Measurement Based on Coherent Optical Detection 199 The first and the second terms on the right side of Equation 2.7.6 are the direct detection components of the optical signal and the LO. The last term is the coherent detection term, which is the result of mixing between the optical signal and the LO. Typically, the LO is a laser operating in continuous waves. Suppose the LO p ffiffiffiffiffiffiffiffiffi has no intensity noise; A LO ¼ P LO is a constant, where P LO is the optical power of the LO. In general, optical power of the LO is much stronger than ~ ~ that of the optical signal such that jA s ðtÞj 2 ( j A s ðtÞ Á A LO j. Therefore the only significant component in Equation 2.7.6 is the last term, and thus p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2:7:7Þ iðtÞ % 2 R eð1 À eÞ cos y P s ðtÞ Á P LO cos ð o IF t þ DfðtÞ Þ ~ ~ where cos y results from the dot product of A s ðtÞ Á A LO , which is the angle of polar- ization state mismatch between the optical signal and the LO. P s (t) ¼ jA s (t)j 2 is the signal optical power. Equation 2.7.7 shows that the detected electrical signal p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi level depends also on the coefficient of the optical coupler e. Since 2 eð1 À eÞ reaches the maximum value of 1 when e ¼ ½, 3-dB couplers are usually used in the coherent detection receiver. In addition, in the ideal case, if the polarization state of the LO matches the incoming optical signal, cos y ¼ 1, therefore the photocurrent of coherent detection is simplified as p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2:7:8Þ iðtÞ % R P s ðtÞ Á P LO cos ðo IF t þ DfÞ