93,99 €
Mehr erfahren.
- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Adopting a novel approach, this book provides a unique "molecular perspective" on plasmonics, concisely presenting the fundamentals and applications in a way suitable for beginners entering this hot field as well as for experienced researchers and practitioners. It begins by introducing readers to the optical effects that occur at the nanoscale and particularly their modification in the presence of biomolecules, followed by a concise yet thorough overview of the different methods for the actual fabrication of nanooptical materials. Further chapters address the relevant nanooptics, as well as the various approaches to combining nanostructures and biomolecules to achieve certain desired functionalities for applications in the fields of probing, sensing and particle manipulation.
For analytical biologists, physical chemists, materials scientists and medicinal chemists.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 358
Veröffentlichungsjahr: 2014
Ähnliche
Table of Contents
Cover
Related Titles
Title Page
Copyright
Foreword
Chapter 1: Introduction
References
Chapter 2: Plasmonic Effects
2.1 Electrical Conductivity in Metal
2.2 Optical Properties and Dielectric Constant
2.3 Plasmons
2.4 Volume Plasmons
2.5 Surface Plasmons and Applications in Life Sciences
2.6 Localized Surface Plasmon
2.7 Combination of SPR and LSPR Approaches
2.8 Nanoholes
2.9 Enhanced Spectroscopies
References
Chapter 3: Nanofabrication of Metal Structures
3.1 Introduction
3.2 Nanofabrication: Top-Down
3.3 Bottom-Up Approaches
3.4 Post-Processing, Combination, and Integration
References
Chapter 4: The Molecular World
4.1 Interaction and Forces between Molecules and Substrates
4.2 Self-assembly Monolayer (SAM)
4.3 DNA
4.4 Peptides and Proteins
4.5 Bioassay Types and Formats
4.6 Nanomedicine: Cell-Nanoparticle Interaction
References
Chapter 5: Measurement and Characterization Techniques
5.1 Parameters of Interest
5.2 Far-Field Optical Techniques
5.3 Near-Field Optical Techniques
5.4 High-Resolution Microscopy
References
Chapter 6: Molecular Plasmonics: Life Sciences Applications
6.1 Marker
6.2 Sensor
6.3 Local Field Control by Plasmonic Nanostructures
6.4 Light-Induced Manipulation
References
Chapter 7: Molecular Plasmonics for Nanooptics and Nanotechnology
7.1 Plasmonic Lithography
7.2 Nanopositioning for Nanooptics
7.3 Nanopositioning for Ultrasensitive Bioanalytics
7.4 Integration of Molecular Constructs
7.5 Plasmonic Properties Control by Using Molecular Assembly
References
Index
End User License Agreement
Pages
XI
XII
1
2
3
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
25
24
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
105
106
114
107
108
109
110
111
112
113
115
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
157
158
159
160
161
162
163
164
165
166
167
169
170
171
172
173
Guide
Cover
Table of Contents
Foreword
Chapter 1: Introduction
List of Illustrations
Figure 1.1
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
Figure 2.8
Figure 2.9
Figure 2.10
Figure 2.11
Figure 2.12
Figure 2.13
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
Figure 3.10
Figure 3.11
Figure 3.12
Figure 3.13
Figure 3.14
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 5.1
Figure 5.2
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Figure 6.9
Figure 7.1
Figure 7.2
List of Tables
Table 2.1
Table 5.1
Related Titles
Kumar, C.S. (ed.)
Nanomaterials for the Life Sciences
10 Volume Set
2011
Print ISBN: 978-3-527-32261-9, also available in digital formats
Li, S., Singh, J., Li, H., Banerjee, I.A. (eds.)
Biosensor Nanomaterials
2011
Print ISBN: 978-3-527-32841-3, also available in digital formats
Krüger, Anke
Carbon Materials and Nanotechnology
2010
Print ISBN: 978-3-527-31803-2, also available in digital formats
Kim, Dae Mann
Introductory Quantum Mechanics for Semiconductor Nanotechnology
2010
Print ISBN: 978-3-527-40975-4
Chi, Lifeng (ed.)
Nanotechnology
Volume 8: Nanostructured Surfaces
2010
Print ISBN: 978-3-527-31739-4
Wolfgang Fritzsche and Marc Lamy de la Chapelle
Molecular Plasmonics
Authors
Dr. Wolfgang Fritzsche
Leibniz Inst. Photon. Technol. (IPHT)
Nano Biophotonics Dept.
