行政院國家科學委員會專題研究計畫 成果報告
D 型光纖漸逝場特性之分析與感測器上之應用(2/2)
計畫類別： 個別型計畫 計畫編號： NSC92-2212-E-006-018- 執行期間： 92 年 08 月 01 日至 93 年 07 月 31 日 執行單位： 國立成功大學機械工程學系（所） 計畫主持人： 李森墉 計畫參與人員： 彭祈程 報告類型： 完整報告 處理方式： 本計畫涉及專利或其他智慧財產權，1 年後可公開查詢 中 華 民 國 93 年 7 月 13 日行政院國家科學委員會補助專題研究計畫
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D 型光纖漸逝場特性之分析與感測器上之應用(2/2)
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NSC 92-2212-E-006-018
執行期間：92 年 8 月 1 日 至 93 年 7 月 31 日
計畫主持人：李森墉
共同主持人：羅裕龍
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執行單位：國立成功大學 機械系
Abstract
In this thesis, the commercially available D-shaped polarization maintain optical fiber is utilized to fabricate D-shaped optical fiber Surface plasmon resonance (SPR) sensor to solve the hardness from the fabrication of the general single mode optical fiber SPR sensor by polishing or etching. The general problem that is polarization unstable of single mode optical fiber SPR sensor is also overcome by using the polarization maintain characteristic of the D-shaped optical fiber. Besides, the etching technology of D-shaped optical fiber is fully discussed, and the asymmetrical waveguides theory is used to decide the etching depth and etching rate. What’s more important, a series of D-shaped optical fiber sensors and optical components are developed. Furthermore, the low environment effect common path Heterodyne Interferometry is perfectly used to work with the phase shift measurement for the D-shaped optical fiber SPR sensor.
Index Terms: D-shaped optical fiber, Surface plasmon resonance sensor, evanescent wave refractometer, Metal-clad polarizer, Common-path Heterodyne Interferometry, Birefringent materials.
中文摘要
本文主要是使用商業用的 D 型保極化光纖來製作表面電漿共振感測 器，以解決傳統單模光纖在製作時的困難，且完整的探討 D 型光纖的蝕 刻技術並利用非對稱波導理論來量測蝕刻深度與蝕刻速率。此外，D 型 光纖的保偏極化特性被使用來解決一般存在於單模光纖表面電漿共振感 測器的偏振不穩定現象。藉由蝕刻深度的控制，詳細探討與發展一系列 的 D 型光纖感測器與光學元件。最後，低環境影響之共路徑外差干涉術 被完美的使用來量測表面電漿共振之相位飄移。 關鍵詞：D 型光纖，表面電漿共振感測器，共路外差干涉。Contents
Pages Abstract in Chinese………... I Abstract in English……… II List of Contents………. III List of Figures………VII List of Tables………. XV Chapter1 Introduction 1.1 Preface………. 1 1.2 Research Motive……….……. 1 1.3 Research Methods………... 2 1.4 Overview of Chapters……….. 3
Chapter 2 TheHistory Review 2.1 History Review of SPR Sensors……….……. 10
2.2 History Review of Evanescent Wave Fiber Optic Sensors ………... 11
2.3History Review of Fiber-Type Polarizers……… 12
2.4History Review of Single Mode Optical Fiber SPR Sensors ………... 13
Chapter 3 Basic Theory 3.1 Evanescence Wave ………. 15
3.2 Surface Plasmon Resonance ……….. 17
3.3 Three Layers Optical Waveguide……… 20
Chapter 4 Optical-Type Surface Plasmon Resonance Sensor 4.1 Preface………. 30
4.2 Heterodyne Interferometry and Lightwave Modulation……. 30
4.3 Common-Path Heterodyne Interferometry………. 31
4.4 Measurement Methods of SPR Sensor……… 32
4.5 Parameters Comparison………...33
4.6 Experiments………. 34
4.7 Error Analysis……….. 36
Chapter 5 Fabrication of The D-Shaped Optical Fiber Surface Plasmon Resonance Sensor 5.1 Preface………. 42
5.2 Etching of the D-Shaped Optical Fiber………... 42
5.3 Etching Rate Measurement………..44
Chapter 6 D-Shaped Optical Fiber Evanescent Wave Refractometer 6.1 Introduction………. 54
6.2 Theory………. 55
6.2.1 Phase shift measurement of birefringent model by Common-Path Heterodyne Interferometry…………... 56
refractive index various……… 58
6.3 Experiments and Discuss……… 60
6.4 Conclusion………... 62
Chapter 7 D-Shaped Optical Fiber Metal-Clad Polarizer 7.1 Introduction………. 68
7.2 Theory………. 69
7.3 Experiment……….. 71
7.3.1 Fabrication of D-shaped optical fiber polarizer………. 71
7.3.2 Experimental Setup……… 72
7.4 Results and Discuss………. 73
7.4.1 D-shaped optical fiber polarizer utilizing thick metal cladding method……….. 75
7.4.2 D-shaped optical fiber polarizer utilizing thin metal cladding method……….. 76
7.5 Conclusion………... 78
Chapter 8 D-Shaped Optical Fiber Surface Plasmon Resonance Sensor 8.1 Introduction……… 84
8.2 Theory ……….……….. 85
8.3 Measurement Setup and Experiments ……… 86
8.4 Results and Discuss……….. 87
8.5 Conclusion……… 88
9.1 Conclusion……… 95 9.2 Future Work……….. 96 Bibliography ………... 97
List of Figures
Pages Figure 1.1 The Development of SPR Biosensor Conformation in ideal.
………. 5 Figure 1.2 The Development of SPR Biosensor Conformation in example.
………. 6 Figure 1.3 Refraction Sensors for Evanescent Wave and SPR…………. 7 Figure 1.4 The research method and flow chart………... 8 Figure 1.5 The D-Shaped Optical Fiber Development Structure and Design
Flow……… 9 Figure 3.1 Incidence wave, reflection wave, and refraction wave……... 24 Figure 3.2 P-wave for incidence wave and refraction wave………. 24 Figure 3.3 The dispersion relation for P-wave incidence wave in air and in
metal……… 25 Figure 3.4 The dispersion relation for P-wave incidence wave in air, coupler,
and in metal………. 25 Figure 3.5 The Kretschmann-Structure is used to as the coupler to generate
evanescent wave to excite the SPR………. 26 Figure 3.6 Theoretic curve of the reflection coefficient versus various
incidence angles
θ
with P-wave and S-wave………... 26 Figure 3.7 Theoretic curve of the reflection coefficient versus variousFigure 3.8 Theoretic curve of the reflection coefficient versus various incidence angles θ with optimum Au coating thickness d... 27 Figure 3.9 Theoretic curve of the resonance trough shift with various
overlayer indexes……… 28 Figure 3.10 Theoretic curve of phase shift versus overlayer refractive index
change with fixed-incidence angle that is near the resonance angle 71.5 deg………... 28 Figure 4.1 Optical-Type SPR Intensity Measurement Configuration….. 37 Figure 4.2 Optical-Type SPR Phase Measurement Configuration……... 37 Figure 4.3 Experimental optical-type SPR intensity measurements for air and
water comparing with theoretic curve………. 38 Figure 4.4 Experimental optical-type SPR phase measurement with
fixed-incidence angle that is near the resonance angle……... 38 Figure 5.1 The fabrication flow of the D-shaped optical fiber SPR sensor
………. 47 Figure 5.2 The commercially available D-shaped optical fiber sketch map.
