A \(\mathrm{p}-\mathrm{i}-\mathrm{n}\) photodiode has a responsivity of \(0.8 \mathrm{~A} / \mathrm{W}\) at \(1.55 \mu \mathrm{m}\). The effective resistance of the detector circuit is \(50 \Omega\). The photodiode dark current density is \(1 \mathrm{pA} / \sqrt{\mathrm{Hz}}\). Calculate the NEP of the detector at \(300 \mathrm{~K}\). Include both shot noise and Johnson noise in your calculation. If the area of the detector is \(1 \mathrm{~mm}^{2}\), what is the NEI?