This module discusses energy transfer mechanisms that occur in molecular lasers and explains how the energy flow process affects design and output characteristics of the laser system. Molecular energy states of diatomic and triatomic molecules and the transitions between states are described in detail. Basic characteristics of diatomic molecular lasers are described using the carbon monoxide laser as an example. Most of the module is devoted to study of the carbon dioxide laser as an example of a triatomic molecular laser. Effects of several parameters on typical CO₂ laser output will be described and correlated to the energy transfer processes occurring in the laser gas. A greater discussion of design and construction of CO₂ laser systems is contained in Module 3-9, "CO₂ Laser Systems."

A small CO₂ laser will be operated in the Laboratory section of this module, and output power will be examined as several parameters are varied.

Upon completion of this module, the student should be able to:

1. Draw and label an energy-level diagram representing the first few rotational energy levels in two adjacent vibrational states of a diatomic molecule. On this diagram draw and label the following:

a. A pure rotational transition.

b. A P-branch vibrational-rotational transition.

c. An R-branch vibrational-rotational transition.

d. A Q-branch vibrational-rotational transition.

2. Draw and label an energy-level diagram showing the lasing cascade in a carbon monoxide (CO) molecular laser. Include at least four vibrational levels, several rotational levels within each vibrational level (not necessarily to scale), and one P-branch transition between three successive vibrational-rotational bands. Use this diagram and explain the concept of a lasing cascade.

3. Draw and label diagrams showing symmetric stretch, bending, and asymmetric stretch vibrational modes in a carbon dioxide (CO₂) molecule.

4. Draw and label a simplified energy-level diagram of a CO₂ laser. The drawing should include upper and lower laser levels for two infrared lines, nonradiative transitions to lower vibrational states, and the ground state. Vibrational energy transfer from nitrogen (N₂) molecules should be indicated, along with the two lowest-energy vibrational levels of N₂. All vibrational levels should be labeled with appropriate quantum numbers.

5. Write symbolic expressions for the four energy transfer mechanisms that excite CO₂ molecules to the upper lasing level (001) in a typical CO₂ laser and the two energy transfer mechanisms necessary to move CO₂ molecules from the lower lasing level (100) to the vibrational ground state (000) in a typical CO₂ laser.

6. Explain the concept of lasing due to a partial inversion in a CO₂ laser, and explain why lasing usually occurs on a single P-branch transition in a CW CO₂ laser.

7. For a coaxial, CW CO₂ laser, make a brief statement explaining how and why the output power depends upon each of the following parameters.

a. Tube current.

b. Wall temperature.

c. Gas pressure.

d. Gas flow rate.

8. Explain how gain and loss in a CO₂ laser are affected by varying the diameter of the laser tube.

9. Operate a low-power CW CO₂ laser in the laboratory. Measure output power as a function of tube current, tube pressure, and gas flow rate. Examine effects of the focused and unfocused CO₂ laser beam on various materials.

Before the design, operating parameters, and output characteristics of molecular gas lasers can be understood, the energy transfer processes at work within the gas itself must be understood. This module will encourage this understanding through discussions of the following topics:

· Molecular energy levels—the origin of vibrational and rotational energy levels of molecules.

· Energy levels and molecular transitions—allowed vibrational-rotational states and transitions of molecules.

· Diatomic molecular lasers—an examination of energy transfer in a carbon monoxide (CO) laser as a representative of the group.

· Triatomic molecular lasers—an examination of energy transfer in a carbon dioxide (CO₂) laser as a representative of the group.

· Operating parameters of CO₂ lasers—a correlation of equipment design and output characteristics relative to energy transfer mechanisms within the gas.

Molecular Energy Levels

Gas lasers may operate due to energy transitions between excited states in neutral atoms (HeNe), ions (argon), or molecules. Energy transitions involved in neutral atom and ion lasers are electronic transitions in which an electron in an atom or ion moves from one orbit to another (in the simplified Bohr model) by absorbing or emitting a photon.

