• Optoelectronics

  • FileName: JDWUAH Optoelectronics Ch7.pdf [read-online]
    • Abstract: OptoelectronicsEE/OPE 451, OPT 444Fall 2009 Section 1: T/Th 9:30‐ 10:55 PMJohn D. Williams, Ph.D.Department of Electrical and Computer Engineering406 Optics Building ‐ UAHuntsville, Huntsville, AL 35899

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EE/OPE 451, OPT 444
Fall 2009 Section 1: T/Th 9:30‐ 10:55 PM
John D. Williams, Ph.D.
Department of Electrical and Computer Engineering
406 Optics Building ‐ UAHuntsville, Huntsville, AL 35899
Ph. (256) 824‐2898  email: [email protected]
Office Hours: Tues/Thurs 2‐3PM
JDW, ECE Fall 2009
• 7.1 Polarization 
– A. State of Polarization B. Malus's Law 
• 7.2 Light Propagation in an Anisotropic Medium: 
– A. Optical Anisotropy 
– B. Uniaxial Crystals and Fresnel's Optical Indicatrix
– C. Birefringence of Calcite 
– D. Dichroism
• 7.3 Birefringent Optical Devices 
– A. Retarding Plates 
– B. Soleil‐Babinet Compensator 
– C. Birefringent Prisms 
• 7.4 Optical Activity and Circular Birefringence 
• 7.5 Electro‐Optic Effects
– A. Definitions 
– B. Pockels Effect 
– C. Kerr Effect 
• 7.6 Integrated Optical Modulators
– A. Phase and Polarization Modulation 
– B. Mach‐Zehnder Modulator 
Prentice‐Hall Inc.
– C. Coupled Waveguide Modulators  © 2001 S.O. Kasap
• 7.7 Acousto‐Optic Modulator ISBN: 0‐201‐61087‐6
• 7.8 Magneto‐Optic Effects 
• 7.9 Non‐Linear Optics and Second Harmonic Generation 
JDW, ECE Fall 2009 Chapter 7 Homework:  2,3,7,8,9,11,12,14,15
• Polarization describes the behavior of the electric field vector in an EM wave
• light propagating with random orientation is referred to as unpolarized
• If field oscillations are confined to a well defined line, then the wave is linearly polarized
• Linearly polarized E field oscillations create a plane of polarization between the k and E vectors
• The field vector for a plane wave propagating in z with oscillations along a line in the xy plane is
E = Ex x + E y y
ˆ ˆ Plane of polarization
φ= 180o
E x = E xo cos(ωt − kz ) E E o = xExo‐yEyo
x y
E y = E yo cos(ωt − kz + φ )
^ ^
x xEx
• φ is the phase difference between E −yEy
z E
the x and y terms and yields (a) (b) (c)
angle at which the field lies
off of the x axis (a) A linearly polarized wave has its electric field oscillations defined along a line
perpendicular to the direction of propagation, z. The field vector E and z define a plane of
polarization. (b) The E-field oscillations are contained in the plane of polarization. (c) A
linearly polarized light at any instant can be represented by the superposition of two fields Ex
and Ey with the right magnitude and phase.
JDW, ECE Fall 2009 © 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Circular Polarization
• right circular polarization  ‐ clockwise rotation of the E field as it propagates along k 
• left circular polarization  ‐ counter clockwise rotation of the E field as it propagates along k
• Assume that φ = 90o and that the Exo and Eyo fields have the same amplitude.  Then
E = Ex x + E y y
ˆ ˆ
E x = E xo cos(ωt − kz )
E y = E yo cos(ωt − kz + φ ) = − E yo cos(ωt − kz )
E 2 = E x2 + E y
θ = kΔz
Δz Ey
θ = kΔz
z Ex
A right circularly polarized light. The field vector E is always at right
angles to z , rotates clockwise around z with time, and traces out a full
circle over one wavelength of distance propagated.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
JDW, ECE Fall 2009
Linear and Circular Polarization
y y y y
(a) (b) (c) (d)
x x x x
Exo =1
Exo Exo=1 Exo=1
Eyo =1
Eyo Eyo=1 Eyo=1
φ=0 φ=0
φ = π/2 φ = −π/2
Examples of linearly, (a) and (b), and circularly polarized light (c) and (d); (c) is
right circularly and (d) is left circularly polarized light (as seen when the wave
directly approaches a viewer)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
JDW, ECE Fall 2009
Linear and Elliptical Polarization
• Assume that the magnitude of one vector component in E is larger then the other
