1.5 Population inversion and laser operation C1>C2 C2>C1 “population inversion” LASER: Light Amplification by Stimulated Emission of Radiation First realization: MASER, (M=microwave), Charles Townes, 1953 NH3 Wikipedia.org Osa-opn.org Principle of laser operation Light Amplification by Stimulated Emission of Radiation (LASER) First realization: Theodore Maiman, 1960 l=693.4 nm HRL Laboratories De.wikibooks.org Examples Osa-opn.org De.wikibooks.org Ti:Sa laser (our laboratory) Equations for laser operation Rate of photon production: mode band- # of photons density width per mode 12 gain losses Condition of operation for a laser: 1.6 Interaction of light and matter Laser radiation: number of photons per mode is >1010 In this lecture, the radiation field will be treated classically. Atoms and molcules will be treated quantum-mechanically. Light-matter interaction is greatly simplified by the “dipole approximation”. IR, VIS, UV: OK Dipole approximation is valid when: X-rays: not OK wavelength dimension of light of particle Electric-dipole interaction of linearly polarized light with a system of charged particles: Electric dipole moment charge position Magnetic dipole interaction 1.7 Coherent excitation of a two-level system Reminder: The time-dependent Schrödinger equation (TDSE) All stationary solutions of the TDSE can be written: Superposition principle: Any linear combination of solutions of the TDSE is also a solution of the TDSE: *End of the reminder* Coherent excitation of a N-level system: TDSE: Time-dependent Hamiltonian: Using the molecular eigenstates as a basis, one obtains: Coherently excited 2-level system: Rabi oscillations |2> TDSE: |1> Matrix elements: We define: The time-dependent coefficients of must solve |2> |1> Example 1: The harmonic oscillator • Frequency-domain spectroscopy measures E1-E0, E2-E1, etc. • Time-domain spectroscopy measures the time evolution of: à A coherent superposition (or ”wave packet”) Time evolution of the wave packet: When many levels are coherently prepared by resonant excitation: à The expectation value of the position follows the classical result. Example 2: The linear rigid rotor E/hc J 12B 3 6B 2 2B 1 0 0 • Frequency-domain spectroscopy measures the intervals E1-E0, E2-E1, etc. • Time-domain spectroscopy measures the time evolution of: Revivals of a rotational wave packet q.