探討掃描光學顯微術之一些新功能

國立交通大學

電機資訊學院

光電工程研究所

碩士論文

探討掃描光學顯微術之一些新功能

Exploring New Functionalities of Scanning Optical Microscopy

研究生：王雲漢

指導教授：黃中垚 教授

探討掃描光學顯微術之一些新功能

Exploring New Functionalities of Scanning Optical Microscopy

研究生：王雲漢

Student：Yuen-Han Wang

指導教授：黃中垚

Advisors：Professor Jung Y. Huang

國立交通大學電機資訊學院

光電工程研究所

碩士論文

A Thesis Submitted to

Department of Photonics and Institute of Electro-optical Engineering

College of Electrical Engineer and Computer Science

National Chiao Tung University

in Partitial Fulfillment of the Requirements

for the Degree of

Master

in

Electro-optical Engineering

February 2008

Hsinchu, Taiwan, Republic of China

探討掃描光學顯微術之一些新功能

研究生：王雲漢 指導教授：黃中垚 教授

國立交通大學

光電工程研究所

摘要

本論文的第一個部份是呈現出利用單光子鎖模偵測技術來分析表

面穩定鐵電液晶的動態調制，此技術不但可以有效的抑制拉曼光譜的

直流基底，而且會產生有關特定之拉曼最高點的振幅及相位調制。摻

雜氧化鋅奈米微粒會比未摻雜的表面穩定鐵電液晶以比較有組織性

的狀態隨外加調制電場轉動，並且因此對於高頻率轉動所產生的混亂

效應會有較好的抗性。此方法提供傳統的拉曼顯微術新的功用，對於

探討在薄膜中具有電光主動性之空間分佈及動態調制。

在第二部份我們會藉由表面增強拉曼散射的技術來調查由於奈

米柱的高外觀比例所造成的拉曼散射光譜的方位角相依性以及利用

單光子鎖模偵測技術測量 8CB 分子吸附在銀奈米柱陣列上的拉曼圖

像。最後部份我們藉由近場光學顯微術來分析聚焦高斯光束的輪廓並

得到在繞涉極限之下的 100 奈米解析度。

Exploring New Functionalities of Scanning

Optical Microscopy

Student：Yuen-Han Wang Advisors：Professor Jung Y. Huang

Department of Photonics and Institute of Electro-optical Engineering,

National Chiao Tung University

Abstract

This thesis presents the analysis of the modulation dynamics of surface stabilized ferroelectric liquid crystal (SSFLC) cells with a photon counting lock-in detection technology in the first section. This technique not only can effectively suppress the dc background of Raman spectrum, but also yields useful information about the modulation amplitudes and phases of specific Raman peaks. The SSFLC doped with ZnO nanocrystals was found to be switched with an electric modulation field in a more organized way than the undoped SSFLC and therefore has better resistance to the disordering effect caused by high frequency switching. This method provides conventional Raman spectroscopy with a new functionality for probing the spatial distribution and modulation dynamics of electro-optic active species in a thin film.

In the second section, we investigate the azimuthal dependence of Raman scattering attributed to high aspect ratio of nanorods and the image of phase-sensitive Raman scattering for monolayer 8CB molecule adsorbed on Ag nanorods array substrate by using photon-counting lock-in detection. In last section, we analyze the beam profile of a focused Gaussian beam and the resolution of spot size can be achieved to one hundred nanometers below the diffraction limit by using Scanning Near-field Optical Microscopy (SNOM) technology.

誌謝

在碩士研究過程中，首先非常感謝我的指導教授 黃中垚教授給

予耐心與嚴謹的指導，雖然做此研究遇到些許問題而無法如期完成，

但是在此段時間，也從教授的指導中學到更多解決問題的方法及研究

的態度。

接著非常感謝我的家人，能夠讓我無後顧之憂的做研究，當我遇

到困難時，給予我精神上的支持和自由而無所侷限，讓我有完成此研

究之動力。

最後還要感謝實驗室的明彰學長、立志學長以及柳萱學姊的協助

和指導，還有感謝秉寬、建輝、建佑的相處，讓我擁有這段多樣化且

充滿回憶的日子。

CONTENTS

1. Introduction ………1

a. Lock-In Detection ………...2

b. Polarizable Nano Objects and Their Effects on Raman Scattering Process ….. 4

c. Oblique-Angle Deposition Technique ...6

2. Raman Imaging of Surface-Stabilized Ferroelectric Liquid Crystal Film with Photon Counting Lock-In Detection ………..9

2.1. Introduction ………..9

2.2. Theoretical Background ……….10

2.3. Experiment………..12

2.4. Results and Discussion ………..13

2.4.1. SSFLC Cell with Pure Felix 017/100 ...………....…13

2.4.2. Felix 017/100 SSFLC Cell Doped with nc-ZnO………...18

2.4.3. CV Characteristics of Felix 017/100 SSFLC Cells…...………21

2.5. Conclusion………..24

3. Lock-in Detected Raman Microscopy of Liquid Crystal Molecules on Tilted Silver Nanorods……….26

3.1. Introduction……….………26

3.2. Theoretical Analysis of Surface Enhanced Raman Scattering From Adsorbed Molecules on a Layer of Ag Nanorods …...……...……..…………...……...27

3.2.1.Mie-Scattering ………...………...………27

3.2.2. Surface Enhanced Raman Scattering From Tilted Ag Nanorod…..…..29

3.3. Experimental Apparatus of Surface Enhanced Raman Spectroscopy……...32

3.4. Results and Discussion………....33

3.5. Conclusion……….…..42

3. Probing the Profile of a Focused Gaussian Beam with Scanning Near-Field Optical Microscopy (SNOM)………43

4.1. Introduction……….43

4.2. Theory of Heterodyne SNOM……...………..44

4.3. Experimental Apparatus of SNOM……….46

4.4. The Experimental Results by Using SNOM Technology and Conclusion….48 5. Conclusions and Future Prospect of This Thesis Study…….………....54

List of Table

4-1 The corresponding spot size for different position of the objective lens in z

LIST of FIGURES

1.1: Schematic of lock-in detection algorithm. By combining the output X and Y, we

can extract the magnitude and the phase of interesting signal relative to that of the reference signal used………...4

1.2: The optical extinction of ellipsoidal gold nanoparticles, calculated by using the

quasi-static approximation, with short radius β=5 nm and long radius α varying from 5 nm to 45 nm, corresponding to aspect ratios η=1-9 as indicated, is presented. The inset shows the wavelength of the longitudinal plasmon resonance peak as a function of aspect ratio………..5

1.3: (a) The optical extinction of ellipsoidal gold nanoparticle due to longitudinal

plasmon resonance is calculated by using discrete dipole approximation and showed. For all aspect ratios, the smallest cylinders have a short diameter 2β= 5nm and long diameter 2α=15, 25, and 35 nm, corresponding to aspect ratio η=3, 5, and 7 as indicated, while the width is increased in steps of 5 nm. (b) The longitudinal peak as a function of cylinder width are showed for aspect ratios η=3 (square), 5 (triangles), and 7 (diamonds). And the size-dependence of surface plasmon resonance of spherical particles is also showed (circles) as a function of diameter, calculated by using Mie theory………..5

1.4: (a) Top view and (b) the cross-sectional view SEM images of the sliver nanorods

array on a glass slide. The scale bars represent 2 μm. the top view SEM was measured without additional metallic coating. (c) and (d) represent TEM image of individual silver nanorods. Scale bar is (c) 100 nm and (d) 200 nm………...8

