ENERGY  STORAGE  IN  LASER  MEDIA

     The entire concept of Q-switching relies on the fact that energy can be stored in the lasing medium itself in the form of an excited atomic population at the ULL. The very definition of cavity quality factor (or Q factor) basically defines the situation:

 (1.1)

A large Q factor represents a low-loss resonator that can store a large amount of energy. In Q-switching the Q of the cavity is spoiled (the Q factor is purposely made low), so that it is not resonant and hence lasing is not possible. Energy storage takes place, but rather than within the cavity as for optical energy, energy is stored in the atomic population.

      In a Q-switched laser the laser medium itself is used as a sort of capacitor, storing energy gradually and releasing it in a single burst. Not surprisingly, the capacity of the medium to store energy depends on the lifetime of the upper lasing level (ULL). A long lifetime implies that the lasing species can absorb energy over a long period without losing it to spontaneous emission; hence it has a large storage capacity and is a good candidate for Q-switching.

     Suppose a laser cavity is blocked, so that laser action cannot occur. Unlike previous examples of in this book, CW lasers, where the level of population inversion reaches an equilibrium level, the inversion is now free to build. The primary limit on this inversion is the lifetime of the upper lasing level, which serves to deplete the upper level through spontaneous emission. With continuous pumping the inversion builds until reaching a level equal to the rate of pumping times the lifetime of the upper level. The population rate equation during this interval when the cavity is blocked becomes

 (1.2)

where r_inversion is the rate at which the inversion builds, r_pumping the rate at which the laser is pumped, and ΔN(t) the population difference at any time t. The solution to this equation at any time t becomes

 (1.3)

The solution to this equation is plotted in Figure 1.1, which depicts how the population builds in time. After pumping for one τ_ULL cycle, a population inversion of 66% has built up. After two such time periods, the inversion is at 88% of its maximum value. It is clear that in such a Q-switched laser it is not productive to pump the

Figure 1.1. Energy storage in Q-switched media.

laser medium with energy beyond two or three times the lifetime of the upper lasing level. After this period the population inversion does not really grow much but rather, slowly approaches (and never reaches) the maximum level, as shown in the figure.

      Excess pump energy is essentially wasted. Still, in many lasers, especially those driven by continuous sources such as CW arc lamps, the time during which the laser is pumped may be very long. In this case the Q-switch is also used to allow the laser to fire on command and so when not actively firing, the pump source (the lamps) is kept on, so that the laser is always in a ready state. Implications are that any laser medium may be Q-switched, but it should be evident that the lifetime of the upper lasing level (ULL) must be much longer than the opening time for the Q-switch. For most gas lasers with ULL lifetimes of under a 1 ns, Q-switching simply will not work, since no practical switch exists that can open in considerably less than this time. One of the few exceptions is the carbon dioxide gas laser, which has an exceptionally long ULL for a gas laser, although in practice, Q-switching of a CO₂ laser is rarely done.

       Solid-state lasers, on the other hand, invariably feature long ULL lifetimes. The ruby laser, for example, has a lifetime of 3 ms, and the YAG laser has a lifetime of 1.2 ms. These are ideal candidates for Q-switching, which is a standard option on most solid-state lasers. An interesting practical demonstration of energy storage in solid-state laser media is in the setup procedure of a double-pulse ruby laser for holography. These lasers can output two short (often around 10 ns) pulses spaced a selectable time interval (usually in microseconds) apart. Since flash lamp pulses are quite long compared to the spacing of the output pulses (and flash lamps have a relatively long recovery time, so that they cannot be fired twice in rapid succession), a laser such as this uses a single flash lamp pulse to produce both output pulses by opening and closing the Q-switch twice, rapidly, during the pumping interval. When the pulses are spaced widely apart in time (“widely” being defined as a few hundred microseconds) the rod loses stored energy in the first pulse but is re-pumped by absorbing pump light once the Q-switch is closed. Energy in the rod builds once again, so the pulses are somewhat independent of each other. When the two pulses are only microseconds apart, though, pump light is insufficient to repump the rod during the time between the pulses, so the total energy stored in the rod is divided between the two output pulses. If the switch is opened fully for the first pulse, it can deplete the energy stored in the rod, resulting in a small or nonexistent second pulse. To produce two pulses of equal power, the Q-switch must be opened only partially for the first pulse, closed again, and opened fully on the second pulse to utilize all stored energy remaining in the rod. Not all Q-switches are capable of opening partially (with EO types, discussed below, being employed for essentially all lasers of this type). This process of balancing pulses is usually done by setting the Q-switch to open only slightly for the first pulse and fully for the second pulse, test firing the laser, and observing the relative output power of each pulse. By opening the Q-switch progressively more and more for the first pulse and test firing the laser between adjustments, it will be seen that the first pulse robs power from the second pulse, until they eventually match in amplitude and the balancing is complete.