Chapter 3 Fiber Optics and Integrated Optics Gradient-index
optics the refractive index is the function of space Fiber optics
Optical wave-guide, tele-communication Integrated optics
miniaturized optical system
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True or false statement: The light travels in the straight line
in the air. (1) True (2) False n refractive index -- density of the
air Ttemperature of the air
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How does light travel? If n=constant; Light travels in straight
line If n varying in space; Light travels in curved line! It
follows the law of refraction!refraction
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3.1 Gradient Refractive Index 1.Atmospheric refraction The
light is bending towards the higher index side Sun rising &
setting The true position of the sun is lower than what you see
Looming Lift up the image Mirage Images formed as if there is a
pool of water!
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2. Gradient index lenses Conventional lens: refraction takes
place only at the surface of the lens. Gradient lens: refraction
takes place within the lens. Advantages of gradient lens: Correct
some aberrationreplace the aspherical lens. Can produce very small
lenshard to manufacture in traditional way. Simplify the optical
system a gradient lens can replace a number of homogeneous
lenses.
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a. Radial gradient lenses The index of refraction varies as a
function of distance from the optical axis. Cylindrical symmetry
Positive lens: n higher in the center Negative lens: n higher in
the periphery The end surface can be : plane or spherical for
additional power. r z Optical axis O
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For a positive radial gradient lens, when the shape of the lens
is a cylinder, what will be the distribution of the refractive
index? What about a negative lens? (2) n higher in the periphery
(1) n higher in the center
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b.Axial gradient lenses The surfaces of constant index are
planes and normal to the axis. Correction of spherical aberration
Conventional lens: marginal ray bends more center ray bends less
gradient lens: index is higher near the front higher index material
is removed in periphery marginal ray bends less z r Optical axis
O
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c. Spherical gradient lens The index of refraction varies
symmetrically about a point. The surfaces of content index are
spheres. Example: Crystalline lens of the human eyehuman eye
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GRIN is short for graded-index or gradient index. It refers to
an optical element in which the refractive index varies. More
specifically (from the Photonics Dictionary) a GRIN lens is a lens
whose material refractive index varies continuously as a function
of spatial coordinates in the medium. Also, a graded-index fiber
describes an optical fiber having a core refractive index that
decreases almost parabolically and radially outward toward the
cladding. GRIN
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GRIN lenses come in two basic flavors: RADIAL or AXIAL which
are sometimes refered to as RGRIN and AGRIN respectively. RGRINS
are usually used where you want to add optical power to focus
light. An RGRIN with flat surfaces can focus light just as a normal
lens with curved surfaces does. Thin RGRIN lenses with flat
surfaces are known as WOOD lenses, named after the American
physisist R.W. Wood who did a lot of experimental work with radial
gradients from about 1895 to 1905 and included descriptions of how
to make them in his physics text book (available from OSA).
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d.Manufacture of gradients Methods available: neutron
irradiation chemical vapor deposition polymerization ion stuffing
ion exchange Ag+ diffuse into the glass replace Na+ n(40h)
Theoretically: n=0.15 Practically: n=0.05
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What is an Optical Fiber? An optical fiber is a waveguide for
light consists of : coreinner part where wave propagates cladding
outer part used to keep wave in core bufferprotective coating
jacketouter protective shield can have a connector too 3.2 Fiber
Optics
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Two types of fiber: step-index; gradient fiber Structure :
core(higher n) ; cladding(lower n) Total internal reflection
1. Step-Index fiber NA of a Fiber The NA defines a cone of
acceptance for light that will be guided by the fiber
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90- tt max nfnf ncnc must be > critical angle nini NA in
air
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NA changes with n air water
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NA is sensitive to n 5% change 1% change
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NA and Acceptance angle ii air water
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Two types of fiber with different propagation modes:
single-mode fiber: only single mode is permitted small core
diameter: 8.3(core) /125(cladding) m Multi-mode fiber: several
modes are permitted large core diameter: 50~62.5(core)
/125(cladding) m
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Types of fiber ends beam patterns can be: spherical cylindrical
bundles 90 degree
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Fiber-optic Cable Many extremely thin strands of glass or
plastic bound together in a sheathing which transmits signals with
light beams Can be used for voice, data, and video
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Angle Preservation In an ideal fiber, the angle of incidence
will equal the exit angle. 22 22 22
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example: critical bend radius Rough surfaces, bending, and
other real-world imperfections will case a change in the exit
cone.
