Ultrashort Pulses

Light pulses as generated in mode-locked lasers can be extremely short, especially with passive mode locking. There is no universally accepted definition of “ultrashort”, but the term usually is applied to pulses whose pulse duration is at most a few tens of picoseconds, and often even in the range of femtoseconds.

Ultrashort pulses (or the lasers that produce them) are sometimes called “ultrafast” – even though these pulses are no faster (have no higher velocity) than longer pulses. However, they do have short rise and fall times, and they make it possible to investigate ultrafast processes (→ ultrafast optics). They can also be used for fast optical data transmission, where “fast” means a high data rate, not a high velocity.

Generation of Ultrashort Pulses

Ultrashort light pulses are usually generated with passively mode-locked lasers, but sometimes also with optical parametric amplifiers (possibly using a supercontinuum as input) or with free electron lasers. It is in principle also possible to start with longer pulses and apply some method of pulse compression, but in most cases the input pulses for such compression are already ultrashort.

The article on ultrafast lasers lists some important areas of ultrashort pulse generation, including the generation of few-cycle pulses, where the pulse duration is only a small multiple of an optical cycle (few-cycle pulses).

Case Studies

Parabolic Pulses in a Fiber Amplifier

We explore the regime of parabolic pulse amplification in an Yb-doped single-mode fiber. We find suitable system parameters and investigate limiting effects.

Optical Bandwidth

Intrinsically, ultrashort pulses have a broad optical bandwidth. Even if they are instantaneous frequency is nearly constant throughout the pulse duration, the optical spectrum has a width which is at least of the order of the inverse pulse duration. This is essentially because e.g. for resonantly exciting some medium, a change in optical frequency matters only if it is large enough to cause a significant phase change within the pulse duration [1]. That is the case only if the frequency change is of the order of the inverse pulse duration.

In many cases, the instantaneous frequency of a pulse is approximately constant, and the time–bandwidth product is somewhat below unity. For example, an unchirped Gaussian pulse with a 1 ps pulse duration (full width at half maximum) has an optical bandwidth of ≈0.44 THz. Extremely short pulses (few-cycle pulses) can even have octave-spanning optical spectra, and are thus very far from being monochromatic.

Spatial Properties and Propagation

Concerning their spatial properties, ultrashort pulses are usually generated in the form of laser beams. Essentially, they can be focused to very small spots just as it is possible with stationary beams. However, various limitations come into play particularly in the regime of few-cycle pulses. For example, the broad optical bandwidth of such pulses leads to problems with the chromatic dispersion of lens materials, which leads to chromatic aberrations of the focusing optics unless special correction techniques are employed. This can lead to complicated spatio-temporal effects, which may effectively make the focused pulses longer than the pulses before focusing. Possible measures against such distortions include the use of reflective or diffractive (instead of refractive) optics as well as the careful compensation of various types of aberrations, e.g. using suitable lens combinations.

The propagation of ultrashort pulses in media gives rise to a range of interesting phenomena, particularly when optical nonlinearities are involved. This can be investigated with pulse propagation modeling (see below).

Simulations of Pulse Propagation

In many cases, it is highly relevant to gain a deep understanding of the properties of pulse propagation. Examples are the development of mode-locked fiber lasers, systems for optical fiber communications, and pulse compression setups.

The modeling of pulse propagation is usually indispensable, as experimental exploration is far more cumbersome and limited. For example, there are sophisticated (and expensive) instruments for pulse characterization, but a complete characterization remains difficult, and can usually be applied only to freely accessible pulses – for example, to the output pulses of a laser system, but not to pulses at any location within a laser resonator or a fiber.

There are different kinds of simulation models for pulse propagation, with specific advantages and limitations. See the article on pulse propagation modeling for more details.

Case Studies

Collision of Soliton Pulses in a Fiber

We let two soliton pulses collide in a fiber. Surprisingly, they survive such collisions, even if we involve solitons of higher order.

Case Studies

Soliton Pulses in a Fiber Amplifier

We investigate to which extent soliton pulses could be amplified in a fiber amplifier, preserving the soliton shape and compressing the pulses temporally.

Case Studies

Raman Scattering in a Fiber Amplifier

We investigate the effects of stimulated Raman scattering in an ytterbium-doped fiber amplifier for ultrashort pulses, considering three very different input pulse duration regimes. Surprisingly, the effect of Raman scattering always gets substantial only on the last meter, although the input peak powers vary by two orders of magnitude.

Shaping Ultrashort Pulses

When ultrashort pulses are generated in a mode-locked laser, instead laser they can be subject to various pulse shaping phenomena. For example, a saturable absorber causes high losses to the beginning and sometimes also the end of the pulse, and can thus modify the duration and shape of a pulse. The effects of optical nonlinearities and chromatic dispersion, however, are often much stronger than those of saturable absorbers.

Outside the laser, ultrashort pulses can further be manipulated with various kinds of pulse shapers.

Case Studies

Nonlinear Pulse Compression in a Fiber

We explore how we can spectrally broaden light pulses by self-phase modulation in a fiber and subsequently compress the pulses using a dispersive element. A substantial reduction in pulse duration by more than an order of magnitude is easily achieved, while the pulse quality is often not ideal.

Simulations on Pulse Propagation

Ultrashort pulses change in complicated ways when propagating through a fiber, for example. A suitable simulator is essential for getting complete insight – not only on the resulting output pulses, but also on the pulses at any location in your system. The RP Fiber Power software is an ideal tool for such work.

Characterization of Ultrashort Pulses

There are various methods for pulse characterization. While some only allow the measurement of fundamental pulse parameters such as the pulse duration, others can be used for “complete” characterization in the sense that the whole time-dependent electric field and the spectral phase can be obtained. The results can be visualized in various ways, e.g. with graphs of time- or frequency-dependent functions, or with spectrograms.

Most frequently, one measures pulse durations using autocorrelators.

Related Articles

Bibliography

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