Albert-Einstein-Str. 9
07745 Jena
Germany
Prof. Marc Lamy de la Chapelle
Université Paris 13
Laboratoire CSPBAT UMR7244
74 rue Marcel Cachin
93017 Bobigny
France
Cover
We thank Uwe Klenz for preparing the cover picture.
All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No.: applied for
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Bibliographic information published by the Deutsche Nationalbibliothek
The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.
© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN: 978-3-527-32765-2
ePDF ISBN: 978-3-527-64971-6
ePub ISBN: 978-3-527-64970-9
Mobi ISBN: 978-3-527-64969-3
oBook ISBN: 978-3-527-64968-6
Foreword
Plasmonics continues to blossom. One reason that scientists and technologists continue to move into this topic area is that plasmonics is seen as an important way in which optics, which traditionally works at the length scale of a micron or so, and the molecular world, for which the relevant length scale is nanometers, can be brought together, thus bridging length scales that differ by three orders of magnitude: this is molecular plasmonics. Here, Wolfgang Fritzsche and Marc Lamy de la Chapelle have joined forces to provide a concise and valuable textbook that will greatly assist those joining the field of molecular plasmonics.
It should come as no surprise that Wolfgang Fritzsche is one of the authors – he has been the driving force behind a unique series of biennial international workshops on the theme of molecular plasmonics, which are held in Jena. These workshops have been a great source of information, cultural exchange, and inspiration for those who have been fortunate enough to attend them. The present book displays many of the same attributes, a clear intellectual purpose with a no-nonsense approach to the core activity, helping scientists participate in this very multidisciplinary area of contemporary nanoscience.
The authors provide a clear overview of the contents of their book in the introduction, so I do not need to itemize what you will find in each of the chapters. Instead, let me tell you something about the style. The approach is, in my view, made at just the right level for someone wishing to enter this field, sufficiently detailed, but without having to deal with endless introductory material. As an example, already in Chapter 2 applications are introduced in a natural way, in this case in the context of plasmonic biosensing. This practical approach permeates the rest of the book, for example Chapter 5 contains a very useful table that sets out the relative merits of different characterization techniques used in plasmonics.
One of the dangers of writing a book such as this is for the contents to be too strongly biased toward the specialist interests of the authors, rather than focusing on the needs of the readers. Fritzsche and de la Chapelle have done an admirable job in avoiding this trap by providing a balanced account across a range of topics. Aimed at those entering the field, the value of this book to those already working in the area is also clear to me, I have learnt much from reading the draft manuscript and am sure others will find much of interest here too.
In summary, I am sure Molecular Plasmonics will become a widely read and valuable book to scientists and technologists from a range of disciplines. Looking to the future, I think we can be confident that this field will continue to grow very substantially. Perhaps we will be fortunate enough to have Fritsche and de la Chapelle help us gain an overview of those new developments with a second edition in the years to come.
William Barnes
Exeter
April 2014
1Introduction
Our world is characterized by a wide variety of colors, which arise from various physical effects. A quite special color-inducing effect can be observed, for example, in historical glass objects such as the Roman Lycurgus cup [1] or in medieval church windows. Their brilliant red color in transmission is based on tiny structures of noble metals, mainly gold or silver. These structures have nanoscale dimension, and their color represents an effect that combines nanoscience and nanooptics.
Although the application of this effect has apparently quite a long tradition, the underlying mechanisms remained unclear for most of the time. Such small structures could neither be systematically fabricated nor be visualized till about 150 years ago. Then Faraday approached this problem and placed various techniques in a context for experimental roads for the purposeful fabrication by both physical and chemical means [2]. He could only speculate about the sub-wavelength sizes of the resulting particles because he couldn't actually observe single nanoparticles. Fifty years later, the invention of the ultramicroscope provided the means for a visualization of single nanoparticles, an invention that boosted science then and represented the forerunner of today's dark field techniques for single nanoparticle microscopy as well as spectroscopy [3]. In the decades to come, the introduction of electron microscopy finally allowed a detailed view at the nanoscale [4]. Now the (sub)structure, such as shape or crystallinity, of nanoparticles could be elucidated.
On the theory side, the interaction of light with structures at or even below wavelength dimension was discussed in greater depth by Mie [5]. Based on this and subsequent work, it became possible to predict the optical properties of such metal nanostructures. The fundamental basics of the phenomenon as originating from excited electrons leading to an effect denoted as plasmon were gradually established [6]. This term somehow includes “plasma” as pointing to the origin in electron plasma, and also suggests a quantum nature (like a photon as a quantum of light, a plasmon as a quantum of excited electron plasma).
