few-cycle laser pulses
Fig. 1. Operation mode of a laser. (© ch)
Lasers usually draw on a resonator made up of two (or more) mirrors enclosing the laser medium and reflecting the laser light, see Fig. 1. Once the first photon is spontaneously emitted along the axis of the resonator, i.e. perpendicularly to the mirrors, it is bounced back and forth between the mirrors. Each time it passes the laser medium it stimulates the emission of further photons. The resultant light wave is amplified upon each round trip. This amplification compensates for the loss related to the output of the laser, coupled out through a partially reflecting mirror, see Fig. 1, as well as to parasitic losses. The laser light can build up at many different frequencies, selected by the resonator, within the frequency range where the laser is able to provide amplification, see Fig. 2. Physicists call these selected frequencies the axial modes of the laser.
Fig. 2. Modes of the laser resonator. (© ch)
These laser modes usually “do not know about each other”, i.e. the field oscillations in these modes are independent of each other. Their simultaneous emission therefore leads to laser light with randomly fluctuating intensity. With a technique called laser mode locking, these waves of differing frequency can be “locked” to each other to make sure that at a certain instant the fields of all modes are maximum and point in the same direction, giving rise to a strongly-enhanced resultant field, see box and Fig. 3. This enhancement lasts only for a short period, because the modes have different frequencies and therefore slightly earlier and later their fields point in opposite directions, resulting in a rapid fall of the resultant (sum of all) field strength. As a consequence, laser mode locking results in a short flash of light, the intensity of which becomes very high for a very short while. This light burst circulates in a resonator. A fraction of it is coupled out through the output coupling mirror, resulting in a series of very short light pulses.
Fig. 3. Laser pulse resulting from mode locking. (© ch)
By applying most modern femtosecond technology, see box on the right, these pulses can now be shortened close to the ultimate frontier, the oscillation period of the carrier light wave, which amounts to 2-3 femtosecond for red/near-infrared light. LAP’s state-of-the-art few-cycle laser sources routinely produce intense few-femtosecond, few-cycle laser pulses for a range of applications.
Consider a laser, in which N axial modes (N=7) in the example of Fig. 2 and 3, with all having the same electric field amplitude, E_0. The intensity of such a light wave of electric field amplitude can be written as
I=E_0^2/2Z_0 , where Z_0=377 V/A is a constant referred to as the “impedance of vacuum”. With the electric field inserted in units of {\rm volt}/{\rm cm} ({\rm V}/{\rm cm}) this formula yields the intensity as I = 0.0013\,E_0^2 in units of {\rm watt}/{\rm cm}^2 ({\rm W}/{\rm cm}^2).
If the modes do not know about each other, their simultaneous emission results in laser light of fluctuating intensity. The mean value of this intensity, I_{\rm mean} is equal to N times the intensity of the individual modes. If the modes are phase-locked to each other by some laser mode locking technique to ensure that their wave crests all coincide, as shown in Fig. 3, the sum of their fields leads to a short pulse, with duration of T_{\rm pulse} = T_r/N and with a peak intensity of I_{\rm peak} = N\,I_{\rm mean}.
Here T is the time it takes the laser light to make a round trip in the laser resonator. Typically T amounts to several nanoseconds, 1 nanosecond is one billionth of a second, 1\,{\rm ns} = 10^{-9}\,{\rm s}.
The more modes can be generated and locked to each other, the shorter and more intense pulses can be produced. The larger the amplification bandwidth of the laser medium, see Fig. 1, the more modes can oscillate.
The laser medium with the broadest amplification band is titanium-doped sapphire, invented by Peter Moulton in 1986. It can support more than one million modes in a typical laser resonator. Its nonlinear index of refraction allows efficient locking of these modes, as first demonstrated by Wilson Sibbett and coworkers in 1992. Other than the bandwidth and locking technique, it has to be made sure that the round-trip time in the laser resonator is the same for all frequency components of the ultrashort light pulse, otherwise it would broaden during circulation in the resonator. For the entire bandwidth available, this condition could only be fulfilled with chirped multilayer mirrors, invented by Robert Szipöcs and Ferenc Krausz in 1993. These three innovations led to the reproducible generation of laser pulses of a few femtosecond in duration and comprising merely a few wave cycles.