Internal Reflection and ATR Spectroscopy

Explains the physical principles underlying ATR spectroscopy

Today, attenuated total reflection (ATR) spectroscopy is the most widely used IR spectroscopic technique. Practitioners in the field, however, are generally not very familiar with the underlying physical basis of spectroscopy, often using spectroscopy as a "black box" tool to analyze their samples. This book provides a bridge between electromagnetic theory and spectroscopy, focusing on ATR spectroscopy in particular. Readers will come to a more complete understanding of the physical phenomena underlying spectroscopic measurement and therefore be better able to make use of ATR and other spectroscopic techniques.

Internal Reflection and ATR Spectroscopy is a unique contribution to the field of spectroscopy, offering derivations of the formulae frequently used in the field and examining important underlying physical mechanisms that are typically not addressed in spectroscopy texts. The book features detailed coverage of such topics as:

Light propagation through absorbing materials Reflection at the interface between two media Phenomena of internal reflection and the evanescent wave Reflectance and transmittance of multi–layered samples Analysis of ATR experiments

As they progress through the book, readers will discover discussions of several new phenomena, including a revision of the conventional understanding of the evanescent wave and of the transport of electromagnetic energy through a totally reflecting interface. In addition, the author identifies a new type of internal reflection that enables researchers to observe some unusual fringes. Throughout all the discussions, numerous figures aid in understanding difficult concepts.

Internal Reflection and ATR Spectroscopy is recommended for all students and researchers who use ATR spectroscopy. By helping readers understand the underlying physical principles of ATR spectroscopy, the book makes it possible for them to optimize the use of spectroscopy as an analytical tool.

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 Interface58

5.3 The Evanescent Wave in Absorbing Materials 59

6 Electric Fields at a Totally Internally ReflectingInterface 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– andp–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 Wave73

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 Reflection85

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 aNonabsorbing Substrate 94

11 Multiple Interfaces 97

11.1 Reflectance and Transmittance of a Two–Interface System97

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 inbetween 109

11.8 Unusual Fringes 110

11.9 Penetration Depth Revisited 113

11.10 Reflectance and Transmittance of a Multiple InterfaceSystem 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 ThinFilms 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 Substrate141

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 toConcentration Change 166

16 ATR Spectroscopy of Small Samples 168

16.1 Benefits of Attenuated Total Reflection (ATR) forMicrosampling 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 Reflectance174

17.4 Effect of the Absorption Index of Metal on Reflectance174

17.5 Use of Plasmons for Detecting Minute Changes of theRefractive Index of Materials 175

17.6 Use of Plasmons for Detecting Minute Changes of theAbsorption Index of Materials 178

18 Extraction of Optical Constants of Materials fromExperiments 180

18.1 Extraction of Optical Constants from Multiple Experiments180

18.2 Kramers Kronig Relations 184

18.3 Kramers Kronig Equations for Normal IncidenceReflectance 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 Interface209

20.1 Energy Conservation at a Totally Reflecting Interface209

20.2 Speed of Propagation and the Formation of an EvanescentWave 212

21 Orientation Studies and ATR Spectroscopy 214

21.1 Oriented Fraction and Dichroic Ratio 214

21.2 Orientation and Field Strengths in Attenuated TotalReflection (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

MILAN MILOSEVIC works as a consultant in the field ofoptical spectroscopy for MeV Technologies, LLC. Milan has spent hisentire career in the field of FTIR spectroscopy, developingspectroscopic equipment and building our understanding of thephysical basis of spectroscopy. He has pioneered several devicesfor what have become standard spectroscopic techniques, includingmicro ATR, variable angle ATR, and grazing angle ATR spectroscopy.Holding over fifteen US patents, Milan has authored or coauthoredover thirty peer–reviewed papers on various aspects ofspectroscopy.