Spatially homogeneous polarizations
SPP Spiral Phase Plate
StD Standard Deviation
SVHW Space Variant Half Waveplate
SVQW Space Variant Quarter Waveplate
TE Transverse Electric
TM Transverse Magnetic
ZEP copolymer of -chloromethacrylate and -methylstyrene
71 Abstract
In this thesis the polarization properties of subwavelength structures for di erent appli-
cations in visible region are investigated. Generating radially polarized light is considered
as the main application. However it is further used in designing a polarization array for
shearing interferometry. The subwavelength structures are divided into two main cate-
gories. The metallic and dielectric subwavelength structures are investigated separately.
The rigorous calculations are used to simulate the properties of these structures. The
e ective medium theory is used to explain the general properties. The structures are
fabricated by electron beam lithography followed by dry etching. The characterizations
are done by measuring the Stokes parameters. The advantages and disadvantages of
each design is discussed at the end of the corresponding section.
First the metallic structures are discussed. Investigation of di erent metals shows that
aluminium is preferred for a high extinction ratio polarizer. Two optical resonances are
observed for TM transmission of aluminium subwavelength structures. The vertical cav-
ity modes associated with transmission enhancement are explained with EMT. The rst
cavity mode is utilized to optimize the e ciency of the normal polarizers in this thesis.
The horizontal particle mode is associated to re ection enhancement. Based on this
4resonance an e cient inverse polarizer with high extinction ratio of 7 10 is predicted
for wavelength of 124nm. As the rst application, the aluminium subwavelength struc-
ture is successfully used in polarization array for shearing interferometry. As the second
application "concentric ring metal grating" is fabricated to generate radially polarized
light. The characterization of the propagating mode shows a highly pure polarization
mode without any mode cleaning.
Next,the dielectric structures are discussed. Silicon nitride with high refractive index is
selected for subwavelength dielectric structures in this thesis. Three designs based on
continuous space variant quarter waveplate are fabricated for generating radially polar-
ized light in visible region ( = 632:8nm). However each design lead to some technical
problems that are discussed. These problems are overcome by modifying the design to a
discontinuous space variant subwavelength