Ytterbium-doped Femtosecond Fiber Ampliers
A ber amplier is an optical ber whose core is doped with rare-earth ions such as erbium (Er3+) or ytterbium (Yb3+). If a pump beam is coupled in the ber, the ions are transferred in an excited state, so that the laser signal can be amplied by stimulated emission of photons. Due to the long interaction lengths in optical bers and the ecient heat removal resulting from their high surface to-volume ratio, these ampliers are very well suited for the amplication of high repetition rate signals to high average powers.
The characteristics of a specic amplier, such as its bandwidth and gain, are determined by the doping ions and the hosting material, as will be explained in more detail in the rst part of this section. The following two parts include some considerations on the pump beam, and a discussion of chirped pulse amplication.
Signal Amplication and Gain
The wavelength range which can be amplied by the ber core depends on its spectroscopic properties, which are for their part determined by the dopants and the host itself. In the ber ampliers used in our setup, the doping ion is Ytterbium, which can in principle be described as a two-level system. However, as the ytterbium ions are integrated in the amorphous structure of the silica ber, the electric elds of the surrounding atoms give rise to the Stark eect which causes a splitting and shifting of the initial Yb3+ energy levels. Moreover, since every ion sees slightly dierent electric elds, the individual energy shifts vary from one ion to another. Averaging over all ions thus yields a smooth energy distribution for both levels. Furthermore, it can be assumed that each state is in thermal equilibrium, which means that the ions are most likely in a lower sublevel of the respective manifold. As a consequence, absorption is more likely to take place at lower wavelengths, where ions from a lower sublevel of the ground state are excited, as schematically shown in g. 1.8a. Conversely, emission is favored at higher wavelengths, corresponding to the emission of a photon from a lower sublevel of the excited state. For intermediate wavelengths, both
processes have similar probabilities. The resulting exact absorption and emission cross sections of an Yb-doped silica ber are shown in g. 1.8b.
The amplication process is characterized by the frequency-dependent gain coecient (), which describes the change in photon number per unit length. It is determined by the dierence between the number of absorbed and emitted photons, so that () = N2e() N1a().
General Aspects of Coherent Beam Combining
A schematic of a general MOPA CBC setup is shown in g. 2.1. The beam emitted by the master oscillator is spatially split into N sub-beams, each of which is amplied independently of the others. The channels are then recombined coherently, so that one single, very powerful beam is obtained. This procedure can be interpreted as an extension of the already existing concepts of mode area increase and peak power reduction, since the use of multiple ber ampliers increases the overall available eective area. In the same time, the peak power in a single amplier is largely reduced compared to the one obtained after the coherent combination. In short pulse regimes, this concept can be expanded in the temporal domain, so that a pulse burst is amplied rather than single pulses. After amplication, the burst is recombined temporally so that a single pulse output with increased peak power is obtained.
Furthermore, temporal and spatial beam combining can be implemented simultaneously by using a spatial CBC architecture as amplication stage within the temporal combining setup. In order to ensure an ecient beam combination, all the characteristics of the individual pulses, that is, their spatial and spectral envelopes and phases as well as their polarizations, need to be perfectly matched [49, 50]. The combining eciency is then dened as the ratio between the power in the combined beam Pcomb and the total output power of the ber ampliers Ptot, so that = Pcomb Ptot .
Phase Matching Techniques
As pointed out above, phase dierences among the beams have to be balanced in order to obtain en ecient CBC. For femtosecond setups, this means that all orders of the spectral phase need to be matched. Orders higher than zero are typically constant in time, so that a static adjustment is sucient . This means that the group delay of the dierent channels need to be matched at all orders, so that delay and dispersion dierences among the pulses are suppressed. In contrast, the zeroth order phase uctuates due to acoustic and thermal noises. It is therefore essential to implement a real time phase oset correction. The necessary bandwidth of this correction depends strongly on the employed material and the experimental conditions. For instance, it has been concluded from measurements of phase uctuations in an Yb-doped ber amplier that a bandwidth of at least several kilohertz would be necessary to obtain a phase correction on the order of /10 peak-to-valley. This value is considered as the maximum tolerable residual phase error for an ecient CBC . However, various implementations demonstrate residual phase errors below /40RMS with considerably lower bandwidths in the range of 500 Hz to 1 kHz [20, 52]. An extreme case was reported for the coherent combining of the dierent cores of a multicore ber, where a bandwidth of 2 Hz was sucient due to the low phase dierences among the cores .
Implementation in the XCAN Setup
In the previous section it has been concluded that a tiled aperture arrangement in combination with an interferometric phase measurement technique are best suited for the coherent combination of a very large number of channels. These congurations have thus been implemented in the XCAN setup, and will be presented in more detail in this section.
Tiled Aperture Conguration
In a tiled aperture conguration, highest combining eciencies can be obtained for highest ll factors of the near eld aperture. In consequence, the beam width has to be close to the array pitch, which can be achieved by collimating the beams after having them diverge over a certain distance. This has the side eect that each beam is clipped by its respective collimating lens, so that a certain part of the beam is not correctly collimated and therefore lost for the subsequent combining process, as illustrated in g. 2.3a. Such a conguration results in a side-by-side arrangement of circular beams, so that a hexagonal ber array leads to the highest aperture lling . Such an array is shown in g. 2.3b. Since only completely lled hexagons make sens, this geometry gives rise to odd numbers of combined channels such as N = 7, 19 or 61. This number is related to the normalized diameter ND of the hexagon by N = 1 + 3 4 (N2D 1).
Table of contents :
1.1 Femtosecond Laser Beams
1.1.1 Femtosecond Pulses in Free Space
1.1.2 Femtosecond Pulses in Optical Fibers
1.2 Optical Fibers
1.2.1 Working Principle
1.2.2 Special Types of Fibers
1.3 Ytterbium-doped Femtosecond Fiber Ampliers
1.3.1 Signal Amplication and Gain
1.3.2 Optical Pumping
1.3.3 Chirped Pulse Amplication
2 Coherent Beam Combining
2.1 General Aspects of Coherent Beam Combining
2.1.1 Spatial Combining Architectures
2.1.2 Temporal Beam Combining
2.1.3 Phase Matching Techniques
2.2 Implementation in the XCAN Setup
2.2.1 Tiled Aperture Conguration
2.2.2 Interferometric Phase Measurement
3 Simulations of the Beam Combining Setup
3.1 General Setup
3.2 Microlens Fill Factor
3.3 Spatial Alignment Errors
3.3.1 Misalignments within the Fiber Array
3.3.2 Microlens Array Misalignments
3.4 Spectral Disparities
3.4.1 Spectral Envelope
3.4.2 Spectral Phase
4 Seven Fiber Laser System
4.1 Laser Front End
4.2 Phase Noise Reduction
4.3 Laser Head
4.3.1 Fiber Array Setup
4.3.2 Fiber Array Assembly and Characterization
4.4 Laser Back End
4.5 Experimental Results in Linear Regime
4.5.1 Residual Phase Noise
4.5.2 Combining Eciency
4.5.3 Power Stability
4.5.4 Spatial Beam Shape
4.5.5 Temporal Compression
4.6 Experimental Results in Nonlinear Regime
4.6.1 Residual Phase Noise
4.6.2 Combining Eciency
4.6.3 Power Stability
4.6.4 Spatial Beam Shape
4.6.5 Temporal Compression
5 Conclusion and Outlook