Coupling Between Energy Levels Leads to Optical Bistability

Breck Hitz

Optical bistability exists when an optical system is capable of operating in two modes under identical external conditions. If the optical system is a laser, the most common form of optical bistability is hysteresis in its input-output transfer function (Figure 1).

Figure 1. The most common form of optical bistability in lasers is hysteresis in the input-output transfer function: At a given input power, the laser can produce two different outputs, depending on whether the input power is increasing from below or decreasing from above.

Of course, the millions of transistors in a computer are electrically bistable devices, capable of storing either a one or a zero. The long-term interest in optical bistability stems from the fact that any form of optical computer will require similar devices, capable of storing either ones or zeros and capable of switching between those two states. Optical computing remains many years from becoming a reality, but optical bistability is being explored in numerous laboratories around the globe.

Figure 2. The thulium ion in a Tm,Ho:YLF laser absorbs energy from the pump light and transfers it to the holmium, which does the lasing. First, a 792-nm pump photon boosts the thulium from its ground-state ³H₆ level to the excited ³H₄ level. The excited ion then decays to the ³F₄ level, but the energy lost in this decay lifts another ground-state thulium ion to the ³F₄ level. In other words, a single pump photon has produced two excited ions. Each ion then transfers its energy to the ⁵I₇ level of a holmium ion. This level becomes inverted with respect to the ground-state ⁵I₈ level, and lasing at ∼2 μm occurs. The terminal level of the laser transition is an upper Stark sublevel of ⁵I₈, which has a nonnegligible thermal population. That means it’s a quasi-three-level laser, and small changes in its temperature can have a large impact on its performance.

Bistable layers

In particular, many optically bistable lasers have been investigated during the past 20 years. Most depend on an intracavity saturable absorber, whose absorption characteristics vary depending on whether the incident power is increasing or decreasing. Others depend on thermally induced changes in resonator optics. Recently, scientists at Harbin Engineering University and at Harbin Institute of Technology, both in Harbin, China, have observed bistability in a Tm,Ho:YLF laser. Unlike other optically bistable lasers, the Tm,Ho:YLF laser has a unique arrangement of energy levels that leads directly to optical bistability, without the introduction of a saturable absorber or specially designed resonator optics.

Figure 3. The laser exhibited hysteresis at very low pump powers. Reprinted with permission of Optics Letters.

The thulium ion in a Tm,Ho:YLF laser is a sensitizer, absorbing the energy from the pump light and transferring it to the holmium ion, so that lasing can occur between levels of the holmium ion (Figure 2). The scientists in Harbin saw a normal increase in the laser’s output as they increased the input — except at very low power, where they saw hysteresis (Figure 3). They attribute the hysteresis to the unique energy-level structure of holmium ions and to the transfer of energy among those levels, as well as to the transfer of energy back to the thulium ions.

Figure 4. Two mechanisms can depopulate the ⁵I₇ level in holmium before it becomes inverted with respect to the ground level. First is an energy transfer upconversion (ETU, tinted reddish) in which a thulium ion transfers its energy from the ³F₄ level, boosting the holmium to the ⁵I₅. Second is excited-state absorption (ESA, tinted green), in which a 792-nm pump photon excites the holmium to the ⁵F₄, ⁵S₂ manifold. Ions excited to this manifold subsequently relax to the ground level with the emission of green luminescence.

Depopulating mechanisms

They believe that two mechanisms depopulated the ⁵I₇ level of holmium at low pump powers (Figure 4). These mechanisms prevented the 2-μm laser from reaching threshold until the pump power reached a certain level; i.e., 200 mW in Figure 3. Once the laser reached threshold, however, its stimulated emission overwhelmed the other two mechanisms. When the stimulated emission at 2 μm became dominant, it continued to dominate even as the pump power decreased below the 200-mW threshold observed for increasing pump power.

Figure 5. Because the Tm,Ho:YLF laser is a quasi-three-level system, increasing the rod’s temperature diminishes the population inversion — and also reduces the amount of hysteresis. Reprinted with permission of Optics Letters.

The scientists observed that the hysteresis was critically dependent on the laser rod’s temperature. As the rod’s temperature increases, the thermal populations of the upper Stark levels of the ground state increase, diminishing the population inversion of the quasi-three-level laser. Thus, increasing temperature results in higher laser thresholds and lower output powers. However, rod temperature has virtually no effect on the two nonlasing mechanisms that depopulate the upper laser level (⁵I₇), so the hysteresis decreases with increasing rod temperature (Figure 5).

Optics Letters, Aug. 15, 2007, pp. 2333-2335.