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Fiber Tapers 11 22 d1d1 d2d2 way to change the acceptance
angles of a fiber sometimes used to collimate light
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2. Gradient-Index Fiber Simplification: continuous n change
discrete layers of n From Snells refraction law: At the nth
boundary, at the distance R from the axis: Therefore: With n(R) Sin
I(R) I(R) Until: Sin I (R ) =1 I(R) =90 , The ray return back to
the center( optical axis)
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Additional Fiber Types (All single mode)
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3. Applications A. Transmission of light & image to
illuminate hard to reach places; to conduct light out of small
places Inside heart, digestive tract, stomach, respiratory tract,
lung, etc.
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B. Tele-communication
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advantages: a.light in weight efficient use of space in
conduits b.less expensive c.Free from electrical interference
aircraft, military, security d.Flexible e.Secure to interception
f.Low power lost g.enormous capacity of transmission: WDM/
DWDM(Dense Wavelength Division Multiplexing) Higher data rates over
longer distances-- more bandwidth for internet traffic Problem
remained: Attenuation: power lost ( minimum at 1.55 m) Dispersion:
modal, material (minimum at 1.31 m),
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Types of Dispersion in Fibers modal- time delay from path
length differences - usually the biggest culprit in step-index
material - n( ) : different times to cross fiber -(note: smallest
effect ~ 1.3 m) waveguide - changes in field distribution
-(important for SM) non-linear - n can become intensity-dependent
NOTE:GRIN fibers tend to have less modal dispersion because the ray
paths are shorter
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Effect of Modal Dispersion time modal example:step index~ 24 ns
km -1 GRIN~ 122 ps km -1 initial pulsefarther downfarther
still
Fibers are made of glass - commonly high-quality fused silica
(SiO2) - some trace impurities (usually controlled) Losses due to:
- Rayleigh scattering (~ -4 ) - absorption - mechanical stress -
coatings
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Attenuation Profiles absorption and scattering in fiber page
297 Rayleigh Scattering IR absorption 89% transmission
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Fiber loss: (dB/km) Where, L1,L2 distance from the start of the
fiber, L1 1, L2 2 20years ago: -20dB/km was thought to be the limit
Now: -0.2dB/km fiber is commonly used Single-mode fiber: 50~100KM
Multi-mode fiber: 2~4KM
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Dispersion: The Basics Light propagates at a finite speed
fastest ray slowest ray slowest ray: one entering at highest angle
(high order mode) fastest ray: one traveling down middle (axial
mode) there will be a difference in time for these two rays
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Coupling with Lenses n 3 n 1 n 2 Edge coupling using a lens. i
/2 o /2 n 2 n 3 n 1
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Coupling with Prisms Commercial applications? (sensors)
Research labs Optical fiber tap p n p Prism Field Prism coupling.
The n3n3 region is typically air. n 3 n 2 n 1 Z Film Field
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Review 1.Optical fibers carry modes of light 2.Step-index,
GRIN, single mode & multimode 3.NA is related to acceptance
cone and ns. 4.How Step-index and GRIN fibers propagate light.
5.Factors that change light propagation in fibers: a.mechanical
aspects (bending, tapers, etc) b.attenuation c.dispersion
Integrated optics offers a particularly interesting candidate
for implementing parallel, reversible computing structures
Integrated optics (integrated wave-guide): Miniature dimension of
fiber optics usually manufactured in the way of thin film (
thickness in the order of wavelength) planar guideswide strip
guidesnarrow Beam couplers: guide light to enter the thin film
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PLC Planar Lightwave Circuits Si Wafer Bottom Cladding Top
Cladding Waveguide CoreGuided Light Si SiO 2
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Coupling with Prisms
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Grating Couplers (Input and Output)
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1.Integrated prisms Thin film prisms Thin film prisms thinner
film effective velocity of light thicker filmeffective velocity of
light Refractive gradient prisms light bend towards the high index
side.
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2. Thin film lenses Luneburg lens a flat circular mound Index
being highest in the center, decreasing towards periphery Geodesic
lens dome shaped film: uniform thickness rays follow the shortest
path between two points on a surface
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3.Other Integrated Elements Light modulators: operate on
amplitude,phase, frequency,state of polarization Electrical signal
change Light direction change Light switches, deflectors, Light
scanners 4. Manufacture Earlier way: vacuum depositionTaO, LiNb
coated on a substrate Modern ways: diffusion techniques ion
implantation proton bombardment electron or laser writing
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Monolithic integrated optics Light source, light guiding,
modulating, detection are performed in a single crystal GaAs
gallium arsenide semiconductor material Fiber optical
gyroscope
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Advantages of Integrated-Optic Circuits: Small size, low power
consumption Efficiency and reliability of batch fabrication Higher
speed possible (not limited by inductance, capacitance) parallel
optical processing possible (WDM) Substrate platform type: Hybrid
-- (near term, use existing technology) Monolithic -- (long term,
ultimately cheaper, more reliable) quartz, LiNbO, Si, GaAs, other
III-V semiconductors