The energy-level structure of a molecule is far more complex than that of an atom (or ion) because there are more transition possibilities. Molecules not only have atoms with electronic energy levels, but have their own characteristic vibrational and rotational energy levels as well.

Excited electronic states of a molecule result when an electron in one of its component atoms is in an orbit corresponding to an excited atomic state. While electronic transitions (mainly in the visible and near UV) have been observed in some molecular lasers, they are of lesser importance and will not be considered here. All important molecular lasers operate with the atoms of the molecule in the electronic ground state (except nitrogen lasers which will be discussed briefly in Module 3-10, "Liquid Dye Lasers").

Atoms comprising a molecule contain energy in the form of vibrational motion due to molecular binding forces between the constituent atoms. Simply speaking, atoms of the molecules are bound together by their shared electronic cloud like balls interconnected by springs. They have natural vibrational frequencies (called normal or resonant modes) that depend upon the masses of the particles and the stiffness of the springs. Molecules can move from one vibrational state to another by absorbing or emitting a photon of the proper energy. Each vibrational possibility (mode) for the molecule involves a particular configuration of its total electronic cloud and, thus, is associated with a specific energy. This gives rise to a discrete set of vibrational energy levels, as is the case with electronic energy levels. The effect is to split each of the electronic energy levels for the atoms of the molecule into a series of "almost" equally separated vibrational levels.

In addition, a molecule may undergo quantized rotations about various axes in space. Again, the molecule changes from one energy state to another by absorbing or emitting only certain discrete or quantized amounts of E-M radiation. Rotational energy of the molecule produces further line splitting by subdividing each vibrational energy level into a series of finely spaced rotational levels. Unlike vibrational levels, rotational energy levels are not as equally spaced. The energy difference between two adjacent rotational levels becomes larger as higher rotational energy levels are reached.

Table 1 is a comparison of energies involved in electronic, vibrational, and rotational transitions. Also given are spectral regions of the photons exchanged in each type of transition. The total energy of a molecule is the sum of its electronic, vibrational, and rotational energies. The molecule may move from one energy state to another by emitting or absorbing a photon or through a collision with another atom or molecule or with a free electron. Collision processes also involve the energy of motion or kinetic energy. Many collisional energy transfer processes involve an increase or decrease in the total kinetic energy of the two particles during a collision.

Table 1. Molecular Spectra.

Energy Levels and Transitions in Diatomic Molecules

Diatomic molecules (CO, HF, N₂) are composed of two atoms bound together. Such molecules have only one normal or fundamental vibrational mode. This mode, shown in Figure 1, consists of a stretching of the molecular bond as the two atoms move away from one another, and a shortening of the bond as they are pulled back toward one another. An increase of the amplitude of this motion corresponds to an increased vibrational energy content of the molecule.

Fig. 1
Vibrational and rotational modes of a diatomic molecule.

Diatomic molecules also rotate around an axis perpendicular to the molecular bond and passing through the center of mass of the molecule. An increase in rotational rate about such an axis corresponds to an increase in rotational energy.

Quantization of both vibrational and rotational energies leads to the molecular energy-level diagram shown in Figure 2.

Fig. 2
Vibrational and rotational energy levels in a diatomic molecule (levels not to same scale).

The quantum number V indicates the vibrational state of the molecule, and the quantum number J indicates the rotational state. Vibrational states are nearly evenly spaced and each vibrational state is composed of a large number of rotational states of which the energy spacings increase as J increases. Figure 2 shows the rotational levels of the V = 2 vibrational state only. Rotational levels of the other vibrational states have a similar form. The energy spacing of rotational levels is much less than for vibrational levels.

Four types of energy transitions between molecular states are important in diatomic molecules. These are illustrated in Figure 3 and described below.

Fig. 3
Transitions in a diatomic molecule.