However, the last 20 years witnessed even more trends targeting this fascinating phenomenon. In the 1990s, nanotechnology emerged as a field of importance for a wide range of applications potentially influencing all aspects of our life [7]. This emergence was connected with a boost for novel approaches in fabrication as well as characterization. Methods for nanostructure fabrication and characterization outside of the vacuum-requiring and highly specialized equipment of established nanofabrication labs became available, with examples such as soft lithography or scanning probe techniques (e.g., AFM, atomic force microscope). On the other hand, the attachment of biomolecules onto gold nanostructures became widely established by first demonstrations for uses in nanotechnology [8] as well as bioanalytics [9]. Thereby, the molecular world with its foundation on (bio)molecular synthesis as well as the wide field of life science (especially medical) application became a driving force for a new field that can be described as Molecular Plasmonics. This field combines the optical effects connected with plasmonic excitation especially at the nanostructure scale (localized surface plasmon) with tools as well as potential applications from the molecular-oriented sciences such as chemistry and life sciences (Figure 1.1). Thereby it is focused only on plasmonic effects at nanostructures (thereby addressing the localized surface plasmon), due to its great potential especially in connection with molecular principles and techniques.
Figure 1.1 Foundations of Molecular Plasmonics. Contributions include plasmonic effects at noble metal nanostructures and their interaction with the molecular world.
Owing to the key importance of health, related applications receive special attention. Molecular Plasmonics already provides a plethora of bioanalytical assay principles that often fulfill the requirements of recent trends in bioanalytics such as on-site measurement abilities in combination with sufficient sensitivity, with more developments to come when today's trend will be followed. Techniques based on plasmonic excitation at nanoparticles play a key role in many fields of nanomedicine, a field that promises to diagnose, monitor, control, or target more precise, than conventional, approaches. Other potential applications are found in novel lithographic methods such as plasmonic lithography. Both in the therapeutic aspect of nanomedicine as well as in this lithographic approach, new dogmas like the nanoantenna effect are used in order to apply optical methods with sub-wavelength precision.
This book focuses on this described field. It is based on a discussion of the various plasmonic effects with focus of the localized case. Molecular Plasmonics represents a highly interdisciplinary field, and the key foundations will be the subjects of the following chapters. An important point is nanostructure fabrication, either by conventional lithographic or by chemical synthesis. In addition to the noble metal structures, molecular components are the other key parts of Molecular Plasmonics. Typical examples are then discussed in the following chapters. This introduction of the basic materials will then be complemented by a discussion of the tools, that is, the various characterization techniques employed in the field. These rather introductory chapters lay the groundwork for the presentation of applications of Molecular Plasmonics in its various fields. Trends in Molecular Plasmonics are discussed at the end, giving an outlook into possible future developments in this fascinating field.
This book attempts to connect the various bases of the field together in an adequate ratio and to an appropriate extent, which is certainly highly subjective. The reader may refer to more specialized publications for in-depth discussion of the individual themes such as plasmonics [10] and especially nanoparticle-connected plasmonic effects [11], nanotechnology (including nanostructure fabrication, nanoparticle synthesis, and their characterization) [7, 12], the various biomolecular components and techniques, or the wide field of (bio)analytical applications of Molecular Plasmonics [13].
References
1. Freestone, I., Meeks, N., Sax, M., and Higgitt, C. (2007)
Gold Bull.
,
40
(4), 270.
2. Faraday, M. (1857)
Philos. Trans. R. Soc. London
,
147
, 145.
3. Siedentopf, H. and Zsigmondy, R. (1902)
Ann. Phys.
,
315
(1), 1.
4. Ruska, E. (1987)
Biosci. Rep.
,
7
(8), 607.
5. Mie, G. (1908)
Ann. Phys.
,
25
(3), 377.
6. (a) Pines, D. (1956)
Rev. Mod. Phys.
,
28
(3), 184; (b) Ritchie, R.H. (1957)
Phys. Rev.
,
106
(5), 874.
7. Köhler, J.M. and Fritzsche, W. (2004)
Nanotechnology
, Wiley-VCH Verlag GmbH, Weinheim.
8. (a) Alivisatos, A.P., Johnsson, K.P., Peng, X., Wilson, T.E., Loweth, C.J., Bruchez, M.P. Jr. and Schultz, P.G. (1996)
Nature
,
382
, 609; (b) Mirkin, C.A., Letsinger, R.L., Mucic, R.C., and Storhoff, J.J. (1996)
Nature
,
382
(6592), 607.
