1. A Complete Course in Power Point Second Edition Version 1.0337
Instructor’s Power Point for Optoelectronics and Photonics: Principles and Practices
Second Edition
A Complete Course in Power Point
Chapter 1
ISBN-10:
Second Edition Version
[6 February 2015]

2. Updates and Corrected Slides Class Demonstrations Class Problems
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3. Slides on Selected Topics on Optoelectronics
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4. PEARSON Copyright Information and Permission: Part II
This Power Point presentation is a copyrighted supplemental material to the textbook Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education (USA), ISBN-10: , ISBN-13: © 2013 Pearson Education. The slides cannot be distributed in any form whatsoever, electronically or in print form, without the written permission of Pearson Education. It is unlawful to post these slides, or part of a slide or slides, on the internet.
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5. Copyright Information and Permission: Part I
This Power Point presentation is a copyrighted supplemental material to the textbook Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education (USA), ISBN-10: , ISBN-13: © 2013 Pearson Education. Permission is given to instructors to use these Power Point slides in their lectures provided that the above book has been adopted as a primary required textbook for the course. Slides may be used in research seminars at research meetings, symposia and conferences provided that the author, book title, and copyright information are clearly displayed under each figure. It is unlawful to use the slides for teaching if the textbook is not a required primary book for the course. The slides cannot be distributed in any form whatsoever, especially on the internet, without the written permission of Pearson Education.
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6. Important Note
You may use color illustrations from this Power Point in your research-related seminars or research-related presentations at scientific or technical meetings, symposia or conferences provided that you fully cite the following reference under each figure
From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA

7. Chapter 1 Wave Nature of Light

8. WAVELENGTH DIVISION MULTIPLEXING: WDM

9. EDFA Configurations

10. Erbium Doped Fiber Amplifier

11. Light is an electromagnetic wave
An electromagnetic wave is a traveling wave that has time-varying electric and magnetic
fields that are perpendicular to each other and the direction of propagation z.

12. Ex = Eo cos(tkz + )
Ex = Electric field along x at position z at time t k = Propagation constant = 2/  = Wavelength  = Angular frequency = 2u (u = frequency) Eo = Amplitude of the wave  = Phase constant; at t = 0 and z = 0, Ex may or may not necessarily be zero depending on the choice of origin.
(tkz + ) =  = Phase of the wave This is a monochromatic plane wave of infinite extent traveling in the positive z direction.

13. Wavefront A surface over which the phase of a wave is constant is referred to as a wavefront A wavefront of a plane wave is a plane perpendicular to the direction of propagation The interaction of a light wave with a nonconducting medium (conductivity = 0) uses the electric field component Ex rather than By. Optical field refers to the electric field Ex.

14. A plane EM wave traveling along z, has the same Ex (or By) at any point in a given xy plane.
All electric field vectors in a given xy plane are therefore in phase. The xy planes are of
infinite extent in the x and y directions.

15. Phase Velocity
The time and space evolution of a given phase , for example that corresponding to a maximum field is described by  = tkz +  = constant During a time interval t, this constant phase (and hence the maximum field) moves a distance z. The phase velocity of this wave is therefore z/t. The phase velocity v is

16. Phase change over a distance Dz
 = tkz + 
D = kDz
The phase difference between two points separated by z is simply kz since t is the same for each point If this phase difference is 0 or multiples of 2 then the two points are in phase. Thus, the phase difference  can be expressed as kz or 2z/

17. Exponential Notation
Recall that cos= Re[exp(j)] where Re refers to the real part. We then need to take the real part of any complex result at the end of calculations. Thus, Ex(z,t) = Re[Eoexp(j)expj(tkz)] or Ex(z,t) = Re[Ecexpj(tkz)] where Ec = Eoexp(jo) is a complex number that represents the amplitude of the wave and includes the constant phase information o.

18. Wave Vector or Propagation Vector
Direction of propagation is indicated with a vector k, called the wave vector, whose magnitude is the propagation constant, k = 2/. k is perpendicular to constant phase planes. When the electromagnetic (EM) wave is propagating along some arbitrary direction k, then the electric field E(r,t) at a point r on a plane perpendicular to k is E (r,t) = Eocos(tkr + ) If propagation is along z, kr becomes kz. In general, if k has components kx, ky and kz along x, y and z, then from the definition of the dot product, kr = kxx + kyy + kzz.

19. Wave Vector k E (r,t) = Eocos(tkr + )
A traveling plane EM wave along a direction k

20. Maxwell’s Wave Equation
A plane wave is a solution of Maxwell’s wave equation
Ex = Eo cos(tkz + )
Substitute into Maxwell’s Equation to show that this is a solution.

21. Spherical Wave

22. Examples of possible EM waves
Optical divergence refers to the angular separation of wave vectors on a given wavefront.

