1 Optical Properties of Materials … reflection … refraction (Snell’s law) … index of refraction Index of refraction Absorption

2 Maxwell’s Equations Materials equations

3 Maxwell’s Equations … no free charge … wave equation

The Wave Equation 4

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

6 Amplitude and Intensity of the Propagating Wave

7 Relationship between Dielectric and Optical Constants * dielectric constant = permittivity

Insulator 8 … 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 Reflection: Transmission: (Snell’s law) Same amplitude and phase of wave at the point “0”

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

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

14 Fresnel Equations

15 Fresnel Coefficients Snell

16 Index of Refraction (Experimental Examples)

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

18 Transmission and Reflection Brewster angle – complete polarization of reflected electromagnetic wave (polarization of light) Vacuum  Glass (n=1,5) Vacuum  Glass: n=1.5

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

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

21 Total Internal Reflection n1n1 n2n2 cc Glass (n = 1,5):  c = 41,8° Water (n = 2):  c = 30°

22 Transmission and Reflection with Complex Index of Refraction

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

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25 Transmission and Reflection with Complex Index of Refraction Copper n = 0.14 k = 3.35 R = 95.6 % Vacuum  Copper (n= i)

26 Transmission and Reflection with Complex Index of Refraction Sodium n = k = 1.86 R = 95.8 % Vacuum  Sodium (n= i)

27 Transmission and Reflection with Complex Index of Refraction Gallium n = 3.69 k = 5.43 R = 71.3 % Vacuum  Gallium (n= i)

28 Transmission and Reflection with Complex Index of Refraction Cobalt n = 2.0 k = 4.0 R = 68.0 % Vacuum  Cobalt (n= i)

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

31 Reflection with Complex Index of Refraction Total external reflection vanishes

32 Reflectivity as function of Refractive Index and Absorption Reflectivity increases with increasing index of refraction and an increasing absorption index Fig Reflectivity as function of absorption and refractive index

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

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

35 Reflection and Transmission of a Thin Film Constant wavelength (monochromatic radiation) Thickness of the film is ten times of the wavelength Reflection Vacuum  Glass (n = 1.5, t = 6 μm)  Vacuum, λ = 600 nm Angle of incidence (degree) Intensity (%)

36 Reflection and Transmission of a Thin Film Constant wavelength (monochromatic radiation) Thickness of the film is two times of the wavelength Reflection Vacuum  Glass (n = 1.5, t = 1.2 μm)  Vacuum, λ = 600 nm Angle of incidence (degree) Intensity (%)

37 Reflection and Transmission of a Thin Film Constant wavelength (monochromatic radiation) Thickness of the film is 40 times of the wavelength Reflection Vacuum  Glass (n = 1.5, t = 24 μm)  Vacuum, λ = 600 nm Angle of incidence (degree) Intensity (%)

38 Reflection and Transmission of a Thin Film Different wavelengths (polychromatic radiation) Thickness of film is 1.2  m Different “Colors” are reflected and transmitted differently. Vacuum  Glass (n = 1.5, t = 1.2 μm)  Vacuum, λ = nm Angle of incidence (degree) Intensity (%)