Transcript No Slide Title
y
Plane of polarization
E
x E y E x
x
E x
E
y
E y z
E (a) (b) (c)
(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 and
E y
with the right magnitude and phase.
E x
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
E
z
=
k
z z
E
E y z E x
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)
(a)
y x
(b)
y x
(c)
y
E
x
(d) E
y E xo E yo
= 0 = 1 = 0
E xo E yo
= 1 = 1 = 0
E xo E yo
= 1 = 1 = /2
E xo E yo
= 1 = 1 = /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)
x
(a)
y x
(b)
y
E
x
(c)
y
E
x E xo E yo
= 1 = 2 = 0
E xo
= 1
E yo
= 2 = /4
E xo
= 1
E yo
= 2 = /2 (a) Linearly polarized light with right elliptically polarized. If polarized light.
E yo
= 2
E xo
and = 0. (b) When right elliptically polarized with a tilted major axis. (c) When = = /4 (45 /2 (90 ), the light is ), the light is
E xo
and
E yo
were equal, this would be right circularly © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
E
cos Linearly polarized light
E
TA 2 Light detector TA 1 Polarizer 2 = Analyzer Polarizer 1 Unpolarized light Randomly polarized light is incident on a Polarizer 1 with a transmission axis TA emerging from Polarizer 1 is linearly polarized with on Polarizer 2 (called "analyzer") with a transmission axis TA detector measures the intensity of the incident light. TA direction.
E
along TA 1 , and becomes incident 2 at an angle 1 . Light to TA 1 . A 1 and TA 2 are normal to the light © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Two polaroid analyzers are placed with their transmission axes, along the long edges, at right angles to each other. The ordinary ray, undeflected, goes through the left polarizer whereas the extraordinary wave, deflected, goes through the right polarizer. The two waves therefore have orthogonal polarizations.
y n
2
O x n
1
n
3
z B O A
P
k
A B
z
Optic axis (a) Fresnel's ellipsoid (b) An EM wave propagating along
OP
at an angle to optic axis.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
y
(a)
x n o
=
n
1
z E o E e n e
(0 ) =
n
2 =
n
1
(b)
y x n o
=
n
1
E o E e n e
(90 ) =
n
3
z
= Optic axis
z
= Optic axis
z
= Optic axis
E o
=
E o
-wave and
E e
=
E e
-wave (a) Wave propagation along the optic axis. (b) Wave propagation normal to optic axis © 1999 S.O. K asap,
Optoelectronics
(Prentice Hall)
e
-wave
o
-wave
k z
Optic axis
E
e Q
k
e
E
o P
k
o O k x
E
e
S
e
= Power flow
k
e
k
e
E
oscillations to paper
E
oscillations // to paper Wavefronts (constant phase fronts)
(a) (b)
(a) Wavevector surface cuts in the
xz
plane for
o
- and
e
-waves. (b) An extraordinary wave in an anisotropic crystal with a is not normal to
k
e
. The energy flow (group velocity) is along than
k
e
.
k
e
at an angle to the optic axis. The electric field
S
e
which is different © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Incident ray Optic axis Principal section Principal section
E //
e
-wave
e
-ray
o
-ray
E
o
-wave
Incident wave A calcite rhomb Optic axis (in plane of paper) An EM wave that is off the optic axis of a calcite crystal splits into two waves called ordinary and extraordinary waves. These waves have orthogonal polarizations and travel with different velocities. The
o
-wave has a polarization that is always perpendicular to the optical axis.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
z
,
n e
Optic axis
x
,
n o E e
-wave
E
E e
-wave
(a)
x
,
n o y E o
-wave
(b)
y
,
n o z E o
-wave Optic axis (a) A birefringent crystal plate with the optic axis parallel to the plate surfaces. (b) A birefringent crystal plate with the optic axis perpendicular to the plate surfaces.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
z
= Slow axis Optic axis
E //
E
E //
n e
=
n
3
E
E
n o L L x
= Fast axis A retarder plate. The optic axis is parallel to the plate face. The in the same direction but at different speeds.
o
- and
e
-waves travel © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Half wavelength plate: = š Optic axis
E Input
x
Output
= arbitrary
E
z x
Quarter wavelength plate: = š/2
z z
45
x x
< 45
z
E
x
= 45
z
E
x
(a) (b)
Input and output polarizations of light through (a) a half-wavelength plate and (b) through a quarter-wavelength plate.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
E
1
E
2
d D
Plate
Wedges can slide Optic axis Optic axis
Soleil-Babinet Compensator
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
e
-ray
Optic axis
A B
o
-ray
Optic axis
A E
1
E
1
e
-ray
E
2
E
1
E
2
E
2
B
Optic axis Optic axis
o
-ray
The Wollaston prism is a beam polarization splitter.
