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
True or false statement:
The light travels in the straight line in the air.
(1) True
(2) False
n — refractive index
(n  1)  
ρ-- density of the air
(n  1)  1 / T
T—temperature of the air
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!
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!
山东蓬莱
山东蓬莱
山东蓬莱
深圳海湾
杭州西湖 雪后蜃景
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 aberration—replace the
aspherical lens.
 Can produce very small lens—hard to
manufacture in traditional way.
 Simplify the optical system— a gradient lens can
replace a number of homogeneous lenses.
a. Radial gradient lenses
 The index of refraction varies as a function of
distance from the optical axis.
r
Cylindrical symmetry
n  f (r )
z
O
Optical axis
 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.
For a positive radial gradient lens, when the
shape of the lens is a cylinder, what will be the
distribution of the refractive index?
(1) n higher in the center
(2) n higher in the periphery

What about a negative lens?
b.Axial gradient lenses
 The surfaces of constant index are planes and normal to
n

f
(z
)
r
the axis.
z
 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
O
Optical axis
c. Spherical gradient lens
 The index of refraction varies symmetrically
about a point.
The surfaces of content index are spheres.
y
n  f (r )
r
x
z
Optical
axis
 Example: Crystalline lens of the human eye
GRIN
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 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).
d.Manufacture of gradients
Alumino silcate glass
 Methods available:
neutron irradiation
chemical vapor deposition
polymerization
ion stuffing
loosely bounded
Na---Si---O
Ag
AgCl--silver chloride (500 C molten)
ion exchange
Ag+ diffuse into the glass replace Na+ →
n↑(40h)
Theoretically: n=0.15
Practically: n=0.05
3.2 Fiber Optics
What is an Optical Fiber?
An optical fiber is a waveguide for light
consists of :
core
inner part where wave propagates
cladding outer part used to keep wave in core
buffer
protective coating
jacket
outer protective shield
can have a
connector
too



Two types of fiber: step-index; gradient fiber
Structure : core(higher n) ; cladding(lower n)
Total internal reflection
step-index step-index
singlemode multimode
nc
GRIN
Types of Fibers
nc
nf
nc
nc
nc
nc
nf
nf
1. Step-Index fiber
NA of a Fiber
 max
NA  noutside sin max 
The NA defines a cone of acceptance for light
that will be guided by the fiber
ni
nc
nf
t
90-
max
must be > critical angle
NA  noutside sin max 
n f  nc
2
NAstep 
2
ni
NAstep  n f  nc
2
2
NA in air
NA changes with n
1.4
1.4
1.2
1
NA n f  1.457  1.00
air
0.8
NA n f  1.457  1.33
0.6
water
0.4
0.2
0
0
1.4
1.4
1.5
1.6
nf
1.7
1.8
1.8
NA is sensitive to n
1.4
1.4
1.2
1% change
1
NA n f  1.457  1.00
0.8
NA n f  1.472  1.00
5% change
0.6
NA n f  1.530  1.00
0.4
0.2
0
0
1.4
1.4
1.5
1.6
nf
1.7
1.8
1.8
NA and Acceptance angle
1.4
1.4
1.2
water
1
NA  i  1.00
0.8
air
NA  i  1.33
0.6
0.4
0.2
0
0
0
0
i
15
30
45
i
60
75
90
90
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
Types of fiber ends
beam patterns can be:
spherical
cylindrical
bundles
90 degree
 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
Angle Preservation
In an ideal fiber, the angle of incidence will equal the exit angle.
2

