Question #43945

A monochromatic microwave beam of angular frequency $\omega_0$ is split equally into two paths of an interferometer, with each path carrying an intensity $I_0$. Path 1 is a standard waveguide. Path 2 contains a semiconductor diode acting as a phase modulator. The dynamic resistance of the diode is modulated by an external square-wave voltage signal of angular frequency $\Omega$ (where $\Omega \ll \omega_0$). This modulation causes the phase of the wave in Path 2 to alternate instantaneously between $\phi_0 + \pi/3$ and $\phi_0 - \pi/3$ with a $50\%$ duty cycle, where $\phi_0$ is a tunable static phase shift. The waves from both paths are recombined and directed into a broadband detector that measures the time-averaged intensity $\langle I \rangle$. If the averaging time of the detector is much greater than $2\pi/\Omega$, what is the maximum possible intensity $I_{max}$ and the fringe visibility $V = \frac{I_{max} - I_{min}}{I_{max} + I_{min}}$ recorded by the detector as $\phi_0$ is varied?