The present work deals with the development and application of an acoustic long-period fiber grating (LPG) in conjunction with a special optical fiber (SF). The acoustic LPG converts selected optical modes of the SF. Some of these modes are characterized by complex, yet cylindrically symmetric polarization and intensity patterns. Therefore, they are the guided variant of so called cylindrical vector beams (CVBs). CVBs find applications in numerous fields of fundamental and applied optics. Here, an application to high-resolution light microscopy is demonstrated. The field distribution in the tight microscope focus is controlled by the LPG, which in turn creates the necessary polarization and intensity distribution for the microscope illumination. A gold nanoparticle of 30 nm diameter is used to probe the focal field with sub-wavelength resolution.
The construction and test of the acoustic LPG are discussed in detail. A key component is the piezoelectric transducer that excites flexural acoustic waves in the SF, which are the origin of an optical mode conversion. A mode conversion efficiency of 85% was realized at 785 nm optical wavelength. The efficiency is, at present, mainly limited by the spectral positions and widths of the transducer’s acoustic resonances.
The SF used with the LPG separates the propagation constants of the second-order polarization modes, so they can be individually excited and are less sensitive to distortions than in standard weakly-guiding fibers. The influence of geometrical parameters of the fiber core on the propagation constant separation and on the mode fields is studied numerically using the multiple multipole method. From the simulations, a simple mode coupling scheme is developed that provides a qualitative understanding of the experimental results achieved with the LPG. The refractive index profile of the fiber core was originally developed by Ramachandran et al. However, an important step of the present work is to reduce the SF’s core size to counteract the the appearance of higher-order modes at shorter wavelengths which would otherwise spoil the mode purity.
Using the acoustic LPG in combination with the SF produces a versatile device to generate CVBs and other phase structures beams. This fiber-optical method offers beam profiles of high quality and achieves good directional stability of the emitted beam. Moreover, the device design is simple and can be realized at low cost. Future developments of the acoustic LPG will aim at applications to fiber-optical sensors and optical near-field microscopy.:Abstract / Kurzfassung iii
Table of contents v
1 Introduction 1
2 Fundamentals of optical waveguides 5
2.1 Introduction 5
2.2 Maxwell’s equations and vector wave equations 5
2.3 Optical waveguides 7
2.3.1 Dielectric waveguides 7
2.3.2 Metallic waveguides 9
2.4 Numerical calculation of modes by the multiple multipole program 10
2.4.1 Representation of simulated mode fields 11
2.5 Overview of coupled mode theory 14
2.5.1 Coupled mode equations 14
2.5.2 Co-directional coupling 15
2.6 Summary and conclusions 16
3 Polarization control for fundamental and higher order modes 17
3.1 Introduction 17
3.2 Description of light polarization 18
3.2.1 Stokes parameters and the polarization ellipse 18
3.2.2 Polarization of light beams in free space 20
3.2.3 Polarization of light beams in optical fibers 21
3.3 Short overview of cylindrical vector beam generation 22
3.4 Excitation of cylindrical vector beams in optical fibers 27
3.4.1 Free-beam techniques 27
3.4.2 In-fiber techniques 29
3.5 Polarization control in optical fibers 30
3.5.1 Phase matching and the beat length 30
3.5.2 Polarization-maintaining single-mode fibers 32
3.5.3 Higher-order mode polarization-maintaining fibers 32
3.6 Summary and conclusions 34
4 Simulation of core-ring-fibers 36
4.1 Introduction 36