Pure Rotational Transitions

Pure rotational transitions involve a change in rotational energy only. Such a transition is indicated in Figure 3 by the letter R followed by the number 3 in parentheses, i.e., R(3). The number in parentheses is always the J quantum number of the lower rotational state involved, whether molecular energy is increasing (absorption) or decreasing (emission). The only pure transitions that can occur in most diatomic molecules are those in which the J value changes by one (D J = ± 1). Such a transition, R(3), is shown in Figure 3. This transition is from the J = 4 rotational level to the J = 3 rotational level, within the single vibrational state V = 2. It involves photons in the microwave region.

P-Branch Transitions

These transitions involve (during emission) a decrease in vibrational energy (D V = –1) accompanied by an increase in rotational energy (D J = +1). They are the "shortest" transitions (lowest energy difference) between two vibrational states and, therefore, the most likely vibrational-rotational transitions. They are identified by the letter P followed by the J (rotational) quantum number of the lower vibrational energy state. Figure 3 shows a P(4) transition from the V = 2, J = 3 state to the V = 1, J = 4 state.

Q-Branch Transitions

These are pure vibrational transitions in which there is a change in vibrational energy (D V = +1) but no change in rotational energy (D J = 0). A Q (4) transition is shown in Figure 3, from the V = 2, J = 4 state to the V = 1, J = 4 state.

R-Branch Transitions

These vibrational-rotational transitions involve a decrease in both vibrational and rotational energies during emission (D V = –1, D J = –1). They are the "longest" (highest-energy) vibrational-rotational transitions. Once again, the number of the transition is the J quantum number of the lower vibrational energy state. The R(2) transition in Figure 3 is from the V = 2, J = 3 state to the V = 1, J = 2 state. Notice that the notation "R(2)" might mean either a pure rotational transition (J = 3 to J = 2 in V = 2, for example) or an R-branch transition (V = 2, J = 3 to V = 2, J = 2, as in Figure 3). Since the longer transition is of greater interest, the term R(4) is assumed to refer to an R-branch transition unless it is specified as a pure rotational transition.

To further complicate the situation, the vibrational states are not exactly evenly spaced. A P(4) transition from the V = 4 state to the V = 3 state is not of the same energy (or wavelength) as a P(4) transition from the V = 3 state to the V = 2 state. These two transitions fall in different vibrational bands. The bands commonly are designated by the vibrational transitions involved. Thus, the 5-4 band contains all transitions (P-, Q-, and R-branch) occurring between the V = 5 vibrational state and the V = 4 state. A P_{5 – 4}(6) transition denotes the P-branch transition between the V = 5, J = 5 and V = 4, J = 6 vibrational-rotational energy levels.

Diatomic Molecular Lasers—CO

A number of diatomic molecules are capable of lasing action, and several are of scientific and industrial importance. Mechanisms in all of these lasers are essentially the same. While lasing can be achieved on all four types of transitions previously discussed, the following general rules apply in most cases:

· Lasing on pure rotational transitions can be achieved in a number of molecules in the far infrared and short microwave regions. This, however, is of relatively less importance and will not be considered further in this module.

· Q-branch transitions produce lasing in a few molecules but usually are not present if the P-branch will lase.

· Most diatomic molecular lasers will operate on either the P-branch or R-branch. In these lasers, P transitions are always the strongest. R-branch transitions will lase only in pulsed lasers or, if the P-branch transition is suppressed, in CW lasers.

The carbon monoxide (CO) laser is chosen as a representative diatomic molecular laser for the remainder of this section.

Figure 4 is a simplified energy-level diagram of a CO laser. The spacings of the rotational levels are not shown to scale in this diagram. In a laser, the CO molecule is excited to a high-energy vibrational state by a collision with an electron in the discharge. Average lifetime of the vibrational state is on the order of 10^–3 seconds. Lifetime of a rotational state within the vibrational level, however, is only about 10^–7 seconds. This means that the CO molecule will change rotational levels thousands of times before a vibrational transition occurs. The energies absorbed or released during these rotational transitions are in the form of photons in the far IR or microwave region of the spectrum, or in the form of increased or decreased kinetic energy of the molecules.

Fig. 4
Lasing cascade in electronic ground state of CO.

