Page 80 - High Power Laser Handbook

50 G a s , C h e m i c a l , a n d F r e e - E l e c t r o n L a s e r s Chemical Lasers 51

HF DF
ω vibrational level linear term 4138.73 3000.358
X first anharmonicity correction –90.05 –47.34
B J rotational constant 20.96 11.00
B 1J rotational constant first –0.7958 –0.2936
correction
Table 3.2 HF and DF Energy Level Parameters. All Values are in
Wavenumbers
The first term in Eq. (3.5) corresponds to the behavior of a simple
harmonic oscillator with quantum number v. Allowable values for
v are 0, 1, 2, . . . . The second term corresponds to a first-order anhar-
monic correction illustrating deviation from ideal harmonic
behavior. The third term is associated with the rotational quantum
number J and the associated rigid-rotor rotational energy. Allow-
able values for J are 0, 1, 2, . . . . The fourth term is the Coriolis
effect correction to the rotational energy. More sophisticated
expressions, including 16 terms or more, are also available. The
interested reader can find a more detailed discussion of diatomic
8
energy levels and spectroscopy in Spectra of Diatomic Molecules,
which also provides general information on diatomic molecule
energy-level notation.
It should be noted that diatomic molecules containing hydrogen
are atypical as compared with most single-bond diatomics. The for-
mer have rather large vibrational level separations, substantial
amounts of anharmonicity, and very large rotational constants. This
last feature is a major advantage from a laser standpoint.
The allowed molecular transitions for HF and DF are:

∆ν = +/–1 (3.6a)

∆ J = +/–1 (3.6b)

Moreover, the degeneracy of the E(v, J) level is 2J + 1.
In terms of energy levels, the primary allowed transitions are:

E(ν, J – 1) → E[(ν – 1), J], which is denoted as a P branch.
E(ν, J + 1) → E[(ν – 1), J], which is denoted as an R branch.

The P branch is the dominant lasing transition due to higher gain (see
Sec. 3.3.2). Figure 3.4 shows energy-level diagrams appropriate for
HF and DF lasers (note that vibrational levels are denoted by V as
opposed to ν).