………. 48 Figure 5.3 The nonflat of the D-Shaped optical fiber with stripping off its
plastic coating……….. 48 Figure 5.4 The flat of the D-Shaped optical fiber with stripping off its plastic
coating………. 49 Figure 5.5 D-Shaped optical fiber without well stripping off its plastic coating
………. 49 Figure 5.6 D-Shaped optical fiber with well stripping off its plastic coating
………. 50 Figure 5.7 The Etched D-shaped optical fiber by BOE……… 50
Figure 5.8 Etched D-shaped optical fiber is cleaned by DI water and Nitrogen.
………. 51 Figure 5.9 The evanescent wave detection by using various overlayer
refractive indexes for etching time 40, 60, and 70 minute….. 51 Figure 5.10 The liquid-drop method for (a) the evanescent wave has been
throughout the cladding, and (b) the core has been reached……….. 52 Figure 6.1 The commercially available D-shaped optical fiber sketch map.
………. 64 Figure 6.2 Experimental Setup for measuring the phase shifts due to the
glucose concentrations various by Heterodyne Interferometry, and the angle is defined as the angle between the y-axis and the principle axis………... 64 Figure 6.3 The etched D-shaped optical fiber with the evanescent wave
throughout………... 65 Figure 6.4 Experimental phase shift is measured with various glucose
concentrations and etching depth……… 65 Figure 6.5 Experimental intensity of output light is detected with various
etching depth and incident light, TM-Wave and TE-Wave, for 1cm etching length in D-shaped optical fiber and surrounding refractive index ns ≈ ……… 66 1 Figure 6.6 Three times experimental phase shift is measured with various
glucose concentrations for etching depth8.980 µm, etching length 3 cm and the sensitivity is about 10 deg (mg/ml)⋅ −1……….. 66
Figure 6.7 Experimental stability for pure water (n = 1.33) with per 0.5 min, and maximum phase drift is 1.83o………. 67
Figure 7.1 The D-shaped optical fiber sketch map………... 79 Figure 7.2 The D-shaped optical fiber polarizer sketch map…………... 79 Figure 7.3 Experimental Setup for measuring the polarization characteristics
by utilizing AC signal detecting. And the angle is defined as the angle between the y-axis and the principle axis……….. 80 Figure 7.4 Experimental intensity of output light is detected with various
etching depth and incident light, TM-Wave and TE-Wave, for 1cm etching length in D-shaped optical fiber without metal coating.
………. 80 Figure 7.5 Experimental insertion loss is detected with various etching depth
and incident light, TM-Wave and TE-Wave, for 1cm etching length in D-shaped optical fiber without metal coating…….. 81 Figure 7.6 Experimental extinction ratios is detected with various etching
depth for 1cm etching length in D-shaped optical fiber without metal coating………... 81
Figure 7.7 Experimental insertion loss is detected with various etching depth and refractive index that is for air and pure water for 1cm etching length in D-shaped optical fiber with thick metal coating….. 81 Figure 7.8 Experimental extinction ratio is detected with various etching
depth and refractive index that is for air and pure water for 1cm etching length in D-shaped optical fiber with thick metal coating.
……….… 81 Figure 7.9 Experimental extinction ratio is detected with various etching
depth, metal thickness, and overlayer index………... 83 Figure 7.10 Experimental insertion loss is detected with various etching
depth, metal thickness, and overlayer index………. 83 Figure 8.1 Theoretic curve of the reflection coefficient versus various
overlayer indexes with difference incident angle and Au thickness is 25 nm………... 90 Figure 8.2 Theoretic curve of the phase shifts versus various overlayer
indexes relative to the case of Figure 8.1……… 90 Figure 8.3 Fiber Type SPR Phase Measurement Configuration.……….. 91 Figure 8.4 Experimental extinction ratios is detected with various etching
depth, metal thickness, and overlayer index………... 92 Figure 8.5 Experimental phase shifts is detected with various overlayer index
for sample I and II………... 92 Figure 8.6 Experimental extinction ratios is detected with various etching
depth for sample I. Its sensitivity 247.5 (%/RIU) and resolution
4
Figure 8.7 Experimental phase shifts is detected with various overlayer index for sample I.……… 93 Figure 8.8 Experimental stability is measured for overlayer refractive index
1.408 with per 1 min, and maximum phase drift is about 0.38o……… 94
List of Tables
Pages Table 3.1 The refractive index of the BK7 prism with various wavelength
………. 29 Table 4.1 SPR Biosensor Measurement Parameters………... 40 Table 4.2 The Theoretical Sensitivity and Resolution in other paper……. 40 Table 4.3 Effective Linear Range……… 41 Table 4.4 The Relative-Mean Error with various incline angle
α
……….41 Table 5.1. Etching Depth Measurement……….. 53 Table 8.1 The resolution of D-shaped optical fiber SPR sensor with variousChapter
1 Introduction
1.1 Preface
The study of optical fiber sensors has passed almost thirty years, and various ideas and techniques have been developed [Byoungho, 2003]. However, One of the most important sensor theories is “evanescent wave”, and it also plays a crucial role in biosensor and optical coupler. The basic condition to generate evanescent wave is using the total internal reflection, and the methods to fabricate total internal reflection have been studied in many structure like optical prism, waveguide, optical fiber, and etc. Because of the principle of the transmission of the lightwave, the application of evanescent wave in optical fiber is much suitable and developable.
1.2 Research Destinations and Motivations
Though the evanescent wave has existed due to the propagation of the lightwave by the total internal reflection in the optical fiber, the effective penetration depth of the evanescent wave is about one wavelength that is too small to be obtained. Therefore, there are many methods like etching, polishing, and pulling are researched to remove the cladding to let the energy of the evanescent wave throughout the cladding. In this thesis, the commercially available D-shaped optical fiber is applied to fabricate evanescent wave optical fiber sensor to solve the difficulty of side-polished optical fiber, and it is much easier to etch and control the residual cladding depth. Besides, though the characteristic of the evanescent wave like energy
abortion and phase shift is effectively applied to measure the surrounding refractive index change, its sensitivity is not good enough. Therefore, the electric field enhancing by surface plasmon resonance is used to increase the sensitivity of the evanescent wave sensor. In the figure 1.1 and figure 1.2, the development flow and basic structure for the application of surface plasmon resonance is shown. It can see that in order to reduce the sensor volume, increase the sensitivity, and more applicable, the optical fiber sensor is developed. In order to solve the difficulty of the fabrication in removing the cladding, the commercially available D-shaped optical fiber can be used, and not only the accuracy of cladding removing depth can be increased but the roughness on the interface can be decreased. Besides, the polarization unstable that exists in general single mode fiber SPR sensor can be solved by the polarization-maintaining characteristic of D-shaped optical fiber in this thesis. From the figure 1.2, the prism structure has been generally developed and much studied. In the figure 1.3, the developable relation between the evanescent wave, surface plasmon resonance, and optical fiber are shown. Finally, the D-shaped optical fiber surface plasmon resonance sensor is chosen as the research destination.
1.3 Research Methods
The research methods in this thesis are shown in figure 1.4. In order to research the D-shaped optical fiber surface plasmon resonance sensor, SPR measurement characteristic and D-shaped optical fiber evanescent wave must be discussed first. Then, the metal cladding characteristic must be studied due
to the metal must be coating properly. If all the parameters are obtained, the D-shaped optical fiber SPR sensor can start to work. Therefore, there are four main subject can be developed, and them are shown in figure 1.5. First, the phenomenon of the surface plasmon resonance can be check and measured by using the I. optical-type surface plasmon resonance sensor, and the phenomenon of the evanescent wave refractometer can be check by using II. D-shaped optical fiber evanescent wave refractometer. Secondly, the phenomenon of the surface plasmon resonance for D-shaped optical fiber can be check by III, and the fiber-type polarizer can be developed. If III can be obtained, the phase measurement of IV D-shaped optical fiber surface plasmon resonance sensor may be able to be detected.