2.1: Schematic of SSFLC cell: Z denotes the rubbing direction, which also the layer

normal of the smectic layers of SSFLC. E is the direction of the applied electric field. The polarization angle of the incident polarized light EL is taken as zero when its

polarization direction coincides with the rubbing direction. M on the right diagram denotes the IR dipole, which tilts from the molecular long axis ξ with an angle of β and rotates about the ξ-axis by γ………...10

2.2: (a) DC unmodulated Raman spectrum of a pure SSFLC cell excited at 532 nm. (b)

The amplitude (solid curve) and phase (dashed line) profiles of a lock-in detected Raman spectrum RΨPSD( ,ν Ω)with a modulation frequency Ω=250 Hz measured at the

position p1. (c) The corresponding lock-in detected amplitude (solid curve) after

removing the nonresoant background………...14

2.3: (a) The optical transmittance image of a Felix 017/100 SSFLC cell, and the 2D

distributions of (b) the amplitude, and (c) the phase of the lock-in detected Raman peak at 1609 cm-1 with a modulating frequency Ω=250Hz. Here p1 is the position of measured position 1 and p2 is the position of measured position 2……….16

2.4: The amplitude (filled circles) and phase (open squares) of a phase-resolved

Raman peak (a) at 1118 cm-1 and (b) at 1610 cm-1 at position 1 are presented as a function of modulated frequency Ω in a pure SSFLC cell and the solid curve is the fitting curve………...17

2.5: (a) The optical image of scanned region is taken on a Felix 017/100 SSFLC cell

doped with nc-ZnO by using optical microscopy, and the 2D distributions of (b) the amplitude, and (c) the phase of the lock-in detected Raman peak at 1609 cm-1 with a

modulated frequency Ω=250Hz. Here p1 is the position of measured position 1 and p2 is the position of measured position 2………...19

2.6: (a) DC unmodulated Raman spectrum of a SSFLC cell doped with nc-ZnO

excited at 532 nm. (b) The amplitude (solid curve) and phase (dashed line) profiles of a lock-in detected Raman spectrum RΨPSD( ,ν Ω)with a modulation frequency Ω=250

Hz measured at the position p1. (c) The corresponding lock-in detected amplitude

(solid curve) after removing the nonresoant background……….20

2.7: The amplitude (triangle symbols) and phase (circular symbols) of a

phase-resolved Raman peak at 1609 cm-1 (a) at position1 and (b) at position 2 are presented as a function of modulated frequency Ω in a SSFLC doped with nc-ZnO cell and the solid curve is the fitting curve………..21

2.8: (a) The experimental C-V curves (symbols) and their fitting results (solid lines) of

the SSFLC cells without and with nc-ZnO doping at 1 kHz. (b) The normalized transient electro-optical azimuthal patterns of the pure SSFLC (open squares) and the SSFLC with nc-ZnO doping (filled circles) cells are presented without an electric field………...23

3.1: Schematic of Mie scattering from a substrate coated with tilted Ag nanorods. An

incident polarized optical beam excites the silver nanorods to produce induced dipoles and an optical analyzer located in front of detector is used to analyze the polarization of the scattering signal………..28

3.2: Schematic of surface enhanced Raman scattering from a substrate coated with

3.3: The apparatus used for acquiring polarization-modulating Raman spectrum is

shown. The polarization direction of the incident light is controlled with a Pockel cell excited with a sinusoidal wave of half-wave voltage amplitude………..32

3.4: The Raman spectrum of a monolayer of 8CB molecules on an Ag

nanordos-coated substrate (red solid line) is presented and the black solid line represents the Raman spectrum of bare substrate coated with tilted Ag nanorods without 8CB molecules……….34

3.5: The azimuthal pattern of the Mie scattering intensity from Ag nanorods coated

substrate was measured and shown in filled triangles and the fitting curve to Eq. (3.5) (red solid line) is also included for comparison. (a) The incident excitation beam is

s-polarized while the Mie scattering signal is p-polarized. (b) Both of the incident

excitation beam and the Mie scattering signal are p-polarized……….35

3.6: The azimuthal pattern of SERS signal for 8CB molecules adsorbed on a tilted Ag

nanorods-coated substrate (triangle) and the fitting curve (red solid line) to Eq. (3.10) and (3.12) are presented. (a) The polarization of incident light used is s-polarized and the SERS is p-polarized. (b) Both of the incident light and SERS are p-polarized…..36

3.7: (a) The DC component, (b) the amplitude and (c) the phase image of the

modulated SERS signal at 1609 cm-1 was acquired by using a photon-counting lock-in detection scheme. The incident light was polarization modulated at a frequency Ω=1 kHz………37

3.8: The images of p-polarized SERS peak at 1603 cm-1 of 8CB molecules adsorbed

on a Ag nanorods-coated substrate. The sample was excited with (a) s-polarized and (b)

p-polarized light. The scan area is 1.2×1.2 mm2………...39

3.9: (a) The azimuthal distribution image of the major axis of Ag nanorod projected on

the x-y plane is showed. (b) The histogram of the azimuthal distribution image of (a) is shown in the black solid line and the red dashed curve denotes the fit to a Gaussian distribution function………..39

3.10: The phase map of the modulated SERS intensity at 1609 cm-1 taken from 8CB

monolayer adsorbed on a tilted Ag nanorod-coated substrate. The substrate was oriented to have the tilting plane of Ag nanorods perpendicular to the incident

plane………..40

3.11: The p-polarized SERS image in a region of 1.2×1.2 mm2 of a tilted Ag nanorods-coated substrate. The incident plane was aligned to 0° azimuthal angle of the tilted Ag nanorods and was excited with (a) s-polarized light, and (b) p-polarized………41

4.1: The schematic of interference between Et and Eb is presented……….44

4.2: schematic of experimental setup for SNOM……….46

4.3: The schematic of experimental setup for heterodyne SNOM………...47

4.4: The distribution of optical intensity on a cover glass is collected by the fiber tip. When the focus plane of the SLED at wavelength 1.3 μm focused by the objective lens (0.55/50X) is on a cover glass, the results of twice continuous measurements is showed respectively at (a) and (b) in SNOM experiment……….49

4.5: When the focus plane of the SLED at wavelength 1.3 μm focused by the objective lens (0.55/50X) is at approximately 15 μm (a) below or (b) above the cover glass, the distribution of optical intensity collected by the fiber tip on the cover glass is presented respectively………...50

4.6 (a) Schematic for spot sizes of beam profile focused by the objective lens along z direction at different z position. (b) and (c) present the view of x direction and y direction of (a), respectively……….52

Chapter 1

Introduction

Due to the minimum invasiveness to sample and the most intuitive image to our brain, optical microscopy (OM) had been developed into a convenient and useful tool for biology, chemistry and material science. Several optical processes had been used to form the optical image and reveal a variety of material properties. That enriches OM with many useful flavors, such as fluorescence microscopy, second-harmonic generation microscopy, third-harmonic generation microscopy and stimulated Raman Scattering microscopy. Although highly successful developments are abundant in OM, serious limitations on optical microscopy remain to be conquered. Abbe-Rayleigh criterion is one such limitation, which prevents two point sources with a lateral separation smaller than λ from being resolved by any OM due to the intrinsic wavy 2 nature of optical field. Unfortunately, a typical biomolecule has a dimension about 2 nm, which is two orders of magnitude below the Abbe-Rayleigh criterion on OM at visible light spectrum. There is high demand for OM with resolution surpassing the Abbe-Rayleigh criterion. Researchers around the world are making effort to achieve this goal by developing a variety of novel concepts.

In accompany with the development of super-resolution OM, developing new functionality for OM with an extremely weak signal has attracted significant research interest since its potential application in single molecular detection. In this thesis, we explore the possibility to enhance the functionality of OM.

