MODELOCKING

    Modelocking techniques are used to generate the shortest pulses of light ever produced. There are two ways to look at this technique: in the time domain and the frequency domain. Although the latter approach is required to fully understand the technique, the time domain is the simplest view and will be dealt with first to give us a basic understanding of the technique. In a modelocked laser, energy in the laser itself is compressed into a single packet of light that traverses the laser, reflecting from cavity mirrors and through the gain medium. The pulse inside the cavity is much shorter than the cavity itself: If the cavity was 1 m long, the pulse might typically be 10 cm within this cavity. If the cavity contains a partially reflecting mirror as an output coupler, a short output pulse is transmitted each time the pulse is reflected from that mirror.

       As depicted in Figure 1.1, the modelocked laser consists of a normal Q-switched laser in which the Q-switch is opened at regular intervals corresponding to the transit time of the pulse within the cavity (c/2L). Once per round trip through the laser cavity the Q-switch is opened (Figure 1.1c) to allow the pulse to pass; at all other times the switch is closed to prevent any other light from oscillating in the cavity except for this modelocked pulse. With the modulator in the center of the cavity, it is required to open twice for each round trip of the pulse. If it is placed near one mirror in the cavity (as in the figure), only one opening of the switch is required per round trip.

          The output of a modelocked laser with the configuration described is a continuous series of short pulses. In the case of a laser with mirrors 1 m apart, the pulses will appear at a frequency of c/2L or 150 MHz. Pulse duration depends, among other factors, on the time for which the Q-switch is open as well as the gain bandwidth of the lasing species (which we shall examine when considering the modelocker in the frequency domain). Q-switches for a modelocked laser must open and close in a very short time period. Regular Q-switches, such as the AO modulators used for a Q-switched laser, are generally not fast enough for these purposes. Consider a typical AO modulator that can open and close in 100 ns. The total optical length

Figure 1.1. Modelock pulse development in the time domain.

of a 1-m laser is 2 m, so light makes a round trip through the entire laser in 6 ns. This modulator will clearly not work for modelocking; the modulator must open and close in much less time than the transit time for the pulse in the laser cavity. One possibility for an AO modulator, however, is to set up a standing wave in the modulator. An acoustic wave can be generated that bounces back and forth through the crystal. At two points in the period of the wave there is a point where light is not diffracted (i.e., a node in the standing wave where the electric field is zero), and hence the switch is open at those points. In our example of a 1-m cavity, such a modulator opening at a rate of 150 MHz will modelock the laser. Note that the frequency required of the modelocker increases as the cavity size decreases.

         Compared to AO modulators, EO modulators have much faster opening times of 1 to 2 ns and so can be used directly as modelockers (i.e., no standing-wave scheme is required). A further advantage is that EO modulators can be inserted directly into the cavity without using a polarizer/analyzer filter combination as usually required when used as an optical switch. This is desirable since the inserted device does not absorb large quantities of intracavity light (which the polarizer and analyzer do absorb in a EO switch as used for Q-switching applications). In such an application, the EO modulator is in the open state when light passes through without phase change and in the closed state when it changes the phase of light passing through it. By changing the phase of light passing through the modulator (in the closed state), such light is really shifted in time with respect to unchanged light. Since only certain resonant frequencies can exist in the cavity (i.e., only those with an integral number of wavelengths that fit into the cavity), light waves that are shifted in phase cannot exist and are extinguished by destructive interference. This behavior is outlined in Figure 1.2, in which two waves inside the laser cavity are shown. In the figure, wave 1 passes through the EO cell without a change in phase. This wave satisfies the basic lasing criteria in that an integral number of waves fits inside the laser cavity. Wave 2 is phase-shifted by the modulator (which has varied its index of refraction in response to an external drive signal). This wave no longer satisfies the criteria for a standing wave inside the laser cavity.

        The final method to modelock a laser is to use a saturable dye absorber (also used as a Q-switch). These absorbers also serve to Q-switch the laser at the same time; the output is a pulse train with a Q-switched amplitude envelope. As with a simple Q-switch, an incident pulse inside the laser cavity bleaches (saturates) the dye, which opens the switch, allowing the pulse through it.

Figure 1.2. EO phase shifter as a modelocker.