07 Optical Properties

Question 1

1. Cite the wavelength range for visible light radiation.

Answer 1

400 (violet)-700nm(red)

Question 2

2. Note the relationship between the velocity of electromagnetic radiation in a vacuum, and vacuum values of the electric permittivity and magnetic permeability.

Answer 2

c = 1/sqrt(ε₀µ₀)

c…speed of light in vacuum (300,000 km/s)

ε₀ electric permittivity

µ₀ magnetic permeability

Question 3

3. Given the velocity of electromagnetic radiation in a vacuum as well as the radiation frequency, compute the radiation wavelength.

Answer 3

λ = c/f

Question 4

4. Define photon.

Answer 4

photon is a quantum unit of light

from a quantum-mechanical point of view, electromagnetic radiation is composed of photons - groups or packets of energy that are quantized - that is, they can have only specific values of energy

Question 5

5. Compute the energy of a photon given its frequency and the value of Planck’s constant.

Answer 5

Question 6

6. List three phenomena that may occur with light radiation as it passes from one medium into another.

Answer 6

1. refraction (Licht-Brechung)
2. reflection
3. absorption
4. transmission

Question 7

7. Cite distinctions between optical transparency, translucency, and opacity.

Answer 7

regarding the degree of light transmissivity, materials are classified as follows:

• transparent - light is transmitted through the material with very little absorption and reflection
• translucent - light is transmitted diffusely; there is some scattering within the interior of the material
• opaque - virtually all light is scattered or reflected such that none is transmitted through the material

Question 8

8. (a) Briefly describe electronic polarization that results from electromagnetic radiation-atomic interactions.
   (b) Cite two consequences of electronic polarization.

Answer 8

a) electric field component of a light wave induces a shift of the electron cloud around an atom relative to its nucleus (e- cloud distorts)

b)

1. absorption
2. refraction of light

Question 9

9. Briefly explain how electromagnetic radiation may be absorbed by electron transitions.

Answer 9

electromagnetic (em) radiation may be absorbed by causing the excitation of e- from one energy state to a higher state

Question 10

10. Briefly explain why metallic materials are opaque to visible light.

Answer 10

because of the absorption and then reemission of light radiation within a thin outer surface layer

absorption occurs via the excitation of e- from occupied energy states to unoccupied ones above the Fermi energy level. Reemission takes place by decay electron transitions in the reverse direction

Question 11

11. Note what determines the color of metallic materials.

Answer 11

the color of a metal is determined by the spectral decomposition of the reflected light i.e. of which type of em-frequencies the reflected light is composed of

Question 12

12. Define index of refraction.

Answer 12

light radiation experiences refraction in transparent materials - that is, its velocity is decreased, and the light beam is bent at the interface

indx of refraction = ratio of veolcity in vacuum c (or c₀) to the velocity in the medium

n = c/v = c₀/c

Question 13

13. Calculate the index of refraction for a material given values of its dielectric constant and relative magnetic permeability.

Answer 13

speed of light in the considered material v:

v = 1/sqrt(ε*µ)

ε, µ… elect. and magn. permeability of the material

ε_R = ε/ε₀ >=1 …rel. electr. permittivity = dielectric constant

µ_R = µ/µ₀ …rel. magn. permeability

n = c/v

Question 14

14. Note the influence of atomic/ionic size on index of refraction.

Answer 14

refrection is a consequence of electronic polarization of the atoms or ions

the larger an atom or ion, the greater the index of refraction

Question 15

15. Calculate the reflectivity at an interface for normally incident light given the indexes of refraction for the media on both sides of the interface.

Answer 15

reflectivity R := I_R/I₀

I_R…intensity of the reflected beam

I₀…intensity of the incident beam

for normally incident light we have:

R = [(n2-n1)/(n2+1)]^2

n1. ..index of refraction of medium 1 (where the beam is coming)
n2. ..index o. ref. of medium 2

in all other cases refer to Fresnel formulas

Question 16

16. For high-purity insulators and semiconductors:
    (a) describe the mechanism of photon absorption;
    (b) explain how the magnitude of the band gap energy influences photon absorption;
    (c) cite band gap energy values for which there is no absorption of visible light radiation; and
    (d) cite band gap energy values for which there is only partial absorption of visible light radiation.

Answer 16

pure nonmetallic materials are either intrinsically transparent or opaque:

a) see Fig: photon absorbtion results if a photon´s energy is sufficient to promote valence band -> conduction band elecron transitions
b) see Fig.
c) Eg > 3.1 eV (blue light, λmin = 400nm)
d) 1.8 eV < Eg < 3.1 eV partial absorption, material is colored

opacity results in relatively narrow band gap materials (Eg < 1.8 eV, red light λmax = 700nm)

Question 17

17. For insulators and semiconductors that contain electrically active defects:
    (a) describe the mechanism of photon absorption;
    (b) cite two decay paths that are possible as excited electrons return to their ground states.

