# Fiber Optics Communication Lecture 5. Nature of Light Two approaches – Geometrical (Ray) optics of light reflection and refraction to provide picture.

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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 17 th 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 – E x (z,t) = Re(E)=e x E 0x cos(wt-kz) E and H are perpendicular to direction of propagation i.e. transverse wave

Linear Polarization E always points in the e x 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 3x10 8 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

Snell’s law n1 sin(φ 1 )=n2sin(φ 2 ) or n1 cos(θ 1 ) = n2 cos(θ 2 ) As φ 1 increase, φ 2 approaches pi/2. This φ 1 is critical angle of incidence. If φ 1 > φ c, then total internal reflection Sin (φ c )=n 2 /n 1

Refraction and Reflection Example. Using n1=1.5 (glass) and n2=1(air), φ c = 52 o. Any light incident at angle > 52 o, 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 » e j(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(Φ min )=n 2 /n 1 » n sin θ 0,max = n 1 sin θ c = (n 1 2 -n 2 2 ) 1/2 » θ c =Π/2-Φ c Numerical aperture » NA =n sin θ 0,max = (n 1 2 -n 2 2 ) 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 = (3.6 2 -3.55 2 ) 1/2 =0.598 θ o =36.7 o Thus, all light incident within +/- 36.7 o is accepted NA =n sin θ 0,max = (n 1 2 -n 2 2 ) 1/2 ≈ n1 (2Δ) 1/2

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] Ibn al-HaythamBook of Opticsenergy particles [4]finite speed [5][6][7] [4]Avicenna [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. Pierre GassendiIsaac Newtondiffraction Francesco Grimaldiaether 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.reflection refractionmediumgravitationalOpticksparticle theory of lightLaplaceStephen HawkingGeorge F. R. Ellis

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