Lineamientos curriculares de matemáticas (1998)

For most applications of a frequency comb, the output power of the oscillator itself is insufficient. Besides, an octave spanning spectrum must be generated for thef-2f

interferometer. While this is possible with the light coming directly from the oscil- lator [152] it leaves only few milliwatts for applications, which is only useful when e.g. directly setting up a heterodyne beatnote. In every other case, the light needs to be amplified and this is exactly one of the advantages of fiber lasers. Since doped fibers have a very high gain combined with a practically infinite mode-matching be- tween pump and signal light, they can be used to design highly efficient single-pass amplifiers

Depending on the subsequent application of the light, nonlinear effects may or may not be desirable to happen in the amplifier. They can be beneficial to broaden the spectrum and enable shorter pulses but more often they are detrimental to the pulse shape and should be avoided. A simple solution is to stretch the pulses in a passive fiber section before amplification. This method comes at the price of adding not only linear but also higher order chirp to the pulses which must be compensated for during recompression.

Another problem which is in general encountered when sending light through a fiber is the evolution of its polarization. As previously discussed, standard single- mode fibers will not preserve the polarization but instead rotate it randomly with a high sensitivity to environmental conditions. Thus, when putting a polarizer after the output, uncontrollable modulations in intensity can occur during operation. A solution to this problem is the use of PM fiber, which preserves a linear polarization

Figure 3.14: Spectral modulation due to polarization mode dispersion (red) and its re- duction (black) when the polarization of the incident light matches one of the optical axes of the fiber.

of the incident light when coinciding with the fiber’s optical axis. Aiming for a long- term stable system we have set up an all-PM system, although it is considerably more effort (and hence more expensive). All splices must be carried out with a PM- capable splicing device and at the coupling to and from the fiber, its optical axis must be carefully aligned. Since the two optical axes have a significant difference in group velocity — which is termed polarization mode dispersion — any misalignment will lead to pulse splitting and spectral interference patterns (see figure 3.14).

Doped fiber for setting up an amplifier is available in two conceptually different designs. Either the pump and signal light are guided both in the fiber core or the pump light is guided in the cladding, in which case the cladding must be surrounded by a material with an even smaller index of refraction. Both variations have been tested and are employed in the latest setup. Since the aim was for a long-term stable system, only PM-fibers were used. Especially in the double-clad amplifiers, which require large fiber lengths, the passive stability of the polarization in non-PM fibers is insufficient.

3.5.1

Core-pumped amplifiers

For the pump light to be guided in the same small core as the signal light, the beam profile of the pump diode must be well shaped to enable efficient coupling to a single-mode fiber. Therefore, only small, single emitters can be used, which limits the maximum available power. State-of-the-art diodes can deliver up to 750 mW at 974 nm. More pump power can only be obtained by combining more than one diode either with a polarization combiner or with a narrow band spectral combiner e.g. when using diodes at 974 and 980 nm.

The pump light is combined with the signal light in a WDM and absorbed in the doped fiber within a very short distance. The nominal pump light absorption

of the fibers used in this work is 1200 dB/m or 2000 dB/m at 975 nm. Short fiber sections can thus be employed, which offers two major advantages. First, only a little TOD is accumulated and a simple grating compressor might suffice for decent pulse compression. The second advantage is related to residual back reflections. In doped fibers that have a very high gain, these reflections can mimic a cavity mirror and lead to the onset of lasing when the amplifier is only seeded insufficiently. This can even lead to the destruction of components as described in the next paragraph. In low-power, core-pumped amplifiers this risk is largely reduced, and so far, no damage has been observed when pumping an unseeded amplifier with up to 1 W.

The choice of the optimum length of the gain fiber is best determined empirically. For large fiber lengths, the amplified spectrum narrows and shifts towards longer wavelengths. The reason for this effect is a significant overlap of the absorption and emission band of Ytterbium in the short-wavelength range. Figure 3.15(a) shows that shortening the gain fiber will reduce this reabsorption but eventually cause the absorbed power to decrease and an increasing amount of the pump light to be wasted. The optimum fiber length is thus a compromise between maximum signal output power, spectral bandwidth and peak wavelength.