• Instead of a circle, the wave generates and ellipse as it propagates along k in the z direction
y y y
(a) (b) (c)
x x x
Exo Exo=1 Exo=1
Eyo Eyo=2 Eyo=2
φ=0 φ = π/4 φ = π/2
(a) Linearly polarized light with E yo = 2Exo and φ = 0. (b) When φ = π/4 (45°), the light is
right elliptically polarized with a tilted major axis. (c) When φ = π/2 (90°), the light is
right elliptically polarized. If Exo and Eyo were equal, this would be right circularly
polarized light.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
JDW, ECE Fall 2009
Example:  Elliptical and Circular Polarization
• Show that if the magnitudes, Exo and Eyo, are different and the phases difference is 90o, that 
the wave is elliptically polarized
E = Ex x + E y y
ˆ ˆ
Ex ≠ E y
= cos(ωt − kz )
E xo
Ey ⎛ π⎞
= cos⎜ ωt − kz + ⎟ = − sin(ωt − kz )
E yo ⎝ 2⎠
⎛ E ⎞ ⎛ Ey ⎞
1 = (cos(ωt − kz ) ) + (− sin(ωt − kz ) ) = ⎜ x ⎟ + ⎜ ⎟
2 2
⎜E ⎟ ⎜E ⎟
⎝ xo ⎠ ⎝ yo ⎠
• Equation for an ellipse if the denominators do not equal
• Further, at ωt=0, E =Ex=Exo and  at   ωt=π/2, E =Ey = Eyo
• Thus the field rotates in a clockwise position:    Right Elliptically Polarized
JDW, ECE Fall 2009
Malus’s Law
• A linear polarizer will only allow electric 
field oscillations through the structure along 
some preferred direction
• This preferred direction is called the  Ecos θ
transmission axis and the transmitted light  Linearly
is polarized based on the orientation of the  polarized light E TA 2
Light detector
polarizing medium
TA 1
• Polaroid sheets are common examples of 
linear polarizers Polarizer 2 = Analyzer
• Dichroic crystals such as tourmaline are  Polarizer 1
good polarizer's because they are optically 
anisotropic and attenuate the fields not  Unpolarized light
oscillating along the optical axis of the  Randomly polarized light is incident on a Polarizer 1 with a transmission axis TA 1. Light
crystal emerging from Polarizer 1 is linearly polarized with E along TA 1, and becomes incident
on Polarizer 2 (called "analyzer") with a transmission axis TA 2 at an angle θ to TA 1. A
• Combining two polarizers detector measures the intensity of the incident light. TA 1 and TA 2 are normal to the light
– First generates initial polarization © 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
– 2nd, the analyzer is used to measure 
the degree of polarization of the first 
by reducing field intensity as a function 
of off axis polarization by the analyzer
JDW, ECE Fall 2009
Optical Anisotropy
• We know that electronic polarization in a medium 
depends on crystal orientation
• Materials with isotropic crystal structures typically 
generate uniform polarization along all three 
principle axis and little or no off axis polarization 
• Such materials are said to be optically isotropic and 
A line viewed through a cubic sodium chloride (halite) crystal
have uniform refractive indices for all incident  (optically isotropic) and a calcite crystal (optically anisotropic).
• Crystals with anisotropic crystal structure generate  • In the same manner that crystals have unit 
vectors representing principle axes, their 
different degrees of polarization in different  permittivity and refractive indices also will also 
directions, thereby exhibiting different refractive  have principle indices indicating the different 
indices in different directions refraction characteristics at different angles of 
• Unpolarized light entering an optically anisotropic  incidence
crystal along all but only a few principle angles of  • Crystals with 3 distinct principle axis and two 
incidence breaks into two different directions with  optic axis are biaxial crystals
different polarizations and phase velocities • Crystals with 2 principle axis and 1 optical axis 
are called uniaxial crytals
• Such materials are referred to as birefringent • Uniaxial crystals such as quartz have n2 > n1  
because incident light beams may be doubly  Uniaxial crystals such as calcite are positive
refracted • n3 

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