1. PROPAGATION OF SIGNALS IN OPTICAL FIBER 9/13/11

2. Summary See notes

3. 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 near The critical wavelength (cutoff) will not Be fully guided within the core. NOTE: Single mode operation (with step index) occurs only above λc.

4. Single Moe Fiber - Example See notes

5. 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

6. Loss - Example OTDR Example Numerical Example

7. 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

8. Fiber Bend Loss Multimode Fibers Critical Radius of curvature Large bending loss occurs at Rcm Single-Mode Fibers Note that modes propagating near The critical wavelength (cutoff) will not Be fully guided within the core. NOTE: Single mode operation (with step index) occurs only above λc.

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

10. 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

11. Other factors impacting loss Notes - map

12. 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

13. Rayleigh Scattering Due to density fluctuation in refractive index of material Represented by ϒ R (Rayleigh scattering factor) – (1/m) ϒ R is a function of 1/(λ)^4 Transmission loss factor for one km (unit less) αR= exp(- ϒ R.L); L is the fiber length Attenuation (dB/km) = 10log(1/αR) Rayleigh scattering is dominant in low-absorption window

14. Example Assume for Silica ϒ R = 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.

15. 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.

16. 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

17. 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

18. 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

19. Material Absorption Photon Energy increasing (eV) molecular vibration within the glass  prop. to WL high energy excitation  prop. to eV

20. 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

21. Overtones due to Hydroxyl Impurities

22. Material Absorption – Extrinsic Using lower-water-peak fiber (dry fiber); also known as zero-water peak (by Lucent) the peaks can be eliminated!

23. Polarization Introduction

25. References http://www.gatewayforindia.com/technology/opticalfiber.ht m http://www.gatewayforindia.com/technology/opticalfiber.ht m Senior: http://www.members.tripod.com/optic1999/http://www.members.tripod.com/optic1999/

26. 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