In figure 3.15(b) the major advantage of Yb-doped fibers is demonstrated. Am- plifiers with a slope efficiency of up to 75 % can be realized, which facilitate heat management and require only moderate pump powers. This amplifier is employed for the generation of octave-spanning spectra for the f-2f interferometer as discussed in the previous section.

3.5.2

Double-clad amplifiers

While core-pumped amplifiers have advantages for the pulse evolution due to the short fiber lengths, their limitation in output power is a significant drawback. The alternative is to use so-called double-clad fibers for amplification. In these fibers, the signal light is still guided in the core but the pump light is guided in the cladding, which has a diameter that is about ten times larger. The fiber is thus multimodal for the pump light, significantly relaxing the requirements for the diode modules. Large emitters can be used and lately 25 W at 974 nm have become commercially available from a single diode coupled to a fiber with 105µm core diameter. This advantage is also reflected in the price per Watt pump power, which is at present a factor of 60 lower for the multimode modules with respect to single-mode diodes. A WDM is obviously unsuited for coupling pump and signal light to the same fiber and a different component must be used. Specifically designed, fused pump combiners are available that can couple the light from six multimode pump fibers and one signal fiber to one output fiber with a double-clad structure.

The spatial overlap between the pump light in the large cladding and the signal light in the core is only very small. A fiber with an absorption of 1200 dB/m with the pump guided in a 6µm core has an absorption of only 2.6 dB/m with the pump

(a) (b)

Figure 3.15: (a) Reabsorption in a core-pumped amplifier and corresponding spectral shift. The pump light is coupled to gain fiber (2000 dB/m absorption at 975 nm and4µm core diameter) of various lengths. The shifted short-wavelength edge of the shortest am- plifier and the dip in all spectra at 1080 nm is caused by the WDM for pump coupling. The inset shows the output power at 600 mW pump power and a seed power of 140 mW. With a 10 cm long gain fiber, the pump light is absorbed only insufficiently and adds to the transmitted power. (b) Slope efficiency of the core-pumped amplifier with 20 cm gain fiber.

guided in the cladding. The length of fiber required for efficient amplification thus increases drastically to several meters instead of centimeters. This is the main disadvantage of the double-clad design, when aiming for powers similar to those in core-pumped amplifiers. The typical application, however, is the construction of high-power amplifiers for which long fiber sections in front of the amplifier are needed anyway to stretch the pulses sufficiently to avoid nonlinearities.

Employing double-clad amplifiers increases the problems with residual back re- flections as discussed above. The damage threshold of the fiber, splices or com- ponents can be exceeded if the amplifier is seeded insufficiently, especially when working with high pump powers. Since the purpose of the amplifiers is to replenish the power lost due to mode filtering, they are used after the FPCs. Once the trans- mission of the filter cavity has a brief dip, e.g. due to a mechanical shock or a dust particle crossing the beam, the effect can be a damaged component. To minimize this risk, a fast interlock circuit has been designed to quickly switch off the power supply of the pump diodes in case the seed power drops. Its implementation is de- picted in figure 3.16. The circuit is designed such that it switches the pump diodes off within 70µs after a drop in signal power. The rate of damages is significantly reduced but still not all events can be prevented. An improved version with 10µs response time is currently being tested, which, according to the fiber manufacturer, should completely prevent self-induced lasing.

Figure 3.16: Double-clad amplifiers including an interlock (IL) circuit to prevent self- induced lasing. Only a small fraction (1-10 %) of the signal is used for the interlock.

erations as for core-pumped amplifiers apply. Due to the lower inversion, however, reabsorption is more pronounced and reduces the output spectral bandwidth much more. While the spectrum after core-pumped amplifiers can even be broader than the fundamental spectrum (up to 100 nm by clever exploitation of SPM), no spectra broader than 30 nm could be obtained with double-clad amplifiers when aiming for a decent efficiency.