In chapter 2, photon counting lock-in detected Raman imaging technique was employed to effectively suppress the nonresonant background of Raman spectrum and

information about the modulation amplitude and phase of specific Raman peak was yielded. The phase-sensitive detection of Raman signal reveals that the field-induced reorientation of nc-ZnO doped ferroelectric liquid crystal (FLC) film is more organized and therefore less sensitive to a high-frequency driving field.

In chapter 3, the photon-counting lock-in detection scheme was used to measure surface-enhanced Raman scattering (SERS) intensity of adsorbed molecules. The technique provides unique capability to deduce the orientation of tilted Ag nanorods, which shows the azimuthal distribution of the major axis of Ag nanorod projected on the x-y plane. Theoretical model of surface-enhanced Raman scattering (SERS) from a monolayer of molecules adsorbed on tilted silver nanorods was developed. The model allows us to deduce the polarizability tensor of a silver nanorod.

The key to a successful development of functional photonic devices lies in the fabrication and characterization. Valuable diagnostic tools not only improve our knowledge of photonic devices but also help to establish the design rules. Therefore, in this thesis study, we also developed a heterodyne interferometric scanning near field optical microscopy to reveal the full-field characteristics of photonic devices at the sub-wavelength region. In chapter 4, we described the preliminary results along this target.

In the rest part of this chapter, we review some technical background of the techniques to facilitate the description of this thesis.

a) Lock-in Detection

Lock-in detection is useful for the recovery of a weak signal embedded in a strong background. By using the lock-in detection scheme, we can obtain relationship between an excitation optical field and the emitted optical signal to characterize various molecules or materials. It yields important frequency-domain information about the response of the molecule perturbed by an external force.

Lock-in detection is a phase-sensitive detection (PSD) and can extract signal characteristics relative to a reference. Assuming the reference signal Sref is a

sinusoidal waveform with frequency ωref and phase ψref and the signal Sref with

frequency ωsig and phase ψsig

cos( )

ref ref ref ref

S =A ω t+ϕ (1.1)

cos( )

sig sig sig sig

S = A ω t+ϕ . (1.2)

By multiplying Eq.(1.2) with Eq.(1.1), we obtain

cos( ) cos( ) 1 cos[( ) ( )] 2 1 cos[( ) ( )] 2

ref sig ref ref sig sig

ref sig ref sig ref sig

ref sig ref sig ref sig

X A A t A A t A A t ω ϕ ω ϕ ω ω ϕ ϕ ω ω ϕ ϕ = + + = + + + − + + − . (1.3)

The signal detected with PSD is the two AC components, one at the difference frequency (ωref-ωsig) and the other at the sum frequency (ωref+ωsig). If ωref=ωsig and

reject the high frequency component with a suited band-pass filter, the output signal with difference frequency left

1

cos( ) ~ cos

2 ref sig ref sig s

X = A A ϕ −ϕ A θ . (1.4)

If the reference signal is shifted by 90°, i.e. Arefcos[(ωreft+ψref +90°)], the output will

become

1

sin( ) ~ sin

2 ref sig ref sig s

Y = A A ϕ −ϕ A θ . (1.5)

The above signal processing algorithm can be implemented schematically in Fig. 1.1. By computing the magnitude of the signal vector, the phase dependency is removed. And the amplitude of the signal and the phase difference between reference and interesting signal can be obtained

2 2

( ) _s

_{tan ( / )}1 Y X

θ ₌ −

Fig. 1.1: Schematic of lock-in detection algorithm. By combining the output X and Y,

we can extract the magnitude and the phase of interesting signal relative to that of the reference signal used.

b) Polarizable Nano Objects and Their Effects on Raman Scattering Process

Surface-enhanced Raman spectroscopy is a useful analytical tool for the detection of trace amount of molecules with capabilities of real-time monitoring and molecular specificity [1, 2]. The technique requires minimal sample preparation and is not destructive to sample. The enhancement effect of SERS arises from a substrate with rough metallic structure, such as nanoparticles, nanorods, nanoprisms, core-shell nano-structures, metallic nanohole or particle arrays [3, 4]. The morphology of the metallic structure plays an important role in determining the magnitude of signal enhancement.

Noble metallic nanoparticles, such as gold and silver, exhibit fairly strong surface plasmon resonance in the visible light range. The wavelength at which the surface plasmon resonance occurs is approximately constant for single isolated nanoparticle with size in the low nanometer range [5]. The interaction among nanoparticle arrays can be tunable [6, 7]. Adjusting the geometry or size of

nanoparticle enables tenability of the wavelength of optical resonance from visible to the near-infrared, which is presented in Fig. 1.2 and Fig. 1.3 [8].

Fig. 1.2: The optical extinction of ellipsoidal gold nanoparticles, calculated by using

the quasi-static approximation, with short radius β=5 nm and long radius α varying from 5 nm to 45 nm, corresponding to aspect ratios η=1-9 as indicated, is presented. The inset shows the wavelength of the longitudinal plasmon resonance peak as a function of aspect ratio. [Ref. [8]：E. Stefan Kooij and Bene Poelsema, Phys. Chem. Chem. Phys., 8, 3349 (2006)]

Fig. 1.3: (a) The optical extinction of ellipsoidal gold nanoparticle due to longitudinal

plasmon resonance is calculated by using discrete dipole approximation and showed. For all aspect ratios, the smallest cylinders have a short diameter 2β= 5nm and long diameter 2α=15, 25, and 35 nm, corresponding to aspect ratio η=3, 5, and 7 as indicated, while the width is increased in steps of 5 nm. (b) The longitudinal peak as a function of cylinder width are showed for aspect ratios η=3 (square), 5 (triangles), and 7 (diamonds). And the size-dependence of surface plasmon resonance of spherical particles is also showed (circles) as a function of diameter, calculated by using Mie theory. [Ref. [8]：E. Stefan Kooij and Bene Poelsema, Phys. Chem. Chem. Phys., 8, 3349 (2006)]

We can find that the wavelength of longitudinal plasmon resonant peak moves to long wavelength, i.e., red-shift, when either the aspect ratio or size of ellipsoidal nanoparticle with low nanometers is increased. Besides, the extinction efficiency broadens with increasing ratio or size of ellipsoidal nanoparticle.

Early surface enhanced Raman scattering substrate included a random distribution of roughness produced by oxidation-reduction process on an evaporated thin metal film on a flat substrate [9]. The enhancement contributed from rough metallic structure is weak due to random distribution of roughness. Thus, many researches reported fabricating various nanostructures, such as rough metallic surface by chemical etching [10], silver nanoparticle array fabricated by lithography [11], and electro-deposition of silver on silver films at high potential [12], to improve SERS effect. However, those methods are either expensive, time consuming or irreproducible in preparing the desired surface morphology.

c). Oblique-Angle Deposition Technique

Oblique angle deposition (OAD) was proposed to fabricate metallic nanorods with the advantages of cheapness and time saving.

