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OPTI510R: Photonics
Khanh Kieu
College of Optical Sciences,
University of Arizona
Meinel building R.626
mailto:[email protected]
Announcements
Homework #4 is assigned, due March 25th
Start discussion on optical fibers
Optical fibers
Outline:
• Introduction
• Fiber dispersion and compensation techniques
• Fiber fabrication
• Nonlinear optical effects in fibers
• Fiber amplifiers
• Passive fiber components
Introduction to optical fibers
Outline:
• Brief history
• Geometrical optics description
• Wave optics description
• Fiber modes
• Fiber loss, fiber dispersion
Geometrical description
Contain a central core surrounded
by a lower-index cladding
Two-dimensional waveguides with
cylindrical symmetry
Step-index fiber: refractive index of
the core is uniform
Graded-index fibers: refractive index
varies inside the core
Geometrical description
= NA
Geometrical description
Guided-wave analysis
acore
cladding
for < a
for > a
n1
n2
Guided-wave analysis
Guided-wave analysis
(credit: G. Agrawal)
Guided-wave analysis
(credit: G. Agrawal)
Bessel function basics
)()( rkJru Tl
u(r) =Kl (gr)
(core) (cladding)
Bessel functions of the first kind Modified Bessel functions of
the second kind
Examples of radial distribution u(r) for l=0 and l=3. The proportionality constants
are determined by continuous u(r) and du/dr at r = a.
Zeroth and higher order modes
Eigen-value equation
Eigen-value equation
Classification of modes
(credit: G. Agrawal)
Eigen-value equation
(credit: G. Agrawal)
Linearly polarized modes
Linearly polarized modes
(credit: G. Agrawal)
Fundamental modes
(credit: G. Agrawal)
Fundamental modes
Fundamental modes
Fundamental modes
(credit: G. Agrawal)
Modes profile
http://www.rp-photonics.com
Electric field amplitude profiles
for all the guided modes of
a fiber with a top-hat refractive
index profile (→ step index fiber).
The two colors indicate different
signs of electric field values. The
lowest-order mode (m = 0, n = 1,
called LP01 mode) has an
intensity profile which is similar to
that of a Gaussian beam. In
general, light launched into
a multimode fiber will excite a
superposition of different modes,
which can have a complicated
shape.
Attenuation in optical fiber
Attenuation coefficient (dB/km)
Power transmission ratio as a function of distance z
a =1
L10log10
1
T with T =
P(L)
P(0)
1-z- kmin for )0(
)(e
P
zP
Calculate (dB) through (km-1)
(dB) = 4.343* (km-1)
Sources of attenuation in silica fiber
Absorption
• Vibrational transitions in the IR
• Electronic and molecular transitions in the UV
• Extrinsic absorption from adsorbed water and other impurities
Scattering
• Rayleigh scattering
• Extrinsic scattering from defects due to manufacturing errors
• Raman, Brillouin scattering
Propagation loss in optical fiber
Current loss is < 0.2dB/km for single mode fiberworking around 1550nm
Propagation loss in optical fiber
Predicted the loss in optical fiber could be < 20dB/km
Loss was ~1000dB/km at that time
Propagation loss in optical fiber
1. Low loss optical fiber based
on fused silica
2. Compact, low-cost diode lasers
Internet enablers:
Communication window
Loss performance in fused silica fiber
Water absorption
Communication window
Loss performance in fused silica fiber
10 THz of
bandwidth!
Compared to coaxial
Scattering loss
Light,
D
ObjectD > : Geometrical scattering
Rayleigh scattering is one of the dominant sources of loss in optical fibers
Inelastic scattering: Brillouin, Raman
Rayleigh scattering
I () ~ D6(1 + cos2())/4
(source: Wikipedia)
http://upload.wikimedia.org/wikipedia/commons/5/5e/SDIM0241b.jpghttp://upload.wikimedia.org/wikipedia/commons/5/5e/SDIM0241b.jpg
Infrared absorption
(source: Wikipedia)
Strategy is to use heavier atoms
to lower vibrational energies
Vibrational phonon absorption edgeTransmission window
Bending loss
Bending loss
• Loss mechanism: coupling to non-propagating modes
• Larger loss for longer wavelength (at a given bending radius)
• Smaller loss for higher NA
• Critical bending radius
Bending loss calculation:
• D. Marcuse, QE 2007
Progress in bendable fiber
Bending loss
In Corning Clearcurve
fiber
Progress in bendable fiber
Sources of dispersion in optical fiber
Modal dispersion• Occurs in multimode fibers coming from differences in group velocity for
different modes
Material dispersion• Results from the wavelength dependence of the bulk refractive index
Waveguide dispersion• Results from the wavelength dependence of the effective index in a
waveguide
• Material + waveguide dispersion is termed chromatic dispersion
Polarization mode dispersion• Results from the fact that different polarizations travel at different speeds
due to small birefringence that is present
Nonlinear dispersion – example is self-phase modulation