1.4 Overview of Chapters
In this article, including this chapter, it is divided into nine chapters to discuss, and a brief introduction of other eight chapters is stated in below, respectively:
Chapter 2 History Review, it introduces the history review of the surface plasmon resonance, and the optical fiber grating.
Chapter 3 Theory Analysis, in this chapter, four basic theories that are evanescent wave, surface plasmon resonance, long period fiber grating, and Heterodyne Interferometry will be proved and analyzed.
Chapter 4 Optical-Type Surface Plasmon Resonance Sensor, the primary measurement methods and parameters of surface plasmon resonance will be
discussed. Besides, the relative sensitivity and resolution will be compared also. Finally, the basic Kretschmann coupler will be used to as the surface plasmon resonance sensor, and the relative error will be discussed.
Chapter 5 Fabrication of The D-Shaped Optical Fiber Surface Plasmon Resonance Sensor, the most important etching technology and how to measure the etching depth are discussed and the full fabrication process of the D-shaped optical fiber surface plasmon resonance sensor is described.
Chapter 6 D-Shaped Optical Fiber Evanescent Wave Refractometer, the characteristic of evanescent wave will be utilized to measure the phase shift due the surrounding refractive index various by D-shaped optical fiber.
Chapter 7 D-Shaped Optical Fiber Metal-Clad Polarizer, two methods that are thick metal cladding and thin metal cladding (SPR) are used to fabricate the fiber-type polarizer, and the extinction ratio and insertion loss will be measured.
Chapter 8 D-Shaped Optical Fiber Surface Plasmon Resonance Sensor, the phase measurement method with fixed resonance angle will be used to measure the change of the surrounding refractive index by fiber-type surface plasmon resonance sensor.
Chapter 9 Conclusion and Future Work, the conclusions of this thesis are discussed and the future work are suggested to solve the problem of fiber-type SPR sensors at present.
5 e Pre dicted y F erre ll A nd S te rn 1968 Kr etsc hma nn、 O tto c ou pler (P ris m ) Op tica l F ib er Se nsor In ord er to : 1. Re duc e V olume 2. I ncre ase Sen sitivity Cladding Re move
1. Etch 2. Polish 3. Pull
D-S hap ed Fi be r In orde r to impr ove the me thod to r emove the cla dding 1967 T eng 、 St er n cou ple r (G ra ting ) … … Figure 1.1 The Developm
ent of SPR Biosensor Conform
6 SPR Bi os en so r D-S haped Opt ical Fiber SPR Sensor [Hom ola, et al. , 1999] [K an o, et al. , 1994] [Hom ola, 2003] [Jorgen son et al., 1993] [Joh n ston e e t al ., 1992] Figure 1.2 The Developm
ent of SPR Biosensor Conform
ation in exam
Evanescent wave SPR
R ∆
φ
θ
sp R ∆φ
∆ω
Kretschmann ˇ[a] ˇ[b] ˇ[c] ˇ[d] Prism
Otto (Structure is too hard to be used.)
Grating ˇ[e] ˇ[f] Evanescent wave SPR R ∆
φ
θsp R ∆φ
∆ω
Single-mode fiber ˇ[g] ˇ[h] ˇ[i] ˇ[j] ˇ[k] Multi-mode fiber ˇ[l] ˇ[m] ˇ[m] ˇ[n] Fiber D-fiber ˇ[o] ˇ[p] ☆ ☆Figure 1.3 Developed Refraction Index Sensors for Evanescent Wave and SPR. “ˇ” means it had been developed, and “☆” means it is the developing goal in this thesis.
θ
spis SPR resonance angle, R is reflectivity, ∆ isφ
Phase shift between p-wave and s-wave, and ∆ is wavelength shift.ω
* [a]=[Matsubara et al., 1988] [b]= [Nylander et al., 1982] [c]=[Nelson et al., 1996] [d]=[Zhang et al., 1988] [e]=[Cullen et al., 1987] [f]=[Vukusic, 1992] [g] = [Hideo et al., 1987] [h] = [Rene et al., 1991] [i] = [Fontana et al., 1998] [j] = [Homola, 1995] [k] = [Slavik et al., 2001]
[l]= [Lee et al., 2003] [m] = [Trouillet et al., 1996] [n] = [Jorgenson et al., 1993] [o] = [Muhammad et al., 1993] [p] = [Kooyman, 1991]
SPR Measurement Characteristics Discussion
D-Shaped Optical Fiber Evanescent Wave Discussion
D-Shaped Optical Fiber SPR Sensor
D-Shaped Optical Fiber Metal Cladding Discussion
9
Figure 1.5
The D-Shaped Optical Fiber Developm
ent S
tructure and Design Flow
I. Optical-T
ype Surface Plasm
on
Resonance Sensor
II. D-Shaped Optical Fiber
Evanescent W
ave
Refractom
eter
IV
. D-Shaped Optical Fiber
Surface Plasm
on Resonance
III. D-Shaped Optical Fiber
Metal-Clad Polarizer He -N e L as er Z X Y (, ) 2 o Q λϕ (4 5 ) o EO (9 0 ) o P (0 ) o P P hot ode te ct er L ock -I n A m plif ier F unc ti on G ene ra to r DC-B ia s Fi be r-C oup le r D -S hap ed O ptical Fi be r pol ar iz er C onde ns er L en s H e-N e La se r Z X Y θ (, ) 2 o Q λϕ (4 5 ) o EO (9 0 ) o P (4 5 ) o P P ho todet ect L oc k-I n A m pl if ie r Funct ion G en er at or DC-B ia s He -N e L as er Z X Y (, ) 2 o Q λϕ (4 5 ) o EO (9 0 ) o P (4 5 ) o P P hot od et ec t Loc k-I n A m plifie r F unctio n G ener ato r DC-B ia s F ib er -C oup le r D-F ib er S en sin g S ec tio n C ond enser Lens
Chapter 2 The History Review
2.1 History Review of SPR Sensors
In the early 20th century, Wood [Wood, 1902] observed the phenomenon of anomalous diffraction on diffraction gratings due to the excitation of surface plasma waves and it was first described. In 1930, Rudberg found out the phenomenon of discontinuous energy loss due to an electron throughout the thin metal film. In 1951, Bohm and Pines expressed it as “Plasma Oscillations”. In 1958, Ferrell integrated above two phenomena and predicted “Radiative Surface Plasmon Oscillations” by theory. In 1960 Steinmann confirmed “Radiative Surface Plasmon Oscillations” by experiments.
In 1962, Ferrell and Stern predicted “Surface Plasmon Wave” could be excited by plane polarization wave. Then just in 1967, Teng and Stern brought forward optical excitation of surface plasmon by the method of grating, and in 1968, Kretschmann [Kretschmann et al., 1968] and Otto [Otto, 1986] brought forward optical excitation of surface plasmon by the method of attenuated total reflection. Sine then, Surface Plasmons have been intensively studied and their major properties have been assessed [Raether, 1988], [Boardman, 1982].