At some time, the molecule will be in a rotational state from which a downward P transition has sufficient gain for lasing to occur. Stimulated emission takes place, and the molecule changes energy states by V = –1, J = +1 (P-branch transition).

Figure 4 shows lasing transitions in a pulsed CO laser in which a large number of molecules have been raised to the V = 9 state and in which all lower vibrational states except the ground state have low populations. Several P transitions in the 9-8 band probably will have sufficient gain for lasing to occur. This lasing action quickly populates the V = 8 vibrational level. As V = 7 has a relatively low population, a new population inversion is created and lasing begins in the 8-7 band. This leads to an inversion between V = 7 and V = 6, and so on. This process, called a lasing cascade or ladder, may produce laser output on a hundred distinct transitions during a single laser pulse. The higher-number bands begin lasing first. As more molecules move downward in energy, these higher band transitions die out and are replaced by transitions in the lower bands. Lasing has been achieved in CO gas in 20 bands containing a total of more than 250 separate P transitions. Most of these transitions lie in the V-range of 5 to 25. Table 2 shows a few of these transitions.

Table 2. Laser Transitions in CO Wavelengths in Micrometers.

The lasing cascade is a unique characteristic of most pulsed diatomic molecular lasers and is responsible for the high efficiencies, pulse energies, and peak powers available from these types of systems. In CW diatomic systems, the pumping rate is too low to produce the abundance of wavelengths observed in the pulsed models. Only that transition with the greatest gain within each band will lase. (This phenomenon is discussed in detail in the following section on CO₂ lasers.) The number of bands that have population inversions is also greatly reduced in CW lasers. Often, only a single output wavelength is present at any one time. Other transitions may be made to lase by using a tuning mechanism.

Energy Levels and Transitions in Triatomic Molecules

Triatomic molecules are composed of three atoms bound together (CO₂, H₂0, HCN). They exhibit the same types of energy-level diagrams and transitions as do diatomic molecules and obey the same general rules:

· Pure rotational transitions usually have D J = ± 1 and occur at a rapid rate (10⁷ per second).

· P-branch transitions usually comprise the strongest lasing lines.

· R-branch transitions usually will lase only in pulsed systems or under controlled conditions.

· Q-branch transitions often are absent, and may be ignored in most cases.

The difference between diatomic and triatomic systems arise from the additional fundamental vibrational modes present in triatomic molecules. Because the CO₂ laser is the most important of the triatomic molecular lasers, it is chosen as an example.

There are three normal or fundamental modes of vibration in the CO₂ molecule. Figure 5 shows these modes and gives the energy of the first excited vibrational state for each mode in reciprocal centimeters (1 eV = 8065 cm^–1). They are:

· Symmetric stretch mode (V₁00) - corresponds to a symmetric stretching along with the internuclear axis with both oxygen atoms moving away from or toward the carbon atom at the same time (Figure 5b).

· Bending mode (0V₂) - corresponds to a vibrational bending motion perpendicular to the internuclear axis (Figure 5c).

· Asymmetric stretching mode (00V₃) - corresponds to an asymmetric vibration or stretching along the internuclear axis with both oxygen atoms moving to the left or right together while the carbon atom moves in the opposite direction between them (Figure 5d).

Fig. 5
Normal modes of vibration for CO₂ molecules.

The vibrational energy state of a CO₂ molecule is described by three quantum numbers and is written as follows:

CO₂(V₁V₂V₃)

Thus, CO₂ (000) indicates a molecule in the vibrational ground state; CO₂ (100) indicates the first excited symmetric stretch state; CO₂ (020) indicates two quanta of the excited bending state; and so on. Figure 6 is an energy-level diagram showing the first few vibrational energy levels of CO₂ molecules.

Fig. 6
Vibrational energy levels in the electronic ground state of CO₂.