9. (a) Elghanian, R., Storhoff, J.J., Mucic, R.C., Letsinger, R.L., and Mirkin, C.A. (1997)
Science
,
277
(5329), 1078; (b) Englebienne, P. (1998)
Analyst
,
123
(7), 1599.
10. (a) Maier, S.A. (2007)
Plasmonics: Fundamentals and Applications
, Springer, New York; (b) Ozbay, E. (2006)
Science
,
311
(5758), 189; (c) Shalaev, V.M. and Kawata, S. (2007) in
Advances in Nano-Optics and Nano-Photonics
(eds V.M. Shalaev and S. Kawata), Elsevier, Amsterdam.
11. (a) Bohren, C.F. and Huffmann, D.R. (1983)
Absorption and Scattering of Light by Small Particles
, John Wiley & Sons, Inc., New York; (b) Kreibig, U. and Vollmer, M. (1995)
Optical Properties of Metal Clusters
, Springer, Berlin; (c) Link, S. and El-Sayed, M.A. (2000)
Int. Rev. Phys. Chem.
,
19
(3), 409; (d) Mulvaney, P. (1996)
Langmuir
,
12
(3), 788; (e) Pelton, M., Aizpurua, J., and Bryant, G. (2008)
Laser Photonics Rev.
,
2
(3), 136.
12. (a) Henzie, J., Lee, J., Lee, M.H., Hasan, W., and Odom, T.W. (2009)
Annu. Rev. Phys. Chem.
,
60
, 147.(b) Sardar, R., Funston, A.M., Mulvaney, P., and Murray, R.W. (2009)
Langmuir
,
25
(24), 13840; (c) Tao, A.R., Habas, S., and Yang, P.D. (2008)
Small
,
4
(3), 310; (d) Schmid, G. (Ed.) (2003)
Nanoparticles: From Theory to Application
, Wiley-VCH Verlag GmbH, Weinheim.
13. (a) Penn, S.G., He, L., and Natan, M.J. (2003)
Curr. Opin. Chem. Biol.
,
7
(5), 609; (b) Pissuwan, D., Valenzuela, S.M., and Cortie, M.B. (2006)
Trends Biotechnol.
,
24
(2), 62; (c) Willets, K.A. and Van Duyne, R.P. (2007)
Annu. Rev. Phys. Chem.
,
58
, 267; (d) Wilson, R. (2008)
Chem. Soc. Rev.
,
37
(9), 2028.
2Plasmonic Effects
The plasmon is a quasiparticle that is related, on the one hand, to the electronic properties of the metal, since it is considered a collective oscillation of the free electrons inside the metal or at the interface between a metal and a dielectric material, and, on the other hand, to the optical properties of the metal since the plasmon can be excited by the interaction with a photon. In order to understand the plasmon and its characteristics, it is important to consider both properties and their relationship. Thus, we will first start with the description of such properties and then present the different types of plasmon and their properties.
2.1 Electrical Conductivity in Metal
Free electrons inside a metal essentially govern the electrical conductivity, and the large values reached by this latter parameter are essentially due to the high mobility of these free electrons. They are located in the conduction band of the metal and are weakly bound to the metal atoms. The metal can then be described as an array of positively charged ions (metal atoms including the atomic nucleus and some but not all electrons involved in the atomic bounds; these latter electrons are then located in the valence bands) surrounded by a gas of free electrons, negatively charged. Taking into account such specificities, several models have been proposed to be able to explain the electronic properties of the metal. These models are based on the determination of the conductivity of the metal but also of specific interactions of the electron with their material environment. The conductivity, , can be defined as the capability of a material to produce an electrical current under the excitation of an external electric field (constant or alternative). It is then defined as the coefficient that relied on the current density, , and the external electric field, , such as:
This relation is known as the local Ohm law. Since and are vectorial quantities, can be a tensor.
2.1.1 Drude Model
P. Drude proposed a first model in 1900. In the framework of the classical physics (mechanics and electromagnetism), the electrons are described as a gas and can move freely and independently from each other. It means that there is no interaction between the electrons. There is also no electromagnetic interaction between the electrons and the metallic ions that have a positive charge. The only interaction that occurs is the potential collision of the electrons with the ions. Thus, the Drude model is based only on a mechanistic description of the matter.
The average time between two collisions is named the relaxation time, , and the probability that a collision occurs during a time duration is . Using this model, one can calculate the conductivity, , of the metal in continuous current:
where , is the electron density, e is the electron charge, and is the electron mass.