The oblique incidence of vapor atoms during evaporation can greatly alter the film properties was discovered simultaneously by Knorr, Hoffmann and Smith. The orientation and magnitude of the anisotropy in the resulting morphology of thin film depend on the deposition geometry used. When the angle between the incident direction of vapor atoms and the substrate normal is 45°, a shadowing effect becomes very effective to produce the anisotropy. In addition to the shadowing effect, surface diffusion was also found to be non-negligible [14].

model the morphology of columnar inclination, bundling and cross-sectional shape. For the inclination of columns, four mechanisms had been proposed to interpret the formation of tilted column from the oblique vapor incidence: (1) adaptation of the continuum model for finite atomic size, (2) shadowing, (3) conservation of parallel momentum, and (4) angle-dependent growth. Self-shadowing by surface rough or dust particle was found to play an important role for the effect of bundling. Behind nuclei or dust particle, there is empty area which can not be filled by incident vapor atoms. For cross-sectional shape, the conservation of parallel momentum is important in determining the shape of nuclei. Furthermore, by combining the conservation of momentum and relative oxygen concentration, the ratio between the number of oxygen and vapor atoms can vary along the nucleus contour, causes elongation of nuclei. To model the film texture, the main axes of crystal can change its direction by varying the incident angle of vapor atoms or other deposition parameters. At normal vapor incidence, there is only one planar reference, which is the plane of substrate. But at oblique incidence, the incident plane provides additional reference plane. As a result, textures with three degrees of freedom can be formed in oblique evaporation. Surface diffusion can play an important role in forming the texture. If surface diffusion is decreased significantly, the growth of crystal planes becomes highly dependent on the local incident angle of vapor atoms. There are several advantages for fabricating a layer of nanorods with oblique angle deposition: the controllable column angle, separation between bundling, size and shape of column and characteristic texture, etc. As a result, more and more researchers choose OAD to fabricate metallic nanostructured substrate.

Fig. 1.4 shows the top view and cross-sectional SEM image of a layer of silver nanorods [13]. We can see from the SEM images that the nanorods are not perfectly cylindrical with a variety of irregular shapes of corrugations, needles, and forks of

nanorods.

Fig. 1.4: (a) Top view and (b) the cross-sectional view SEM images of the sliver

nanorods array on a glass slide. The scale bars represent 2 μm. the top view SEM was measured without additional metallic coating. (c) and (d) represent TEM image of individual silver nanorods. Scale bar is (c) 100 nm and (d) 200 nm. [Ref. [13]：Y.-P. Zhao, Stephen B. Chaney,Saratchandra Shanmukh, and Richard A. Dluhy, J. Phys. Chem. B, 110, 3153 (2006)]

Chapter 2

Raman Imaging of Surface-Stabilized

Ferroelectric Liquid Crystal Film with Photon

Counting Lock-in Detection

2.1 Introduction

Raman scattering is an inelastic scattering of a photon which creates (or annihilates) an optical phonon. When a photon bounces off a molecule, the inelastic scattered photon is less energetic and the associated light exhibits a frequency shift. The various frequency shifts associated with different molecular vibrations give rise to a spectrum, which is characteristic of a specific compound. Therefore, Raman spectroscopy has been widely used as a molecular fingerprinting probe to identify molecular species and structures of a complex material. Unfortunately, normal Raman signal not only is extremely weak with a signal at the single-photon counting level, but also is often overwhelmed with elastic scattered photons or fluorescent photons. Although lock-in detection is highly successful in recovering a weak electrical ac signal from large noise background, this phase-sensitive detection (PSD) scheme can not be directly applied to the detection of optical signal at photon counting level. Recently, a computer-based scheme had been developed to yield lock-in detection functionality with a conventional photon counting hardware for the detection of an extremely weak optical signal [15].In this study, we combine the photon counting lock-in technique with Raman microscopy to probe the field-induced reorientation of an electro-optical switching surface stabilized ferroelectric liquid crystal (SSFLC) cell.

The ferroelectric liquid crystals FLCs have significant advantages for display applications compared to the widely used nematic liquid crystals such as the fast response time, wide viewing angle, and bistability of the two stable molecular orientations in the SSFLC molecular structures. [16, 17]We show that this Raman imaging scheme can successfully yield interesting information about the electro-optic active species that are closely related to the applications of SSFLC. Theoretical model of the phase-resolved Raman signal from a molecular normal mode was also formulated to illustrate the underlying principle.

2.2 Theoretical Background

The schematic of a SSFLC cell in a Raman scattering setup is depicted in Figure 2.1. Here Z denotes the rubbing direction, which is also the layer normal of the smectic layers of SSFLC. E is the applied electric field. The polarization angle of the polarized incident light EL is taken as zero when its polarization direction coincides

with the rubbing direction. M on the right diagram, which tilts from the molecular long axis ξ with an angle of β and rotates about the ξ-axis by γ, denotes the molecular normal mode responsible for the Raman scattering.

layer normal of the smectic layers of SSFLC. E is the direction of the applied electric field. The polarization angle of the incident polarized light EL is taken as zero when

its polarization direction coincides with the rubbing direction. M on the right diagram denotes the IR dipole, which tilts from the molecular long axis ξ with an angle of β and rotates about the ξ-axis by γ.

The number of Raman scattered photons from FLC molecules is proportional to the square of projected Raman polarizability αij. Assuming αij for a normal mode with

β=0 to be a tensor with single dominating component αMM, the Y-polarized Raman

signal (Φ=90°) excited by Y-polarized light is proportional to

4 4

0sin (3 sin ( ) sin[3 ( )])

Y Y

R _→ = R θ φ t + φ t (2.1)

Similarly, the Z-polarized Raman signal (Φ=0°) is proportional to

2 2 2

0sin (2 )sin ( )(2 cos [2 ( )])

Y Z

R _→ = R θ φ t + φ t 2 (2.2)

By driving the SSFLC cell with a sinusoidal electric waveform of frequency Ω, the azimuthal angle φ(t) of FLC molecules on the SmC* cone can be modulated with an applied electric field E(Ω), which results in a modulated Raman signal from the electro-optical switching SSFLC cell.

For a theory of phase-sensitive detection (PSD), the analytical procedure of PSD at a given wavenumber ν typically involves a multiplication of the time-resolved Raman spectrum R(ν, t) with cos[Ωt + ΨPSD] followed by normalized integration over

a period of T: 0 2 ( , ) ( , ) cos( ) PSD T PSD R R t t T φ ν Ω =

∫

Applying Eq. (2.3) to all wavenumber ν of the spectrum leads to a data vector where the time-resolved Raman spectra R(ν, t) and RΨPSD( , )ν Ω of Eq. (2.3) are treated like

modulation frequency Ω and phase setting ΨPSD. For the special cases with ΨPSD =0° and ΨPSD =90°, RΨPSD( ,ν Ω) is equivalent to the in-phase and out-of-phase

components: 0 0 90 0 2 ( , )cos[ ( , )] ( , ) ( , )cos( ) 2 ( , )sin[ ( , )] ( , ) ( , )sin( ) PSD PSD T T R R R t T R R R t T ν ν ν ν ν ν ν ν ° ° Ψ = Ψ = Ω Ω Ω Ω Ω Ω Ω Ω Δ = = Δ = =

∫

∫

Here R( , )ν Ω and Δ(ν ,Ω) are the absolute modulation amplitude of the Raman signal

and the corresponding phase shift. These are the main parameters important for the interpretation of a modulation experiment and can be determined from the measured phase-resolved spectra RΨPSD=0°( , )ν Ω and RΨPSD=90°( , )ν Ω by using

2 2 0 90 90 0 ( , ) ( , ) ( , ) , sin[ ( , )] ( , ) / ( , ) cos[ ( , )] ( , ) / ( , ) PSD PSD PSD PSD R R R R R R R ν ν ν ν ν ν ν ν ν ° ° ° ° Ψ = Ψ = Ψ = Ψ = Ω Ω Ω Ω Ω Ω Ω Ω Ω = + Δ = Δ = with (2.5)

Thus, the purpose of the PSD in modulation spectroscopy is the evaluation of phase-resolved spectra RΨ_PSD( , )ν Ω .

2.3 Experiment

The laser used in our Raman imaging apparatus with photon-counting lock-in detection is a 60 mW CW diode-pumped solid state laser operating at 532 nm. The laser was weakly focused with a lens of 20-cm focal length to yield an elliptical spot 90μm×60μm on the sample at an incident angle of 45°. The SSFLC cell was driven with a sinusoidal electric waveform of frequency Ω. The Raman scattered photons were collected with a lens, and filtered by using a Raman notch filter and a spectrograph. The photons were detected with a cooled photomultiplier tube and processed by a single-photon counting module. The lock-in amplitude and phase were

retrieved from the photon-counting pulses with the lock-in photon counting software developed by Dieter Braun [15].

