What is a pulsed laser？

The most direct way to generate laser pulses is to add a modulator outside the continuous laser. This method can generate the fastest picosecond-level pulses. Although it is simple, it wastes light energy and the peak power cannot exceed the continuous light power. Therefore, a more efficient way to generate laser pulses is to modulate the laser cavity, storing energy in the off time of the pulse train and releasing it in the on time. The comparison of the two methods is as follows:

The four commonly used techniques for generating pulses through laser cavity modulation are gain switching, Q-switching (loss switching), cavity emptying and mode-locking.

The gain switch generates short pulses by modulating the pump power. For instance, semiconductor gain-switched lasers can generate pulses ranging from a few nanoseconds to a hundred picoseconds through current modulation. Although the pulse energy is low, this method is very flexible, such as providing adjustable repetition rate and pulse width.

Strong nanosecond pulses are generally generated by Q-switched lasers. The laser is emitted within several round trips in the cavity, and the pulse energy ranges from a few millijoules to several joules, which is specifically related to the size of the system.

Medium-energy (generally below 1 μJ) picosecond and femtosecond pulses are mainly generated by mode-locked lasers. There are one or more ultrashort pulses in continuous cycles within the laser resonance cavity. Each time the cavity pulse passes through the output coupling mirror, it emits one pulse, and the repetition frequency is generally between 10 MHz and 100 GHz. The following figure shows a fully normal dispersion (ANDi) dissipative soliton femtosecond fiber laser device. The vast majority of it can be built using Thorlabs standard components (fiber, lens, mounting seat and displacement stage).

Cavity venting technology can be applied not only to Q-switched lasers to obtain shorter pulses but also to mode-locked lasers to increase pulse energy at a lower repetition rate.

Time-domain and frequency-domain pulses
The linear shape of a pulse varying with time is generally simple and can be represented by Gaussian and sech² functions. Pulse time (also known as pulse width) is most commonly expressed by the half-height width (FWHM) value, which is the width across which the optical power is at least half of the peak power. Nanosecond-level short pulses are generated by Q-switched lasers, and ultra-short pulses (USP) ranging from tens of picoseconds to femtoseconds are produced by mode-locked lasers. High-speed electronics can only measure pulses of tens of picoseconds at the fastest. Shorter pulses can only be measured by pure optical techniques, such as autocorrelators, FROG and SPIDER.

If the pulse shape is known, the relationship among pulse energy (Ep), peak power (Pp), and pulse width (tp) is calculated according to the following formula:

Among them, fs is a coefficient related to the pulse shape, approximately 0.94 for Gaussian pulses and about 0.88 for sech² pulses, but in general, it is approximately calculated as 1.

The bandwidth of a pulse can be expressed by frequency, wavelength or angular frequency. If the bandwidth is small, the wavelength and frequency bandwidths are converted using the following formula, where λ and ν are the central wavelength and frequency respectively, and Δλ and Δν are the bandwidths expressed in terms of wavelength and frequency respectively.

Bandwidth limit pulse
For a specific pulse shape, the spectral width of the pulse is the smallest when there is no chirp. At this time, we call it the bandwidth-limited or Fourier transform limit pulse. The product of its pulse time and frequency bandwidth is a constant, and this constant is called the time-bandwidth product (TBP). The time-bandwidth products of the bandwidth-limited Gaussian and sech² pulses are approximately 0.441 and 0.315, respectively. Based on this, the chirp quantity of the actual pulse and the cumulative group delay dispersion can also be calculated.

Therefore, the narrower the pulse width, the wider the Fourier spectrum required. For instance, the bandwidth of a 10 fs pulse must be at least on the order of 30 THz, while the bandwidth of an attosecond pulse is even greater, and its center frequency must be much higher than any visible light frequency.

Factors influencing pulse width

Although the pulse width of nanosecond or longer pulses hardly changes during propagation, even over long distances, ultrashort pulses may be affected by various factors:

Dispersion may cause significant pulse broadening, but it can be re-compressed with the opposite dispersion. The following figure shows the working principle diagram of the Thorlabs femtosecond pulse compressor compensating for microscope dispersion.

Nonlinearity generally does not directly affect pulse width, but it will cause the bandwidth to widen, making the pulse more susceptible to dispersion during propagation.

Any type of optical fiber (including other gain media with limited bandwidth) may affect the bandwidth or the shape of the ultrashort pulse, and a reduction in bandwidth may lead to time broadening. There are also cases where the pulse width of strongly chirped pulses shortens as the spectrum Narrows.