1. Lecture 8

2. Comparison of modulaters sizeCapacitanceInsertion loss Chirping Electro- absorption smalllowerhighersome Electro-optic type (LiNbO3) largehigherlowernone

3. Optical Receiver Converts optical signals to electrical signals. Photons to electrons. Consider the noise at the receiving side using SNR or BER.

4. Optical Receiver

5. Photon Statistics Poisson Distribution P( ) = Probability that N photons will arrive during time interval T. N = number of photoelectrons produced in time interval T. = rT = the average number of photoelectrons in time T. r = average rate at which photoelectrons are produced.

6. Photon Statistics N/P(N) 00.10.5151020 010.9040.60650.3680.00674.5x10 -5 2x10 -9 100.09040.3033 200.00450.0758

7. Photon Statistics

10. The Poisson distribution has the interesting property that the variance and the mean are equal. Mean square deviation in N = average value of N.

11. Gaussian probability Gaussian probability distribution function is a good approximation to Poisson distribution function for sufficiently large, say.

12. Gaussian probability

13. Assume that the variance and the meal are equal as in Poisson distribution, we have

14. Probability of error in digital communication

15. Average number of electrons in time T for “0” transmitted = Average number of electrons in time T for “1” transmitted = Probability of error is the area of tail of Gaussian distribution.

16. Probability of error in digital communication If equal number of “1’s” and “0’s” transmitted, then the probability of error is equal to ‘bit error rate’ or BER.

17. Probability of error in digital communication The area under a curve to one side of a point  =  is given by a Q-function.

18. Probability of error in digital communication

20. Assume

21. Probability of error in digital communication

22. Relate BER to electrical signal-to-noise ratio (SNR) in receiver. n s = number of photoelectrons per time interval produced by turning light on.  = root mean square deviation in number of photoelect.rons per time interval

23. Probability of error in digital communication Assume

24. Probability of error in digital communication (SNR) 1/2 SNRSNR(dB)BER 4.621.113.310 -2 7.454.817.310 -4 9.488.419.510 -6 11.2125.420.910 -8 12.6158.822.010 -10 14.2201.623.010 -12 15.4237.123.710 -14

25. Example In an optical communications experiment, an average of m1, photons is detected when a “1” is transmitted and m 0 when a “0” is transmitted. What is m 1 for error rates of 10 -3 and 10 -10, if (a) m 0 = 0 and (b) m 0 = 1. Assume Poisson statistics.