4.2 Model geometries for index-tailored optical fiber 37
4.2.1 Special fiber and fabrication 37
4.2.2 Elliptical core boundaries 39
4.2.3 Overview of the applied MMP Models 41
4.3 Simulation results for circular core geometry 43
4.3.1 Mode fields 43
4.3.2 Scaling of the core radii 43
4.3.3 Wavelength dependence 48
4.4 Simulation results for non-circular geometry 50
4.4.1 Mode fields 50
4.4.2 Effects of individual rotation angles 53
4.4.3 Wavelength dependence 56
4.5 Summary and conclusions 61
5 Long period fiber gratings 63
5.1 Introduction 63
5.2 Principle of long-period fiber gratings 64
5.2.1 Results from coupled mode theory 64
5.2.2 Types of long-period gratings 65
5.2.3 Properties of acoustic long-period fiber gratings 67
5.3 Acoustic long-period grating setup 68
5.3.1 Transducer 69
5.3.2 Mechanical coupling 72
5.3.3 Acoustic dispersion of an optical fiber 75
5.3.4 Optical setup 77
5.3.5 Comparison to other acoustic LPG geometries 81
5.4 Experimental results 82
5.4.1 Transmission spectra 82
5.4.2 Discussion of transmission results 88
5.4.3 Direct mode field observation 93
5.4.4 Discussion of mode field observations 97
5.4.5 Time behavior and grating amplitude modulation 99
5.5 Summary and conclusions 101
6 Application of higher order fiber modes for far-field microscopy 104
6.1 Introduction 104
6.2 Complex beams in high-resolution far-field microscopy 104
6.3 Theoretical considerations 106
6.4 Experimental details 111
6.5 Results 114
6.6 Discussion 118
6.7 Summary and conclusions 122
7 Summary and outlook 124
Acknowledgments 139
Publications related to this work 142
List of figures 144
List of tables 150
List of acronyms 151 / Diese Arbeit behandelt die Entwicklung und Anwendung eines akustischen langperiodischen Fasergitters (LPG) in Verbindung mit einer optischen Spezialfaser (SF). Das akustische LPG wandelt ausgewählte optische Modi der SF um. Einige dieser Modi weisen eine komplexe, zylindersymmetrische Polarisations- und Intensitätsverteilung auf. Diese sind eine Form der so genannten zylindrischen Vektor-Strahlen (CVBs), welche in zahlreichen Gebieten der wissenschaftlichen und angewandten Optik zum Einsatz kommen. In dieser Arbeit wird eine Anwendung auf die hochauflösende Lichtmikroskopie demonstriert. Die fokale Feldverteilung wird dabei durch die Auswahl der vom LPG erzeugten Modi, welche zur Beleuchtung genutzt werden, eingestellt. Als Nachweis wird die entstehende laterale Feldverteilung mithilfe eines Goldpartikels (Durchmesser 30 Nanometer) vermessen.
Aufbau und Test des akustischen LPGs werden im Detail besprochen. Eine wichtige Komponente ist ein piezoelektrischer Wandler, der akustische Biegewellen in der SF anregt. Diese sind die Ursache der Umwandlung optischer Modi. Die maximale Konversionseffizienz betrug 85% bei 785 nm (optischer) Wellenlänge. Die Effizienz ist derzeit hauptsächlich durch die Lage der akustischen Resonanzfrequenzen des Wandlers und deren Bandbreite begrenzt.
Die benutzte SF spaltet die Ausbreitungskonstanten von Polarisationsmodi zweiter Ordnung auf, sodass diese individuell angeregt werden können und weniger anfällig gegen über Störungen der Faser sind, als das bei gewöhnlichen, schwach führenden Glasfasern der Fall ist. Das zu Grunde liegende Brechzahlprofil des Faserkerns wurde von Ramachandran et al. entwickelt. Für diese Arbeit wurde jedoch die Ausdehnung des Profils verkleinert – ein erster Schritt um Anwendungen bei kürzeren optischen Wellenlängen zu ermöglichen. Es werden numerische Simulationen mit der Methode der multiplen Multipole zur Berechnung der Modenfelder und den zugehörigen Propagationskonstanten vorgestellt. Diese zeigen u. a. den starken Einfluss von geometrischen Veränderungen des Faserkerns. Basierend auf den Simulationsergebnissen wird ein einfaches Kopplungsschema für die Modi entwickelt, welches ein qualitatives Verständnis der experimentellen Ergebnisse ermöglicht.
