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 xiii1 Introduction to Spectroscopy 11.1 History 11.2 Definition of Transmittance and Reflectance 61.3 The Spectroscopic Experiment and the Spectrometer 101.4 Propagation of Light through a Medium 131.5 Transmittance and Absorbance 151.6 S/N in a Spectroscopic Measurement 162 Harmonic Oscillator Model for Optical Constants 202.1 Harmonic Oscillator Model for Polarizability 202.2 Clausius–Mossotti Equation 252.3 Refractive Index 262.4 Absorption Index and Concentration 293 Propagation of Electromagnetic Energy 313.1 Poynting Vector and Flow of Electromagnetic Energy 313.2 Linear Momentum of Light 343.3 Light Absorption in Absorbing Media 353.4 Lambert Law and Molecular Cross Section 364 Fresnel Equations 394.1 Electromagnetic Fields at the Interface 394.2 Snell’s Law 414.3 Boundary Conditions at the Interface 424.4 Fresnel Formulae 434.5 Refl ectance and Transmitance of Interface 444.6 Snell’s Pairs 464.7 Normal Incidence 474.8 Brewster’s Angle 474.9 The Case of the 45° Angle of Incidence 484.10 Total Internal Reflection 495 Evanescent Wave 555.1 Exponential Decay and Penetration Depth 555.2 Energy Flow at a Totally Internally Reflecting Interface 585.3 The Evanescent Wave in Absorbing Materials 596 Electric Fields at a Totally Internally Reflecting Interface 616.1 Ex, Ey, and Ez for s-Polarized Incident Light 616.2 Ex, Ey, and Ez for p-Polarized Incident Light 627 Anatomy of ATR Absorption 677.1 Attenuated Total Reflection (ATR) Reflectance for s- and p-Polarized Beam 677.2 Absorbance Transform of ATR Spectra 697.3 Weak Absorption Approximation 707.4 Supercritical Reflectance and Absorption of Evanescent Wave 737.5 The Leaky Interface Model 768 Effective Thickness 798.1 Defi nition and Expressions for Effective Thickness 798.2 Effective Thickness and Penetration Depth 808.3 Effective Thickness and ATR Spectroscopy 828.4 Effective Thickness for Strong Absorptions 849 Internal Reflectance near Critical Angle 859.1 Transition from Subcritical to Supercritical Reflection 859.2 Effective Thickness and Refractive Index of Sample 879.3 Critical Angle and Refractive Index of Sample 8810 Depth Profiling 9210.1 Energy Absorption at Different Depths 9210.2 Thin Absorbing Layer on a Nonabsorbing Substrate 9310.3 Thin Nonabsorbing Film on an Absorbing Substrate 9410.4 Thin Nonabsorbing Film on a Thin Absorbing Film on a Nonabsorbing Substrate 9411 Multiple Interfaces 9711.1 Reflectance and Transmittance of a Two-Interface System 9711.2 Very Thin Films 10011.3 Interference Fringes 10111.4 Normal Incidence 10211.5 Interference Fringes and Transmission Spectroscopy 10411.6 Thin Films and ATR 10811.7 Internal Reflection: Subcritical, Supercritical, and in between 10911.8 Unusual Fringes 11011.9 Penetration Depth Revisited 11311.10 Reflectance and Transmittance of a Multiple Interface System 11612 Metal Optics 12112.1 Electromagnetic Fields in Metals 12112.2 Plasma 12612.3 Reflectance of Metal Surfaces 12712.4 Thin Metal Films on Transparent Substrates 13012.5 Curious Reflectance of Extremely Thin Metal Films 13212.6 ATR Spectroscopy through Thin Metal Films 13413 Grazing Angle ATR (GAATR) Spectroscopy 13613.1 Attenuated Total Refl ection (ATR) Spectroscopy of Thin Films on Silicon Substrates 13613.2 Enhancement for s- and p-Polarized Light 13713.3 Enhancement and Film Thickness 13913.4 Electric Fields in a Very Thin Film on a Si Substrate 14113.5 Source of Enhancement 14313.6 GAATR Spectroscopy 14514 Super Grazing Angle Reflection Spectroscopy (SuGARS) 14714.1 Reflectance of Thin Films on Metal Substrates 14714.2 Problem of Reference 14814.3 Sensitivity Enhancement 15015 ATR Experiment 15115.1 Multiple Reflection Attenuated Total Reflection (ATR) 15115.2 Facet Reflections 15515.3 Beam Spread and the Angle of Incidence 15615.4 Effect of Facet Shape 15815.5 Beam Spread and the Number of Reflections in Multiple Refl ection ATR 16015.6 Effect of Beam Alignment on Multiple Reflection ATR 16215.7 Change in the Refractive Index of the Sample due to Concentration Change 16616 ATR Spectroscopy of Small Samples 16816.1 Benefits of Attenuated Total Reflection (ATR) for Microsampling 16816.2 Contact Problem for Solid Samples 17017 Surface Plasma Waves 17217.1 Excitation of Surface Plasma Waves 17217.2 Effect of Metal Film Thickness on Reflectance 17317.3 Effect of the Refractive Index of Metal on Reflectance 17417.4 Effect of the Absorption Index of Metal on Reflectance 17417.5 Use of Plasmons for Detecting Minute Changes of the Refractive Index of Materials 17517.6 Use of Plasmons for Detecting Minute Changes of the Absorption Index of Materials 17818 Extraction of Optical Constants of Materials from Experiments 18018.1 Extraction of Optical Constants from Multiple Experiments 18018.2 Kramers–Kronig Relations 18418.3 Kramers–Kronig Equations for Normal Incidence Reflectance 18719 ATR Spectroscopy of Powders 19219.1 Propagation of Light through Inhomogeneous Media 19219.2 Spectroscopic Analysis of Powdered Samples 19319.3 Particle Size and Absorbance of Powders 19519.4 Propagation of Evanescent Wave in Powdered Media 19820 Energy Flow at a Totally Internally Reflecting Interface 20920.1 Energy Conservation at a Totally Reflecting Interface 20920.2 Speed of Propagation and the Formation of an Evanescent Wave 21221 Orientation Studies and ATR Spectroscopy 21421.1 Oriented Fraction and Dichroic Ratio 21421.2 Orientation and Field Strengths in Attenuated Total Reflection (ATR) 21722 Applications of ATR Spectroscopy 22022.1 Solid Samples 22022.2 Liquid Samples 22022.3 Powders 22122.4 Surface-Modified Solid Samples 22122.5 High Sample Throughput ATR Analysis 22122.6 Process and Reaction Monitoring 222Appendix A ATR Correction 224Appendix B Quantification in ATR Spectroscopy 227Index 237