ABSTRACT
Suppose, the field Eˆ2 is a coherent laser field (local oscillator) of a large amplitude α, whereas the signal (detected) field is weak.
As a result, the terms proportional to 〈bˆ†bˆ〉 and 〈bˆ†〉, 〈bˆ〉 dominate over those without bˆ† and bˆ. Hence, the terms independent of the amplitude of the local oscillator can be discarded. Thus, we can
ignore the term β〈aˆ†aˆ〉, and denoting 〈bˆ〉 = |α| exp(iφ), 〈bˆ†〉 = |α| exp(−iφ), the resultant light intensity at the detector is then
I ≈ (1− β) |α|2 + 2 |α| √
β (1− β) 〈Eˆφ〉 , (6.102) where 〈
Eˆφ 〉 = 1
2i
(〈aˆ〉e−iφ − 〈aˆ†〉eiφ) , (6.103) and φ is the phase of the laser. The first term on the right-hand side
of Eq. (6.102) is equal to the intensity of the reflected coherent beam.
The second term is an interference term between the coherent
and the signals beams. This term contains the phase-dependent
quadrature amplitude of the signal beam.
