Graduate Optics

1
Graduate Optics

• Polarization

2
Polarization
Page 4.1

• Because light produces transverse waves (crests
  and troughs perpendicular to the direction of
  propagation), the light waves can be polarized

3
Polarization
Page 4.1

• Natural light oscillates (produces electric
  fields) randomly in all directions
• This means it is unpolarized

Natural Light
4
Polarization
Page 4.1

• Rope Analogy

5
Polarization Rope Analogy
Page 4.1
Apply a vertical flick to the rope (like
cracking a whip)
6
Polarization Rope Analogy
Page 4.1
7
Polarization Rope Analogy
Page 4.1

• Snapping a taut rope vertically at the free end
  causes a vertically oscillating wave to propagate
  horizontally along the length of the rope.
• This is analogous to plane polarized light

8
Vertically Polarized Light
Page 4.1
9
Polarization
Page 4.1

• The wire-grid polarizer

10
Wire Grid Polarizer
Fig 1, P4.1
11
Wire Grid Polarizer
Page 4.2
Natural Light
12
Wire Grid Polarizer
Page 4.2
Natural Light
13
Wire Grid Polarizer
Page 4.2
14
Wire Grid Polarizer
Page 4.2
P-state Light
15
Polarization
Page 4.2

• Dichroic crystal

16
Dichroic Crystal
Page 4.2

• Behaves like a wire grid polarizer
• The optic axis direction is like the transmission
  axis of the wire grid - light interacts minimally
  with the crystal

17
Dichroic Crystal
Fig 2, P4.3
Electric field components parallel to the optic
axis are minimally absorbed by the crystal
Optic Axis Direction
EF components perpendicular to the optic axis are
strongly absorbed by the crystal
18
Dichroic Crystal
Page 4.3

• Dichroic crystal is not a perfect polarizer
• Beside plane polarizing light, the crystal also
  absorbs certain l s more strongly than others

19
Dichroic Crystal
Page 4.3

• Incident white light may therefore be emitted,
  e.g. as plane polarized green light
• this means that the crystal must absorb red more
  strongly
• This is the origin of the term dichroic (two
  color).

20
Dichroic Crystal
Page 4.3
Optic Axis Direction
Under normal conditions, polarized light looks
the same as unpolarized light
White light in
Green light out
21
Polaroid H-Sheet
Page 4.4

• Analogous to a wire grid polarizer
• A sheet of clear PVA is heated, then stretched
  linearly, aligning the long hydrocarbon chains
• The sheet is then dipped in iodine, which
  attaches to the parallel hydrocarbon chains ?
  iodine wire grid

22
Polaroid H-Sheet

• The EF incident parallel to the iodized
  hydrocarbon chains is absorbed
• The orthogonal (perpendicular) EF is freely
  transmitted
• Plane polarized light is emitted
• Crossing two polaroid H-sheets results
  (theoretically) in zero light transmission (some
  violet leak)

23
Polaroid H-Sheet
Fig 3, P4.4
OpticAxis
OpticAxis
Optic Axis(? to page)
P-State Light
24
Birefringent Polarizer
Page 4.5

• Anisotropic (structurally asymmetric) crystals
  refract light differently depending on direction
  of incidence). Example calcite
• Light incident along the optical axis is
  refracted normally
• Light incident from any other direction splits
  into two orthogonally polarized beams

25
Fig 4, P5
26
Birefringence
Page 4.5

• Structural anisotropy ? optical anisotropy
• refractive index differs between axes
• If atoms within two axes differ from the third
  axis, structural anisotropy ? birefringence
• refractive index along two axes differs from
  third
• basis for ordinary and extraordinary rays