E
1 is orthogonal to the plane of the paper and also to the optic axis of the first prism.
E
2 is in the plane of the paper and orthogonal to
E
1 .
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
E
E
z
E
Levo
z z
Dextro
E
Quartz
L
Optic axis An optically active material such as quartz rotates the plane of polarization of the incident wave: The optical field
E
rotated to
E
. If we reflect the wave back into the material,
E
rotates back to
E
.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Input
y
E
x
E
L
y x
y
E
R x y y y
Output
E
x
x
x
E
L
E
R
Slow Fast Vertically polarized wave at the input can be thought of as two right and left handed circularly polarized waves that are symmetrical,
i.e.
at any instant If these travel at different velocities through a medium then at the output they are no longer symmetric with respect to angle to
y
.
y
, ., and the result is a vector
E
= at an .
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
y n
2 =
n o z n
1 =
n o x
KDP, LiNbO 3
(a)
y
n
2 KDP
E a z n
1
(b )
x
45
x n
1
n
2
z y E a
(c)
x
LiNbO 3 (a) Cross section of the optical indicatrix with no applied field, applied external field modifies the optical indicatrix. In a KDP crystal, it rotates the principal axes by 45 to
x
and
y
and
n
1 and
n
2 change to
n
1
n
1 = and
n
2
n
2 =
n o
(b) The . (c) Applied field along and
n
2 .
y
in LiNbO 2 modifies the indicatrix and changes
n
1 and
n
2 change to
n
1 © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Input light
E
y
V
E
x d E a x y
E
y z
E
x z
Output light Tranverse Pockels cell phase modulator. A linearly polarized input light into an electro-optic crystal emerges as a circularly polarized light.
E a
is the applied field parallel to
y
.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
QWP
Input light
P V
Crystal
y A
Transmission intensity
I o
Detector
Q
x z
0
V
V
Left: A tranverse Pockels cell intensity modulator. The polarizer their transmission axis at right angles and
P
polarizes at an angle 45 Transmission intensity vs. applied voltage characteristics. If a quarter-wave plate ( is inserted after
P
, the characteristic is shifted to the dashed curve.
P
and analyzer
A
have to
y
-axis. Right:
QWP
) © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
(a)
E a x z n o n e n o y
(b)
Input light
E
z E a y
E
z
Output light
E
x x
(a) An applied electric field, via the Kerr effect, induces birefringences in an otherwise optically istropic material. (b) A Kerr cell phase modulator.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Coplanar strip electrodes
V
(
t
) Polarized input light LiNbO 3
L
EO Subst rate
y x z
Waveguide Thin buffer layer
d E a
LiNbO 3 Cross-section Integrated tranverse Pockels cell phase modulator in which a waveguide is diffused into an electro-optic (EO) substrate. Coplanar strip electrodes apply a transverse field
E a
through the waveguide. The substrate is an
x
-cut LiNbO 3 and typically there is a thin dielectric buffer layer (
e.g.
~200 nm thick SiO 2 ) between the surface electrodes and the substrate to separate the electrodes away from the waveguide.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
In
C A B V
(
t
) Electrode
B
Waveguide
A
EO Substrate
D
Out LiNbO 3 An integrated Mach-Zender optical intensity modulator. The input light is split into two coherent waves
A
and
B
, which are phase shifted by the applied voltage, and then the two are combined again at the output.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
x z
Top view Cross-section Coupled waveguides
n A A d n B B n s
Input
P A
(0)
B A P B
(
L o
)
P A
(
L o
)
E E A E B P A
(
z
)
L o x
(a) (b)
P B
(
z
)
z
(a) Cross section of two closely spaced waveguides
A
and
B
(separated by
d
) embedded in a substrate. The evanescent field from
A
extends into
B
and vice versa.
Note:
n A
and
n B
>
n s
(= substrate index).
(b) Top view of the two guides
A
and
B
that are coupled along the
z
-direction. Light is fed into
A
at
z
= 0, and it is gradually transferred to light been transferred to
A
in the same way.
