This thesis concentrates on the physics and fiber optics side of the CPA system, but it is worth noting that some additional mechanical and electrical engineering is necessary for realizing such a laser system in practice. All the laser diodes need drivers, which are optimally computer controllable. The AOM pulse picker requires additional electronics that use a monitor photodiode to synchronize with the incoming pulse train and generate the correct driving signal. Other monitor diodes and possibly thermocouples should act as failsafe to shut down the laser system in case of abnormal operation. The power amplifier, including the tapered fiber, the multimode pump diodes, and the pump coupling optics must be actively cooled to maintain constant temperature and output power and to avoid damage due to overheating. All these things require real engineering work that is not considered here in any detail.
4 EVALUATION OF THE DESIGN BY NUMERICAL SIMULATIONS
This chapter presents numerical simulations of the complete designed CPA laser system starting from the pulses generated by the seed laser and ending with the compressed pulses after the gratings. In effect, the seed pulse is propagated computationally through each piece of fiber and each component in the system. Gain in the active fibers is mod-elled using rate equation simulations while the actual ultrashort pulse propagation is cal-culated with the generalized nonlinear Schrödinger equation. Since the components for this laser system design actually exist, the simulations strive to use their realistic parame-ters from their datasheets where possible. Some starting parameparame-ters were unfortunately unavailable and have been substituted by educated guesses or estimates. The text states clearly the points where this has been necessary. Similarly, some physical effects or de-tails are beyond the scope of this thesis either because of the difficulty in implementing them or, more commonly, because of their impact on the modelling results was consid-ered very limited. The text also includes a mention wherever the physical model could be improved by considering those additional effects.
The first half of this chapter goes through the laser design piece by piece in sequential order to show how each part is modelled and how it affects the pulse propagating through it. For this purpose, the simulation uses the seed pulse from the experimentally build mode-locked fiber laser, which allows evaluating the seed laser’s suitability for the CPA system at the same time. After the component-by-component analysis, the model for the complete system is used to study the effect of tuning the amplifiers’ pump currents and the stretcher’s dispersion as well as using a Gaussian seed pulse.
The ultrafast pulse is described numerically as an array of complex numbers correspond-ing to the discretized complex amplitude in either the spectral or time domain. As men-tioned in section 2.5.3, the two descriptions are equivalent, and it is possible to switch be-tween them by Fourier transforming. This also has a practical consequence as it means that the scales of the simulation arrays in time and spectral domain are similarly linked.
The table below table 4.1 shows the parameters of the simulation arrays used in all the ultrafast simulations in this chapter. The spectral domain is presented as using wave-length units for convenience, though in reality the simulation array consists of equally spaced points in frequency and the wavelength resolution varies slightly from the low to high-frequency side of the array.
Table 4.1. The time and wavelength ranges and resolutions used in the discretized GNLSE simulation arrays.
Parameters of the pulse simulation array
Time resolution 72 fs
Time range 1.2 ns
Wavelength resolution 3.1 pm
Wavelength range 50 nm
Center wavelength 1040 nm
Number of points 16384
The parameters are determined by the requirement to model both stretched and com-pressed pulses in the CPA system. First, the time window must be long enough to ac-commodate a pulse hundreds of picoseconds long so that no energy can escape from the window to the sides, whereupon it would appear on the other side, distorting the simulation results. At the same time, the time grid must be dense enough to describe a compressed sub-picosecond pulse. In this case, a <100 fs resolution is acceptable given that the seed’s spectral width (see section 4.1.1) is too narrow to support<0.5 ps pulses. The number of data points is typically set as a power of two to leverage the most efficient fast Fourier transform (FFT) algorithms. Consequently, the best choice is 214 points, which leads to a time resolution of 72 fs. The spectral range and resolution follow from the time domain parameters as expected with the Fourier transform. No-tably, the spectral range excludes wavelengths around 1090 nm where stimulated Raman scattering would appear. This is a conscious decision to reduce the computational load and based on the following reasons. The simulations presented in this chapter suggest that poor pulse compression due to self-phase modulation becomes the limiting factor of the CPA system earlier than significant SRS is expected to be generated based on experiments. The second reason to exclude Raman wavelengths is that modelling SRS accurately in a fiber amplifier is simply difficult as it also requires accurate modelling of background noise caused by amplified spontaneous emission and spontaneous Raman scattering, because these provide the seed signal for SRS.