Title: Modeling and control of optical pulse amplifiers for ultra-short laser pulses
Language: English
Authors: Deutschmann, Andreas 
Qualification level: Doctoral
Advisor: Kugi, Andreas 
Issue Date: 2019
Number of Pages: 167
Qualification level: Doctoral
The amplification of high-energy laser pulses is usually done using regenerative amplifiers. The population inversion due to continuous pumping over a comparatively long period is transferred into an incoming laser pulse in very short time by cycling it through the excited laser medium several times. While the total energy of the resulting pulses in essentially limited by the storage capacity of the laser medium, the extremely high power densities of short pulses can destroy the medium due to self-focusing effects at significantly lower energies. This limitation can be avoided by using known chirped pulse amplification techniques, where the incoming pulse is spread in time using positive dispersion first and amplified in a spectrally homogeneous way afterwards. Finally, the amplified pulse is recompressed using negative dispersion. The assumption of spectrally homogeneous amplification profiles is increasingly violated for ultra-short pulses due to their required spectral bandwidth. Additionally, the optical nonlinearities of the laser medium lead to self-induced phase distortions, wherefore suitable input filters are used to counter the increasingly incomplete recompression. If regenerative amplifiers are operated at fast repetition rates, the intrinsic coupling of subsequent pulses can destabilize the amplifier's dynamics and lead to so-called period-doubling bifurcations above a critical pumping power. For safety reasons, those operational regimes are typically avoided despite their potentially beneficial properties. Alternative methods for the generation of high-energy pulses rely on the coherent superposition of the individual pulses of a pulse burst. Ensuring high efficiency of this so-called ``pulse stacking'' requires precise amplitude and phase relations between subsequent pulses. A promising technique to simultaneously generate and amplify such pulse bursts relies on the Vernier effect by operating regenerative amplifiers with a slightly detuned resonator. However, the nonlinear coupling of all individual pulses significantly complicates the precise control of the pulse burst's energy distribution. In all those cases, the availability of programmable optical filters strongly suggests the application of automatic control concepts. The overall goal of this thesis is thus to take a look at optical amplifiers from a dedicated control engineering perspective and investigate suitable control methods. First, a detailed nonlinear infinite-dimensional model of such amplifiers is derived based on the nonlinear Schrödinger equation and the description of the interaction of the pulses with the doped ions of the laser medium. This mathematical model is subsequently used to create arbitrarily shaped pulses using iterative learning control methods. To this end, the coupling of subsequent pulses due to the complex population dynamics is neglected to describe the spectral input-output behavior by a reduced linear model. Using a Wiener-filtering-based learning approach, adaptive learning control laws are developed that do not rely on precisely calibrated (atomic) models or a chosen operating point. In a second step, the previously neglected pulse-to-pulse dynamics are investigated by ignoring the spectral properties of the laser medium to obtain a simplified energy-based description in form of a nonlinear discrete-time system. Depending on the available measurement quantities, different feedback schemes are developed to stabilize otherwise unstable operating points. This allows to operate pulse amplifiers with very high gains that can be safely steered into (or through) otherwise unstable regions. Finally, these methods are transferred to the generation and amplification of pulse bursts. By extending the energy-based description one is able to obtain settings of the input filter that produce the desired steady-state pulse bursts by solving a constrained optimization problem. Possible deviations due to model or parameter uncertainties can be eliminated using iterative learning control methods while the pulse-to-pulse dynamic can be influenced by feedback methods simultaneously.
Keywords: Regelungstechnik; optische Verstärker; adaptive Pulsformung; mathematische Modellierung; Stabilisierung; iterativ lernende Regelung; Erzeugung von Pulszügen; Layserdynamik; nichtlineare Schrödingergleichung
automatic control; optical amplifier; adaptive pulse shaping; mathematical modeling; feedback stabilization; iterative learning control; pulse burst generation; laser dynamics; nonlinear schrödinger equation
URI: https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-129460
Library ID: AC15467700
Organisation: E376 - Institut für Automatisierungs- und Regelungstechnik 
Publication Type: Thesis
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