In alternative current, one should include the frequency of the current in the conductivity as:
2.1.2 Drude–Lorentz Model
H. A. Lorentz modified the Drude model in 1905 by including the contribution of the valence electrons and included an elastic force that corresponds to the interaction of the valence electrons with the positively charged nucleus. This force depends on the distance of the electron from its equilibrium position.
2.1.3 Drude–Sommerfeld Model
In the two latter models, the electrons were considered a classical object and not as a quantum one. Thus, the Sommerfeld model considers the electron as a fermion and its energetic distribution is determined by the Fermi–Dirac distribution and not by the Maxwell–Boltzmann one as P. Drude did in his model.
In the following, we will limit ourselves to the Drude or the Drude–Lorentz models, which give a simple description of the electron and of the electronic and optical properties with sufficient accuracy for this book.
2.2 Optical Properties and Dielectric Constant
The optical properties determine the behavior of a material when it interacts with light. Since light is an electromagnetic wave, it essentially interacts with the electrons inside the metal. Such interaction is then directly connected with the electronic properties of the material and the electrons interaction with their environment.
The main parameter that describes the optical properties of a material is its dielectric constant, , which depends on the excitation frequency. The complex dielectric constant expresses the dielectric response of a metal to electromagnetic radiation:
The real part represents the degree of metal polarization induced by the external electrical field, and the imaginary part determines the phase shift of this polarization and it includes losses. The different models presented earlier can describe dielectric constants of metals.
can be determined using the description of the electron motion inside the metal. If we limit our description to the Drude–Lorentz model, the interaction of the electrons with the metallic ions can be described as two forces:
a damping force (introduced by P. Drude).
an elastic force (introduced by H. A. Lorentz to correct the Drude model)
When excited by an electromagnetic wave, the electrons are also submitted to a third force, the Coulomb force known as:
with , the excitation electric field. This latter one is an oscillating field and thus can be described as , with , its amplitude and its frequency.
The electron motion can be deduced from the second Newton's law since:
The resolution of this equation gives the time dependence of such as:
We can then notice that the electrons oscillate at the same frequency as the external field and that the oscillation amplitude depends on the frequency value. This one will be maximal for a specific value of . This latter condition is a resonance condition, for which the absorption of the light will be at its maximum.
The electron motion induces a dipolar moment inside the material. This dipolar moment is proportional to the electron displacement:
with , a unitary vector in the displacement direction, the electric susceptibility, and , the dielectric constant of the vacuum.
Since is equal to 1 + , we can deduce its dependence with as:
with , the plasma frequency, and , the eigen frequency.
Moreover, the plasma frequency is directly related to the conductivity calculated in the Drude model (Section 2.1).
A general expression can be given between the dielectric constant and the conductivity of the material such as:
with the value of the dielectric constant when .
In the Drude model, the term of disappears and the dielectric constant can be calculated as:
Thus, the different expressions of by the Drude or the Drude Lorentz models give us the behavior of the metal when it is excited by an electromagnetic field. This behavior depends essentially on its frequency. The electromagnetic field induces the oscillation of the electrons within the metal. As explained previously, at a specific frequency, this oscillation can be in resonance with the field, whereas at other frequencies, the electron motion is damped. At the resonance conditions, the oscillation corresponds to the plasmon. The resonance condition depends on the dielectric constant values and also on the dimensionality of the metal geometry. This condition can be predicted by its theoretical expressions. However, especially for gold being one of the most important metal for plasmonic applications, this model needs corrections, so that usually experimentally measured values are used for .
For the sake of clarity, plasmons and plasmon resonances are used here as synonyms, and the term polariton (which includes the interaction of plasmons with photons) is not applied because it does not add to a better understanding of the discussed effects with regards to molecular plasmonics.
2.3 Plasmons
Depending on the dimensionality of the metal structure, different modes of plasmonic oscillation can be distinguished:
Volume plasmons
Surface plasmons (SPs)
Localized (surface) plasmons (LSPs).
2.4 Volume Plasmons
The volume plasmon is defined inside an infinitely large, crystalline metal structure (bulk material) and corresponds to an oscillation of the whole electron cloud in all the metal. This occurs when the dielectric constant of the metal is null (condition for the propagation of an electromagnetic wave inside the metal). With such condition, we can deduce from the Drude model (Equation (2.12)) that the volume plasmon oscillates at the plasma frequency . Metals are then transparent for higher energy radiation, but do not transmit light with frequencies below this volume plasmon frequency .
The SP was observed for the first time in 1930 by electron energy loss spectroscopy. Indeed, some losses have been detected when the electron energy was a multiple of [1].
