Internal Reflection and ATR Spectroscopy

MILAN MILOSEVIC works as a consultant in the field of optical spectroscopy for MeV Technologies, LLC. Milan has spent his entire career in the field of FTIR spectroscopy, developing spectroscopic equipment and building our understanding of the physical basis of spectroscopy. He has pioneered several devices for what have become standard spectroscopic techniques, including micro ATR, variable angle ATR, and grazing angle ATR spectroscopy. Holding over fifteen US patents, Milan has authored or coauthored over thirty peer-reviewed papers on various aspects of spectroscopy.

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 Refl ectance 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 45degree 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 Defi nition 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 Refl ection (ATR) Spectroscopy of Thin Films on Silicon Substrates 136 13.2 Enhancement for s- 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 Refl ection 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 B Quantification in ATR Spectroscopy 227 Index 237