Preface ...................................................... xiii
1 Introduction to Spectroscopy ................................. 1
1.1 History ................................................. 1
1.2 Definition of Transmittance and Reflectance ............. 6
1.3 The Spectroscopic Experiment and the Spectrometer ...... 10
1.4 Propagation of Light through a Medium .................. 13
1.5 Transmittance and Absorbance ........................... 15
1.6 S/N in a Spectroscopic Measurement ..................... 16
2 Harmonic Oscillator Model for Optical Constants ............. 20
2.1 Harmonic Oscillator Model for Polarizability ........... 20
2.2 Clausius-Mossotti Equation ............................. 25
2.3 Refractive Index ....................................... 26
2.4 Absorption Index and Concentration ..................... 29
3 Propagation of Electromagnetic Energy ....................... 31
3.1 Poynting Vector and Flow of Electromagnetic Energy ..... 31
3.2 Linear Momentum of Light ............................... 34
3.3 Light Absorption in Absorbing Media .................... 35
3.4 Lambert Law and Molecular Cross Section ................ 36
4 Fresnel Equations ........................................... 39
4.1 Electromagnetic Fields at the Interface ................ 39
4.2 Snell's Law ............................................ 41
4.3 Boundary Conditions at the Interface ................... 42
4.4 Fresnel Formulae ....................................... 43
4.5 Reflectance and Transmitance of Interface .............. 44
4.6 Snell's Pairs .......................................... 46
4.7 Normal Incidence ....................................... 47
4.8 Brewster's Angle ....................................... 47
4.9 The Case of the 45° Angle of Incidence ................. 48
4.10 Total Internal Reflection .............................. 49
5 Evanescent Wave ............................................. 55
5.1 Exponential Decay and Penetration Depth ................ 55
5.2 Energy Flow at a Totally Internally Reflecting
Interface .............................................. 58
5.3 The Evanescent Wave in Absorbing Materials ............. 59
6 Electric Fields at a Totally Internally Reflecting
Interface ................................................... 61
6.1 Ex, Ey, and Ez for s-Polarized Incident Light .......... 61
6.2 Ex, Ey, and Ez for p-Polarized Incident Light .......... 62
7 Anatomy of ATR Absorption ................................... 67
7.1 Attenuated Total Reflection (ATR) Reflectance for
s- and p-Polarized Beam ................................ 67
7.2 Absorbance Transform of ATR Spectra .................... 69
7.3 Weak Absorption Approximation .......................... 70
7.4 Supercritical Reflectance and Absorption of
Evanescent Wave ........................................ 73
7.5 The Leaky Interface Model .............................. 76
8 Effective Thickness ......................................... 79
8.1 Definition and Expressions for Effective Thickness ..... 79
8.2 Effective Thickness and Penetration Depth .............. 80
8.3 Effective Thickness and ATR Spectroscopy ............... 82
8.4 Effective Thickness for Strong Absorptions ............. 84
9 Internal Reflectance near Critical Angle .................... 85
9.1 Transition from Subcritical to Supercritical
Reflection ............................................. 85
9.2 Effective Thickness and Refractive Index of Sample ..... 87
9.3 Critical Angle and Refractive Index of Sample .......... 88
10 Depth Profiling ............................................. 92
10.1 Energy Absorption at Different Depths .................. 92
10.2 Thin Absorbing Layer on a Nonabsorbing Substrate ....... 93
10.3 Thin Nonabsorbing Film on an Absorbing Substrate ....... 94
10.4 Thin Nonabsorbing Film on a Thin Absorbing Film on
a Nonabsorbing Substrate ............................... 94
11 Multiple Interfaces ......................................... 97
11.1 Reflectance and Transmittance of a Two-Interface
System ................................................. 97
11.2 Very Thin Films ....................................... 100
11.3 Interference Fringes .................................. 101
11.4 Normal Incidence ...................................... 102
11.5 Interference Fringes and Transmission Spectroscopy .... 104
11.6 Thin Films and ATR .................................... 108
11.7 Internal Reflection: Subcritical, Supercritical, and
in between ............................................ 109
11.8 Unusual Fringes ....................................... 110
11.9 Penetration Depth Revisited ........................... 113
11.10 Reflectance and Transmittance of a Multiple
Interface System ...................................... 116
