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 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 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