Lecture 4b Fiber Optics Communication Link 1. Introduction 2 Lecture 4b  Fiber Optics Communication Link 1. Introduction   2. Optical Fiber, Physical Background 3.  The Light Transmitters and the Receivers as a Components of the Fiber Optic Communication Links 4. Light Emitting Diodes 5. Transmitters 6. Driving Circuits 7. Receivers 8. p-i-n Photodiode 9. Transceivers and Repeaters 10. Fiber Optic Communication Link Rise Time and Bandwidth Bandwidth 11. Communication Link Power Budget 12. Connectors 13. Conclusion

1. Wide bandwidth: Fiber optic system uses light as a carrier with 1013 to 1014 Hz. Radio waves are 106 to 1010 Hz. Electrical signals have frequencies up to 108 Hz. The maximum bandwidth of the transmitted signals is 10% of the carrier. 2. Low loss: The typical attenuation of a 1 GHz bandwidth digital signal in an optical fiber is 0.1 dB per km. A 100 MHz bandwidth signal in RG‑58/U coaxial cable has attenuation of 130 dB per km. 3. Electromagnetic immunity: Electrical fields do not affect light signals.   4. Light weight and small size: 1 km of optical fiber cable weighs about 10 kilograms. A 1 km copper wire with the same signal carrying capacity would weigh 700 kg. 5. Safety: There is no possibility of a short circuit in a fiber optic system, eliminating the hazard of sparks in an electrical cable. 6. Security: Optical fiber is harder to tap than electrical wire. Unwanted tapping over the length of the fiber can usually be detected.

A. Index of Refraction C= 3×108 meters per second, but it is reduced when it passes through matter. The index of refraction n: speed of light in a vacuum, 3×108 m/s speed of light in the given material c wavelength of light in a vacuum wavelength of light in the given material X ray,

for various materials. Index of refraction and speed of light Free space (vacuum) 1.0 3×108 m/s Air at sea level 1.003 2.99×108 m/s Ice 1.31 2.29×108 m/s Water 1.33 2.26×108 m/s Glass (minimum) 1.45 2.07×108 m/s Glass (maximum) 1.80 1.67×108 m/s Diamond 2.42 1.24×108 m/s

B. Refraction with Snell's Law 1 : The incident angle (from the surface normal) 2 : The angle of refracted light (from the surface normal) n1 : index of refraction in the incident medium n2 : index of refraction in the refracting medium   Light that is not absorbed or refracted will be reflected. The incident ray, the reflected ray, the refracted ray, and the normal to the surface will all lie in the same plane.

D. Multimode Step Index Fiber We want to find the critical case of total internal reflection at the core-cladding boundary. Using Snell’s Law with 2 = 90º, we can find the critical angle CR :

C. Total internal reflection   C. Total internal reflection Total internal reflection when 1 > CR .

Critical angle refraction=90

Since we can relate r, CR to angle CR by simple geometry, and we can make the approximate n0  = 1, this equation can be simplified: The negated and shifted sine function is identical to the cosine, and we can relate this cosine to the sine by the trigonometric identity: In equation (3.4), this sine was found above in terms of n1  and n2 : For n1   n2 , we can simplify the numerical aperture calculation:

Number of modes E. Modal Dispersion Dispersion means the difference in arrival time of the light rays at the output end of an optical fiber. Modal dispersion is caused by the difference in rays path (with equal wave length) due to variation in light incidence angles at the input end. It occurs only in multimode fibers Material dispersion is related to the variation of light velocity in a given fiber material due to the difference in propagated light wave. Number of modes

A Input pulse Output pulse LMax t Critical angle LMin For instance, if n1  = 1.5 and  = 0.01, then the numerical aperture is 0.212 and the critical angle  r,cr,  is about 12.5 degrees.

i  = 0 and path length=L (fiber length). The longest path occurs for  i = i, CR and can be estimated as: For  = 0.002 in a small-step index optical fiber:

B Mbps 150 1 1 150 L km

F. Bandwidth of a Multimode Optical Fiber To estimate the bandwidth of an optical fiber, we can convert from a bit transfer rate to a bandwidth. In one signal period, two bits can be transferred, so the maximum signal frequency is simply one-half the bit transfer rate. Light frequencies used in fiber optic systems use a carrier frequency between 1014 and 1015 Hz (105 to 106 GHz). The theoretical bandwidth of a fiber optic system is about 10% of the carrier frequency, or up to 10,000-100,000 GHz!

There are two reasons for attenuation: Scattering; Absorption: G. Attenuation Attenuation ranges from 0.1 dB/km (single-mode silica fibers) to over 300 dB/km (plastic fiber). There are two reasons for attenuation: Scattering; Absorption: Attenuation (dB) =

3. Classification of optical fibers and their characteristics

 multimode step inde   multimode graded index  single-mode step index

4. Light Emitting Diodes

Sources of losses of light power due to mismatches: A source, with an output diameter of 100m and an NA of 0.30 is connected to a fiber with a core diameter of 62.5m and NA of 0.275. The  and the are as follows:

LED driver circuits

p-n Photodiode, (p-i-n)

The important characteristics of receivers are: Signal-to-noise ratio (S/N) is expressing the quality of signal in a system. In decibels, S/N is equal to the signal power in decibels minus the noise power in decibels. S/N (dB) = 10 log10( S/N ) = 10 log10( S ) - 10 log10( N ). If the signal power is 50 W (-13 dBm) and the noise power is 50 nW (-43 dBm), the S/N is 1000, or 30 dB. Bit-error rate (BER) is related to S/N. The BER is the ratio of the incorrectly received bits to correctly transmitted bits. A ratio of 10-9 means that one wrong bit is received for every 1 billion transmitted bits. Responsivity (R) is the ratio of the photodiode's output current to the input optical power; it is expressed in Amperes /Watt (A/W). A p‑i‑n photodiode typically has a responsivity of around 0.4 to 0.6 A/W. A responsivity of 0.6 A/W means that incident light having 50 W of power results in 30 A of current. Rise time For most components, rise time and fall time are assumed to be equal. The response time of the receiver characterizes its bandwidth. Sensitivity specifies the weakest optical signal that can be detected. Sensitivity can be expressed in microwatts or dBm. A sensitivity of 1 W is the same as a sensitivity of ‑30 dBm.

Receivers

Transceivers and Repeaters

System Rise Time and Bandwidth

Communication Link Power Budget

Connectors