**UFRJ**

# Capítulo 20 Materiais Ópticos

(Parte **1** de 2)

20 Photonic Materials

Which, if any, of the materials listed in Table 20–1 could cause the beam of photons to continue at an angle of 18 to 20 from the normal of the material’s surface?

Solution:Assuming that the beam originally is passing through air or a vacuum,

In Table 20–1, only ice, water, and Teflon have an index of refraction between 1.236 and 1.367.

Solution:The index of refraction for polystyrene is 1.60. Since the incident angle uiis 20 , the angle of the beam as it passes through the polystyrene block will be:

216The Science and Engineering of MaterialsInstructor’s Solution Manual

From the sketch, we can find the displacement of the beam expected if no refraction occurs:

We can also find the displacement of the beam when refraction occurs:

Because of refraction, the beam is displaced 1.820 1.095 0.725 cm from its path had no refraction occurred.

20–12Abeam of photons passes through air and strikes a soda-lime glass that is part of an aquarium containing water. What fraction of the beam is reflected by the front face of the glass? What fraction of the remaining beam is reflected by the back face of the glass?

Solution:The fraction of the beam reflected by the front face is:

The fraction of the remaining beam reflected from the back face of the glass is:

20–13We find that 20% of the original intensity of a beam of photons is transmitted from air through a 1-cm thick-material having a dielectric constant of 2.3 and back into air. Determine the fraction of the beam that is (a) reflected at the front surface, (b) absorbed in the material, and (c) reflected at the back surface. (d) Determine the linear absorption coefficient of the photons in the material.

Solution:The dielectric material has an index of refraction of:

(a)The fraction of the beam reflected at the front surface is:

(b)The fraction transmitted through the material is 0.2; therefore the linear absorption coefficient of the materials is:

0.725 cm

After reflection, the intensity of the remaining beam is

Before reflection at the back surface, the intensity of the beam is: The fraction of the beam that is absorbed is therefore

(c)The fraction of the beam reflected off the back surface is:

20–14Abeam of photons in air strikes a composite material consisting of a 1-cm-thick sheet of polyethylene and a 2-cm-thick sheet of soda-lime glass. The incident beam is 10 from the normal of the composite. Determine the angle of the beam with respect to the normal as the beam (a) passes through the polyethylene, (b) passes through the glass, and (c) passes through air on the opposite side of the composite. (d) By what distance is the beam displaced from its original path when it emerges from the composite?

Solution:The figure shows how the beam changes directions, and the amount that the beam is displaced from the normal to the point of entry, as it passes through each interface.

(a)As the beam passes from air into polyethylene (which has an index of refraction of 1.52), γ = 6.69 polyethylene glass

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(b)When the beam enters the glass (which has an index of refraction of 1.50), the new angle is:

(c)When the beam emerges from the glass back into air, the final angle is:

When the beam then reaches the glass-air interface, it has been displaced an additional:

The total displacement is therefore x y 0.351 cm. If the beam had not been refracted, the displacement would have been:

The beam has therefore been displaced 0.529 0.351 0.178 cm from its original path.

Therefore the maximum angle that the incoming beam can deviate from the fiber axis is:

Solution:

nteflon nglass sinui sinut

original intensity after the stimulus is removed.

Solution:

Solution:We can use the information in the problem to find the relaxation time for the material.

20–30By appropriately doping yttrium aluminum garnet with neodymium, electrons are excited within the 4fenergy shell of the Nd atoms. Determine the approximate energy transition if the Nd:YAG serves as a laser, producing a wavelength of 532 nm. What color would the laser beam possess?

Solution:The energy transition is:

The wavelength of 532 nm is 5320 Å or 5.32 10 5cm. This wavelength corresponds to a color of green.

(a) ZnO (b) GaP (c) GaAs (d) GaSb (e) PbS

Solution:The incident beam must have an energy greater than the energy gap of the material in order for luminescence to occur. The energy of the incident photons is:

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From Chapter 18 and literature values, the energy gaps of the five materials are:

ZnO:3.2 eV GaP:2.24 eV GaAs:1.35 eV GaSb:0.67 eV PbS:0.37 eV

Consequently the photons, having energy 1.655 eV, will be able to excite electrons in GaAs, GaSb, and PbS; however electrons will not be excited in ZnO and GaP.

20–32Determine the wavelength of photons produced when electrons excited into the conduction band of indium-doped silicon (a) drop from the conduction band to the acceptor band and (b) then drop from the acceptor band to the valence band (see Chapter 18).

Solution:The acceptor energy in Si–In is 0.16 eV; the energy gap in pure Si is 1.107eV. The difference between the energy gap and the acceptor energy level is 1.107 0.16 0.947 eV.

(a)The wavelength of photons produced when an electron drops from the conduction band to the acceptor band, an energy difference of 0.947 eV,is:

(b)The wavelength of photons produced when the electron subsequently drops from the acceptor band to the valence band, an energy difference of 0.16 eV, is:

(Parte **1** de 2)