[40 points] Lineshape Function and Spontaneous Emission An optical material is placed in an optical resonator designed specifically so that there is only one mode for the atoms to interact with. The resonant wavelength of the molecular transition is 0=600nm, the associated transition bandwidth is v=200GHz, its spontaneous lifetime is tsp=2ns, and the refractive index of the material system is n=1.5. Let us assume that the resonator supports a single mode that corresponds to the wavelength close to the atomic resonance, but not exactly matching it: =600.05nm. Assume the volume V= 100cm3 for the resonator. Evaluate the probability density of the spontaneous emission for sucl an atomic transition at the resonant wavelength and at the wavelength corresponding to the supported longitudinal mode, and compare the two values