Since this volume plasmon can be excited only inside the metal, it has therefore no direct implication for surface-oriented sensors and applications, as it is the focus of this book.
2.5 Surface Plasmons and Applications in Life Sciences
2.5.1 Surface Plasmons in a Flat Metallic Film
In the case of a surface, the conditions are different since the plasmon is produced by the discontinuity of the electric field at the surface. This discontinuity creates a transverse surface wave confined at the metal surface (evanescent wave).
To model this SP, we consider an interface between a metal and a dielectric medium (see Figure 2.1). The metal is supposed to be semi-infinite to have to consider only one interface. The dielectric constants are and for the metal and the dielectric media, respectively. The electric fields at the interface are expressed as:
in the dielectric medium and
in the metal with in the interface direction and perpendicular to the surface.
Figure 2.1 Typical setup for a (propagating) SPR sensor. Light is coupled by a prism into a thin (gold) metal layer, which holds on the other side biorecognition elements for target molecule binding resulting in a changed molecular layer thickness (and thereby in a changed local refractive index).
Maxwell's equations as well as the boundary conditions at the interface give:
This leads to:
and
One can then deduce the dispersion relation of the surface wave along the interface:
If we use the dielectric constant calculated in the Drude model (Equation (2.12)), one can determine the dispersion relation as:
When is close to zero, the frequency is also close to zero; but one can remark that the value of is also close to . It means that the SP dispersion curve is tangential to the light dispersion curve () but with always a lower value compared to (the SP curve is below the light curve). For a high value of , the frequency becomes constant and takes the value of .
This relation describes an electromagnetic wave that propagates along the surface and is based on longitudinal electronic oscillations parallel to the metal surface. This wave is called surface plasmon (SP) or delocalized surface plasmon (DSP) since it can propagate on distance largely higher than its own wavelength.
As an SP propagates along the surface, it loses energy. The propagation length is defined as the lateral distance for the SP intensity to decay by a factor of , and is caused by damping due to losses in the metal. Since the SP intensity along the direction decreases as , the SP decay length can be defined as . For a light wavelength of 633 nm, is about 9 µm for gold and 60 µm for silver. Moving up in wavelength, for example, into the 1.5 µm near-infrared telecom band, this value increases toward 1 mm for silver.
Moreover, the SP has an evanescent character. Indeed, from Equations (2.17) and (2.18), it can be deduced that . If and then and is complex. Thus, the electric field falls off exponentially perpendicular to the metal surface. Typical decay lengths are in the order of half wavelength of the involved light, which means about 200 nm for visible light. The field in this direction is said to be evanescent or near-field in nature and is a consequence of the bound, non-radiative nature of SPs, which prevents power from propagating away from the surface. At low frequencies, the SP penetration depth into the metal is commonly approximated using the skin depth formula. In the dielectric, the field falls off far more slowly.
A key prerequisite for the formation of a propagating SP is the coupling of a light wave to a SP at a metal dielectric interface. This coupling requires that the component of light's wavevector that is parallel to the interface matches the wavevector of the SP. To be excited by a photon, a phase matching between the light and the SP is required. It means that the frequencies and the wavevectors of both the light and the SP are equal ( and ). In other words, it also means that it should have an intersection between the light and SP dispersion curves (the intersection point corresponds to the phase matching). As the light dispersion curve () is always above the SP dispersion curve, SPs cannot be excited directly by light incident onto a smooth metal surface. The wavevector of light has to be increased to match that of the SP (the light dispersion curve is then shifted to the right and as a consequence, it can cross the SP dispersion curve). This can be done by using attenuated total reflection (ATR) or diffraction. The coupling between the photon and the SP is then called surface plasmon polariton (SPP).
This light/SP coupling is performed in a coupling device (coupler), such as based on a prism, a waveguide, or a grating [2]. Therefore, prism couplers are the most frequently applied method. In the Kretschmann configuration of the ATR method, a light wave passes through a high refractive index prism and is totally reflected at the base of the prism, thereby generating an evanescent wave that penetrates into the thin metal film [3]. This evanescent wave propagates along the interface, and the light wavevector can be adjusted (to match that of the SP and thereby realize coupling) by controlling the angle of incidence. In fact, the light wavevector is projected along the prism surface ( direction) and the wavevector component at the prism/metal interface takes a new value: , with , the incident angle of the excitation light and , the prism refractive index.
