Optical Fiber Communications 4th Edition by Gerd Keiser

Exercise 21

Consider the following Taylor series expansion of the optical-power-versus-drive-current relationship of an optical source about a given bias point:
y ( t ) = a 1 x ( t ) + a 2 x 2 ( t ) + a 3 x 3 ( t ) + a 4 x 4 ( t )
Let the modulating signal x ( t ) be the sum of two sinusoidal tones at frequencies 1 and 2 given by
x ( t ) = b 1 cos 1 t + b 2 cos 2 t
( a ) Find the second-, third-, and fourth-order intermodulation distortion coefficients B mn (where m and n = ± 1, ±2, ±3, and ±4) in terms of b 1 , b 2 , and the a i.
( b ) Find the second-, third-, and fourth-order harmonic distortion coefficients A 2 , A 3 and A 4 in terms of b 1 , b 2 , and the a i.