The surface-stabilized ferroelectric liquid crystal (SSFLC) cells consist of two ITO-glass plates coated with polyimide alignment layers (RN1182 from Nissan Chemical), which had been rubbed undirectionally along the Z-axis as shown in Figure 1. The substrates were separated by 1.5μm-thick spacers to maintain a cell gap closing to the half-wave thickness d_{λ/ 2} =λ/ 2Δ n 1.9μmestimated with

and λ=0.633 μm. Felix 017/100, a FLC mixture from Clariant inc. (Germany), was used in view of its potential device applications [18].

0.17

n

Δ 

The ZnO nanoparticles used had been caped with 3-(trimethoxysilyl) propyl methacrylate (TPM) during the synthesis process of nc-ZnO. The bandgap and the photoluminescence peak of the TPM-caped ZnO nanocrystals were found to be 3.54 eV and 518 nm, indicating the averaged diameter of the nanoparticles to be about 3.2 nm [19]. An appropriate amount of nc-ZnO powder was added into the pure Felix 017/100 to 1.0% by weight. The mixture was homogenized with ultrasonic at 85℃ for 40 min and then cooled down to room temperature in vacuum. The desired FLC material in the isotropic phase was filled into the test cells and then the test cells were cooled slowly to 35℃ to yield a stable SmC* phase.

2.4 Results and Discussion

2.4.1. SSFLC Cell with Pure Felix 017/100

A SSFLC cell with pure Felix 017/100 was investigated first with Raman spectroscopy without applying an electric modulation field. The cell was excited with a Y-polarized 532-nm laser beam. The resulting dc Raman spectrum exhibiting clearly five major Raman peaks is presented in Fig. 2.2 (a). We can attribute these

peaks at 1610 cm-1, 1505 cm-1, and 1326 cm-1 to the C=C stretching modes of benzene ring, the 1446 cm-1 peak to the C=C stretch of pyrimidine ring, and the 1118 cm-1 to the C-O-C motion [20].

900 1200 1500 1800 2100 70000 80000 90000 In ten s ity (ar b. u n it s) Wavenumber(cm-1) (a) 900 1200 1500 1800 2100 0 1500 3000 4500 6000 1610cm-1 1118cm-1 _ampl. phase Wavenumber(cm-1) Amp li tude(arb. un its) (b) 0 90 180 270 360 P h a s e (de gr ee ) 900 1200 1500 1800 2100 0 1200 2400 3600 4800 ampl. phase Wavenumber(cm-1) A m pl itu d e (a rb. u n it s) 1610cm-1 1505cm-1 1446cm-1 1326cm-1 1118cm-1 (c) 0 90 180 270 360 Phase(degree)

Fig. 2.2: (a) DC unmodulated Raman spectrum of a pure SSFLC cell excited at 532

nm. (b) The amplitude (solid curve) and phase (dashed line) profiles of a lock-in detected Raman spectrum RΨPSD( ,ν Ω) with a modulation frequency Ω=250 Hz

measured at the position p1. (c) The corresponding lock-in detected amplitude (solid

curve) after removing the nonresoant background.

When a photon-counting lock-in detection scheme is employed, the amplitude and phase of the Raman scattered light from the SSFLC cell driven by an electric field with a sinusoidal waveform of frequency Ω=250 Hz are presented in Fig. 2.2 (b). The nonresonant background clearly observable in Fig. 2.2 (a) is suppressed effectively by the lock-in detection scheme. The residual nonresonant signal is most likely to originate from the light scattering from the field-induced refractive index variation.

The three Raman peaks at 1326 cm-1, 1446 cm-1, and 1505 cm-1 disappear owing to the comparable amplitudes 180° phase difference with that of the nonresoant background. The phase of the nonresonant signal, which can be determined from the measured values in the nonresonant region, was found to be about 90°. By using the phase angle, we can remove the residual nonresonant background from the spectrum shown in Fig. 2.2 (b). The resulting lock-in detected Raman amplitudes (solid curve) are presented in Fig. 2.2 (c). The 90° phase angle of the nonresonant signal also causes the measured phase of Raman peak to vary from Δ~320° at 1610 cm-1, to 60° at 1505 cm-1, 180° at both 1446 cm-1 and 1326 cm-1, and Δ~120° at 1118 cm-1, depending upon their corresponding peak heights.

An optical transmittance image of the Felix 017/100 SSFLC cell is shown in Fig. 2.3 (a).Two defects can be observed in the scanned area of 1500μm×1500μm. The corresponding 2D distributions of the amplitude and the phase of the modulated Raman peak at 1610 cm-1 with Ω=250Hz are presented in Fig. 2.3 (b) and 2.3 (c). Both the dc Raman peak (not shown) and the modulated Raman signal amplitude at 1610 cm-1 (Fig. 2.3 (b)) are very weak inside the defects, indicating the defects to be voids without FLC molecules. To further verify the functionality of the lock-in detected Raman imaging technique, two sites (labeled by p1 and p2 in Figs. 2.3 (b) and 2.3 (c)) were chosen for further examination. Here the site 1 was chosen to reflect the general characteristics of the SSFLC cell and the site 2, which exhibits an enhanced electro-optic modulation response, was selected to reveal the influences on FLC from the rim of a void defect.

Fig. 2.3: (a) The optical transmittance image of a Felix 017/100 SSFLC cell, and the

2D distributions of (b) the amplitude, and (c) the phase of the lock-in detected Raman peak at 1609 cm-1 with a modulating frequency Ω=250Hz. Here p1 is the position of measured position 1 and p2 is the position of measured position 2.

In the frequency-domain, an SSFLC cell driven by a sinusoidal electric waveform can yield a change of the Raman scattered light and a phase shift between the scattered light and the driving waveform. The relationship between the driving field and the modulated Raman response can be expressed in terms of a transfer function H(Ω) 2 0 0 0 ( , ) ( ) 1 ( ) ( ) [ ] 1 -( ) PSD R E H E L i E R τ ν ν Ψ Ω Ω Ω Ω Ω Δ ₌ Δ ₌ + E Ω Δ _(2.6)

HereE0is an appropriate normalization parameter for the driving field and R0( )ν is

the DC intensity of the Raman peak, ΔE(Ω)denotes the AC amplitude of the driving electric field and ΔRΨPSD( ,ν Ω) the amplitude of phase-resolved Raman peak.

The experimental results of the 1118 cm-1-peak from the position 1 as a function of modulation frequency Ω are presented in Fig. 2.4 (a). The measured phases of the modulated Raman response are shown with open symbols and the measured magnitude shown with filled symbols. Since the transfer function of modulation phase can only be affected by the modulation dynamics, we therefore determine the phase relaxation time from the fit of the measured phase of the Raman response at 1118 cm-1 to Eq. (2.6). The fitting results in a relaxation time of 6.27×10-3 sec. Unlike to the phase relaxation process, the magnitude of the modulated Raman response can be affected by either the modulation dynamics of the FLC molecules or the FLC molecular alignment (see Eqs. (2.1-2.2)). Since the FLC molecules could be aligned to form a lower ordered structure with a high-frequency driving field, a modulus transfer function with shorter relaxation time (and therefore wider 3-dB bandwidth) than that revealed by the phase function shall be revealed. This is exactly what we had observed in Fig. 2.4 (a), where the modulus transfer function of the modulated Raman response can be fitted to a solid curve with τ=1.54×10-3 sec, which is about 4 times shorter than that (dashed curve) with the phase relaxation time τ=6.27×10-3 sec. The reduction factor from the phase relaxation time to the magnitude relaxation time becomes a useful parameter to reflect the disordering effect of the FLC alignment from the high-frequency driving condition.

