Propagation of Signals in optical fiber

9/13/11

Summary• See notes

Single Mode Fiber • Avoids the delay between different rays • Only one mode (ray) is propagated • Thus, we need to select the right relationship between the

wavelength and core diameter

Note that modes propagating nearThe critical wavelength (cutoff) will notBe fully guided within the core. NOTE: Single mode operation (with step index) occurs only above λc.

Single Moe Fiber - Example• See notes

Attenuation • Transmission loss is the main limiting factor in optical

communication systems • Limiting how far the signal can be transmitted

• Transmission loss in fiber is much less than copper (<5 dB/km)

• Loss in dB = 10log Pi / Po • Pi/Po = 10 ^(dB/10) • Attenuation (dB) = αL = 10log(Pi/Po) ; • Loss per unit length is represented by α is in dB/km• Also represented as follow (z=length from the source, and P(z) is

the power at point z.

• Example

Loss - Example• OTDR Example• Numerical Example

Fiber Bend Loss• Radiation loss due to any type of

bending • There are two types bending

causing this loss • micro bending

• small bends in the fiber created by crushing, contraction etc causes the loss

• macro bending• fiber is sharply bent so that the light

traveling down the fiber can not make the turn and gets lost

Radiation attenuation coefficient = αr = C1 exp(-C2 x R)

R = radius of the curvature; C1 & C2 are constants

Fiber Bend Loss• Multimode Fibers

• Critical Radius of curvature• Large bending loss occurs at Rcm

• Single-Mode Fibers

Note that modes propagating nearThe critical wavelength (cutoff) will notBe fully guided within the core. NOTE: Single mode operation (with step index) occurs only above λc.

Fiber Bend Loss - Example• In general, the refractive index difference:

Example of cutoff Wavelength • Find the cutoff wavelength for a step index fiber to exhibit

single mode operation when n1=1.46 and core radius=a=4.5 um. Assume Δ=0.25%

λc = 1.214 um

Typical values are a=4μm,Δ=0.3%, λ=1.55 μm

Note that if V becomes larger than 2.405 multimode fiber

Other factors impacting loss• Notes - map

Scattering• When some of the power in one propagation mode is

transferred into a different mode Loss of power in the core

• Power Scattering• Linear : Po is proportional to Pi, and there is no frequency change

– thus the power propagated is proportional to mode power • Two types: Rayleigh and Mie

• Nonlinear : The power propagation results in frequency change • Type types: Stimulated Brillouin Scattering & Stimulated Roman

Scattering

Rayleigh Scattering• Due to density fluctuation in

refractive index of material• Represented by ϒR (Rayleigh

scattering factor) – (1/m)• ϒR is a function of 1/(λ)^4• Transmission loss factor for one km

(unit less) αR= exp(-ϒR.L); L is the fiber length

• Attenuation (dB/km) = 10log(1/αR)

• Rayleigh scattering is dominant in low-absorption window

Example• Assume for Silica ϒR = 1.895/(λ^4); and we are operating

at wavelength 0.63um. Find attenuation due to Rayleigh scattering in a 1-km of fiber. Repeat the same problem for wavelengths of 1 um and 1.3 um.

Mie Scattering • Linear scattering can be due to inhomogeneities in fiber

• This is due to having non-perfect cylindrical structure or code-cladding refractive index difference along the fiber

• When such inhomogeneities > λ/10 Mie Scattering is significant

• Mie scattering can be removed by removing imperfections in the glass manufacturing or increasing Δ.

Nonlinear Scattering • Nonlinearity is primarily due to high power level, high bit-rate (when

we have to transmit over long distances) • Resulting in frequency change

• Stimulated Brillouin Scattering (SBS)• A backward gain (emission is stimulated), opposite to direction of

propagation when a threshold power is reached depleting the transmitted power

• The stimulated light has a shorter wavelength creating interfering with similar possible wavelengths

• Exists only above a certain power threshold • PB (in watts) = 4.4*10-3*d^2*λ^2*α( in dB/km)*V

• [this is relatively low threshold]

• V is Bandwidth in GHz; d is code diameter (2a) in um; λ in um• Beyond PB optical frequency shifts• More critical than SRS

Nonlinear Scattering• Stimulated Roman Scattering (SRS)

• Power from lower wavelength channels is transferred to higher wavelengths

• Exists only above a certain power threshold • PR = 5.9*10-2*d^2 (in um)*λ (in um)*α( in dB/km) [in watts]• d is code diameter (2a);

Example

Material Absorption • A major loss factor is material absorption

• Dissipation of optical power in the waveguide due to material composition and fabrication process

• Absorption can be Intrinsic or Extrinsic • Intrinsic

• Interaction of different components of the glass (due to impurities)• Has two components

• Ultra violate absorption – high energy excitation (lower wL high eV higher excitation more heat more loss

• Infrared Absorption – molecular vibration within the glass heat

Material Absorption

Photon Energy increasing (eV)

molecular vibration within the glass prop. to WL

high energy excitation prop. to eV

Material Absorption – Extrinsic • Due to waveguide impurities (the glass) – major source of

attenuation • Metallic impurities – metallic ions e.g., copper and chromium);

depending on their WL• This is why some glasses are colored (e.g., they have copper ion –

thus, absorbing some lights passing through others)• Hydroxyl (OH) impurities (main factor)

• Key factors in generating overtones

Overtones due to Hydroxyl Impurities

Material Absorption – Extrinsic • Using lower-water-peak fiber (dry fiber); also known as

zero-water peak (by Lucent) the peaks can be eliminated!

Polarization• Introduction

References• http://www.gatewayforindia.com/technology/opticalfiber.ht

m• Senior: http://www.members.tripod.com/optic1999/

Communication Systems

Basic Blocks

• Three basic components • Source and Transmitter • Destinations and Receiver • Communication channel

(medium)

• Communication channel • Wired • Wireless• Glass • Water and or materials

Coverage and Topology

• Coverage (public network) • LAN • MAN • WAN

• Topology • Bus • Ring • Mesh • Star