 Solution

Adjacent longitudinal cavity modes obey $2nL=m{\lambda }_0$. Neglecting optical dispersion in estimating their spacing,Hence the gain interval accommodatespossible longitudinal cavity modes. The exact integer depends on the positions of the interval endpoints and resonances. This counts available resonances; mode competition and actual laser threshold can reduce the number that oscillates. More accurately, the spacing uses the group refractive index instead of $n$.

A broad multimode spectrum suffers differential delay through optical fiber group velocity dispersion, broadening transmitted pulses. Near $800\mathrm{nm}$, ordinary silica optical fiber attenuation is also larger than in the long-distance windows near $1.3$ and $1.55\mu \mathrm{m}$. These limitations concern this short-wavelength, simple multimode device: suitably engineered single-frequency semiconductor lasers at telecommunications wavelengths are useful communication sources.