0 600 1200 1800 2400 3000 0 800 1600 2400 3200 ampl. phase Frequency(Hz) Amplit ude( ar b. unit .) (a) 0 50 100 150 200 250 Pha s e (deg ree) 0 600 1200 1800 2400 3000 800 1600 2400 3200 ampl. phase Frequency(Hz) A m p lit ud e (ar b. un it s ) (b) 240 260 280 300 320 340 Phase (d egr ee )

Raman peak (a) at 1118 cm-1 and (b) at 1610 cm-1 at position 1 are presented as a function of modulated frequency Ω in a pure SSFLC cell and the solid curve is the fitting curve.

The experimental results of the 1610 cm-1-peak from the position 1 as a function of Ω are presented in Fig. 2.4 (b). The relaxation time of the modulated Raman magnitude is deduced to be 6.7×10-4 sec, which is about 8.7 times shorter than the corresponding phase relaxation time 5.8×10-3 sec. A large reduction factor for the 1610 cm-1-peak indicates that the disordering effect at high-frequency driving is more distinctive for the more rigid C=C stretching mode.

The modulus transfer function of the modulated Raman response at 1118 cm-1 at the position 2 yields a relaxation time of 6.05×10-3 sec, which is about 4.9 times shorter than the measured phase relaxation time 1.23×10-3 sec. The relaxation time for the 1610 cm-1-peak from the position 2 decreases from 5.53×10-3 sec (phase) to 5.44×10-4 sec (amplitude), which is even larger (10.2) than that (8.7) from the position 1, revealing clearly the influence on FLC from the rim of a void defect.

2.4.2. Felix 017/100 SSFLC Cell Doped with nc-ZnO

We reported in our previous study that the electro-optical response of FLC can be improved by doping with zinc oxide nanocrystals [21]. This method opens up an effective nonsynthetic way to yield promising new FLC materials.

The optical transmittance image of a Felix 017/100 SSFLC doped with nc-ZnO cell is shown in Fig. 2.5 (a). The 2D distributions of the amplitude and the phase of the lock-in detected Raman signal at 1610 cm-1 with a modulated frequency 250 Hz are presented in Fig. 2.5 (b) and 2.5 (c). The optical image shown in Fig. 2.5 (a) indicates the lower right portion of the scanned area to be different from the rest part. Fig. 2.5 (b) reveals that FLC in this region produces weaker modulated Raman peak, indicating that the FLC is disordered to result in weaker electro-optical response. Two

sites labeled with p1 and p2 were chosen for further examination. Position 1 represents a location with general characteristics and position 2 was selected to reveal the structure with enhanced electro-optical response.

Fig. 2.5: (a) The optical image of scanned region is taken on a Felix 017/100 SSFLC

cell doped with nc-ZnO by using optical microscopy, and the 2D distributions of (b) the amplitude, and (c) the phase of the lock-in detected Raman peak at 1609 cm-1 _with

a modulated frequency Ω=250Hz. Here p1 is the position of measured position 1 and p2 is the position of measured position 2.

The dc Raman spectrum of the nc-ZnO doped SSFLC cell excited with a Y-polarized laser beam at 532 nm is presented in Fig. 2.6 (a). The Raman spectrum is very similar to that shown in Fig. 2.2(a), except that the 1118 cm-1 peak from the C-O-C motion is weaker while the C=O group at 1763 cm-1, which contributes to the nonvanishing spontaneous polarization of this FLC material in SmC*, is more distinctive. When the photon counting lock-in detection is employed, the amplitude and phase of the lock-in detected Raman spectrum with a sinusoidal waveform of

Ω=250 Hz are presented Figs. 2.5 (b). The phase of the nonresonant signal was found to be about 330°. By using the phase angle, we can remove the nonresonant background from the spectrum shown in Fig. 2.5 (b). The resulting lock-in detected Raman amplitudes (solid curve) are presented in Fig. 2.5 (c). The modulated Raman signal exhibits a phase angle Δ~330° at 1610 cm-1 and Δ~140° at 1118 cm-1, which are similar to that of Fig. 2.2 (b). However, the phase of the C=C stretching modes was found to be about 330°, which is in phase with the nonresonant signal. As pointed out previously, the nonresonant signal is most likely to originate from the light scattering from the field-induced refractive index variation. The zero phase difference between the modulated nonresonant signal and the C=C stretching peaks suggests that doping SSFLC with nc-ZnO appears to result in a more organized field-induced reorientation process. 900 1200 1500 1800 2100 56000 64000 72000 80000 In tensi ty(arb. un it s) Wavenumber(cm-1) (a) 900 1200 1500 1800 2100 0 2000 4000 1326cm-1 1446cm-1 1520cm-1 1610cm-1 ampl. phase Wavenumber(cm-1) A m plit ude (a rb. un it s ) 1118cm-1 0 90 180 270 360 P h ase(degree) (b) 900 1200 1500 1800 2100 0 2000 4000 ampl. phase Wavenumber(cm-1) A mplit ude(arb. units) 1610cm-1 1520cm-1 1446cm-1 1326cm-1 (c) 1118cm-1 0 90 180 270 360 Ph ase (de gre e)

Fig. 2.6: (a) DC unmodulated Raman spectrum of a SSFLC cell doped with nc-ZnO

a lock-in detected Raman spectrum RΨPSD( ,ν Ω)with a modulation frequency Ω=250

Hz measured at the position p1. (c) The corresponding lock-in detected amplitude

(solid curve) after removing the nonresoant background.

The measured transfer function of the Raman peak at 1610 cm-1 from the positions 1 and 2 are presented in Figs. 2.7 (a) and 2.7 (b). The solid curves are the fitting results to Eq. (2.6). The relaxation time deduced from the measured magnitude at 1610 cm-1 from the position 1 is 9.89×10-4 sec, which is about 5 times shorter than 4.98×10-3 sec of the phase relaxation time. At position 2 (Fig. 2.7 (b)) the amplitude relaxation time becomes 6.81×10-4 sec, which is about 3.5 times shorter than the corresponding phase relaxation time 2.36×10-3. Since the reduction factor from the phase relaxation time to the amplitude relaxation time is useful to reflect the disordering effect in the FLC alignment originating from high-frequency switching. Our results indicate that the field-induced reorientation dynamics of the nc-ZnO doped SSFLC film at the position 2 is more organized and therefore less sensitive to the high-frequency driving induced disordering.

0 600 1200 1800 2400 3000 0 1400 2800 4200 ampl. phase Frequency(Hz) Am pl itu de(arb. u ni ts) (a) 260 280 300 320 340 Phas e(degr ee ) 0 600 1200 1800 2400 3000 0 1400 2800 4200 ampl. phase Freqency(Hz) A m pli tu de (a rb .uni ts) (b) 240 260 280 300 320 340 Phase(deg ree)

Fig. 2.7: The amplitude (triangle symbols) and phase (circular symbols) of a

phase-resolved Raman peak at 1609 cm-1 (a) at position1 and (b) at position 2 are presented as a function of modulated frequency Ω in a SSFLC doped with nc-ZnO cell and the solid curve is the fitting curve.

