Transcript Fiber Optics Communication

Fiber Optics Communication
Lecture 5
Nature of Light
• Two approaches
– Geometrical (Ray) optics of light reflection and
refraction to provide picture of propagation
– Light is treated as electromagnetic field that
propagates along waveguide
Nature of Light
• Until 17th century it was believed that light consists of minute
particle that were emitted by luminous sources. These particle
traveled in straight lines. This theory adequately described large
scale optical effects such reflection and refraction but failed to
describe finer scale phenomena such interference and diffraction
• In 1864, Maxwell theorized that light waves are electromagnetic in
nature
– Polarization effects indicated that light waves are transverse
• In this wave optics view, electromagnetic wave radiated by a small
optical source can be represented by a train of spherical wave fronts
with source at center
• When wavelength of light is much smaller than the object (opening)
it encounters, the wave fronts appear as straight lines to this object
– Large scale optical effects such as reflection or refraction can be
analyzed by simple geometrical process of ray tracing. This is referred
to as ray or geometrical optics
Linear Polarization
• A plane wave linearly polarized that varies
harmonically as it travels in z-direction can be
expressed as
– Ex(z,t) = Re(E)=exE0xcos(wt-kz)
• E and H are perpendicular to direction of
propagation i.e. transverse wave
Linear Polarization
• E always points in the ex
direction
Circular Polarization
• Circularly polarized light
consists of two
perpendicular
electromagnetic plane
waves of equal amplitude
and 90° difference in
phase.
Elliptical Polarization
• Elliptically polarized
light consists of two
perpendicular waves of
unequal amplitude
which differ in phase by
90°
• E rotates and change its
magnitude as a function
of w (angular
frequency)
Quantum Nature of Light
• In dealing with interaction of light and matter
such as emission, and absorption of light,
neither particle theory nor wave theory is
appropriate. Instead quantum theory which
indicates that optical radiation has particles as
well as wave properties
• Light energy emitted or absorbed is always in
discrete units called quanta or photons
Quantum Nature of Light
• The relationship between E and frequency v of a
photon is
• E=hv
• h=6.625x10-34 J.s Planck’s constant
• An electron in an excited state can drop to a
lower state separated from it by an energy hv by
emitting a photon of exactly this energy
• When light is incident on an atom, a photon can
trasfer its energy to an electron within this atom
i.e. exciting it to a higher enger level.
Optical Laws And Definitions
• Refractive index
• In free space light travels at speed 3x108 m/s
• c=λv
• Upon entering a dielectric medium the wave travels at
speed v which is equal
– v= c/n (n=1,1.33,1.5 for air, water, and glass repectively)
Refraction and Reflection
Refraction and Reflection
• Snell’s law
• n1 sin(φ1)=n2sin(φ2) or
• n1 cos(θ1) = n2 cos(θ2)
• As φ1 increase, φ2 approaches pi/2 . This φ1 is critical
angle of incidence.
• If φ1 > φc , then total internal reflection
• Sin (φc )=n2/n1
Refraction and Reflection
• Example. Using n1=1.5 (glass) and n2=1(air),
φc = 52o. Any light incident at angle > 52o , is
totally reflected back.
• In addition, when light is totally internally
reflected, a phase δ occurs in the reflected
wave
Optical Fiber Modes and
Configurations: Fiber Types
• Optical Fiber: dielectric (normally cylindrical)
waveguide that operates at optical
frequencies.
• Transmission properties are dictated by fiber
structural characteristics
• The propagation of light along a waveguide
can be described in terms of a set guided
electromagnetic waves called modes of the
waveguide
Fiber Types
• These modes are referred to
as bound or trapped modes of
waveguides
• Optical Fiber structure
– Core
– Cladding
• Reduces scattering loss that results
from discontinuities at core
• Mechanical support
• Protect core from contaminants
– Coating
Fiber Types
• Single mode
sustains on mode
of propagation
• Multimode
supports many
modes
Fiber Types
• Advantages of Multimode
– Larger core radii makes it easier to launch optical power
into the fiber and facilitate connecting of similar fiber
– LEDs can be used
• Disadvantage
– Intermodal dispersion (when optical pulse is launched into
fiber, optical power is distributed over all of the modes.