Up to 1982, SPR started to popular in optical measurement after Nylander and Liedberg first used SPR for gas detection [Nylander et al., 1982], [Liedberg et al., 1983], [Liedberg et al., 1993]. Since then SPR sensing has been receiving continuously growing attention from scientific community.
Since 1992, integrated optical waveguide for SPR sensors [Lambeck, 1992] is pioneered, and then various groups have developed SPR-sensing devices using slab and channel single-mode integrated optical waveguides. In 1993, Jorgenson and Yee [Jorgenson et al., 1993] first used optical fibers for SPR sensing that was based on wavelength modulation in multimode optical fibers with partly removed cladding and metal film deposited symmetrically around the exposed section of the fiber core.
2.2 History Review of Evanescent Wave Fiber Optic Sensors
In [Lamb, 2002], Hirschfed first introduced the concept of the evanescent wave in 1965. In 1975, Kronick and Little put this concept into practice for immunoassays. At the same time 1974, Hesse used a fiber optic-based sensor for O2 and iodide. In 1984, the first evanescent wave fiber optic
immunosensor was developed by Hirschfeld, and it was further optimized by Andrade et al. in 1985 and Sutherland et al. in 1984. In 1991, the ellipsometry was used to fabricate the optical fiber immunosensor [Kooyman et al, 1991]. The relative phase retardation due the surrounding refractive index various can be measured by detecting the polarization change. In the same year, simple interferometer for evanescent field refractive index sensing was designed [Rene et al, 1991], and the theoretic sensitivity was calculated. In 1993, the D-shaped optical fiber was made as polarimetric optical-fibre sensor for biochemical measurements [Heideman et al., 1993], and it also used the ellipsometry. In 1998, the D-shaped optical fiber was made as polarimetric D-fiber sensor for chemical applications by using fringes counting
[Muhammad, 1998].
2.3 History Review of Fiber-Type Polarizers
In 1980, the first single-mode fiber-optic polarizer was fabricated by using birefringent crystal [Bergh, 1980], and the characteristic of different refractive index for different polarization was used to separate the TE wave and TM wave. In order to overcome the large volume from birefringent crystal, the metal characteristic of the attenuation difference between the TE mode and TM mode was used to fabricate the metal-clad fiber-optic polarizer [Eickhoff, 1980], [Hosaka et al., 1982], [Hosaka et al.,1983]. By this way, the extinction ratio can be increased with decreasing the cladding thickness between the metal and the core. However, the insertion loss will become large when the deep etching depth is arrived. Therefore, it was hard to obtain high extinction ratio and low insertion loss at the same time by the thick metal-clad method. In 1986, because the SPR had started to popular in optical measurement, the SPR phenomenon was used to fabricate the thin metal-clad fiber-optic polarizer [Feth, 1986]. By SPR method, the high extinction ratio and low insertion loss could be obtained at the same time with special matching condition. Since then, the fiber-type SPR polarizer had been widely studied. In 1995, a Hi-Bi single-mode fiber experiencing a periodic perturbation was used to fabricate in-line fiber polarizer [Wang et al., 1995]. The periodic perturbation could be produced by a periodic microbending, acoustic waves, or a photorefractive index grating. Recently, resonant tunneling [Arun Kumar
et al, 1997], LPG in birefringent optical fibers [Ortega et al., 1997], and FBG with locally pressed [Torres et al. 2003] were individual brought forward, and all these designs used the characteristic of the fiber grating different mode coupling due the different core refractive index.
2.4 History Review of Single Mode Optical Fiber SPR Sensors
In 1993, Jorgenson and Yee [Jorgenson et al., 1993] first used optical fibers for SPR sensing that was based on wavelength modulation in multimode optical fibers with partly removed cladding and metal film deposited symmetrically around the exposed section of the fiber core. In 1995, Homola [Homola, 1995] used intensity modulation in single mode optical fibers which were side-polish and coated with a thin metal film. These SPR sensors suffered from modal noise and polarization instability. In order to overcome the polarization instability, two methods were developed. In the first method [Homola et al., 2001], light from a polychromatic light source passes a Lyott fiber optic depolarizer which produces unpolarized light which was then coupled into a fiber optic SPR sensing element, and then the transmitted light was analyzed with a spectrograph. The second method [Piliarik et al., 2003] uses a polarization-maintaining fiber to control polarization of light in the fiber-optic SPR sensing element. However, the SPR measurement dynamic range of single mode optical fiber was restricted near the refractive index of cladding. Therefore, in 1998, a thin tantalum pentoxide overlayer was used to tune the operation range of the sensor to desired region of the refractive indices [Slavý´k et al., 1998]. In 2001, a tapered fiber was used to require
simper technology than the polishing technique, and the different surface plasma modes supported by the metal film can be excited by the fiber mode [Diez et al., 2001].
Chapter 3 Basic Theory
In this chapter, there will be four crucial basic theories that will be proved and analyzed, and these four basic theories will be the foundation stone to establish the follow experimental principles and conformations.
3.1 Evanescence Wave [趙凱華 et al.,1992]
As is known to everyone, if the angle of the incidence light is large than the critical angle of the total reflection, the energy of the incidence light will be reflected totally. However, this phenomenon doesn’t mean that there will not exist refraction light. In fact, there will exist a special phenomenon that is the total energy of the refraction light will decay exponentially with the distance far from the interface, and the prove are as follows:
First, the mathematic model of incidence wave, reflection wave, and refraction wave (like figure3.1) can be described by the electromagnetic wave of Maxwell’ theory as (3.1.1), (3.1.2), (3.1.3). 1 1 1 1 1 1 1 1 exp[ ( )] exp[ ( )] E E k r H H k r i t i t
ω
ω
= ⋅ − = ⋅ − (Incidence-Wave) (3.1.1) 1 1 1 1 1 1 1 1 exp[ ( )] exp[ ( )] E E k r H H k r i t i tω
ω
′ = ′ ′⋅ − ′ ′ = ′ ′⋅ − ′ (Reflection-Wave) (3.1.2) 2 2 2 2 2 2 2 2 exp[ ( )] exp[ ( )] E E k r H H k r i t i tω
ω
= ⋅ − = ⋅ − (Refraction-Wave), (3.1.3) and ki =( , , )k k kix iy iz ,i=1,2;r =( , , )x y z ;ω ω
1, ,1′ andω
2 are the incidentlight frequency, reflective light frequency, and refractive light frequency respectively. Then researching for k , and due to the continuum of the 2 z
boundary condition in the interface, k can be represented as follows: 2 z
2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 ( ) z x x x n k k k k k k k n = − = − = − , (3.1.4)
and by introducing the geometry relation k can be rewritten as follows: 2 z
2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 ( ) sin ( ) sin z n n k k k k n θ n θ = − ⋅ = − . (3.1.5)
Then, there are some key points to be discussed: if n2 > then n1 k2 z∈ R
if n2 < then n1 k may be I2 z ∈
By the Snell’s Law, we can find the critical angle condition:
2 1
sin c
n
n =
θ
(3.1.6)Then k2 z can be rewritten as follows in critical angle condition:
2 2 2z 1 (sin )c sin 1 k =k θ − θ (3.1.7) So, if i1> then ic k2 z∈ . I Let 2 2 2z 1 (sin )c sin 1
k =k θ − θ =iκ lead back to (3.1.3) and become
| | 2 2 2 | | 2 2 2 exp[ ( )] exp[ ( )] z x z x e i xk t e i xk t κ κ
ω
ω
− − = − = − E E H H (3.1.8)Now, it can clear to see that the magnitude of the refraction wave will decay exponentially with the distance far from the interface, and it is called “Evanescent Wave”.
