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

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