Instructor’s Power Point for Optoelectronics and Photonics: Principles and Practices

Second Edition

ISBN-10: 0133081753Second Edition Version 1.0337

[6 February 2015]

A Complete Course in Power Point

Chapter 1

Updates andCorrected Slides

Class Demonstrations

Class Problems

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Slides on Selected Topics on

Optoelectronics

may be available at the author website

http://optoelectronics.usask.ca

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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: 0132151499, ISBN-13: 9780132151498. © 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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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: 0132151499, ISBN-13: 9780132151498. © 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.

Copyright Information and Permission: Part I

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From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, © 2013 Pearson Education, USA

Chapter 1 Wave Nature of Light

WAVELENGTH DIVISION MULTIPLEXING: WDM

EDFA Configurations

Erbium Doped Fiber Amplifier

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.

Ex = Eo cos(tkz + )

Ex = Electric field along x at position z at time tk = 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.

(tkz + ) = = Phase of the wave

This is a monochromatic plane wave of infinite extent traveling in the positive z direction.

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.

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.

The time and space evolution of a given phase , for example that corresponding to a maximum field is described by

= tkz + = 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

kt

zv

Phase Velocity

The phase difference between two points separated by z is simply kz

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 kz or 2z/

Phase change over a distance Dz

= tkz + D = kDz

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(tkz)] or

Ex(z,t) = Re[Ecexpj(tkz)]

where Ec = Eoexp(jo) is a complex number that represents the amplitude of the wave and includes the constant phase information o.

Exponential Notation

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(tkr + )

If propagation is along z, kr 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, kr = kxx + kyy + kzz.

Wave Vector or Propagation Vector

Wave Vector k

A traveling plane EM wave along a direction k

E (r,t) = Eocos(tkr + )

Maxwell’s Wave Equation

02

2

2

2

2

2

2

2

t

E

z

E

y

E

x

Eoro

Ex = Eo cos(tkz + )

A plane wave is a solution of Maxwell’s wave equation

Substitute into Maxwell’s Equation to show that this is a solution.

Spherical Wave

)cos( krtr

AE

Examples of possible EM waves

Optical divergence refers to the angular separation of wave vectors on a given wavefront.

Gaussian Beam

Wavefronts of a Gaussian light beam

The radiation emitted from a laser can be approximated by a Gaussian beam. Gaussian beam approximations are widely used in photonics.

Gaussian Beam

Intensity = I(r,z) = [2P/(pw2)]exp(-2r2/w2)

q = w/z = l/(pwo) 2q = Far field divergence

The intensity across the beam follows a Gaussian distribution

Beam axis

The Gaussian Intensity Distribution is Not Unusual

I(r) = I(0)exp(-2r2/w2)

The Gaussian intensity distribution is also used in fiber opticsThe fundamental mode in single mode fibers can be approximated with a

Gaussian intensity distribution across the fiber core

Gaussian Beam

zo = pwo2/l

2q = Far field divergence

2/12

2122

oo w

zww

2

oo

wz

2/12

122

oo z

zww

Rayleigh range

Gaussian Beam

Real and Ideal Gaussian Beams

2/12

2

2

122

ororr w

Mzww

)/(2

ror

o

ror w

w

wM

Definition of M2

Real Gaussian Beam

2/12

2

2

122

ororr w

Mzww

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.

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.

Gaussian Beam in an Optical Cavity

mm20m24.1

m25)mm1(2122

2/12

oo

oo z

zw

z

zww

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

Refractive Index

Maxwell’s Wave Equation in an isotropic medium

02

2

2

2

2

2

2

2

t

E

z

E

y

E

x

Eoro

Ex = Eo cos(tkz + )A plane wave is a solution of Maxwell’s wave equation

orok 1

v

The phase velocity of this plane wave in the medium is given by

The phase velocity in vacuum is

oook 1

c

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

Phase Velocity and er

oor 1

ν

Phase Velocity and er

oor 1

ν

r

cn

vRefractive index n definition

Refractive Index n

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

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

ko Free-space propagation constant (wave vector) ko 2π/o Free-space wavelengthk Propagation constant (vave vector) in the medium Wavelength in the medium

ok

kn

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

Refractive Index and Propagation Constant

Refractive Index and Wavelength

lmedium = l /n

kmedium = nkIn free space

It is customary to drop the subscript o on k and l

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

Refractive Index and Isotropy

n depends on the wavelength

22

222at2

21

o

o

eo cm

ZeNn

Dispersion relation: n = n(l)

23

2

23

22

2

22

21

2

212 1

AAAn

Sellmeier Equation

lo = A “resonant frequency”

Nat =Number of atoms per unit volumeZ = Number of electrons in the atom (atomic number)

The simplest electronic polarization gives

n depends on the wavelength

n = n-2(hu)-2 + n0 + n2(hu)2 + n4(hu)4

Cauchy dispersion relationn = n(u)

n depends on the wavelength

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

When two perfectly harmonic waves of frequencies and + and wavevectors kk 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

vg

ddk

Group Velocity and Group Index

Two slightly different wavelength waves traveling in the same direction result in a wavepacket that has an amplitude variation that travels at the group velocity.

Group Velocity

dk

dgv

Group Velocity

Consider two sinusoidal waves that are close in frequency, that is, they have frequencies and + . Their wavevectors will be kk and k + k. The resultant wave is

Ex(z,t) = Eocos[()t(kk)z] + Eocos[( + )t(k + k)z]

By using the trigonometric identity

cosA + cosB = 2cos[1/2(AB)]cos[1/2(A + B)] we arrive at

Ex(z,t) = 2Eocos[()t(k)z][cos(tkz)]