27
Calcite Light shone parallel to Optic Axis
Fig 5, P6
Remember wave amplitude is perpendicular to
direction of propagation
28
Calcite Light shone parallel to Optic Axis
Same index no in all directions ? to direction of
propagation
zero birefringence
All waves normal ? no polarization by
birefringence
29
Calcite Light shone perpendicular to Optic Axis
Fig 6, P7
Index lower parallel to optic axis (ne) ? wave
propagates faster than ordinary wave
maximum birefringence
Faster extraordinary wave emerges ahead of
ordinary wave
n e lt n o
30
Calcite Faces oblique to Optic Axis (? incidence)
Fig 7, P8
emergent waves separate (and extraordinary ahead
of ordinary wave)
intermediate birefringence
Basis of many prismatic and beam-splitting
systems
n e lt n o
31
Wave Properties Ordinary Extraordinary Rays,
Oblique Optic Axis
Fig 8, P9
32
Ordinary Extraordinary Rays (Oblique OA)
Page 4.9

• Ordinary ray refracts normally into crystal and
  becomes plane polarized refracted wavefronts
  remain ? to the plane of incidence
• Extraordinary ray
• refracts in a different direction
• becomes plane polarized (orthogonal to o-ray)
• slows down (retarded) to a lesser extent than
  o-ray
• Refracted wavefront is not normal to the plane of
  incidence

33
Calcite Birefringence
Halite (isotropic)
Calcite (anisotropic)
34
Calcite and crossed H-sheets
35
Q. Explain the effect indicated by the arrow
36
Q. Explain the effect indicated by the arrows
37
Q. Explain the effect indicated by the arrow
38
Q. Explain the effect indicated by the arrow
39
Birefringent Polarizer

• The extraordinary ray will be optically cut out
  in an optical system that simply requires
  plane-polarized light
• In other systems, the difference in speed between
  the e- and o-waves is used to produce
  interference effects or circular polarization
  effects in the recombined emergent wave ?
  retarding plates, or wave plates

40
Quarter-Wave Plate
Fig 9, P.10
extraordinary wave (faster through crystal)
ordinary wave (retarded in crystal)
90? (quarter wavelength) phase difference
linearly polarized incident light (45? to optic
axis)
41
Producing Circular Polarization
Fig 10, P.11
Adding the two wave amplitudes produces a net
amplitude of continually changing orientation ?
helical pattern
component waves must have equal amplitude to
produce circular polarization ? plane wave must
be incident 45? to optic axis of quarter-wave
plate
42
Elliptical Polarization
Fig 11, P.12
component waves of unequal amplitude produce
elliptical polarization (incident plane wave not
45? from optic axis of wave plate)
43
Circular Polarization in Nature

• The Scarab Beetles exocuticle reflects only
  left circularly polarized light, and
  extinguishes right circularly polarized light
• This beetles exocuticle could therefore be used
  to detect the state of polarization of circularly
  polarized light ? acts as an analyzer

44
Circular Polarization in Nature

• The helicoid crystalline structure of the Scarab
  Beetles exocuticle is remarkably similar to the
  structure of a liquid crystal display.
• Liquid crystals make use of birefringence to
  change display characteristics as applied voltage
  is varied

45
Another Species of Scarab Beetle
46
ANALYZERSDetection of Polarized Light
Page 4.13
47
Detection of Polarized Light

• All we see emerging from a dichroic crystal is a
  color that differs from the incident light - we
  do not see its state of polarization
• A birefringent crystal may produce two emergent
  waves, but we cannot detect the state of
  polarization (plane of vibration of each wave)
  under normal conditions.

48
Dichroic Crystal
Optic Axis Direction
Under normal conditions, polarized light looks
the same as unpolarized light
White light in
Green light out
49
Analyzers Polarized Light

• An analyzer is any device that can distinguish
  the appearance of polarized light (between
  transmission and extinction axes)
• To be able to detect the state of polarization of
  light, the analyzer itself must have polarizing
  properties

50
Polarization Analyzers
Page P13
Consider light incident at a polarizer to
comprise two components, one parallel to and
one perpendicular to the transmission axis of the
polarizer
51

• e.g. (oblique) Plane polarized light incident at
  a polarizer with vertical transmission axis
• resolve incident light into vertical (parallel)
  and horizontal (perpendicular) components

EV
E
EV E cos q
EH E sin q
EH
52
Polarization Analyzers

• The component (P-state) incident perpendicular to
  the transmission axis is extinguished,
  resulting in zero transmission in this direction
• The component parallel to the transmission axis
  is 100 transmitted

53
Polarization Analyzers

• What happens if we produce plane polarized light
  that is then incident at an acute angle to an
  analyzer (rather than parallel or perpendicular
  to the transmission axis)?