Answer 17

a) photon absorbtion again happens via a valence-band-conduction band electron excitation, the impuritiy energy level from the defect lies within the band gap

b)

1. emission of two photons involving e- decay first into an impurity state (donor or acceptor state) and finally to the ground state
2. generation of both a phonon (excitation of a periodic, elastic arrangement of atoms with an energy dE) and a photon as an excited e- falls first into an impurity level and finally back to its ground state

Question 18

18. Calculate the intensity of nonabsorbed radiation that passes through a transparent medium of specified thickness, given the intensity of nonreflected radiation incident on the front face, as well as the absorption coefficient for the particular medium.

Answer 18

Question 19

19. Determine the intensity of radiation that emerges from the back face of a transparent solid of specified thickness, given the intensity of radiation that impinges on the front face, and, in addition, values of the material’s reflectance and absorption coefficient.

Answer 19

Question 20

20. (a) Briefly explain why some semiconducting materials appear colored.
    (b) Now explain the source of color in many insulating materials.

Answer 20

a) Because their band gaps are within the range of visible light 1.8eV to 3.1eV. Thus, the fraction of the visible light having energies greater than Eg is selectively absorbed by valence band -conduction band electron transitions. Some of this absorbed radiation is reemitted when e- falls back to ground state. This frequency is not necessarily the same as of the absorption. As a result, the color depends on the frequency distribution of both transmitted and reemitted light beams.
b) specific impurities introduce electron levels within the forbidden band gap. Light radiation is absorbed by valence band-conduction band electron transitions, some of which is then reemitted at spec. wavelengths as a consequence of e- transitions to and from these impurity levels. The non-absorbed or transmitted light mixed with reemitted light determines the color of the material.

Question 21

21. (a) For inherently transparent dielectric materials (e.g. glass, some plastics), note three sources of internal scattering that can lead to translucency and opacity.
    (b) Briefly explain why internal scattering occurs for each of these sources.

Answer 21

a)

1. in polycrystalline materials that have anisotropic indices of refraction
2. two-phase materials
3. materials containing small pores
4. highly crystalline polymers

b) because light beam experiences interior reflection and/or refraction e.g. anisotropic index of refraction in polycrystalline materials, grain boundaries give rise to refraction and reflexion

Question 22

22. Briefly explain why amorphous materials are normally transparent.

Answer 22

Highly amorphous materials, which means there are no crystalline phases, have little or no scattering and are therefore transparent.

Question 23

23. (a) Describe the phenomena of luminescence and electroluminescence.
    (b) Distinguish between fluorescence and phosphorescence.

Answer 23

with luminescence, energy is absorbed as a consequence of electron excitations, which is subsequently reemitted as visible light

electroluminescence is the phenomenon by which light is emitted as a result of electron-hole recombination (annihilation = Vernichtung of the electron) events that are induced in a forward-biased diode

b) when light is reemitted less than 1s after excitation it´s called fluorescence (residence time in trapped state is rel. long >10^8s)

for longer reemission times, the term phosphorescence is used (residence times <10^8s)

Prof. Holl was not happy with this definition

Question 24

24. Briefly describe the phenomenon of photoconductivity.

Answer 24

is the phenomenon by which the electrical conductivity of some semiconductors may be enhanced by photo-induced electron transitions, by which additional free e- and holes are generated

used in photovoltaic cells

Question 25

25. Briefly describe the operation of a semiconductor light-emitting diode.

Answer 25

works with the phenomenon of electroluminescence

forward biased pn junction attracts e- on the n-side toward the junction, where some them pass into (“inject”) the p-side. Recombination occurs and the energy is in the form of photons of light.

Question 26

26. Briefly describe the construction of and operation of (a) the ruby laser, and (b) the semiconductor laser.

Answer 26

coherent and high-intensity light beams are produced in lasers by stimulated electron transitions

a) a beam is generated by e- that decay back into their ground Cr³⁺ states from metastable excited states (example of a pulsed laser)
The generation of one photon by the decay transition of an electron, induces the emission of other photons that are all in phase with one another. – This cascading effect produces an intense burst of coherent light.

b) beam results from the recombination of excited electrons in the conduction band with valence band holes

Question 27

27. List and describe the functions of various components for an optical fiber communications system.

Answer 27

Question 28

28. Explain the transmission of digitized signals through optical fibers.

Answer 28

interference-free, rapid, intense

Question 29

29. Note and briefly explain functions of the several components that are found in an optical fiber.

Answer 29

• a core through which the pulses of light propagate
• cladding, which provides for total internal reflection and containment of the light beam within the core
• coating, which protects the core and cladding from damage

Question 30

30. Explain what precautions are taken to minimize scattering and attenuation of a light beam that passes through an optical fiber.

Answer 30

extremely pure and high-quality fibers

no impurities or other defects that absorb, scatter and thus attenuate the light beam
no bubbles and surface defects

presence of Cu, Fe, and Va is detrimental (schädlich), reduce concentration to several ppb

core roundness is critical, extremely tight tolerances