In Kombination bilden die SF und das LPG ein vielseitiges Gerät zur Erzeugung von CVBs und anderen Strahlen mit komplexer Phasenstruktur. Die Methode besticht durch hohe Qualität des Strahlprofils, stabile Abstrahlrichtung, einfachen Aufbau, elektronische Steuerbarkeit und geringe Materialkosten. Zukünftige Weiterentwicklungen des akustischen LPGs zielen auf die Anwendung in faseroptischen Sensoren und in der optischen Nahfeldmikroskopie ab.:Abstract / Kurzfassung iii
Table of contents v
1 Introduction 1
2 Fundamentals of optical waveguides 5
2.1 Introduction 5
2.2 Maxwell’s equations and vector wave equations 5
2.3 Optical waveguides 7
2.3.1 Dielectric waveguides 7
2.3.2 Metallic waveguides 9
2.4 Numerical calculation of modes by the multiple multipole program 10
2.4.1 Representation of simulated mode fields 11
2.5 Overview of coupled mode theory 14
2.5.1 Coupled mode equations 14
2.5.2 Co-directional coupling 15
2.6 Summary and conclusions 16
3 Polarization control for fundamental and higher order modes 17
3.1 Introduction 17
3.2 Description of light polarization 18
3.2.1 Stokes parameters and the polarization ellipse 18
3.2.2 Polarization of light beams in free space 20
3.2.3 Polarization of light beams in optical fibers 21
3.3 Short overview of cylindrical vector beam generation 22
3.4 Excitation of cylindrical vector beams in optical fibers 27
3.4.1 Free-beam techniques 27
3.4.2 In-fiber techniques 29
3.5 Polarization control in optical fibers 30
3.5.1 Phase matching and the beat length 30
3.5.2 Polarization-maintaining single-mode fibers 32
3.5.3 Higher-order mode polarization-maintaining fibers 32
3.6 Summary and conclusions 34
4 Simulation of core-ring-fibers 36
4.1 Introduction 36
4.2 Model geometries for index-tailored optical fiber 37
4.2.1 Special fiber and fabrication 37
4.2.2 Elliptical core boundaries 39
4.2.3 Overview of the applied MMP Models 41
4.3 Simulation results for circular core geometry 43
4.3.1 Mode fields 43
4.3.2 Scaling of the core radii 43
4.3.3 Wavelength dependence 48
4.4 Simulation results for non-circular geometry 50
4.4.1 Mode fields 50
4.4.2 Effects of individual rotation angles 53
4.4.3 Wavelength dependence 56
4.5 Summary and conclusions 61
5 Long period fiber gratings 63
5.1 Introduction 63
5.2 Principle of long-period fiber gratings 64
5.2.1 Results from coupled mode theory 64
5.2.2 Types of long-period gratings 65
5.2.3 Properties of acoustic long-period fiber gratings 67
5.3 Acoustic long-period grating setup 68
5.3.1 Transducer 69
5.3.2 Mechanical coupling 72
5.3.3 Acoustic dispersion of an optical fiber 75
5.3.4 Optical setup 77
5.3.5 Comparison to other acoustic LPG geometries 81
5.4 Experimental results 82
5.4.1 Transmission spectra 82
5.4.2 Discussion of transmission results 88
5.4.3 Direct mode field observation 93
5.4.4 Discussion of mode field observations 97
5.4.5 Time behavior and grating amplitude modulation 99
5.5 Summary and conclusions 101
6 Application of higher order fiber modes for far-field microscopy 104
6.1 Introduction 104
6.2 Complex beams in high-resolution far-field microscopy 104
6.3 Theoretical considerations 106
6.4 Experimental details 111
6.5 Results 114
6.6 Discussion 118
6.7 Summary and conclusions 122
7 Summary and outlook 124
Acknowledgments 139
Publications related to this work 142
List of figures 144
List of tables 150
List of acronyms 151
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:27304 |
| Date | 05 November 2013 |
| Creators | Zeh, Christoph |
| Contributors | Eng, Lukas M., Zhan, Qiwen, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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