Even if the Kretschmann configuration is the most used and the most appropriate to excite and observe SP, another configuration can be used. This one was first proposed by A. Otto and is called Otto configuration (this configuration was actually proposed before the Kretschmann one) [4]. In both configurations, the SP is excited by an evanescent field produced at the prism surface in ATR but in the Kretschmann configuration, the evanescent field is transmitted inside the thin metal layer (few tens of nanometers), whereas it is transmitted in a thin layer of air in the Otto configuration.
In the case of a diffraction grating, the wavevector becomes , with , the incoming light angle, , the diffraction order ( is an integer) and , the grating constant.
2.5.2 Biosensor Applications
The biosensoric application of SPR uses the change of the resonance condition of the SP when an analyte is deposited at the metallic film surface [5]: The maximum excitation of SPs is detected by monitoring the reflected power from a prism coupler as a function of incident angle or wavelength (Figure 2.1). Indeed, from the Equation (2.21), one can deduce that the frequency of the SP depends on the dielectric constant of the medium above the metallic layer (). Any change of then induces a shift of the resonance condition of the plasmon and as a consequence, a shift of the phase matching with the light. For a fixed light wavelength, , and a fixed angle, it induces a measurable change in the reflectivity of the metallic layer. To recover the phase matching, it is possible to change the excitation condition (), by modifying either the angle of reflection of the incident light (for a fixed light wavelength) or the light wavelength (for a fixed angle ).
This technique can be used to observe nanometer changes in thickness, density fluctuations, or molecular adsorption. In order to realize specificity, a biorecognition element is used at the sensor surface, such as DNA complementary to the analyte (target) DNA, or antibodies specific for the protein or cell type of interest. Such systems are widely applied, because they are able to detect molecular interactions in real-time and under physiological condition. In these SPR biosensors, the analyte quantification is carried out by detection of the binding reaction, however, the increase in the refractive index produced by the adsorption of small molecules may not be sufficient to be detected directly, and sandwich or competitive assay methods may need to be used (cf. Section 4.5).
One limitation of this original method is the low throughput. SPR imaging configurations allow for the parallel readout of a whole array of sensor areas [6]. Therefore, a beam of monochromatic light passes through a prism coupler and is made incident on a thin metal film at an angle of incidence near the coupling angle. The reflected light intensity depends on the coupling strength between the incident light and the SP and can be correlated with the distribution of the refractive index at the metal film surface.
2.6 Localized Surface Plasmon
In the previous case, the light/metal interaction occurs only at the metal surface since the light cannot penetrate deeply inside the metal. Indeed, the wave intensity decreases exponentially inside the metal. The decay length of the wave is estimated using the imaginary part of the wave vector. From the Equations (2.11) and (2.16), it comes that:
The electromagnetic wave and its intensity inside the metal can be expressed as follows:
One can deduce the decay length, :
The decay length is also called the skin depth of the metal. For metals, the conductivity value is high and the penetration depth of the electromagnetic field is limited to a few tens to a few hundreds of nanometers. In fact, since the electromagnetic wave interacts strongly with the free electrons of the metal, a shielding effect occurs that restricts the penetration of the wave. This latter one is then reflected. For gold and silver, the skin depth is at 633 nm equal to 81 and 105 nm, respectively.
Thus, when light meets metal nanostructures, the nanostructure size is lower than the skin depth and the whole nanostructure interacts with the light. The whole cloud of rather freely movable conduction band electrons is displaced with respect to the positively charged ions of the metal lattice (Figure 2.2a). A dipole results, and represents a restoring force. So the nanostructure can be considered a light wave-driven harmonic oscillator in a first approximation. It is driven by the light wave and damped by heat production (due to Ohmic losses) and scattering (radiative) losses (scattering occurs as a re-emission of a photon). This electron cloud oscillation is called the localized surface plasmon (LSP). The term localized is used as the plasmon is confined within the nanostructure and cannot propagate as the previous DSP. The excitation light can enter in resonance with the plasmon (localized surface plasmon resonance, LSPR) for a specific energy corresponding to a proper mode of oscillation of the electrons within the nanostructure (Figure 2.2b). As any oscillator, this LSPR energy depends on the chemical nature of the metal, on the geometry (size and shape) of the nanostructure and on its local environment (surrounding medium or coupling with other nanostructures). The resonance can be observed by extinction spectroscopy (see Section 5.2.2 for more details). The extinction spectrum represents the efficiency of the interaction of the light with the nanostructure depending on the frequency or the wavelength of the light. The maximum of the extinction spectrum corresponds to the LSPR. In fact, the extinction spectrum consists of two distinct features: an absorption band and a scattering band. Both these bands depend essentially on the size of the nanostructure.
