282 Short fiber Characterization of Optical Devices Waveform generator Transmitter under test Wideband receiver High-speed oscilloscope Trigger Figure 3.2.7 Block diagram of time-domain measurement of optical transmitter. domain waveform characterization in Section 2.8, where both electrical domain sampling and optical domain sampling were presented. More detailed descrip- tions of time-domain waveform measurement and eye diagram evaluation are given in Chapter 5, where we discuss optical transmission systems. 3.2.2 Measurement of Frequency Chirp Frequency chirp is the associated frequency modulation when an optical transmitter is intensity modulated. Frequency chirp usually broadens the spec- tral bandwidth of the modulated optical signal and introduces additional performance degradation when the optical signal propagates through a disper- sive media. The origins and physical mechanisms of frequency chirp in directly modulated laser diodes and in electro-optic external modulators were discussed in Chapter 1; here we discuss techniques of measuring the frequency chirp. Let's consider an optical field that has both intensity and phase fluctuations: p ffiffiffiffiffiffiffiffiffi ð3:2:5Þ EðtÞ ¼ PðtÞ e jfðtÞ ¼ exp f jfðtÞ þ 0:5 lnPðtÞ g where PðtÞ ¼ jEðtÞj 2 is the optical power. In this expression, the real part inside the exponent is 0:5 lnPðtÞ and the imaginary part is f(t). The ratio between the derivatives of the imaginary part and the real part is equivalent to the ratio between the phase modulation and the intensity modulation, which is defined as the chirp parameter: a lw ¼ 2 dfðtÞ=dt dfðtÞ=dt ¼ 2P dfln PðtÞg=dt dPðtÞdt ð3:2:6Þ The frequency deviation is equal to the time derivative of the phase modula- tion, Do ¼ dfðtÞ=dt; therefore the intensity modulation-induced optical fre- quency shift is a lw 1 dP Do ¼ ð3:2:7Þ 2 P dt