2.4.3. CV Characteristics of Felix 017/100 SSFLC Cells

orientation of the FLC molecules is changed. The FLC molecules can be aligned parallel or antiparallel to the positive field direction. The transition from the antiparallel state to the parallel state is accompanied with a change in the direction of polarization. This gives rise to a nonlinear contribution to the capacitance value of the ferroelectric. Hence the ferroelectric capacitance consists of linear as well as nonlinear parts [22] ( ) LC lin ext dp A C C dV d = + (2.7)

where Clin denotes the linear capacitance, Vext the applied voltage, A and d the area

and the thickness of the capacitor, respectively. The nonlinear part of the FLC capacitance relating to the polarization reversal can be deduced by using the Preisach model, which assumes that the individual dipoles of the FLC film add up to yield the total polarization and each of them exhibits a rectangular hysteretic loop. The external applied field can interact with the dipoles and changes their directions.

Assuming the direction of the dipoles in thermal equilibrium to follow a Gaussian distribution, the total polarization P of the FLC film can then be expressed as [23]

( ext) tanh[ ( ext c )]

P V =FP δ V V± (2.8)

Here the parameter F is used to depict the non-saturated behavior of the loop; δ is a constant with r r 1 P / log( ) / 1 P / s c s P V P δ = + − (2.9) Ps denotes the saturated polarization (or the spontaneous polarization), and is the

mean value of the individual coercive voltage. The (+) sign refers to an increase of

V

c

V±

ext, and the (-) sign indicates a decrease of Vext. (FPs) carries the meaning of the

(2.7) with (2.8), the FLC capacitance with multiple dipolar species can be expressed as 2 ( ) cosh ( ( )) s i i LC lin i i ext Ci FP A C C V V d δ δ ± = +

∑

Eq. (2.10) shows that the capacitance peak in the C-V curve shall coincide with the polarization reversal point with the peak height relating to the amount of switchable polarization [25].

Figure 2.8 (a) shows the measured data of the undoped SSFLC (open circles) and the nc-ZnO doped SSFLC (filled triangles) at an applied field frequency of 1 kHz. The corresponding fitting curves to Eq. (2.10) are presented with solid lines. As shown in the Fig. 2.8 (a), the undoped SSFLC cell needs three Preisach terms to yield a satisfactory fit, while for the doped SSFLC only one term is sufficient. This result suggests that ZnO nanocrystals effectively tie together the surrounding FLC dipolar species and simplify their field-induced switching behaviors. The sub molecular binding effect is possible in view that ZnO nano dots possess fairly large dipole moments and can interact the FLC molecules via dipolar interaction.

-12 -6 0 6 12 0.00 1.50x10-9 3.00x10-9 4.50x10-9 6.00x10-9 _{CV characteristics @1 kHz} SSFLC

SSFLC with nc-ZnO doping

C a paci ta n c e C Cel l (F)

Applied Voltage (Volt)

0 1 2 0 30 60 90 120 150 180 210 240 270 300 330 0 1 2 N o rmal iz ed O p ti cal Tran s m issi o n

No electronic field applied SSFLC with nc-ZnO doping SSFLC

Fig. 2.8: (a) The experimental C-V curves (symbols) and their fitting results (solid

lines) of the SSFLC cells without and with nc-ZnO doping at 1 kHz. (b) The normalized transient electro-optical azimuthal patterns of the pure SSFLC (open squares) and the SSFLC with nc-ZnO doping (filled circles) cells are presented without an electric field.

The patterns of normal optical transmittance through the undoped (open symbols) and the doped (filled symbols) SSFLC cells, which were positioned between a crossed polarizer-analyzers setup, are presented in Figure 2.8 (b). By rotating the SSFLC cells about the beam propagation direction, an azimuthal pattern with four-folded lopes was observed [26]. The dark state has a fairly small light leakage, indicating that both of the two SSFLC cells possess fairly high quality of molecular alignment. The bright state of the doped SSFLC cell yields 2.6 times larger optical transmittance than that of the undoped cell. The result supports the notion that the intermolecular binding effect via nc-ZnO doping produces a higher ordered alignment to result in an improved optical transmissive property.

2.5 Conclusion

In summary, we had applied photon counting lock-in detected Raman imaging technique to investigate the modulation dynamics of surface stabilized ferroelectric liquid crystal with or without doping of ZnO nanocrystals. The technique not only effectively suppresses the nonresonant background of Raman spectrum, but also yields the information about the modulation amplitude and phase of specific Raman peak. The reduction factor from the phase relaxation time to the amplitude relaxation time is useful to reflect the disordering effect of the FLC alignment from the high-frequency driving. The field-induced reorientation dynamics of the nc-ZnO doped SSFLC film is generally more organized and therefore less sensitive to the high frequency driving induced disordering. The result is also supported by the CV characterization. We propose the ZnO nano dots to act as an effective molecular binder by tieing together surrounding FLC dipolar species and yield a 2.5-time improvement in the optical transmittance of nc-ZnO-doped SSFLC. The method

reported here opens up an effective non-synthetic way to yield promising new FLC materials.

Chapter 3

Lock-In Detected Raman Microscopy of Liquid

Crystal Molecules on Tilted Silver Nanorods

3.1 Introduction

The phenomenon of inelastic light scattering by molecular vibration was discovered by C. V. Raman in 1928. To observe this effect, an optical beam is used to illuminate a material and the scattered photons are detected with the help of a sensitive photon detector and a spectrograph. The scattered photons are frequency shifted from the incident excitation photons. The frequency-shifted optical signal consists of two components, the scattering process leading to red-shift frequency is called Stoke scattering and that with blue-shift frequency is called anti-Stoke scattering. The spontaneous Raman scattering is a rather weak process. The intensity of spontaneous Raman signal is orders of magnitude weaker than fluorescence. Surface enhanced Raman scattering (SERS) was discovered thirty years ago [27,28] with the capability to detect a monolayer of molecules adsorbed on roughened noble metal electrodes. Afterwards the technique was developed into a powerful and sensitive spectroscopic tool for chemical analysis. This technology usually utilizes rough metallic surfaces, such as nanoparticles, core-shell nanostruture and nanorods, to yield local field enhancement with plasmon resonance. Due to their extremely high aspect ratio, nanorods and nanowires were found to be effective in producing SERS [13, 29].

In this chapter, surface enhanced Raman scattering from a monolayer of cyano biphenyl (8CB) liquid crystal molecules adsorbed on a tilted silver nanorods coated substrate is studied theoretically and experimentally. The tilted Ag nanorods were

fabricated with oblique angle deposition (OAD) technique [30]. OAD belongs to a physical vapor deposition process in which the incident atoms are deposited on a substrate at a large incident angle with respect to the surface normal of the substrate. By using oblique angle deposition to fabricate tilted nanorods, the size and shape of nanorods can be controlled. The tilt angle of nanorods with respect to the surface normal and the texture in an oblique angle deposited film can be adjusted.

3.2 Theoretical Analysis of Surface Enhanced Raman

Scattering From Adsorbed Molecules on a Layer of Ag

Nanorods

3.2.1 Mie-Scattering

Light scattering occurs as long as there is fluctuation in the optical property of

material. Considering that a dielectric particle with a polarizability of

α ω

exposed to a polarized optical field EG₀, the induced dipole

p

G

p

( )

ω

=

α ω

( )

⋅

E

G

G

I

(3.1) The polarizability depends on the shape and size of particle, the optical property of material and the optical frequency used. Due to the time-varying behavior of the incident optical field, the induced dipole moment oscillates and can radiate at the oscillating frequency.

For a silver rod with a length of ~2000 nm and diameter of ~100 nm, its polarizability can be expressed as [27]

11 21 31 21 11 31 31 31 33 r α α α α α α α α α α ⎡ ⎤ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ I

.

In view of the geometrical symmetry and physical properties of the nanorod, there are only four independent components instead of nine in a general case. The schematic of Mie scattering from Ag nanorods is presented in Fig. 3.1.

polarizer

Ag nanorod array Ag thin film

substrate

analyzer

incident exciting radiation

Mei-scattering radiation polarization direction I induced dipole of scatterer r x y z x' y' z' θ φ θ α

Fig. 3.1: Schematic of Mie scattering from a substrate coated with tilted Ag nanorods.