3.2 Surface Plasmon Resonance [Raether, H., 1988]
In 1962, Ferrell and Stern predicted “Surface Plasmon Wave” could be excited by plane wave, and it exists a resonance condition [Raether, H., 1988]: 1 2 0 1 2 sp k k
ε ε
ε ε
= + . (3.2.1)“Resonance” means that if the incidence light satisfies some conditions, the total energy will couple into the plasmon on the metal interface, and the evidence can be derived as follows:
First, for p-wave, the mathematic model of incidence wave and refraction wave (like Figure3.2) can be described by the electromagnetic wave of Maxwell’ theory as (3.2.2), (3.2.3) [Raether, H., 1988].
For z > 0: 1 = 01exp (i k x k zx1 + z1 −
ω
t) (0,= Hy1,0)exp (i k x k zx1 + z1 −ω
t) H H 1= 01exp (i k x k zx1 + z1 −ω
t) (= Ex1,0,Ez1)exp (i k x k zx1 + z1 −ω
t) E E (3.2.2) For z < 0: 2 = 02exp (i k x k zx2 + z2 −ω
t) (0,= Hy2,0)exp (i k x k zx2 + z2 −ω
t) H H2 = 02exp (i k x k zx2 + z2 −
ω
t) (= Ex2,0,Ez2)exp (i k x k zx2 + z2 −ω
t)E E
(3.2.3)
By fulfilling Maxwell’s equation, for free space and two infinite plane: 1 i i i E H c t
ε
∂ ∇ × = ∂ K (3.2.4) 1 i i H E c t ∂ ∇ × = − ∂ K (3.2.5) 0 iEiε
∇ ⋅ K = (3.2.6) 0 i H ∇ ⋅ K = (3.2.7)and the continuum relation on the boundary:
1 2 x x E = E 、Hy1 = Hy2、
ε
1Ez1 =ε
2Ez2 (3.2.8) 1 2 x x x k = k =k . (3.2.9) It can get: 1 2 0 1 2 0 z z k k Dε
ε
= + = (3.2.10) 2 2 ( )2 x zi i k k cω
ε
+ = (3.2.11)Then by (3.2.10) and (3.2.11), it can derive out:
1 2 0 1 2 x k k
ε ε
ε ε
= + (3.2.11)Because
ε
2 =ε
2′ +iε
2′′, (3.2.11) can be rewritten as (3.2.12).x x x
; 1/ 2 2 1 2 1 3/ 2 2 1 2 2 2 1 2 ( ) ( ) 2( ) x x k c k c
ω ε ε
ε
ε
ω ε ε
ε
ε
ε
ε
′ ′ = ′ + ′ ′′ ′′ = ′ ′ + (3.2.13)Then now, we only care for the real part because the imaginary part just means a damping term or internal absorption. So, k′ describes the x
phenomenon (wave vector) of the surface plasmon wave (SPW) in the x-direction. Therefore, the resonance condition of SPW can be written as:
2 1 2 1 x k c
ω
ε ε
ε
ε
′ ′ = ′ + (3.2.14) Generally, let 2 2ε
= (3.2.15)ε
′ 2 1 2 1 x x k k cω
ε ε
ε
ε
′ ′ = = ′ + (3.2.16) Define 1 2 1 2 x k cω
ε ε
ε ε
= + (ε ε
、1 2∈R) (3.2.17)Equation (3.2.17) is called the resonance condition of surface plasmon wave. Comparing Equation (3.2.11) and (3.2.17), if special case
ε
2 < , 0ε
1 > , and 02 1
|
ε
|> is chosen (EX: air-metal interface), the inequationε
kx cω
> and complex wave number kzi∈ can be obtained. Complex wave number in I
the z-direction means nonradiative surface plasmon wave, and the energy will decay exponentially with the distance far from the interface. However, if the s-wave is proved by the same way, the result of SPR cannot be obtained. In other words, the surface plasmon wave only can be excited by p-wave. Besides, the surface plasmon wave cannot be excited directly by the lightwave from the analysis of [Raether, H., 1988]. In Figure3.3, the dispersion relation for the lightwave in air and for the metal are shown, and these two cures have no intersection. It means that the lightwave cannot excite the surface plasmon wave directly. In order to overcome this problem, the couplers have been brought forward. At present, primary three coupling structures that have been used to enhance the momentum of the lightwave are the prism coupler, (like Kretschmann-Structure and Otto-Structure), grating coupler, and waveguide coupler that can be shown in Figure 1.2. If the coupler is used and the dispersion relation for the lightwave and the metal has the intersection, it can be shown in Figure 3.4. In other words, the surface plasmon wave may have the chance to be excited by the coupling light wave, and another way to express this phenomenon is that the surface plasmon wave can be exited by the evanescent wave from the prism coupler.
3.3 Three Layers Optical Waveguide
In this section, the three layers optical waveguide theory is used to analyze and simulate the electric field of surface plasmon wave. Besides, there are two main measuring methods will be discussed. One is the resonance trough shift due to the overlayer index. Another is the phase difference that is between the
P-wave and S-wave shift due to the overlayer index. In Figure 3.5, the Kretschmann three layers optical waveguide structure is shown. By the Fresnel’s Formula, we can analyze what parameters may affect the performance of SPR (surface plasmon resonance), and the Fresnel’s Formula are as follows:[ Yu et al.,2001]
12 13 12 13 exp(2 ) , , 1 exp(2 ) q q iz q q q iz r r ik d r q p s r r ik d + = = + ; (3.2.1) / , q q i j q i iz ij q q i iz i j Z Z k q p r Z k q s Z Z
ε
− = = = = + , (3.2.2) 2 1/ 2 0( 0sin ) iz i k =kε ε
−θ
(3.2.3) 0 k cω
= (3.2.4) Plot ( )Rpθ
and ( )Rsθ
in Figure 3.6 by MATLAB for the incident light isHe-Ne laser 633 nm, the overlayer index n is 1, the Au coating is 46 nm 3
and where Rp( )
θ
, ( )Rsθ
are defined as | 2 | pr , | 2 | s
r . From the theoretic curve, it can know that only the P-wave can excite the surface plasmon resonance. By the above Formula we can understand that the parameters: metal film thickness(d)、the frequency of the incidence light(
ω
)、the incidence angle(θ
)、and the permittivity (ε1、ε2、ε3) will affect the reflection coefficient(Rp). However, the frequencyω
has been decided by using He-Ne laser (the wave length is 633 nm), and the material of prism in this experiment is BK7 (its refractive index can be known at the Table 3.1 [Lambda]), and for the He-Ne laser 633 nm the permittivity of the Au film is2 11.6798 1.1722i
ε
= − + . Now, if we take the air as the measured sample, the reflection coefficient (Rp) will only depend on the parameters θ and d. Therefore, if we can find the appropriate parameters θ and d, we can get the maximum sensitivity of the measurement system, and the most appropriate parameters θ and d can be found by using MATLAB to calculate and the result is shown in Figure 3.7. By the Figure 3.7 and Figure 3.8 we can known that when d=45~54(nm), system has the maximum resonance trough at0
43
θ
= . In other words, it has the maximum sensitivity atθ
=430, and withthis method we can find the optimization coating thickness on the Kretschmann-Structure. In Figure 3.9, when the overlayer index n changes, 3
the resonance trough will shift. Therefore, the overlayer index change can be detected by measuring the resonance trough shift.