54
Fig 12, P13
E cos q
55
Polarization Analyzers

• The amplitude of light incident at the analyzers
  transmission axis (subtending an angle q with the
  polarizers transmission axis) is given by

56
Malus Law
Page 4.14

• Re-expressing the equation in terms of light
  intensity (square of amplitude), we get Malus
  Law

57
Malus Law Examples

• For an angle of 25O between polarizer and
  analyzer transmission axes

58
I0
emergent intensity?
I0 cos2 q
TA
Unpolarized white light
I0 cos2 q
TA
Polarizer
I25
Analyzer
59
Malus Law Crossed Polaroids

• When the angle between polarizer and analyzer
  transmission axes is 90

60
emergent intensity?
I0
I0 cos2 q
Unpolarized white light
I0 cos2 q
TA
TA
Polarizer
I90
Analyzer
61
Malus Law Crossed Polaroids

• It is easy to determine when zero intensity is
  emitted from the analyzer (no light is seen)
• Then, provided we know the orientation of the
  analyzers transmission axis, the polarizers
  transmission axis must be 90O away

62
Haidingers Brushes - the eyes Analyzer

• The human macula contains an analyzer that (under
  specific viewing conditions) can entoptically
  differentiate the transmission and extinction
  axes of P-state light
• The macular analyzer has polarizing properties
  and is dichroic (selectively absorbing blue light)

63
Macula lutea
64
Haidingers Brushes

• Haidingers brushes appear optimal when viewing a
  rotating plane polarizer through a blue filter

65
Appearance of Haidingers Brushes under optimum
conditions
66
Haidingers Brushes Dichroic RA Theory
WHITE LIGHT
BLUE LIGHT
67
Polarimetry
68
Polarimetry Crossed Polarizers
Fig 13, P.15
Vertical plane-polarized light has no horizontal
component ? zero light emitted through an
analyzer with horizontal transmission axis
69
Polarimetry Crossed Polarizers
Fig 14, P.16
70
Polarimetry Crossed Polarizers
Linear polarizers transmit all wave components
to their transmission axis and absorb all ?
components
Fig 14, P.16
71
Polarimetry Crossed Polarizers
The middle polarizer with oblique transmission
axis transmits components in all orientations
except ? to its transmission axis. This includes
a transmitted horizontal component
Fig 14, P.16
72
Polarimetry Crossed Polarizers
The horizontal component transmitted by the
middle polarizer is also transmitted by the
analyzer
Fig 14, P.16
73
Polarimetry Crossed Polarizers
Polarimeters use crossed polarizers in this way
to analyze or exploit the polarizing properties
of test materials
Test polarizer
Fig 14, P.16
74
The Plane Polariscope
Fig 15, P.17
A birefringent test material with oblique optic
axis is placed between crossed polarizers
75
The Plane Polariscope
Fig 15, P.17
The incident vertically polarized light is
split into orthogonal ordinary and extraordinary
componentsby the birefringent test material
76
The Plane Polariscope
Fig 15, P.17
If refractive index is higher for the
extraordinary wave (most materials), the e-wave
will be retarded upon emerging from the crystal
77
The Plane Polariscope
Fig 15, P.17
The horizontal transmission axis of the
analyzer transmits only the horizontal
component of the e- and o- waves
78
The Plane Polariscope
Fig 15, P.17
The two emergent waves have the same state of
polarization, but are out of phase due to
retardation in the birefringent material
79
The Plane Polariscope
Fig 15, P.17
This produces an interference pattern that is
dependent on the relative indices (e versus o)
and thickness of the birefringent test material
80
The Plane Polariscope
Fig 15, P.17
In the figure, the test material produces
slightly less than ?/4 retardation. This
produces partial destructive interference. ?/2
retardation would cause total destructive
interference
81
Polarimetry Applications
Page 4.18

