- #1
roam
- 1,271
- 12
Homework Statement
The input signal to the interferometer shown in the picture below is given by:
$$E_{\text{in}}=\sqrt{P}\exp\left(j\omega_{0}t+\frac{jD(t)\pi}{2}+j\varphi_{p}(t)\right). \tag{1}$$
##P## is the power that is received. The delay present in one arm of the interferometer is ##T_b##.
I want to calculate the intensity/optical power at the output of the interferometer.
Homework Equations
For two waves ##\sqrt{I_{1}}\exp(j\varphi_{1})## and ##\sqrt{I_{2}}\exp(j\varphi_{2})##, the resulting interference equation is:
$$I=I_{1}-I_{2}+2\sqrt{I_{1}I_{2}}\cos\varphi \tag{2}$$
where ##d## is the delay distance, and ##\varphi = \varphi_2 - \varphi_1##.
The Attempt at a Solution
So from the interference equation:
$$P_{\text{out}}=2P\left[1+\cos\left(\frac{2\pi d}{\lambda}\right)\right]=2P\left[1+\cos\left(\frac{2\pi cT_{b}f}{c}\right)\right]$$
$$=2P\left[1+\cos\left(2\pi T_{b}f\right)\right]=2P\left[1+\cos\left(T_{b}\omega\right)\right]. \tag{3}$$
Is this correct?
The context of this problem is in telecom. ##\omega_0## represents the carrier frequency, ##D(t)## is the actual data that has to be recovered. However ##D## is absent from (3) so I am thinking that my result is probably not correct.
Any explanation would be greatly appreciated.