However, it knows that the reflection coefficient r , p r can be defined s
as (3.2.5) | | i p p p r = r eϕ , | | i s s s r = r eϕ , (3.2.5) and then | | | | p s i p p s s r r e r r ϕ ϕ− = . (3.2.6)
From equation (3.21)~(3.24), it can get (3.2.7) ( , ) p s r r n r =
θ
, (3.2.7)and if the overlayer refractive index change, equation (3.2.6) can be written as (3.2.8) 0 0 0 ( ) ( ) | | | | | | | | p p s s i p p i i s s r r e e e r r ϕ +∆ϕ −ϕ +∆ϕ = ϕ ∆ϕ; 0 p0 s0
ϕ
=ϕ
−ϕ
, ∆ = ∆ − ∆ (3.2.8)φ
φ
pφ
s Comparing equation (3.2.7) and (3.2.8), the phase shift ∆ between theφ
P-wave and S-wave is the function of the incident angle
θ
and overlayer refractive index n : 3( )∆ = ∆
ϕ
ϕ θ
、∆ = ∆ϕ
ϕ
( )n3 , (3.2.9) In Figure 3.10, the theoretic curve, ∆ = ∆ϕ
ϕ
( )n3 , of phase shift versusoverlayer refractive index change with fixed-incidence angle that is near the resonance angle of water is shown.
In the Appendix A, the simple four layers optical waveguide theory is used to simulate and analyze the electric field distribution of surface plasmon wave. This is because the zero cladding thickness cannot be arrived due to the asymmetric optical waveguide theory, and the four layers optical waveguide equivalent is necessarily discussed. However, it can be predicted that thicker residual cladding thickness can decrease the sensitivity of D-shaped optical fiber SPR sensor.
1
θ
x z 1θ
′ 2θ
Figure 3.1 Incidence wave, reflective wave, and refractive wave
x
z
2ε
1ε
E
Figure 3.3 The dispersion relation for P-wave incidence wave in air and in metal. [Raether, 1988]
Figure 3.4 The dispersion relation for P-wave incidence wave in air, coupler, and in metal. [Raether, 1988]
θ
1n
2n
3n
Figure. 3.5 The Kretschmann-Structure is used to as the coupler to generate evanescent wave to excite the SPR
Figure 3.6 Theoretic curve of the reflection coefficient versus various incidence angles
θ
with P-wave and S-waveFigure 3.7 Theoretic curve of the reflection coefficient versus various incidence angles θ with various Au coating thickness d
Figure 3.8 Theoretic curve of the reflection coefficient versus various incidence angles θ with optimum Au coating thickness d
Figure 3.9 Theoretic curve of the resonance trough shift with various overlayer indexes
Figure 3.10 Theoretic curve of phase shift versus overlayer refractive index change with fixed-incidence angle that is near the resonance angle 71.5 deg.
Table 3.1 The refractive index of the BK7 prism with various wavelength [Lambda] Index Wavelength 1.51947 532nm 1.51509 633nm 1.51118 780nm 1.5107 800nm 1.50663 1064nm 1.50065 1550nm
Chapter 4 Optical-Type Surface Plasmon Resonance Sensor
4.1 Preface
In order to study the effect of the coating on D-shaped optical fiber, we first research the Kretschmann-Structure (coating on the prism) as the Figure3.5. At present, there are primary two kinds of prism-type coupler that are Kretschmann-Structure and Otto-Structure to excite the surface plasmon wave. In this chapter, the Kretschmann-Structure is used to excite the surface plasmon wave, and it can be shown in Figure.3.5 also. The reason why the Kretschmann-Structure be used is because it is easier and more practicable than the Otto-Structure to used, and the theory has been analyzed in section 3.3, and the measurement methods of SPR sensor and parameters comparison are discussed in the section 4.4 and 4.5. Finally, the experiment result and error will be discussed in section 4.6 and 4.7.
4.2 Heterodyne Interferometry and Lightwave Modulation
Just as its name implies, it means that it needs the external machine-made to modulate the frequency or phase in order to form the difference of frequency between two light wave, and the purpose of the forming frequency difference is in order to interfere. Of course, the purpose of interference for light wave is easier to be detected. So now, what the most important key technologies are modulation of light wave and the methods of heterodyne interferometry. In the rough, there are two type methods to
modulate light wave. One is mechanical type and another is electrical type. The main ideal of the mechanical type modulation is Doppler frequency shifting like PZT (piezoactuated miniature translation stage), the moving diffraction gratings method, and the circumvolving wave plate method. Besides, the main ideal of the electrical type modulation is crystal modulation, like Zeeman Laser, Photoelastic Modulator, Acousto-Optic Modulator, and Electro-Optic Modulator.
4.3 Common-Path Heterodyne Interferometry
It knows that the frequency of light wave is too fast to be detected for electric instrument, so the interference plays a crucial role in optical measurement. However, best one of the methods to measure the phase difference between p-wave and s-wave is “Common-Path Heterodyne Interferometry ”. The common-path heterodyne interferometry has an important characteristic that is p-wave and s-wave go through the same path completely, so they get the same effect from the environment completely. Finally, when doing interference, the completely the same effect from the environment will be canceled. In other words, the common-path Heterodyne Interferometry can avoid the effect from the environment like temperature, vibration, humidity, pressure …etc. However, there are two parameters can be discussed in the common-path heterodyne Interferometry. One is the amplitude change, and another is the phase difference. Besides, how to make a heterodyne lightwave is developed. At present, the Zeeman laser and EO modulator are generally used to generate a heterodyne lightwave, and the
demodulation technology is also much studied. If the sawtooth voltage waveform from the function generator is used to modulate the lightwave by EO modulator, and the amplitude of the sawtooth voltage waveform is large than the half-wave voltage, the output lightwave can retain the sine waveform, and it is much easy to be demodulation with lock-in amplifier. Therefore, this modulation technology will be used in the follow experimental configuration.
4.4 The Measurement Methods of SPR Sensor
Generally speaking, there are five kinds of measurement methods for SPR sensors. They are the detecting of the resonance angle shifting due to the refractive index changing (
θ
SP), the detecting of the phase difference between p-wave and s-wave due to the refractive index changing and for fixing incidence angle (∆ ), the detecting of the intensity changing due to theϕ
refractive index changing and for fixing incidence angle ( Rp−min ), the detecting of the resonance wavelength shift due to the refractive index changing (∆ ), and the detecting of the phase difference between p-waveω
and s-wave due to the incidence angle changing. The theoretical sensitivity and resolution of the first three kinds of measurement methods are as Table. 4.1. The theories are calculated in the condition of prism-based system (BK7), gold 46 nm, He-Ne laser 633nm, and analyzing the dielectric constant from 1.8 to 1.9. However, it can be checked with Table 4.2 catching from reference [Homola et al., 1999], and the theoretical sensitivity and resolution ofθ
SP are the same asθ
SP in Table 4.2, excepting for Rp−min. Besides, thetheoretical resolution of ∆ agrees with the value in reference [Shen et al.,
ϕ
1999]. Comparingθ
SP and ∆ , it can know that the theoretical resolutionϕ
of ∆ is about 2 times greater thanϕ
θ
SP. So, the method of the detecting of the phase difference between p-wave and s-wave due to the refractive index changing and for fixing incidence angle exist a excellent potential to measure. Though the instrument resolution of the phase detecting (≈10−2deg) is stillnot enough for comparing with the resolution of the angle detecting (≈10−4deg), the former one is effective and has better potential for accuracy
measurement.