• Detection of stress patterns in thermally
  hardened spectacle lenses

82
Spectacle Lens Polariscope

• When a glass spectacle lens is thermally
  hardened, characteristic regional stress patterns
  develop
• Stress patterns impart refractive index
  variations across the lens, making it
  stress-birefringent
• When the lens is placed between the crossed
  polarizers of a Polariscope, variable
  birefringence-induced retardation across the lens
  produces interference patterns
• These interference patterns correlate with the
  regional stress variations
• The Polariscope also detects high-stress regions
  on any lens (glass, plastic, polycarbonate, etc.)
  that make it more susceptible to failure
  (shattering)

83
Polycarbonate viewed through Polariscope
Fig 16, P18
84
High Stress Regions viewed with Polariscope
Photoelastic fringes on plastic showing high
stress regions and cracks in the material
85
Polarimetry Applications
Page 4.20

• Detection of stress patterns in thermally
  hardened spectacle lenses
• Retinal Nerve Fiber Layer (RNFL) Scanning Laser
  Polarimetry (SLP) used for early glaucoma
  detection

86
RNFL Scanning Laser Polarimetry (SLP)

• SLP used to assess retinal nerve fiber layer
  (RNFL) thickness across the optic disc
• Measures retardation of polarized light reflected
  from the retina
• Each RNF bundle contains (cylindrical)
  microtubules (lt ?) which are form-birefringent
• Microtubule optic axis aligned with RNF bundles
  with retardance proportional to thickness.
• Optic axis is the slow axis (higher nO lower nE
  ).

87
SLP the near infrared laser double passes the
retinal nerve fiber layer and is split into two
parallel (orthogonally polarized) rays by the
birefringence of the RNFL. The two rays travel
at different speeds, and this retardation
directly correlates to the thickness of the RNFL
88
RNFL Scanning Laser Polarimetry (SLP)

• Near the disc, microtubule optic axis
  distribution is approximately radial.
• In a normal eye
• retardance is higher in superior and inferior
  disc
• retardance is lower in temporal and nasal disc
• Q. What does this indicate about relative RNFL
  thickness Sup Inf vs. Temp Nas?

A. The RNFL is thicker superiorly and inferiorly
89
SLP
Fig 18, P20
90
Polarization by Reflection
Page 4.21

• When light is incident at a small angle (to the
  normal) to a surface, it obeys Fresnels Law of
  reflectance.
• At larger angles of incidence, a higher
  proportion is reflected
• In addition, both the reflected and refracted
  beams become partially polarized

91
Polarization by Reflection
Fig 19, P21
Incident unpolarized beam
reflected beam
refracted beam
92
When the reflected and refracted waves are 90O
apart, the reflected beam is completely plane
polarized
Incident unpolarized beam
reflected beam
refracted beam
93
Incident unpolarized beam
reflected beam
refracted beam
94
Brewsters Law
Page 22

• What angle of incidence will result in a
  reflected and refracted beam that are 90O apart?

• We call this angle of incidence Brewsters angle

95
Brewsters Law
Page 23

• Brewsters angle is determined by the ratio of
  refractive indices across the interface. e.g. for
  an air/glass interface

96
Brewsters Law Applications

• Unpolarized light incident vertically on a
  horizontal surface at Brewsters angle produces a
  specularly reflected beam that is horizontally
  polarized
• Vertically polarized light incident on a
  horizontal surface at Brewsters angle results in
  zero reflected light

97
Brewsters Law Applications

• This is the basis of Polaroid sunglasses
• Polaroid sunglasses are made from polaroid sheet
  with transmission axes vertical
• The lenses do not transmit horizontally polarized
  light

98
Polarizing Sunglasses
99
Brewsters Law Applications

• All of the light reflected at Brewsters angle
  from a horizontal surface (e.g. water) will be
  absorbed by the polaroid sunglasses.
• Not all light reflects at Brewsters angle, but
  the majority of light reflecting from flat
  horizontal surfaces is horizontally polarized

100
Fig 20, P 24