The initial demonstration of an ultrafast pulsed laser system in 1966, where 40 ps pulses from a mode-locked YAlG:Nd laser was reported [54]. The first demon-stration of an ultrafast semiconductor LD was 12 years later when a 20 ps pulsed GaAlAs LD was reported in 1978 [52], and demonstration of 5 ps passively mode-locked pulses from a GaAlAs LD was reported in 1980 [55]. These were arguably the most notable advancements in the acceleration of the ps optoelectronics field in general. Advancement into the sub-ps arena was made with the demonstration of a mode-locked dye laser that generated 200 fs pulses [56], and pulse stretch-ing and compression methods usstretch-ing diffraction gratstretch-ings and dispersion prisms [57, 58] allowed the generation of even shorter fs optical pulses.
Mode-locking of gas or other solid-state laser types such as the Ti:Sapphire is still conducted today in much the same way as it was around the time of their first demonstration. The laser cavity itself is constructed with a certain length, Lcavity, which determines the oscillation frequency of the circulating longitudinal modes as described by the following equation:
fosc= c
2nmedLcavity (1.2.1.1)
Figure 1.3: Principle of mode-locking of multiple oscillating longitudinal laser modes.
where nmed is the refractive index of the laser gain medium. Intuitively, this indicates that a longer cavity can support a greater number of oscillating lon-gitudinal modes, and this is sketched in Figure 1.3. It should be noted here that the colours used in the pulse profile on the right of this sketch are simply to clarify that the pulse consists (optically) of the available modes oscillating as shown on the left, and give some idea of the separation of these constituent wave-lengths throughout the pulse. This concept is useful in visualising the spectral distribution of optical pulses as discussed later in this section.
It can be seen that each theoretically supported longitudinal optical mode which interferes constructively in the cavity oscillates with a frequency difference of fosc, but only those energies supported by the laser gain medium will be absorbed and/or emitted accordingly. This determines the gain bandwidth limits of the laser (range of supported optical modes) and this in turn sets the lower limits on the output pulsewidth and upper limits on energy, as we shall see. In the general case, the temporal overlap of circulating optical cavity modes is supported by the balance between the temporal ‘lagging’ effects of group velocity dispersion (GVD) and the ‘accelerating’ effects of self-phase modulation. The maintenance of the ultrashort pulse may be further enhanced by the ‘self-starting’ effect of Kerr lens mode-locking (KLM) [59], which utilises the inherent self-focussing of the beam due to the variance of refractive index with wavelength in the medium and the corresponding collapse of the modes’ temporal spread. If the total bandwidth δf = N ×foscis comprised of N number of modes each separated by an oscillating
frequency fosc, the temporal spread δτp of the output pulse is given by Equation 1.2.1.2.
δτp = β
δf, (1.2.1.2)
where β is assigned here to account for the output pulse profile. The rise and fall times of the pulse determines which β-factor to use. For example, the propagation of a pulse with slowly rising and falling edges such as a saw-tooth ‘delivers’ the bulk of the pulse energy effectively over a longer time than a top-hat-like pulse profile, even if the full-width half-maximum (FWHM) happened to be the same for both pulses. It should be noted that neither of these pulse profile types will be observed in ultrafast laser pulses – Gaussian (β = 0.4413), sech2 (β = 0.315) or Lorenzian (β = 0.2206) profiles are generally observed. These pulse profiles are used as ‘templates’ in the fitting of experimentally obtained laser pulses so that an accurate measurement of the pulse duration δτp can be made. The formulas for the approximation of the temporal intensity profile of each pulse type are given as:
The definition of τp and corresponding pulse profiles are essentially ideal case solutions for the minimum theoretical temporal spread of each pulse profile type.
The product of δτp and δf is therefore a common measure of the ‘purity’ of a laser pulse, referred to as the time-bandwidth product (TBWP). The sketch in Figure 1.3 indicates some spectral spread in the mode-locked output pulse, although this is not intended as an accurate depiction of the frequency spread as such. An optical pulse in real laser systems consists of a broad range of longitudinal wavelengths which naturally propagate through the medium with different effective refractive indices, which gives rise to GVD. This delay between the long and short wavelengths is referred to as chirp.
The principles and management of spectral chirp in laser systems are relevant in this work to the extent that optical pump signals are generally chirp-compensated in real THz systems. In time-domain systems, the pump pulse should ideally be as short as possible to obtain a broad working THz spectral range, described in more detail in Section 1.2.4.1. Mode-locked laser pulses are short because the range of longitudinal modes have been ‘locked’ in phase-space such that there is a very narrow region of the propagating signal wherein the peaks of (ideally) all modes interfere constructively, and this amplitude peak circulates in the cavity.
If there is a temporal offset between long-and short-wavelength mode peaks, τp will increase and the peak power will decrease accordingly. The peak power is dependent upon τp because optical energy which is restricted (or well-defined ) in the time domain will correspondingly be amplified (or ‘broadened’) in the energy domain, according to the uncertainty principle. This leads to the relationship between the laser average optical power Pave, peak power Pp, and ‘duty cycle’ as given by:
Duty cycle ≡ δτpfrep = Pave
Pp , (1.2.1.6)
where frepis the repetition rate of the circulating pulse in the cavity and the peak power in the pulse is inversely proportional to the pulsewidth as Pp ≈ E/δτp where E is the total pulse energy.
Mode-locked femtosecond pulses are generated in a Ti:Sapphire laser system by considering these principles, among other design considerations. In this system, a green pump beam is used to optically pump the Ti:Sapphire crystal and, once properly aligned, allows a circulating beam of peak wavelength around 800 nm to be emitted from the crystal output facet. This may then be steered through focussing and compression optics to obtain a mode-locked optical pulse signal with a τp which may be finely controlled using a pair of compensation prisms as shown in Figure 1.4.
The first prism diffracts the incoming beam into a spatially separated range of wavelengths with a linearly increasing time-of-flight delay applied across the spectrum (part “A”). The second prism recollimates the diffracted beam, by which point each optical mode will have propagated the same optical path length and been delayed to roughly the same temporal location. This is effectively the actual spectral chirp compensation stage, but the beam then consists of a broad range of spatially laterally chirped wavelengths (part “B”). This is compensated
Figure 1.4: Basic optical schematic of the Ti:Sapphire laser system.
by retro-reflecting the beam back through the prism pair where they may be extracted as a refocussed, chirp-compensated simultaneous ‘bunch’ of modes as an ultrashort pulse.
This is now a well-established method for the generation of ultrashort laser pulses, and has been significantly developed and improved for the production of even shorter pulsewidths approaching the few-fs limit (e.g. [60]). The method for mode-locking of semiconductor LDs is somewhat different, and is discussed in the next section.