PROPAGATION OF SIGNALS IN OPTICAL FIBER 92011 Light

PROPAGATION OF SIGNALS IN OPTICAL FIBER 9/20/11

Light Characteristics • Particle Characteristics • Light has energy • Photons are the smallest quantity of monochromatic light • That is light with single frequency • The energy of a photon is described by E= hf (h=6. 6260755 E-34 joule-sec) and f is the frequency of light • Energy of light depends on its speed: E=mc^2 (Einstein’s Eqn. ) • The relationship between frequency and speed: v=c/λ • Speed of light changes as it enters denser materials • Wave Characteristics • Described by a series of equations

Photometric Terms • Flux • Rate of optical energy flow (number of photons emitted per second • Illuminous density • Rate emitted in a solid angle

Light Properties • Light is electromagnetic radiation • Impacted by many parameters: reflection, refraction, loss, polarization, scattering, etc. • Light of a single frequency is termed monochromatic • Any electromagnetic wave is governed by a series of equations • In this case ε and μ are relative

** Wave Equation • Phase velocity • Group velocity • Velocity at which pulses propagate: 1/β 1 • Change of rate of group velocity is proportional to β 2 • When β 2=0 pulse does not broaden! Propagation constant for monochromatic wave • Defined by β=ωn/c = 2πn/λ = kn • k is the wave number k=2π/λ (spatial frequency) • Thus, for core β 1 = k. n 1 • That is kn 2 < β <kn 1 • Effective index = neff = β/k • The speed at which light travels is c/neff

Polarization • Remember: light is an electromagnetic wave • Electric field and magnetic field • When E and H fields have the same strength in all directions light is un-polarized • As light propagates through medium field interact and their strengths changes light become polarized • If the E field associate with the EM wave has no component in the direction of propagation is said to be Traverse E-field (TE) • Thus, only Ex and Ey exist n the fundamental mode • Same for TM • Collectively, it is called a TEM wave

Directional Relation Between E and H For Any TEM Wave k (x, y, z) E (x, y, z) H (x, y, z) Phasor Form Note: E and H may have x & y components However, they travel in Z direction and They are perpendicular to each other!

Polarization - General • Polarization is the orientation of electric field component of an electromagnetic wave relative to the Earth’s surface. • Polarization is important to get the maximum performance from the propagating signal • There are different types of polarization (depending on existence and changes of different electric fields) • Linear • Horizontal (E field changing in parallel with respect to earth’s surface) • Vertical (E field going up/down with respect to earth’s surface) • Dual polarized • Circular (Ex and Ey) • Similar to satellite communications • TX and RX must agree on direction of rotation • Elliptical • Linear polarization is used in Wi. Fi communications

Polarization - General z E-Field is Going up/down respect to Earth! (Vertical Polarization) (x, z) (y, z) E-Field is Rotating (or Corkscrewed) as they are traveling Propagating parallel to earth o Polarization is important to get the maximum performance from the antennas n The polarization of the antennas at both ends of the path must use the same polarization n This is particularly important when the transmitted power is limited

Factors Impacting Polarization • A number of factors can impact polarization • Reflection • Refraction • Scattering • These factors in turn depend on material property • Transparent materials • Isotropic • Refractive index, polarization, and propagation constant do not change along the medium • Anisotropy • Electrons move with different freedom in different directions • As light hits the medium the refracted light splits, each having a different polarization • This property is referred to as Birefringence in fiber – modes of propagation have different propagation constants (polarization modes Ex & Ey) • Birefringence in fiber can be used for filtering

Example – Fiber Birefringence • The birefringence property pulse spreading • Lithium Niobate • We refer to this as polarization-mode dispersion

Numerical Example – Fiber Birefringence

Dispersion • Different components of light travel with different velocity , thus, arriving at different time • This results in pulse broadening • Dispersion types • Polarization Mode Dispersion • Intermodal Dispersion • Chromatic Dispersion

Chromatic Dispersion • So how much a pulse is broadened? • Depends on the pulse shape • Let’s assume a specific family of pulses called chirped Gaussian Pulses (chirped means frequency is changing with time) • They are not rectangular! � • Used in RZ modulation • Chirped pulses are used in high-performance systems • If To is the initial width, Tz is pulse width after distance z, with κ being the chirp factor:

Chromatic Dispersion • In a single mode fiber different spectral components travel with different velocities (proportional to β 2) • Chromatic Dispersion parameter D = 1(2πc/λ^2)β 2 • Expressed in terms of ps/nm-km • No chromatic dispersion when β 2 = second derivative = 0 • D=Dm + Dw • Due to material dispersion n λ • Different wavelengths travel at different speeds • More significant • Due to waveguide dispersion n 2<neff<n 1; P neff • neff depends on how propagated power is distributed in cladding or core • Power distribution in core and cladding is a function of wavelength • Longer wavelength more power in cladding • Thus, even if n(λ) = constant wavelength change result in power distribution change neff change •

Chromatic Dispersion The total dispersion D is zero about 1. 31 um We want to operate around 1. 55 um (low loss) let’s shift the zero-dispersion point to 1. 55 um! This is done by changing Dw (Dm cannot be changed too much) Negative dispersion

Example • Consider a 2. 5 Gb/s SONET system operating over a single mode fiber at 1. 55 um with dispersion length of 1800 km. Find Tz/To after Z = 2 LD. Assume an unchirped Gaussian pulse • LD = To^2/β 2 • Z=2(LD) Tz/To = sqrt(1+4)=2. 24 • Note To=0. 2 nsec (half bit interval) • What if κ is negative?

Chirp Factor • If chirp factor is negative the pulse goes under compression first and then it broadens

Example of Single Mode Chromatic Dispersion

Dealing with Dispersion • Different approaches • Dispersion-shifted Fiber • Dispersion Compensated Fiber • Dispersion Flattened Fiber • Basic idea • Change the refractive index profile in cladding and core • Thus introducing negative dispersion

References • http: //www. gatewayforindia. com/technology/opticalfiber. ht m • Senior: http: //www. members. tripod. com/optic 1999/