Assume an InGaAsP-InP laser diode that has a resonator cavity equal to \(250 \mu \mathrm{m}\). The peak radiation is at \(\lambda=1.55 \mu \mathrm{m}\). The refractive index of InGaAsP is 4. The optical gain bandwidth (as measured between the \(50 \%\) intensity points) is assumed for this problem to be \(2 \mathrm{~nm}\). What is the mode integer of the radiation peak? What is the separation \(\Delta \lambda\) between the modes of the cavity? How many of the modes are within the gain band of the laser? What is the reflection coefficient and reflectance at the ends of the resonator cavity, which we will assume at the ends of the InGaAsP crystal? The beam divergence full angle is \(5^{\circ}\) in the \(x\)-direction and \(20^{\circ}\) in the \(y\)-direction. Estimate the \(x\) and \(y\) dimensions of the cavity?

Assume a Gaussian beam with the waist located at the output of the cavity where we assume that its waist size approximates the \(x\) and \(y\) dimensions of the cavity.