Gain medium

A common solid-state laser material consists of an optically transparent host such as glass (mostly SiO2), YAG, sapphire (Al2O3), etc., doped with a small amount of a rare earth ions (the rare earths are those elements with atomic numbers from 57 to 71 with two of the most important being Nd 60 and Er 68 ). The active atom is the rare earth and usually acts as if it was triply ionized since the outermost three electrons are involved in the bonding (the solid-state material is charged neutrally).

Some of the unique laser properties arise because of a subtle point appearing in nature. In the rare earths, the active electron participating in the optical transition is one of the 4f electrons that is shielded by electrons in the larger n = 5 and 6 shells (or orbits). One of the consequences is that the energy levels of rare earths are only weakly dependent on the host lattice. Thus, while there are small changes in the wavelengths of the RE laser depending on the host lattice, those changes appear in the third or fourth significant figure. Per usual, we depend upon experiment to identify the character of the quantum states, the energy levels, any nonradiative quenching rates, branching ratios, the Einstein coefficients, and the transition probabilities.

The characteristics of the quantum states are usually specified by the spectroscopic name to the following scheme.

superscript = number[Letter]subscript = number

The letter symbol indicates the orbital angular momentum quantum number according to the following prescription:

Letter S P D F G H I etc.

L = 0 1 2 3 4 5 6 etc.

The numerical value for the superscript = 2S+1, where S is the spin angular momentum. The numerical value for the subscript = J, where J is total angular momentum quantum number.

A level such as ⁴I9/2 (the ground state of the neodymium) is referred to as

“quartet-I-nine-halves” and from its “name”, we immediately know that the degeneracy of that level is g = 2J+1 = 10. In other words, there are 10 different orthogonal wavefunctions describing this state.

A common solid state laser material is made by doping a rare earth, neodymium, into a variety of host materials, with the most common ones being amorphous glass and crystalline YAG. In each case, the active atoms participate as if they were triply ionized, Nd³⁺, with energy levels and broadening of the states dependent on the host lattice. The dopant (1% to 3%) goes into the amorphous glass at random sites, and thus each Nd³⁺ ion “sees” a slightly different environment. On the other hand, the Nd³⁺ substitutes for Y³⁺ in the cubic crystal of YAG, and thus each of these dopant atoms sees more or less identical environments. It should come as no surprise then that the glass laser transition is inhomogeneously broadened with a comparatively wide line, whereas the YAG transition line widths are much smaller. While the YAG and the glass laser resemble each other, both lasing at λ₀ ~1.06 µm, they are sufficiently different to warrant separate discussions.

Pure YAG is an optically isotropic crystal with a cubic structure characteristic of garnets. Because of the difference in size of the Nd³⁺ that is substituted for Y³⁺

(about 3%), one is limited in the amount of neodymium that can be included to about 1%; otherwise, the crystal becomes severely strained. Because the active atoms are in a well defined environment, the energy levels are well defined and narrow and are shown in Fig. 2.10 part (a) with a greater detail in Fig. 2.10 part (b) where the

dominant laser transition at λ₀ =1.064 µm is shown as the transition between the upper state of the ⁴F3/2 at 11507 cm^-1 and the lower state ⁴I11/2 at 2110 cm^-1. In Fig.

2.10 part (c) the energy levels are shown presuming that the host lattice was cooled to liquid nitrogen temperatures [53]. Specific data on the various transitions, arranged in order of wavelength, are given in Tables 2.2 and 2.3.

Figure 2.10. Energy level for neodymium in YAG. (a) Structure of Nd:YAG showing the pumping routes with the percentages referring to a pump with a broad spectral output, (b) details of the manifold at 300K showing the dominant transition, the semiconductor laser pumping route are also shown, the number in parentheses is energy levels at 77 K [53].

(a) (b)

Table 2.2: Characteristics of a typical Nd:YAG laser rod

Table 2.3: Detailed data on ⁴F3/2 → ⁴I13/2, ⁴I11/2, ⁴I9/2 transitions

The typical pumping route, such as a flash lamp, is also indicated in with approximately 10% of the absorbed energy going directly to the upper laser manifold

4F3/2 and the remainder going to the higher states. Also shown is the route for the case of a semiconductor laser pumping the YAG using radiation near 808 nm. For the most

part, the ions promoted to ⁴F5/2, ⁴H9/2 and so on return to the ⁴F3/2 level for participation in the laser action. The lower laser level ⁴I11/2, decays with a lifetime of

~30 ns, but that radiation is strongly absorbed by the host lattice and thus that energy shows up as heat. Fortunately, YAG has a high thermal conductivity and this unwanted energy can be removed by conduction. The system can be operated either cw or pulsed, mode locked or Q-switched [54]. By using frequency doubling techniques, the output wavelength can be converted to the “green” with a diffraction limited TEM00 mode as the output. The entire system of diode laser pumped solid-state laser can be contained in a compact volume compare to a thumb size or smaller.