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2.1.3: Modelocking

In the previous section we demonstrated that in order to get short light pulses, laser must

  1. Generate light in as wide frequency range as possible and
  2. The modes with different frequencies must have identical phases

Therefore, the first requirement for an ultrashort (1 ps and shorter) pulsed laser is a broad gain spectrum. This explains why gas lasers are not especially attractive for short pulse generation: emission lines of gases are very narrow, which makes it impossible to amplify wide range of frequencies. Therefore, historically first ‘real’ ultrafast lasers were dye lasers, where the gain profile covers the entire fluorescence spectrum of a dye molecule (which can be up to 50 nm wide in the visible range). Dyes are also not especially attractive as lasing media: organic molecules tend to degrade when they are excited and de-excited multiple times, therefore, the dye solutions must be circulated for refreshment, employing large and noisy pumps. When hoses crack, dyes spray over the entire lab, making almighty mess. Some dye molecules have even been found to be carcinogenic. Additionally, wavelength tuning with a single dye is only possible across a relatively narrow spectral range. For different range of wavelengths, dyes must be replaced – a long and messy process. For these reasons, laser engineers found a way to replace dyes with solid state media: almost all biophysical and physicochemical research uses ultrafast lasers based on titanium-doped sapphire (Ti:Sapphire, Ti:Al2O3) lasers allowing the generation of light in the spectral range from 690 to 1050 nm. The maximum gain is around 800 nm, which is the wavelength corresponding to the carrier frequency of Ti:Sapphire pulses. In the recent years, solid-state lasers employing other active media, such as Yb:KGW crystals have gained in popularity, but Ti:Sapphire remains a main workhorse of ultrafast science.

            So, how do we make the laser to generate all the modes in step (with equal phases)? The general idea is that, similarly to a Q-switched laser, laser cavity must be supplemented by a component that damps the lasing action (increases cavity losses), when the laser operates in continuous wave (cw, random mode phases) regime. On the other hand, this component should encourage lasing when the phases of different modes (accidentally) fall in step. There are several solutions for this, but we will only discuss one, called Kerr lens modelocking, because this is one of the simplest and most widely used modelocking mechanism in Ti:Sapphire laser systems.

            Kerr effect in optics is the dependence of refractive index of a medium on the intensity of the light propagating therein. In such medium, the refractive index can be described in the following way:

                                                                                                                              ,

where n0 is the conventional (linear) refractive index, observed at low light intensities. A laser beam intensity distribution in the plane perpendicular to the beam propagation direction is usually similar to Gaussian, i.e. the intensity is low at the sides and high at the center. When such beam propagates in the medium with nonlinear refractive index, the refractive index change is highest in the center and lowers at the edges. Thus, the medium obtains refractive index profile similar to that of a lens and the beam starts to focus (fig. 6A). The tighter the focusing is, the higher is the intensity of the beam, and the stronger lensing effect can be achieved. Therefore, when the beam starts to self-focus, it will keep contracting in size until other phenomena kick in to limit the focus (e.g. diffraction, or breakdown of the medium). We note that such self-focusing is only possible at high light intensities (because the refractive index change is proportional to the intensity). Now, given the same amount of pump light, the intensity will always be higher in the pulsed regime, where all the energy is concentrated in the peak of the pulse, rather than spread over time. This, in turn, means that self-focusing will be a lot stronger, when the laser is modelocked: all modes are in phase and strong pulse is generated instead of continuous wave operation.  Let us now insert an aperture in the cavity (an opaque plate with a hole in the center) that will only allow the focused beam to pass. Then the modelocked light will be able to freely travel in the cavity and be amplified. If the laser is inclined to misbehave and lase with randomly phased modes, such lasing will be discriminated against by the aperture (the beam does not get focused and a large portion of light is stopped by the aperture – losses increase). This way, a “natural selection” of lasing is established: only modelocked light is amplified, and all other types of generation are discriminated against. In fact, when the laser becomes modelocked, it is hard to kick out of this operation regime: the pulsed operation consumes the entire population inversion and CW operation gets no chance to start. Loosely speaking, the laser ‘rather waits’ for the next pulse than starts lasing in CW – there is simply no juice left after the previous pulse.

 

 

Fig. 1) A: focusing of light due to Kerr effect: when light propagates in nonlinear medium, refractive index change is highest in the center of the beam (where light intensity is high), and lower in the sides (intensity is low).

The resulting refractive index profile resembles a lens and focuses the beam. The focused beam results in higher refractive index change, etc. B: modelocking in the laser cavity using Kerr lens. When laser operates in pulsed mode (modes are in phase), the peak intensity in the pulse is higher and the resulting Kerr lens focuses the beam, allowing it to pass the spatial filter: lasing is efficient (thick black line depicts the beam). In CW mode, (thin dashed line), electric field intensity is insufficient for self-focusing to occur and lasing does not start because of the losses on the spatial filter.

 

Ti:Sapphire laser operating in the described fashion is called an oscillator.   It will generate a train of pulses, the duration of which can be down to a few tens of femtoseconds (with special care one can get down below 10 fs). The repetition frequency of the pulses matches cavity round trip time, usually around 80 MHz, or 12.5 ns between consecutive pulses. The energies of pulses are in the range of 1-6 nJ.