Figure 2.2 Localized surface plasmon resonance (LSPR). (a) The light-induced displacement of the electron cloud in noble-metal nanostructures at resonance [7]. (b) This effect leads to the typical LSP resonance curve (here: spherical 30 nm Au particles) and the resulting color of solutions of such particles.
2.6.1 LSP in Spherical Nanoparticles
In 1908, G. Mie proposed a theoretical model for optical extinction (as sum of absorption and scattering) of spherical noble-metal nanoparticles [8].
The Mie theory can be used to calculate the extinction coefficient and more especially the cross section of the particle, , defined as , the absorption and the scattering cross sections, respectively. In the case of a metallic sphere with a radius and embedded by a dielectric medium (), the Mie theory gives an explicit formulation of the and the , the is then deduced from the two last cross sections as:
with and the electric and magnetic susceptibilities related to the scattered field. These coefficients can be calculated using the spherical harmonics.
The values of depending on directly give the extinction spectrum of the spherical nanoparticle and thus the position of the plasmon resonance. This latter one is red-shifted and broadened when the radius of the nanoparticle increases.
The Mie theory describes precisely the light-matter interaction for (Figure 2.3) spherical structure, giving analytical solutions. The cross section formulas are not easy to use and are sometimes hard to interpret or to get information on the underlying physics.
These formulas can be simplified by using specific approximations. The most known and used one is the quasi-static or Rayleigh approximation. In this case, the nanoparticle diameter is supposed to be small compared to the excitation wavelength (; this approximation is notably valid when ) and then the electric field amplitude is supposed to be constant inside the nanoparticle (no dephasing inside the nanoparticle). In such approximation, the cross sections can be calculated as:
with the volume of the particle ( for spherical particle).
Other parameters often used are the absorption, scattering, and extinction yields, which are defined as the normalization of the cross section by the geometrical cross section of the nanoparticle, that corresponds to its surface () [9].
is maximum when . This condition of resonance depends on the dielectric constant of the metal and of the surrounding medium. It determines the position of the plasmon resonance for small nanoparticles. For example, a nanoparticle of silver or of gold in air () exhibits a plasmon resonance at 354 or 484 nm, respectively (This resonance position is a good approximation for nanoparticle with diameter lower than 30 nm).
Figure 2.3 (a,b) Extinction (sum of absorption and scattering) and scattering efficiencies for gold nanoparticles with different diameters (calculated for ) [8]
Reproduced with permission. Copyright © 1908 WILEY-VCH Verlag GmbH & Co. KGaA. [10] Reproduced with permission. Copyright © 2010 Nova Science Publishers, Inc.
The relative weight of the absorption and scattering processes is another interesting topic. As is proportional to the volume of the nanoparticle, whereas is proportional to , by increasing the particle diameter, the scattering cross section gains more influence on the extinction compared to the absorption cross section. For small radius (<30 nm for silver particles), applies Figure 2.3. It means that the incident light is only absorbed by the particle and a very small quantity is effectively scattered. At the opposite, for large radius (>100 nm for silver or gold particles), the extinction spectrum is dominated by the scattering process ().
Even if the extinction efficiency depends on the particle size, the condition of resonance does not depend on this parameter. It means that whatever the nanoparticle size, the plasmon resonance is always calculated at the same spectral position, which is in contradiction with the Mie theory. This can be explained since the cross sections have been determined in the quasi-static approximation and then for small nanoparticles compared to the excitation wavelength. To consider larger nanostructure which can no more be described in the quasi-static approximation (diameter larger than ), it is then necessary to add some correction factors in the cross section formula.
These corrections are:
the radiation damping
the dynamic depolarization
These factors are then used in the expressions of the cross sections that should be rewritten as follows:
with
The maximum of the extinction cross section is now reached for:
The resonance condition is changed and depends on the size of the nanosphere, as expected, and on the dielectric constant of the surrounding medium.
This latter parameter is of first importance in sensing issues. The local refractive index of the surrounding medium increases (i.e., larger value of ) when, for example, molecules bind at the particle surface in aqueous solution. Because the dielectric constant () of gold and silver decreases with increasing wavelength [11], Equation (2.37) shows that an increase in red-shifts the resonance wavelength as well as increases the extinction at resonance – a property that forms the base of optical transduction of receptor-analyte binding in the intraparticle type of LSPR sensing as discussed later [12]. Also substrate effects change the optical properties of individual particles and can lead to a red-shift compared to the situation in solution [13].