23. Wavefronts of a Gaussian light beam
Gaussian Beam
The radiation emitted from a laser can be approximated by a Gaussian beam. Gaussian beam approximations are widely used in photonics.
Wavefronts of a Gaussian light beam

24. The intensity across the beam follows a Gaussian distribution
Gaussian Beam
The intensity across the beam follows a Gaussian distribution
Beam axis
Intensity = I(r,z) = [2P/(pw2)]exp(-2r2/w2)
q = w/z = l/(pwo)
2q = Far field divergence

25. The Gaussian Intensity Distribution is Not Unusual
The Gaussian intensity distribution is also used in fiber optics
The fundamental mode in single mode fibers can be approximated with a Gaussian intensity distribution across the fiber core
I(r) = I(0)exp(-2r2/w2)

26. Gaussian Beam
2q = Far field divergence
zo = pwo2/l

27. Gaussian Beam
Rayleigh range

28. Real and Ideal Gaussian Beams
Definition of M2

29. Real Gaussian Beam Real beam
Correction note: Page 10 in textbook, Equation (1.11.1), w should be wr as above and wor should be squared in the parantheses.

30. Gaussian Beam in an Optical Cavity
Two spherical mirrors reflect waves to and from each other. The optical cavity contains a Gaussian beam. This particular optical cavity is symmetric and confocal; the two focal points coincide at F.

32. Refractive Index
When an EM wave is traveling in a dielectric medium, the oscillating electric field polarizes the molecules of the medium at the frequency of the wave The stronger is the interaction between the field and the dipoles, the slower is the propagation of the wave

33. Refractive Index

34. Maxwell’s Wave Equation in an isotropic medium
A plane wave is a solution of Maxwell’s wave equation
Ex = Eo cos(tkz + )
The phase velocity of this plane wave in the medium is given by
The phase velocity in vacuum is

35. Phase Velocity and er
The relative permittivity r measures the ease with which the medium becomes polarized and hence it indicates the extent of interaction between the field and the induced dipoles. For an EM wave traveling in a nonmagnetic dielectric medium of relative permittivity r, the phase velocity v is given by

36. Refractive Index n
Phase Velocity and er
Refractive index n definition

37. Optical frequencies
Typical frequencies that are involved in optoelectronic devices are in the infrared (including far infrared), visible, and UV, and we generically refer to these frequencies as optical frequencies
Somewhat arbitrary range:
Roughly 1012 Hz to 1016 Hz

38. Low frequency (LF) relative permittivity er(LF) and refractive index n.

39. Refractive Index and Propagation Constant
ko Free-space propagation constant (wave vector) ko 2π/ o Free-space wavelength k Propagation constant (vave vector) in the medium  Wavelength in the medium
In noncrystalline materials such as glasses and liquids, the material structure is the same in all directions and n does not depend on the direction. The refractive index is then isotropic

40. kmedium = nk lmedium = l /n Refractive Index and Wavelength
It is customary to drop the subscript o on k and l
kmedium = nk
In free space
lmedium = l /n

41. Refractive Index and Isotropy
Crystals, in general, have nonisotropic, or anisotropic, properties Typically noncrystalline solids such as glasses and liquids, and cubic crystals are optically isotropic; they possess only one refractive index for all directions

42. n depends on the wavelength
Dispersion relation: n = n(l)
The simplest electronic polarization gives
Nat =Number of atoms per unit volume
Z = Number of electrons in the atom (atomic number)
lo = A “resonant frequency”
Sellmeier Equation

43. Cauchy dispersion relation n = n-2(hu)-2 + n0 + n2(hu)2 + n4(hu)4
n depends on the wavelength
Cauchy dispersion relation
n = n(u)
n = n-2(hu)-2 + n0 + n2(hu)2 + n4(hu)4

44. n depends on the wavelength

47. Group Velocity and Group Index
There are no perfect monochromatic waves We have to consider the way in which a group of waves differing slightly in wavelength travel along the z-direction

48. Group Velocity and Group Index
When two perfectly harmonic waves of frequencies  and  +  and wavevectors kk and k + k interfere, they generate a wave packet which contains an oscillating field at the mean frequency  that is amplitude modulated by a slowly varying field of frequency . The maximum amplitude moves with a wavevector k and thus with a group velocity that is given by

49. Group Velocity
Two slightly different wavelength waves traveling in the same direction result in a wave
packet that has an amplitude variation that travels at the group velocity.

51. Group Velocity
Consider two sinusoidal waves that are close in frequency, that is, they have frequencies  and  + . Their wavevectors will be kk and k + k. The resultant wave is Ex(z,t) = Eocos[()t(kk)z] Eocos[( + )t(k + k)z] By using the trigonometric identity
cosA + cosB = 2cos[1/2(AB)]cos[1/2(A + B)] we arrive at Ex(z,t) = 2Eocos[()t(k)z][cos(tkz)]