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Pulse Trains

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

Light pulses are flashes of light, often with very short pulse durations. They are often generated with lasers, but sometimes with other kinds of light sources such as flash lamps. In many cases, one does not generate single pulses, but regular sequences of pulses, called pulse trains, which may last over long times, for example days or weeks. Typically, one has regularly spaced pulses with constant parameters, i.e., periodic pulse trains.

Parameters of Pulse Trains

Optical pulse trains are typically characterized by the following parameters:

• The pulse repetition rate in units of Hertz tells how many pulses occur within one second. In some cases, extremely high pulse repetition rates of many gigahertz or even more than one terahertz occur. The pulse spacing is the inverse of the pulse repetition rate.
• The duty cycle is the ratio of pulse duration and pulse spacing – in other words, the fraction of time in which there is light. For example, a Q-switched laser with 10 ns pulse duration and 1 kHz repetition rate has a duty cycle of 10 ns / 1 ms = 10⁻⁵. Mode-locked femtosecond lasers exhibit rather short pulse spacings of e.g. 10 ns, but due to the very short pulse duration they can nevertheless have duty cycles similar to those of Q-switched lasers. A small duty cycle implies that the peak power is much higher than the average power.
• Various parameters can be used to characterize each single pulse, in particular the pulse energy, pulse duration, optical pulse bandwidth and chirp. In many cases, the pulse parameters are quite constant within a pulse train, although in some cases substantial fluctuations are observed.
• Additional specifications applied to different kinds of noise. In particular, there is the timing jitter, which can be extremely low for some mode-locked lasers. Other aspects are the pulse-to-pulse coherence and the carrier–envelope offset frequency noise. Also, there are various kinds of noise of the pulses themselves. Due to the discrete nature of the pulses in a train, noise specifications e.g. for the pulse energy are technically somewhat different from those for intensity noise of continuous-wave lasers.

Lasers Generating Pulse Trains

The most common types of laser sources producing pulse trains are repetitively Q-switched lasers and mode-locked lasers.

With Q-switched lasers, pulses can also be generated at irregular time intervals, but regular pulsing is most common. The pulse repetition rate is then often somewhere between 10 Hz and 100 kHz, although more extreme values are possible. Even if the trigger source of an actively Q-switched laser exhibits very precise timing, the laser pulses can exhibit a slightly variable time delay due to fluctuations in laser gain (e.g. as a result of fluctuating pulse energy from a flash lamp used as pump source). This can lead to some substantial level of timing jitter.

Mode-locked lasers naturally produce pulse trains at a very high pulse repetition rate (typically between 50 MHz and a few gigahertz), which is usually the inverse round-trip time of the laser resonator: an output pulse is obtained each time when the (single) circulating intracavity pulse hits the output coupler mirror. At least over short time spans, the resonator length is quite precisely constant, and there may be only a very low level of timing noise introduced by quantum noise influences via the gain medium and vacuum noise entering the laser mainly through the output coupler. Therefore, the pulse-to-pulse timing jitter can be extremely small (on an attosecond timescale), corresponding to a very low power spectral density of the timing noise at high noise frequencies. However, the low-frequency noise, corresponding to a longer time intervals, is usually orders of magnitude stronger due to various types of noise influences.

Pulse Repetition Rate Multiplication and Division

Even after generation of a pulse train, the repetition rate can be modified in both directions:

• There are methods of repetition rate multiplication. For example, one may use a beam splitter to obtain two pulse trains and a second beam splitter to interleave those to obtain one pulse train with twice the original pulse repetition rate. (The resulting device may look like a Mach–Zehnder interferometer, although interference effects are not utilized.) That method can be repeated for obtaining higher multiplication factors. Another possibility is injection locking of a mode-look laser with a higher repetition rate.
• For the reduction of the pulse repetition rate by a factor <$N$>, one may use a pulse picker which transmits only every <$n$>th pulse. That is often used when amplifying ultrashort pulses with reduced pulse repetition rates to achieve higher pulse energies and peak powers.

Pulse Bursts

In some cases, one deals with pulse bursts, which are pulse trains with a quite limited duration, for example corresponding to only a couple of pulses or a few hundred pulses. A burst mode laser source may emit such bursts in a regular fashion, where the repetition rate of the bursts is usually orders of magnitude lower than the repetition rate within a burst.

In some cases, the pulse spacing within one burst is not constant, and/or one has a variable pulse energy in the burst. As an unintentional effect, one sometimes obtains a drop of pulse energy during a burst due to gain saturation, although that can to some extent be compensated with certain means.

For more details, see the article on burst mode lasers.

More to Learn

Encyclopedia articles:

• light pulses
• ultrashort pulses
• timing jitter
• pulse characterization
• mode-locked lasers

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