B
along
z
. At
z
=
L o
, all the
B
. Beyond this point, light begins to be transferred back to © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
P B
(
L o
)/
P A
(0) 100% 0 Transmission power ratio from guide
A
to guide
B
over the transmission length
L o
as a function of mismatch
V
3)
/L o
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Waveguides
V
(
t
)
L o A
In Fibers Electrode LiNbO 3
B V
(
t
) Cross-section
d A E a B
LiNbO 3 Coupled waveguides An integrated directional coupler. Applied field two guides and changes the strength of coupling.
E a
alters the refractive indices of the © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Acoustic absorber Incident light Acoustic wave fronts Induced diffraction grating Diffracted light Through light Piezoelectric crystal Modulating RF voltage Interdigitally electroded transducer Traveling acoustic waves create a harmonic variation in the refractive index and thereby create a diffraction grating that diffracts the incident beam through an angle 2 .
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Incident optical beam
A B
Diffracted optical beam
A' B' x
Acoustic wave
x n
min
n
max
n
min
n
max
O P Q
si n
O' v
acoustic si n Acoustic wave fronts
n
min
n
ma x
n
Simplified
n
min Actual
n
ma x
n
Consider two coherent optical waves scattered) from two adjacent acoustic wavefronts to become angle
A
and
B
being "reflected" (strictly, is exaggerated (typically this is a few degrees).
A'
and
B'
. These reflected waves can only constitute the diffracted beam if they are in phase. The © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Polarizer Light Reflected light
E
Source
E
y
Faraday medium
B
E
E
Reflector The sense of rotation of the optical field magnetic field for a given medium (given Verdet constant). If light is reflected back into the Faraday medium, the field rotates a further come out as
E
with a 2
E
depends only on the direction of the rotation with respect to
E
.
in the same sense to © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
E o P
+
P P
-
E o E o E
E o P
+
P
-
t t P
sin
t
-cos2
t
DC
t
(a) (b) (c)
(a) Induced polarization vs. optical field for a nonlinear medium. (b) Sinusoidal optical field oscillations between
E o
result in polarization oscillations between
P
+ and
P
. (c) The polarization oscillation can be represented by sinusoidal oscillations at angular frequencies (fundamental), 2 (second harmonic) and a small DC component.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Second harmonics Fundamental
v
1
k
1
S
1
S
2
S
3
k
2
v
2 Crystal As the fundamental wave propagates, it periodically generates second harmonic waves (
S
1 ,
S
2 ,
S
3 , ...) and if these are in phase then the amplitude of the second harmonic light builds up.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Laser Nd:YAG = 1064 nm KDP Optic axis IM = 1064 nm = 532 nm Filter = 532 nm A simplified schematic illustration of optical frequency doubling using a KDP (potassium dihydrogen phosphate) crystal. IM is the index matched direction at an angle (about 35 ) to the optic axis along which the laser beam onto the KDP crystal and the collimation of the light emerging from the crystal are not shown.
n e
(2 ) =
n o
( ). The focusing of © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
x z E x E y
Wire-grid polarizer
E y y
The wire grid-acts as a polarizer
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
I
y p
(
t
) Oscillating molecular dipole
y z z
(a)
E E
Oscillating dipole along
y x
(a) A snap shot of the field pattern around an oscillating dipole moment in the
y
direction. Maximum electromagnetic radiation is perpendicular to the dipole axis and there is no radiation along the dipole axis. (b) Scattering of electromagnetic waves from induced molecular dipole oscillations is anisotropic.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
(b)
o-ray
Absorber 38.5
e-ray Calcite Optic axis
Air-gap The Glan-Foucault prism provides linearly polarized light © 2001 S.O. Kasap,
Optoelectronics and Photonics: Principles and Practices
(Prentice Hall)
L
-polarized
R
-handed quartz
L
-handed quartz
R
-polarized The Fresnel prism for separating unpolarized light into two divergent beams with opposite circular polarizations (
R
= right,
L
= left; divergence is exaggerated) © 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
R s
= 50 A Light in B
L D W
Light out
z V s R s Z
A EO Crystal A
C
EO B B
L R p
(a) (b)
(a) A step voltage is suddenly applied to an EO modulator. (b) An inductance
L
with an equivalent parallel resistance
R p
is placed across the EO crystal modulator to match the capacitance
C EO
.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)
Incident optical beam,
k
, Acoustic wave,
K
2 Diffracted optical beam,
k
2
k
k K
Wavevectors for the incident and diffracted optical waves and the acoustic wave.
© 1999 S.O. Kasap,
Optoelectronics
(Prentice Hall)