 ni



 1 
n

f





2

2
example: critical bend radius
Rough surfaces, bending, and other real-world imperfections will
case a change in the exit cone.
Fiber Tapers
2
d1
d2
1
d1 sin 1   d 2 sin 2 
• way to change the acceptance angles of a fiber
• sometimes used to collimate light
2. Gradient-Index Fiber
Simplification: continuous n change → discrete layers of n
From Snell’s refraction law:
n1 sin I1  n2 sin I 2
At the nth boundary, at the distance R from the axis:
n1 sin I 1  n( R) sin I ( R)
Therefore:
n( R) sin I ( R)  cons tan t
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)
r
Escaping Ray
2 o
Light Source
Trapped Ray
2o
GRIN CORE
Additional Fiber Types
Index Profile
(All single mode)
Field Intensity
Simple Step
Depressed cladding
dispersion
flatened
Alpha-1
dispersion
shifted
W-Type
Segmented
profile
Radius
Radius
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.
B. Tele-communication
Information
Source
electrical
Information digital signal
encoder
Optical transmitter
Multiplexing
optical signal
Signal
Modulator
Optical fiber
Relay station
Light source
Optical fiber
Relay station
Multimedia
output
Information
decoder
electrical
digital signal
Demodulating
Demultiplexing
optical signal
Optical receiver
Optical fiber
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),
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
Effect of Modal Dispersion
initial pulse
time
modal example:
farther down
farther still
time
step index
GRIN
time
~ 24 ns km -1
~ 122 ps km-1
4. Bel & Decibel (dB): Comparative unit
Input: 1 output: 2
Attenuation
Bel → Log10
2
1
Decibel (dB) → 10  Log10
2= 101 → 1Bel → 10dB
2= 1001 → 2Bel → 20dB
2= 1 → 0Bel → 0dB
2= 1/2 → 10lg0.5 → -3dB
2
1
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
Attenuation Profiles
page 297
IR absorption
Rayleigh
Scattering
89% transmission
absorption and scattering in fiber
Fiber loss:
10
 2 ( )
 ( ) 
 Log10
L2  L1
1 (  )
(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
Dispersion: The Basics
Light propagates at a finite speed
fastest ray
slowest ray
fastest ray: one traveling down middle (“axial mode”)
slowest ray: one entering at highest angle (“high order” mode)
there will be a difference in time for these two rays
Coupling with Lenses
n3
n1
n2
Edge coupling using a lens.
 /2
o
 /2
i
n2
n1
n3
Coupling with Prisms
n3
Prism Field
p
np
Z
n1
n2
Film Field
Prism coupling. The n3 region is typically air.
• Commercial applications?
(sensors)
• Research labs
• Optical fiber tap
Review
1. Optical fibers carry modes of light
2. Step-index, GRIN, single mode & multimode
3. NA is related to acceptance cone and n’s.
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
3.3 Integrated Optics
 Integrated optics ∽Integrated circuit
Electronics
Photonics
1970’s
Tubes & transistors
decreasing size
1960’s
Integrated circuits
1980’s
VLSI
2000’s
Fiber optics
discreet components
1970’s
Planar optical
waveguides
1980’s
Integrated optical
circuits
1990’s
Molecular electronics
Photonic crystals
Electronics
Photonics
fiber
wire
10
15
f ~ 10 Hz
f ~ 10 Hz
sig in
sig out
control beam
v
5
~ 10 m/s
elec
Strong elec-elec interaction
v
8
~ 10 m/s
phot
Weak phot-phot interaction
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 guides—wide
strip guides—narrow
 Beam couplers: guide light to enter the thin film
PLC – Planar Lightwave Circuits
Top Cladding
SiO2
Bottom Cladding
SiO2
Si Wafer
Si
Waveguide Core
Guided Light
Coupling with Prisms
AIR
n1 FILM
n2
n1
n2
Coupled Wave Amplitude
Placement of the input beam for a prism coupler.
(a) Energy is fed back into the prism from the film.
(b) The beam is positioned for maximum efficiency.
The amplitude of the wave in the film is shown in
both cases.
Wave
Amplitude
Film
Prism output coupling. The two
propagating modes couple out of the
prism at different angles. The shape
of the top beam is sketched.
Grating Couplers (Input and Output)
(a)
(b)
AIR
AIR
n1
n1
FILM
n2
n 2 Coupled
Wave
Amplitude
Grating couplers. (a) Periodic dielectric array.
(b) Dielectric layer having a periodic variation
in refractive index.
FILM

PL
n2


n1
n2
1.Integrated prisms

Thin film prisms
thinner film– effective velocity of light ↑
thicker film—effective velocity of light ↓

Refractive gradient prisms
light bend towards the high index side.
incident
light
substrate
another layer of material
exit light
incident
light
n higher
n lower
exit light
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
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 deposition—TaO, LiNb coated on a substrate
Modern ways: diffusion techniques
ion implantation
proton bombardment
electron or laser writing
 Monolithic integrated optics
Light source, light guiding,
modulating, detection
are performed
in a single crystal
GaAs — gallium arsenide
— semiconductor material
Fiber optical gyroscope
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
homework
 2,3,5
 Translation(E to C)