CO₂ molecules also rotate in the same manner as diatomic molecules and with the same result; each vibrational state is split into a number of rotational levels. One exception worth noting is the absence of some rotational states due to symmetry conditions of the molecule. The asymmetric stretching mode of coo contains only odd rotational levels (J-1, 3, 5, …). Symmetric modes (bending and symmetric stretch) contain only even rotational levels (J-0, 2, 4, …). This occurs because CO₂ is a symmetric molecule (0 = C = 0). It does not occur for H – C º N or other asymmetric molecules.

Triatomic Molecular Lasers–—CO₂

Any of a variety of energy transfer mechanisms may be employed in triatomic molecular lasers. The CO₂ laser is used as an example here for two reasons: First, it is the most frequently used triatomic molecular laser medium; second, it employs, to a large extent, all of the energy transfer mechanisms found in other triatomic molecular lasers. Popularity of the CO₂ laser stems as well from its relative inexpensiveness, great efficiency, and the fact that it emits in an atmospheric window, i.e., there is little absorption at its lasing wavelength by the atmosphere. Figure 7 is a simplified energy-level diagram of a CO₂ laser. Only the important vibrational levels are shown. Other vibrational levels and all rotational levels are excluded from the diagram for simplicity.

Fig. 7
Energy-level diagram for CO₂ laser showing vibrational energy transfer from N₂.

The two strongest lasing transitions in CO₂ are (001) è (100) centered at 10.6 m m, and (001) è (020) centered at 9.6 m m. The 10.6-m m line is the strongest line and will be the only one considered during the remainder of the discussion. All energy transfer mechanisms are essentially the same for both the 10.6-m m and 9.6-m m laser transitions.

The excitation processes of the CO₂ laser are shown in Figure 8. These are the general processes used to establish population inversions in most triatomic molecular lasers.

Fig. 8
Population mechanisms in a CO₂ laser.

Figure 8a shows the collision of a CO₂ molecule in the ground state with an energetic free electron. Some of the kinetic energy of the electron is absorbed by the CO₂ molecule, raising the molecule to the upper lasing level (001) (V₃ = 1). While this energy transfer mechanism is very effective in diatomic systems and some triatomic systems, it is not very effective in CO₂.

Figure 8b shows a much more efficient population mechanism. It involves the addition of nitrogen (N₂) to the lasing medium. The nitrogen molecule is excited to its V = 1 state by an electron collision. The nitrogen V = 1 state is very close in energy to the CO₂ (001) state, making a resonant transfer of energy from the excited N₂ molecule to the ground state CO₂ molecule highly probable. Thus, the excited N₂ molecule collides with a CO₂ molecule in the ground state (000) and transfers its energy to the CO₂ molecule, raising the CO₂ molecule to the (001) state. The N₂ molecule returns to its ground state (V = 0) and soon is excited by another electron collision, repeating the process. The energy difference of 18 cm^–1 between the two states is compensated for by a decrease in kinetic energy after the collision. In a low-pressure nitrogen discharge, approximately 30 percent of the N₂ molecules are in the V = 1 state at any given time, thus providing constant excitation for the CO₂ molecules.

From the (001) state lasing occurs on the 10.6-m m line. This results in an increased population of the CO₂ (100) (V₁ = 1) lower laser state. If the population of this state rises greatly, the population inversion is destroyed and lasing stops. Figure 9a shows the depopulation mechanism for removing CO₂ molecules from the (100) state. CO₂ (100) collides with ground state CO₂ (000) to result in two CO₂ (010). The slight energy difference appears as increased kinetic energy of the molecules. This process is very efficient as long as the population of the (010) level is low. Unfortunately, a CO₂ molecule in the (010) state tends to stay there for a relatively long period of time (10^–2 sec) and the population of this state increases rapidly. This problem may be solved by the addition of a third gas. Figure 9b shows the depopulation of CO₂ (010) by helium atoms. When CO₂ (010) collides with a low-speed He atom, the CO₂ molecule drops to the ground state and the He atom carries away the excess energy in the form of increased kinetic energy (heat). Addition of helium to the gas mixture increases the depopulation rate of the CO₂ (010) level by as much as 40 times.