Each mode travels at slightly different velocity. This means
modes arrive at the fiber end at slightly different times,
causing pulse to spread out in time. This is known as
intermodal dispersion or intermodal dispersion
• Intermodal dispersion can be reduced using graded
index profile. Thus, graded index fiber have much
larger bandwidth than step index fiber
Fiber Optics Propagation
• Electromagnetic light guided along a fiber can be represented
by a superposition of bound modes. Each mode consists of
simple EM configurations. For light field with radian frequency
w, a mode traveling in z direction has time and z dependence
» ej(wt-βz)
– β (z component of wave propagation constant).
– For guided modes, β can assume discrete value
• Two methods
– Ray tracing
• Good approximation to light acceptance and guiding properties of fiber
when fiber radius to wave length is large
• More direct physical interpretation of light propagation characteristics
– Modal Analysis uses electromagnetic analysis
• Single mode fiber
• Coherence, interference phenomena
• Fiber bent loss
Step Index Fiber
• For step index fiber,
» n2 = n1 (1-Δ),
» Δ is core-cladding index difference or index difference,
value nominally 1-3% for multimode and 0.2 to 1 % for
single mode.
• Since n1>n2, EM energy is made to propagate
along fiber through internal reflection
Ray Optics Representation
• From snell’s law, for total internal reflection
» Sin(Φmin)=n2/n1
» n sin θ0,max = n1 sin θc = (n12-n22)1/2
» θc =Π/2-Φc
• Numerical aperture
» NA =n sin θ0,max = (n12-n22)1/2 ≈ n1 (2Δ)1/2
Example
• Compute the numerical aperture and
acceptance angle for the symmetrical AlGaAs
slab waveguide where n1=3.6, n2=3.55
• Solution
NA =n sin θ0,max = (n12-n22)1/2 ≈ n1 (2Δ)1/2
NA = (3.62-3.552)1/2=0.598
θo=36.7o
Thus, all light incident within +/- 36.7o is accepted
EM spectrum
Particle theory
•
•
•
Ibn al-Haytham (Alhazen, 965-1040) proposed a particle theory of light in his Book of Optics
(1021). He held light rays to be streams of minute energy particles[4] that travel in straight lines
at a finite speed.[5][6][7] He states in his optics that "the smallest parts of light," as he calls them,
"retain only properties that can be treated by geometry and verified by experiment; they lack all
sensible qualities except energy."[4] Avicenna (980-1037) also proposed that "the perception of
light is due to the emission of some sort of particles by a luminous source".[9]
Pierre Gassendi (1592-1655), an atomist, proposed a particle theory of light which was
published posthumously in the 1660s. Isaac Newton studied Gassendi's work at an early age,
and preferred his view to Descartes' theory of the plenum. He stated in his Hypothesis of Light of
1675 that light was composed of corpuscles (particles of matter) which were emitted in all
directions from a source. One of Newton's arguments against the wave nature of light was that
waves were known to bend around obstacles, while light travelled only in straight lines. He did,
however, explain the phenomenon of the diffraction of light (which had been observed by
Francesco Grimaldi) by allowing that a light particle could create a localised wave in the aether.
Newton's theory could be used to predict the reflection of light, but could only explain
refraction by incorrectly assuming that light accelerated upon entering a denser medium
because the gravitational pull was greater. Newton published the final version of his theory in
his Opticks of 1704. His reputation helped the particle theory of light to hold sway during the
18th century. The particle theory of light led Laplace to argue that a body could be so massive
that light could not escape from it. In other words it would become what is now called a black
hole. Laplace withdrew his suggestion when the wave theory of light was firmly established. A
translation of his essay appears in The large scale structure of space-time, by Stephen Hawking
and George F. R. Ellis.