Optical Properties of Materials Index of Refraction Reflection

Optical Properties of Materials Index of Refraction … Reflection … Refraction (Snell’s law) … Index of Refraction Absorption 1

Maxwell’s Equations Materials equations 2

Maxwell’s Equations If no free charge is present 3

Maxwell’s Equations If no free charge … the wave equation 4

The Wave Equation Complex index of refraction Complex dielectric constant 5

Refraction and Absorption k … wave vector … angular frequency c … velocity of light n … index of refraction … electrical conductivity Complex permittivity: permittivity and losses Complex index of refraction: refraction and absorption 5

Amplitude and Intensity of the Propagating Wave Amplitude Propagating wave Absorption Intensity 7

Relationship between Dielectric and Optical Constants Dielectric constant = permittivity 8

Insulator … non-conducting material … no absorption, no losses … the index of refraction is a real quantity 9

Penetration Depth … dependent on frequency (wavelength) and absorption 10

Penetration Depth and Absorption (Examples) * absorption = damping 11

Reflection and Transmission 1 2 “ 0” Same amplitude and phase of wave at the point “ 0” Reflection: Transmission: (Snell’s law) 12

Electric and Magnetic Field The vectors of the electric and magnetic fields are perpendicular to the propagation direction of the wave. The original wave: 13

Electric and Magnetic Field The transmitted wave: The reflected wave: 14

Fresnel Equations 15

Fresnel Coefficients Snell law 16

Index of Refraction (Experimental Examples) 17

Materials with different refractive indices are very important for complex optical systems 18

Polarization of a Propagating Wave An electromagnetic wave can be decomposed into two linear polarized waves. … a constant phase shift of two linear polarized waves describes an elliptically polarized wave 19

Transmission and Reflection Vacuum Glass: n=1. 5 Brewster angle – complete polarization of reflected electromagnetic wave (polarization of light) Vacuum Glass (n=1, 5) 20

Transmission and Reflection Vacuum Germanium: n=5, 3 Vacuum Germanium (n=5, 3) 21

Brewster angle Vacuum Germanium: n=5, 3 Vacuum Germanium (n=5, 3) 22

Optical Reflection Glass (n=1, 5) Vacuum Total internal reflection Glass (n=1, 5) Vacuum 23

Total Internal Reflection n 2 c n 1 Glass (n = 1, 5): c = 41, 8° Water (n = 2): c = 30° 24

Transmission and Reflection with an Incident Angle of 0° Interface material - vacuum: 25

Transmission and Reflection with Complex Index of Refraction 26

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Transmission and Reflection with Complex Index of Refraction Vacuum Copper (n=0. 14 -3. 35 i) Copper n = 0. 14 k = 3. 35 R = 95. 6 % 28

Transmission and Reflection with Complex Index of Refraction Vacuum Sodium (n=0. 0481. 86 i) Sodium n = 0. 048 k = 1. 86 R = 95. 8 % 29

Transmission and Reflection with Complex Index of Refraction Vacuum Gallium (n=3. 69 -5. 43 i) Gallium n = 3. 69 k = 5. 43 R = 71. 3 % 30

Transmission and Reflection with Complex Index of Refraction Vacuum Cobalt (n=2. 0 -4. 0 i) Cobalt n = 2. 0 k = 4. 0 R = 68. 0 % 31

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Reflection with Complex Index of Refraction Influence of absorption (weakening, damping) on the reflection 33

Reflection with Complex Index of Refraction Total external reflection vanishes 34

Reflectivity as function of Refractive Index and Absorption Reflectivity increases with increasing index of refraction and an increasing absorption index Fig. 11. 2 Reflectivity as function of absorption and refractive index 35

Refractive Index as function of Wavelength Material (Sphalerite) Color of Materials (Rutile) Fig. 11. 5 Refractive index as function of absorption index and absorption coefficient as function of wavelength for Si (a), KCl (b) and Cu (c). 36

Reflection and Transmission of a Thin Film Fresnel coefficients at the interfaces: Phase shift: 37

Reflection and Transmission of a Thin Film Intensity (%) Vacuum Glass (n = 1. 5, t = 6 μm) Vacuum, λ = 600 nm Constant wavelength (monochromatic radiation) Reflection Thickness of the film is ten times of the wavelength Angle of incidence (degree) 38

Reflection and Transmission of a Thin Film Intensity (%) Vacuum Glass (n = 1. 5, t = 1. 2 μm) Vacuum, λ = 600 nm Constant wavelength (monochromatic radiation) Reflection Thickness of the film is two times of the wavelength Angle of incidence (degree) 39

Reflection and Transmission of a Thin Film Vacuum Glass (n = 1. 5, t = 24 μm) Vacuum, λ = 600 nm Intensity (%) Constant wavelength (monochromatic radiation) Reflection Thickness of the film is 40 times of the wavelength Angle of incidence (degree) 40

Reflection and Transmission of a Thin Film Vacuum Glass (n = 1. 5, t = 1. 2 μm) Vacuum, λ = 300 -600 nm Different wavelengths (polychromatic radiation) Intensity (%) Thickness of film is 1. 2 m Different “Colors” are reflected and transmitted differently. Angle of incidence (degree) 41