激光原理课件chapter3

W12 uv"uv 'dR
2
(3.1.11)
This means the transition must occur vertically: A→A’; B→B’
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Principles and Technologies of lasers
Chapter 3 Energy Levels, Radiative, and Nonradiative Transitions in Molecules and Semiconductors
(2J+1)-fold degenerate rotational level
P( J ) (2 J 1) exp BJ ( J 1) / kT
(3.1.9)
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Principles and Technologies of lasers
Chapter 3 Energy Levels, Radiative, and Nonradiative Transitions in Molecules and Semiconductors
V”=0
1/ 2
(For polyatomics, there is a Q-branch, where DJ=0).
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Principles and Technologies of lasers
Chapter 3 Energy Levels, Radiative, and Nonradiative Transitions in Molecules and Semiconductors
Dp 2 2 DEe ~ ~ 2m m a2
(3.1.1)
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Principles and Technologies of lasers
Chapter 3 Energy Levels, Radiative, and Nonradiative Transitions in Molecules and Semiconductors
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Principles and Technologies of lasers
Chapter 3 Energy Levels, Radiative, and Nonradiative Transitions in Molecules and Semiconductors
(1) vibronic transitions Nuclear separations do not change during a radiative transition (Franck-Condon principle). Transition probability between v” and v’ (different electronic states) is
Principles and Technologies of lasers
Chapter 3 Energy Levels, Radiative, and Nonradiative Transitions in Molecules and Semiconductors
3.1.2. Level Occupation at Thermal Equilibrium The probability of occupation of a given rotational level of the lowest vibrational state can be written as
DEr 2 m m 2 DEe DEv Ma2 M M
2 1/ 2
(3.1.6)
where m is the mass of the electron and M is the mass of the atom. And
m ~ 10 4 M
(so DEr is one-hundredth of DEv)
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J: rotational quantum number
3 2 1 J’=0
v: vibrational quantum number
V’=1
DJ=+1, P-branch
DJ=-1, R-branch
Er 2 J ( J 1) / Ma2
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3 2 1 J”=0
2 2 m DEr 2 DEe Ma 2 M m DEv M
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Principles and Technologies of lasers
Chapter 3 Energy Levels, Radiative, and Nonradiative Transitions in Molecules and Semiconductors
3.1.3. Stimulated Transitions
Principles and Technologies of lasers
Chapter 3 Energy Levels, Radiative, and Nonradiative Transitions in Molecules and Semiconductors
3.1. MOLECULES
Qualitatively describing the features of molecule for gas and organic dye lasers. 3.1.1. Energy Levels Molecular energies: 1. Electronic energy Ee Since Dx~a, from the uncertainty principle, Dx Dp ~ we have Dp ~ / a (the uncertainty in momentum). Kinetic energy
We find the most heavily populated level is not the ground level (J=0), but the J which satisfies the relation
(2J 1)m 2kT / B
1/ 2
(3.1.10)
For simple molecules at room temperature, the molecular population is distributed among several rotational levels of the ground vibrational state.
Three types transitions among energy levels of a molecule: (1) Transitions between two rotational-vibrational levels of different electronic states (vibronic transitions, near-uv spectral region) (2) Transitions between two rotational-vibrational levels of the same electronic state (rotational-vibrational transitions, nearto middle-infrared spectral region) (3) Transitions between two rotational levels of the same vibrational state, e.g., v” = 0, of the ground electronic state (pure rotational transitions, far-infrared spectral region)
(2) rotational-vibrational transitions A transition between two vibrational levels of the same electronic state. For such a transition the quantum mt Dv = ± 1. We did not consider the rotational transition on the above cases. If we include rotational transitions in consideration, according to election rule of DJ=J”-J’=±1, there are two sets of lines: P-branch (DJ=+1) and Q-branch (DJ=-1).
lines are evenly separated in frequency by the amount of 2B/h. The amplitude are different because of the different populations in rotational levels of the ground state. Each line is broadened 10 by same line broadening mechanism.
3. Rotational energy Er
According to quantum mechanics, for a homonuclear diatomic molecule,
Er 2 J ( J 1) / Ma2
where J is the rotational quantum number. The energy difference between two consecutive quantum number is
2. Vibrational energy Ev
Ev 0 ,
x" k0 x,
2
for harmonic oscillators, k x" 0 x 0

x" x 0, where