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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.
2. Einstein's Prediction
7.1 Stimulated Emission of Radiation
Assume first: an ensemble of atoms is in thermal equilibrium and not subject to an external radiation field.
Light from bulbs are due to spontaneous emission
1. Many wavelengths 2. Multidirectional 3. Incoherent
1. Monochromatic 2. Directional 3. Coherent
Coherence
thermal equilibrium system absorption and spontaneous emission take place side by side N2 < N1, absorption dominates: an incident quantum is more likely to be absorbed than to cause emission.
explains why it is so difficult to achieve laser emission in the X-ray range, where is rather high
7.1 Stimulated Emission of Radiation
3. Population Inversion
populations in the two states, N2 / N1.
N2 N1

e E2 / T e E1 / T
Or
N 2N 1e(E 2E 1)/T
plot the energy in the higher state relative to that in the lower state, versus the population in these states(E versus N), the result is an exponential curve known as a Boltzmann distribution.
• 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 the form of quanta h . -- spontaneous emission
Einstein's coefficients: A21, B21, B12
ຫໍສະໝຸດ Baidu
Einstein's relations
B21 = B12
A21 8 h3
B21
c3
(1) the coefficients for both stimulated emission and absorption are numerically equal
rate of the spontaneous transition: P21N2 A21
A21: constant of proportionality N2 : number of atoms (per unit volume) in the higher state
7.1 Stimulated Emission of Radiation
Its rate is
P 12 N 1B 1u 2
B12 : constant of proportionality.
7.1 Stimulated Emission of Radiation
Transitions between energy states
7.1 Stimulated Emission of Radiation
Assume 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.
Emission: the downward transition, E2 E1, population N : the number of atoms, per unit volume, that
exist in a given state.
given by Boltzmann's equation
Example: An incandescent or fluorescent light bulb produces incoherent light. All of the atoms in the phosphor of the bulb radiate with random phase.
Stimulated vs Spontaneous Emission
考试时间：2019.1.4 上课时间和教室
Chapter 7.
Lasers
(acronym)
Light Amplification by Stimulated Emission of Radiation
The History
1916, Einstein predicted the stimulated emission. 1954, Townes and co-workers developed a Microwave
(2) the ratio of the coefficients of spontaneous versus stimulated emission is proportional to the third power of the frequency of the transition radiation
Stimulated 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.
Coherent: 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 at any instant).
Its rate is
P 2 1N 2B 2u 1
B21 : constant of proportionality u(): energy density (J m-3), function of frequency .
the two phase is opposite : the impulse transferred counteracts the oscillation, energy is consumed, and the system is raised to a higher state -- absorption.
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 Stimulated Emission of Radiation
1. Boltzmann Distribution
2. the transitions that occur between different energy states
absorption: the upward transition from a lower energy state to a higher state, E1 E2
Amplifier by Stimulated Emission of Radiation(maser) using ammonia, NH3. 1958, Schawlow and Townes showed that the maser principle could be extended into the visible region . 1960, Maiman built the first laser using ruby as the active medium. From then on, laser development was nothing short of miraculous, giving optics new impetus and wide publicity.
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.
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.
7.1 Stimulated Emission of Radiation
the two phases coincide:a quantum of the field may cause the
emission of another quantum. -- stimulated emission.
NeE/T
E : energy lever of the system : Boltzmann's constant T : absolute temperature.
7.1 Stimulated Emission of Radiation
Boltzmann's ratio or relative population : the ratio of the
population inversion condition a majority of atoms in the higher state, N2 > N1 on return to the ground state, the system will probably lase.
Incandescent vs. Laser Light