4.5 Parameters Comparison
At present, the method of detecting the resonance angle shift due to the refractive index changing has been the commercial production, and the high resolution has arrived 5 10× −7 (RIU). In Table 4.1, three kinds of
measurement methods are compared. However, although the sensitivity of the resonance angle shift is only 200 (deg/RIU), the resolution of the rotation machine and intensity detection to detect the angle shift is high to about
4
1 10× − (deg). For the method of detecting the intensity various near the resonance angle, the sensitivity is about 1388 (%/RIU) and the resolution is about 1.4 10× −4(RIU). For the third method that is detecting the phase
difference between p-wave and s-wave due to the refractive index changing with fixing incidence angle, a super high sensitivity about 3.8 10× 4(deg/RIU)
is calculated by theory. So, this method is potential to measure the extreme minim change in refractive index. However, the general resolution of the phase detection is only about 1 10× −2(deg), and this is the limit that leads to
system resolution 2.6 10× −7(RIU) about the same as the first method. Even if
this, this method still possesses high potential to develop the phase measurement in SPR optical fiber sensor.
4.6 Experiment
In this section, the intensity measurement and phase measurement of the surface plasmon resonance are detected by the measurement configuration in Figure 4.1 and Figure 4.2. In Figure 4.1, the polarizer is used to generate TM wave to excite the surface plasmon wave, the rotator is used to change the incident angle, and finally the output intensity can be detected by the power meter. By using the optical-type SPR intensity measurement configuration, the different resonance trough can be found with different measuring sample when changing the angle of the incident light. In Figure 4.3, the theoretical curves and experimental data are compared, and the phenomenon of the surface plasmon resonance can be ensured. For the air measurement, the experimental data coincides with the theoretical curves. However, for the water measurement, the experimental trough is wider. This may because of not pure water is used. In Figure 4.2, a simple common-path Heterodyne Interferometry is used to measure the phase difference shift between the s-wave and p-wave, and the relative Jones Matrix can be expressed as follows:
(45 ) ( , ) ( , ) (45 ) (90 ) 2 o o o o out in E = A ⋅SPR
ρ ϕ
∆ ⋅Hλ
ϕ
⋅EO ⋅E ; (4.2.10) exp ( ) 0 ( , ) 0 1 i SPRρ ϕ
∆ = ρ
ϕ
+ ∆ϕ
(4.2.11)Where the
ρ ρ ρ
= p / s is defined as the reflective coefficient ratio between p-wave and s-wave, and ∆ the phase difference between p-wave andϕ
s-wave due to the SPR phenomenon. Because the birefringent characteristic of the SPR, the Jones Matrix of the SPR Kretschmann-Structure can be expressed as the equation (4.2.11). (90 )oin
E is the electric field of the input light wave with the angle of the polarization90o, which is He-Ne laser 633nm.
(45 , )o
EO Γ is the electric-optic modulator with the modulation voltage Γ and the angle of the principle axis 45o. ( , )
2
o h
H
λ ϕ
is the half wave plate, and the angle difference of the principle axis between the EO modulator and the SPR prism can be calibrated by changing the angle oh
ϕ
of ( )o h Hϕ
. (45 )oA is the analyzer with its angle of the principle axis 45o. If the EO
modulator is modulated by sawtooth wave whose amplitude is larger than the half-wave voltage, the output intensity can be the same as sin-wave, and the half wave plate can be adjusted to let the principal axis of the EO modulator align the principal axis of the prism. Then the output intensity can be written as (4.2.12), and the parameter o
h
ϕ
from half wave plate will disappear.2 1 2
| | [1 2cos( )] 2
out out
0 0
p s
ϕ ϕ
= −ϕ
. (4.2.13)The phase shift ∆ from p-wave can be detected from the output lightwave,
ϕ
and the initial phase differenceϕ
between the p-wave and s-wave is constant. Besides, the phase shift ∆ is the function of the overlayerϕ
refractive index. Therefore, the change of the overlayer refractive index can be detected by measuring the phase shift ∆ . In Figure 4.4, theϕ
concentration of the alcohol is measured at the resonance angle for n = 1.333, and the theoretical curves and experimental data are compared. The sensitivity of experiment is about 1.3 10 (deg/× 4 RIU), the sensitivity oftheory is about 3.8 10 (deg/× 4 RIU) , and the resolution of the lock-in
amplifier is about 1 10 (deg)× −2 . Finally, the resolution of the experiment is
about 7.7 10 (× −7 RIU), and it is agreed with the theory resolution in Table
4.1.
4.7 Error Analysis
In above section, if the change of the refractive index is small, the linear dependence can be used. However, how small the change of the refractive index is enough will be discussed in the Table 4.3. In the Table 4.3, the error and the sensitivity can be obtained with various measurement range of the dielectric constant. Besides, if the principal axis of the EO modulator misaligns the principal axis of the prism, the measurement error will happen.
In Table 4.4, the relative-mean error relation will be discussed with various incline angles
α
that is the angle difference of principal axis between the EO and SPR.He-Ne Laser Polorizer(0) Z X Y
θ
Power MeterFigure 4.1 Optical-Type SPR Intensity Measurement Configuration
He-Ne Laser Z X Y θ ( , ) 2 o H λ ϕ (45 )o EO (90 )o P (45 )o P Photodetect Lock-In Amplifier
Function Generator DC-Bias
0 0.2 0.4 0.6 0.8 1 30 35 40 45 50 55 60 65 70 75 80 85 The Angle of Incident Light (deg)
Normalized Intensity.
theory-air theory-water exp-air exp-water
Figure 4.3 Experimental optical-type SPR intensity measurements for air and water comparing with theoretic curve
20 40 60 80 1.329 1.3295 1.33 1.3305 1.331 1.3315 1.332 Measurement Refractive
The phase change (deg)
Theory Experiement
Figure 4.4 Experimental optical-type SPR phase measurement with fixed-incidence angle that is near the resonance angle.
Table 4.1 SPR Biosensor Measurement Parameters for prism-based BK7, Au coating 46nm, wavelength 633nm, analyze with the refractive index 1.33.
Measurement
Parameters
θ
SP p minR − ∆
ϕ
Sensitivity 1.9 10× 2(deg/ RIU ) 1388( % / RIU ) 3.8 10× 4(deg/ RIU )
Resolution (RIU ) 5 10× −7 1.4 10× −4 2.6 10× −7 Resolution [Ref.] 5 10× −7 [Homola et al., 1999] 5 5 10× − [Homola et al., 1999] 7 3 10× − [Shen et al., 1999]
*
θ
SP: the resonance anglemin p
R − : the intensity reflectivity at the resonance angle
ϕ
∆ : the phase shift due to the SPR (for dynamic range ∆ <n 3.7 10× −3)
Table 4.2 The Theoretical Sensitivity and Resolution in other paper [Homola et al., 1999]
Table 4.3 Effective Linear Range The Measurement Range of
Dielectric Constant Error Sensitivity
DCU ∆n(RIU) deg/DCU deg/RIU
3 1.8 1.0 10± × − 7.45 10× -4 39.84 % 246.245 3.7858 10× 4 4 1.8 5.0 10± × − 3.73 10× -4 9.78 % 248.360 3.8183 10× 4 4 1.8 1.0 10± × − 1.86 10× -4 4.08 % 249.05 3.8289 10× 4 5 1.8 2.5 10± × − 4.66 10× -5 3.66 % 249.000 3.8281 10× 4 5 1.8 1.0 10± × − 1.86 10× -5 0.09 % 249.500 3.8358 10× 4
* DCU: Unit Dielectric Constant RIU: Unit Refractive Index
Table 4.4 The Relative-Mean Error with various incline angle
α
73.4incidence
θ = , ε =1.8 10± −4, ∆ =ε 10−5
α (deg) Relative-Mean Error
0.00 0.00 %
0.25 5.27 %
0.50 11.31 %
0.75 19.40 %
Chapter 5 Fabrication of the D-Shaped Optical Fiber Surface
Plasmon Resonance Sensor
5.1 Preface
In this chapter, the fabrication process will be described in section 5.1 and 5.2, and the method how to determine the etching depth is discussed also. Finally, the Au metal will be evaporated by E-Beam (electron-beam evaporator). In Figure 5.1, the full fabrication flow of the D-shaped optical fiber SPR sensor is described, and it will be discussed in next section.