12 Metal Optics ............................................... 121
12.1 Electromagnetic Fields in Metals ...................... 121
12.2 Plasma ................................................ 126
12.3 Reflectance of Metal Surfaces ......................... 127
12.4 Thin Metal Films on Transparent Substrates ............ 130
12.5 Curious Reflectance of Extremely Thin Metal Films ..... 132
12.6 ATR Spectroscopy through Thin Metal Films ............. 134
13 Grazing Angle ATR (GAATR) Spectroscopy ..................... 136
13.1 Attenuated Total Reflection (ATR) Spectroscopy of
Thin Films on Silicon Substrates ...................... 136
13.2 Enhancement for 5- and p-Polarized Light .............. 137
13.3 Enhancement and Film Thickness ........................ 139
13.4 Electric Fields in a Very Thin Film on a Si
Substrate ............................................. 141
13.5 Source of Enhancement ................................. 143
13.6 GAATR Spectroscopy .................................... 145
14 Super Grazing Angle Reflection Spectroscopy (SuGARS) ....... 147
14.1 Reflectance of Thin Films on Metal Substrates ......... 147
14.2 Problem of Reference .................................. 148
14.3 Sensitivity Enhancement ............................... 150
15 ATR Experiment ............................................. 151
15.1 Multiple Reflection Attenuated Total Reflection
(ATR) ...................................................... 151
15.2 Facet Reflections ..................................... 155
15.3 Beam Spread and the Angle of Incidence ................ 156
15.4 Effect of Facet Shape ................................. 158
15.5 Beam Spread and the Number of Reflections in
Multiple Reflection ATR ............................... 160
15.6 Effect of Beam Alignment on Multiple Reflection
ATR ................................................... 162
15.7 Change in the Refractive Index of the Sample due to
Concentration Change .................................. 166
16 ATR Spectroscopy of Small Samples .......................... 168
16.1 Benefits of Attenuated Total Reflection (ATR) for
Microsampling ......................................... 168
16.2 Contact Problem for Solid Samples ..................... 170
17 Surface Plasma Waves ....................................... 172
17.1 Excitation of Surface Plasma Waves .................... 172
17.2 Effect of Metal Film Thickness on Reflectance ......... 173
17.3 Effect of the Refractive Index of Metal on
Reflectance ........................................... 174
17.4 Effect of the Absorption Index of Metal on
Reflectance ........................................... 174
17.5 Use of Plasmons for Detecting Minute Changes of the
Refractive Index of Materials ......................... 175
17.6 Use of Plasmons for Detecting Minute Changes
of the Absorption Index of Materials .................. 178
18 Extraction of Optical Constants of Materials from
Experiments ................................................ 180
18.1 Extraction of Optical Constants from Multiple
Experiments ........................................... 180
18.2 Kramers-Kronig Relations .............................. 184
18.3 Kramers-Kronig Equations for Normal Incidence
Reflectance ........................................... 187
19 ATR Spectroscopy of Powders ................................ 192
19.1 Propagation of Light through Inhomogeneous Media ...... 192
19.2 Spectroscopic Analysis of Powdered Samples ............ 193
19.3 Particle Size and Absorbance of Powders ............... 195
19.4 Propagation of Evanescent Wave in Powdered Media ...... 198
20 Energy Flow at a Totally Internally Reflecting Interface ... 209
20.1 Energy Conservation at a Totally Reflecting
Interface ............................................. 209
20.2 Speed of Propagation and the Formation of an
Evanescent Wave ....................................... 212
21 Orientation Studies and ATR Spectroscopy ................... 214
21.1 Oriented Fraction and Dichroic Ratio .................. 214
21.2 Orientation and Field Strengths in Attenuated Total
Reflection (ATR) ...................................... 217
22 Applications of ATR Spectroscopy ........................... 220
22.1 Solid Samples ......................................... 220
22.2 Liquid Samples ........................................ 220
22.3 Powders ............................................... 221
22.4 Surface-Modified Solid Samples ........................ 221
22.5 High Sample Throughput ATR Analysis ................... 221
22.6 Process and Reaction Monitoring ....................... 222
Appendix A ATR Correction ..................................... 224
Appendix В Quantification in ATR Spectroscopy ................. 227
Index ......................................................... 237
|
