Coherence — Question 8

Question 8

Visibility can be limited by both coherence and intensity imbalance

Two parallel-polarized beams have intensities $I_1=9$ and $I_2=1$ in the same units. Their measured fringe visibility is 0.45. Model the intensity by $I=I_1+I_2+2\sqrt{I_1I_2}|\gamma|\cos\delta$, with $0\leq|\gamma|\leq1$.

1. Infer the modulus of the complex degree of coherence.

2. If the stronger beam is attenuated until both intensities are 1 while coherence is unchanged, calculate the new extrema and visibility.

Question 8 - Solution

Visibility can be limited by both coherence and intensity imbalance

(a) Method and calculation

$$V=\frac{2\sqrt{I_1I_2}}{I_1+I_2}|\gamma|=\frac6{10}|\gamma|.$$$$\boxed{|\gamma|=0.45/0.60=0.75}.$$

(b) Interpretation and further calculation

$$I_1^\prime=I_2^\prime=1:\quad I^\prime=2+1.5\cos\delta.$$$$\boxed{I^\prime_{\max}=3.5,\quad I^\prime_{\min}=0.5,\quad V^\prime=0.75}.$$

Physical check

Balancing beam powers removes the imbalance penalty, but cannot make the visibility exceed the underlying coherence modulus.