5.2 Etching of the D-Shaped Optical Fiber
In order to generate well etching flat, the BOE (Buffered Oxide Etch) is used to etch the D-shaped optical fiber instead of HF (Hydrofluoric Acid). This is because the BOE has lower etching rate. Besides, the BOE etching is only effective for SiO2, and the plastic coating covering on the D-shaped optical fiber cannot be removed. Therefore, the etching length can be determined by controlling the length of the bare fiber, and the etching depth can be determined by controlling the etching time. However, the etching rate is dependent on the temperature and concentration of the BOE. Thus, the etching temperature must be controlled if the accuracy etching depth is required. In this thesis, the D-shaped optical fiber is the commercially available D-shaped optical fiber from KVH. Because of the special geometric structure of D-shaped optical fiber that the distance dcore flat− between the
core and the flat is only 9 µm and the diameter dcladding is about 70 µm , the necessary etch depth is controlled less than 9 µm . For the general signal-mode optical fiber, the etching depth about 50 µm must be obtained to let the evanescent wave throughout. In Figure 5.2, the commercially available D-shaped optical fiber basic structure is shown, and because of the elliptical core, it exist birefringent characteristic. In other word, it is one kind of polarization maintaining optical fiber. Before etching, the plastic coating must be stripped off about 1 cm, and it can be shown in Figure 5.3. and Figure 5.4. By observing these two images, it can be checked that the cladding of the D-shaped optical fiber exists a flat indeed. Then etching it by BOE with proper etching time. In Figure 5.5 and Figure 5.6, the etched D-shaped optical fibers are shown. However, if the plastic coating does not strip well, the boundary will no smooth like Figure 5.5, and if it done well like Figure 5.6, it will be effective for Au metal coating. Before Au metal coating, the flat of the D-shaped optical fiber must be found and fixed. In Figure 5.7 and Figure 5.8, the flat of the D-shaped optical fiber is found by microscope. It is important to let the flat toward upward, because the Au metal must be coated on the flat to be excited surface plasmon resonance. However, it can clear to see that fiber in Figure 5.7 is dirty and with much fouling. Therefore, it is necessary to clean the bare optical by using DI water and nitrogen after etching. In Figure 5.8, the D-shaped optical fiber is much clean than the fiber in Figure 5.7, and then the Au metal can be coated on it. In order to excited surface plasmon resonance, the thickness of the Au metal must be matched. Therefore, Au metal thickness about 40, 30, and 20 nm will be coated on the flat by using
electron-beam evaporator. Because the coating thickness is much thin, the deposition rate is better slower than 0.5 Ao/ sec . Generally specking, the attachment of the Au metal for SiO is not well, and the 2 TiO is usually 2
used to enhance the attachment between the Au and SiO . However, it still 2
may become a sacrifice layer.
5.3 Etching Rate Measurement
For the application of the evanescent wave, the distance between the polishes surface and the core region of the fiber is an important parameter. However, it is difficult to measure experimentally using standard optical and mechanical instruments. At present, three methods are used to obtain an estimate of the cladding thickness. The first one uses a mechanical comparator and requires measuring the thickness of the substrate and comparing it with the substrate thickness fiber without polishing. The second method is to measure the oval polished section of the fiber. However, these two methods yield fairly accurate relative results but fail to provide an absolute value of the remaining cladding thickness. The third method is brought forward by [Digonnet et al., 1985], and it called liquid-drop method. Shown in Figure 5.10 (a), if the evanescent wave is throughout, the phenomenon can be described in it, and it means that in case (a) the transmission is unchanged for the liquid refractive index up to the index that is the same as the cladding index. When the liquid index large than the cladding index, the guidewave will be strongly coupled out of the fiber. In
case (b), if the etching depth reaches the core region, the transmission will be significant attenuation, and the attenuation will decrease with increase the liquid index until the cladding index is reached.
In this thesis, the portion theory of the third method is used to determine the etching depth, and the measurement principle is using the asymmetric waveguide theory. This is because the experiment in this thesis (Figure 5.9) does not totally accord with the third method. In Figure 5.9, the two phenomenons in Figure 5.10 happen at the same time. For all case, the attenuation will decrease with increase the liquid index until the cladding index is reached. Therefore, the main measurement method is according to the asymmetric waveguide theory. It knows that the modes of symmetric slab waveguides are simpler than those of asymmetric slab because they can be expressed either as even or odd field distributions, and the lowest order mode of a symmetric slab waveguides does not have a cutoff frequency. However, all modes of asymmetric slab waveguides become cutoff if the frequency of operation is sufficiently low [Marcuse, 1974]. Therefore, when the core of the D-shaped optical fiber exposes to the air, the all modes will cutoff. By this phenomenon, the etching depth and etching rate will be obtained. In other word, when the transmission light cutoff, the etching depth 9 µm is arrived. In Table 5.1, the etching depth and rate are measured and calculated. D(I) and D(II) mean different D-shaped optical fiber from various manufacturer. “Obvious” means using the microscope to check the etching depth. In view of this, the etching rate must be calibrated afresh when using different D-shaped
Plastic Coating Stripping Off
Optical Cladding Removing (Etching by BOE)
Cleaning by DI Water and Nitrogen
Transmission Light Testing
The D-Flat Finding by Microscope
The D-Flat Fixing
Au Metal Coating on The D-Flat
D-Shaped Optical Fiber SPR Sensor
70 cladding d ≈ µm 9 core flat d − ≈ µm
cladding
core
Figure 5.2. The commercially available D-shaped optical fiber sketch map.
Figure 5.3. The nonflat of the D-Shaped optical fiber with stripping off its plastic coating
Figure 5.4. The flat of the D-Shaped optical fiber with stripping off its plastic coating
Figure 5.5. D-Shaped optical fiber without well stripping off its plastic coating
Figure 5.6. D-Shaped optical fiber with well stripping off its plastic coating
Figure 5.8. Etched D-shaped optical fiber is cleaned by DI water and Nitrogen. 0 0.2 0.4 0.6 0.8 1 1.2 1 1.1 1.2 1.3 1.4 1.5 1.6
Overlayer Refractive Index
Output Intensity (Voltage)
.
40min 60min 70min
Figure 5.9. The evanescent wave detection by using various overlayer refractive indexes for etching time 40, 60, and 70 minute.
Figure 5.10. The liquid-drop method for (a) the evanescent wave has been throughout the cladding, and (b) the core has been reached. [M. J. F Digonnet
et al., 1985]
![Figure 3.3 The dispersion relation for P-wave incidence wave in air and in metal. [Raether, 1988]](https://thumb-ap.123doks.com/thumbv2/9libinfo/8993283.284083/40.892.230.635.124.457/figure-dispersion-relation-wave-incidence-wave-metal-raether.webp)
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