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1、Chapter 7. Lasers Light Amplification by Stimulated Emission of Radiation (acronym)The Historyv1916, Einstein predicted the stimulated emission.v1954, Townes and co-workers developed a Microwave Amplifier by Stimulated Emission of Radiation(maser) using ammonia, NH3.v1958, Schawlow and Townes showed
2、 that the maser principle could be extended into the visible region .v1960, Maiman built the first laser using ruby as the active medium. vFrom then on, laser development was nothing short of miraculous, giving optics new impetus and wide publicity.7.1 Stimulated Emission of Radiation 1. Boltzmann D
3、istribution 2. the transitions that occur between different energy statesv absorption: the upward transition from a lower energy state to a higher state, E1 E2v Emission: the downward transition, E2 E1, v population N : the number of atoms, per unit volume, that exist in a given state. given by Bolt
4、zmanns equationE : energy lever of the system k : Boltzmanns constant T : absolute temperature. 7.1 Stimulated Emission of Radiation vBoltzmanns ratio or relative population : the ratio of the populations in the two states, N2 / N1.Orvplot the energy in the higher state relative to that in the lower
5、 state, versus the population in these states(E versus N), the result is an exponential curve known as a Boltzmann distribution.v When the Boltzmann distribution is normal, it means that the system is in thermal equilibrium, having more atoms in the lower state than in the higher state. 7.1 Stimulat
6、ed Emission of Radiation 2. Einsteins Prediction vAssume first: an ensemble of atoms is in thermal equilibrium and not subject to an external radiation field. At higher temperatures, a certain number of atoms is in the excited state; on return to the lower state, these atoms will emit radiation, in
7、the form of quanta h . - spontaneous emission rate of the transition: the number of atoms in the higher state that make the transition to the lower state, per second. lifetime of the transition: the reciprocal of the rate of transition. rate of the spontaneous transition:A21: constant of proportiona
8、lityN2 : number of atoms (per unit volume) in the higher state7.1 Stimulated Emission of Radiation vAssume next: the system is subject to some external radiation field. one of two processes may occur, depending on:the direction (the phase) of the field with respect to the phase of the oscillator.7.1
9、 Stimulated Emission of Radiation the two phases coincide:a quantum of the field may cause the emission of another quantum. - stimulated emission.Its rate isB21 : constant of proportionality u(): energy density (J m-3), function of frequency .the two phase is opposite : the impulse transferred count
10、eracts the oscillation, energy is consumed, and the system is raised to a higher state - absorption. Its rate isB12 : constant of proportionality. 7.1 Stimulated Emission of Radiation Transitions between energy states 7.1 Stimulated Emission of Radiation Einsteins coefficients: A21, B21, B12Einstein
11、s relations B21 = B12(1) the coefficients for both stimulated emission and absorption are numerically equal(2) the ratio of the coefficients of spontaneous versus stimulated emission is proportional to the third power of the frequency of the transition radiationexplains why it is so difficult to ach
12、ieve laser emission in the X-ray range, where is rather high7.1 Stimulated Emission of Radiation 3. Population Inversion v thermal equilibrium systemabsorption and spontaneous emission take place side by side N2 N1on return to the ground state, the system will probably lase. Incandescent vs. Laser L
13、ightLight from bulbs are due to spontaneous emission1. Many wavelengths2. Multidirectional3. Incoherent1. Monochromatic2. Directional3. CoherentCoherenceCoherent: If the phase of a light wave is well defined at all times (oscillates in a simple pattern with time and varies in a smooth wave in space
14、at any instant).Example: a laser produces highly coherent light. In a laser, all of the atoms radiate in phase.Incoherent: the phase of a light wave varies randomly from point to point, or from moment to moment.Example: An incandescent or fluorescent light bulb produces incoherent light. All of the
15、atoms in the phosphor of the bulb radiate with random phase. Stimulated vs Spontaneous EmissionStimulated emission requires the presence of a photon. An “incoming” photon stimulates a molecule in an excited state to decay to the ground state by emitting a photon. The stimulated photons travel in the same direction as the incoming photon.Spontaneous emission does not require the presence of a photon. Instead a molecule in the excited state can relax to the ground state by spontaneously emitting a photon. Spontaneously emitted photons are emitted in all directions.two-le
