Question

Artificial rubies have an atomic system consisting of three main energy levels and can be used to produce short pulses of laser light. The energies of these levels are Eo, E1 and E2, in increasing order of energy (a) Write down an expression giving the relative population of the energy levels Eo and E1 at thermal equilibrium. b) Explain what is meant by the term population inversion. Described how this is achieved in a three-level laser system Photons of wavelength 550 nm can be used to excite the ruby system. This results in the production of coherent light of wavelength 694 nm (c) Use the above information to draw the energy level diagram for the ruby laser, giving the energies for the excited states with respect to the ground state in eV. (d) Under spontaneous emission, the lifetime of the E1 level is ~10-3 s. Use the Heisenberg Uncertainty Principle to estimate the linewidth of the laser light due to lifetime of the state e) The energy state E is, in reality, composed of two nearly degenerate energies with an energy difference of 0.002 eV. Estimate the linewidth due to the splitting of the E1 state and briefly comment on the answer you obtain.

Answer 1

(a) A₂₁/B₂₁ =hw³/6.36/3.18².c²

where A21 & B21 are the coefficient of proportionality from higher to lower state

(b) Population inversion - Initially all the particles at the ground state when we provide energy the shifted at higher energy level i.e. E₂ & E₃, where E₂ is the metastable state its life time is 10^-8s. Then we see that there is less particles at ground state & more at higher state which means to be the population transfer os inversion