An incident polarized optical beam excites the silver nanorods to produce induced dipoles and an optical analyzer located in front of detector is used to analyze the polarization of the scattering signal.

In Fig.3.1, we project the incident optical field in the laboratory coordinate system (x, y, z) onto the coordinate system (x’, y’, z’) of Ag nanorod, where z’-axis is aligned to parallel to the long axis of the nanorod. The relationship between the laboratory coordinates system and the nanorod’s coordinates system is described by the

transformation TI

1 0 0 cos sin 0 cos sin 0

0 cos sin sin cos 0 cos sin cos cos sin

0 sin cos 0 0 1 sin sin sin cos cos

T ϕ ϕ ϕ ϕ θ θ ϕ ϕ θ ϕ θ ϕ θ θ θ θ ϕ θ ⎡ ⎤ ⎡ ⎤ ⎡ ⎢ ⎥ ⎢ ⎥ ⎢ =_⎢ − _{⎥ ⎢}− _{⎥ ⎢}= − − ⎢ ⎥ ⎢ ⎥ ⎢− ⎣ ⎦ ⎣ ⎦ ⎣ I ϕ θ ⎤ ⎥ ⎥ ⎥⎦ , (3.3)

where θ denotes the angle between the z- and z’-axis and ψ is the angle between the x- and x’-axis. The incident optical field in the nanorod’s coordinate system can then be found to be 0 0 0 0 x y z E 0 E E T E ⎡ ′ ⎤ ⎢ ⎥ ′ =_⎢ ′ _⎥= ⋅E ⎢ _′ ⎥ ⎣ ⎦ G I G , (3.4)

The Mie scattering intensity by Ag nanorod can be written as 2

-1

ˆ

sca s r ˆi

I = e T⋅I ⋅αI ⋅ ⋅T eI , (3.5)

where eˆ_i and eˆ_s are the unit vectors of the incident optical exciting field and the

Mie scattering field in the laboratory coordinates system. In the simplest case, the polarizability of the silver nanorod can be a diagonal form when the induced dipoles can only be generated to along to the direction of optical field. However, an induced dipole perpendicular to the optical field may be produced by a more general optical driving pattern of valence electrons. In the case of our silver nanorod, the non diagonal terms of α ωI_r( ) turn out to be non negligible.

3.2.2 Surface Enhanced Raman Scattering From Tilted Ag Nanorod

When the molecule of interest is located closed to a polarizable body, the effect of the electromagnetic interaction will occur. The effective electric field EG experienced by the molecule is composed of the incident polarized radiation and a dipole field from the nearby induced dipole. In Fig. 3.2, the schematic of surface enhanced Raman scattering is presented. In brief, two kinds of Raman scattering field are taken into account: one is the direct Raman scattering from the molecule of interest without nanorod and the other is an indirect Raman scattering from an

0

interaction between adsorbed molecule and nanorod [28]. Ag nanorod array Ag thin film substrate incident polarized exciting radiation direct Raman scattering radiation indirect Raman scattering radiation case 1 case 2 _{case 3} oscillating dipole α θ x y z x' y' z' θ φ

Fig.3.2: Schematic of surface enhanced Raman scattering from a substrate coated

with tilted Ag nanorods.

We describe the molecular polarizability with αm

I

and the nearby polarizable body is

a silver nanorod with polarizability

α

I

. This leads to induced dipoles with the following expressions: 0 0 ( ) ( ) m m m r r r r m P E E M P P E E M P α α α α = ⋅ = ⋅ + ⋅ = ⋅ = ⋅ + ⋅ G _I G _I G I G G _I G _I G I G , (3.6)

where PG_m and PG_r are the induced electric dipole of the molecule and nanorod,

respectively; 3 with

ˆ ˆ (3 - ) /

MI = nn II d dG denoting the distance between the

molecule and the center of mass of the nanorod; ˆn=d dK/ ; and II a unit tensor. By

expressing Eq. (3.6) in terms of the incident optical field EG₀, we obtain

-1 0 0 -1 0 0 ( - ) [ ] ( - ) [ ] eff m m m r m r eff r r r m r m P E I M M I M E P E I M M I M E α α α α α α α α α α = ⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ + ⋅ ⋅ = ⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ + ⋅ ⋅ G _I G I _I I _{I I} I I _I G _I G I _I I _I I _I I I _I G G . (3.7)

reduced to 0 0 0 [ ] [ ] eff m m m r eff r r r m 0 P E I M E P E I M α α α α α α = ⋅ = ⋅ + ⋅ ⋅ = ⋅ = ⋅ + ⋅ ⋅ G _I G _I I I _I G _I G _I I I _I E G G . (3.8)

Notice that the Raman polarizabilityα_m can be associated with normal mode coordinates, the total Raman polarizability becomes

[ ] [

tot eff eff m m

Raman Q m r Q M r r Q Q Q ] m M Q α α α α = Δ ∂ α +α = Δ ∂ + ∂ ⋅ ⋅α +α ⋅ ⋅∂ ∂ ∂ ∂ ∂ I I _{I I} I I I I I I _{. (3.9)}

The total Raman scattering intensity from the molecules adsorbed on Ag nanorods is given by 2 -1 ˆ _RAMtot R ˆi I∝ e ⋅TI ⋅αI ⋅ ⋅T eI , (3.10) where and are the unit vectors of the incident exciting field and the Raman scattering field in the laboratory coordinates system.

i

ˆe ˆe_R

There are three geometries for the molecules to lie on the silver nanorods: In the case 1, where the long axis of adsorbed molecule lies along to the x’-axis of the nanorod coordinates system, the probability for a molecule to take this adsorbed geometry is assumed to be ρx'. The resulting polarizability αm

I becomes 0 0 0 0 0 0 0 0 m α α ⎡ ⎤ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ I . (3.11)

Inserting Eq. (3.11) into Eq. (3.9) and Eq. (3.10), the Raman scattering intensity from the adsorbed molecule in this case is denoted by I1. Similarly, for the case 2 where the

long axis of adsorbed molecule lies along to the y’-axis of the nanorod coordinates system, the probability for a molecule to take this adsorbed geometry is ρ . The _y'

Raman scattering intensity is denoted by I2. And for the case 3 where the long axis of

probability for a molecule to take this adsorbed geometry is ρz'. The Raman scattering intensity is I3. Thus, when we take into account the three cases, the total

Raman scattering intensity Itot shall be equal to

' 1 ' 2 ' 3

tot x y z

I = ρ I +ρ I +ρ I . (3.12)

3.3 Experimental Apparatus of Surface Enhanced Raman

Spectroscopy

The nanorods coated substrate is prepared with oblique-angle vapor deposition (OAD) method as detailed by Dr. Zhao, et al. [31]. It was made with 20-nm Ti, 500-nm Ag film and a layer of 2000-nm long silver nanorods. We deposited a drop of 30μM 8CB/Isopropyl Alcohol (IPA) solution on the Ag nanorods-coated substrate, a monolayer of 8CB molecule will be formed. The apparatus used for acquiring polarization-modulating Raman spectrum of 8CB monolayer is depicted in Fig. 3.3.

Solid-state laser

532 nm Polarizer pockel cell Mirror Mirror Lens f=10cm Rotation stage Analyzer Lens f=10cm Spectrograph Objective lens Color filter Color filter high-voltage supply

Fig. 3.3: The apparatus used for acquiring polarization-modulating Raman spectrum

is shown. The polarization direction of the incident light is controlled with a Pockel cell excited with a sinusoidal wave of half-wave voltage amplitude.