We have measured the optical properties of films of the organic semiconductors PTCDA (3,4:9,10-perylene-tetracarboxylic dianhydride) and HBC (peri-hexabenzocoronene), prepared by Organic Molecular Beam Expitaxy (OMBE), on different substrates by means of Differential Reflectance Spectroscopy (DRS). The optical setup enables us to directly follow the thickness dependent optical properties of the organic films, starting from submonolayer coverage up to thicker films on the order of 20 monolayers (ML) film thickness. Due to the different optical nature of the different substrates used, i.e., mica, glass, Au(111), and HOPG, the direct interpretation of the DRS signal is not feasible. Therefore, we have proposed a method by which the calculation of the optical constants n (index of refraction) and k (absorption index) of thin films on arbitrary substrates from just one spectral measurement (in our case the DRS) becomes possible. The results fulfill a priori a Kramers-Kronig consistency and no specific model is needed to express the spectral behavior of the optical constants. Based on our method, we have successfully calculated the optical constants, and therefore the absorption behavior, of films of different thickness of PTCDA on mica, glass, Au(111), and HOPG, as well as of HBC on mica, glass, and HOPG. Extrinsic effects due to island growth or the presence of a polarizable substrate (screening) have been accounted for. We have introduced a finite dipole model which considers the extended geometry and anisotropy of the organic molecules. The calculated absorption behavior is discussed in great detail in terms of spectral changes with varying film thickness, different growth modes, degree of ordering of the films, interactions with the substrates and oscillator strength. A direct observation of a monomer-dimer transition in solid films could be observed for the first time. Our results indicate an exciton delocalization over about 4 molecules for both molecules.

For consistent electrochemical impedance spectroscopy (EIS) measurements, several important conditions must be met. The measurements should be made in a linear region of the characteristic of the Device Under Test (DUT), which should be kept causal and stable throughout the measurement time. Violation of these conditions requires extensive special signal processing or can invalidate the entire measurement. As the measurement procedure consists of applying an excitation signal and measuring the response signal, the excitation signal plays a critical role in the quality of the measurement. It should have a small amplitude to meet the linearity and stability conditions while maintaining a sufficient signal-to-noise ratio. This is particularly important for electrochemical systems, which change their state during long measurement times for low frequency excitations. Multi-frequency signals, such as multisine signals, outperform sine-sweep signals in meeting these conditions because they include multiple frequencies within the same signal and can, therefore, significantly reduce measurement time. These signals must be optimized to ensure that the amplitude remains within the linearity range and that the signal power density per frequency is maximized. Until now, optimization procedures have been performed primarily for the requirements of specific applications, resulting in the lack of a universal methodology. In this thesis, we propose, for the first time, a novel methodology for designing multisine signals, reducing measurement time, maximizing the excitation signal power, maintaining the linearity range, and thereby ensuring system stability even at low frequencies in the mHz range. Within a comprehensive approach, various aspects are considered, such as optimizing the frequency selection, reducing the signal duration, and maintaining the linearity range. To evaluate the consistency of measured impedance spectra, we propose a novel method based on the regularized linear Kramers-Kronig (rLKK), which is robust to distortions and noise. Three novel phase optimization methods have been developed, tailored to the desired frequency density at low frequencies and the specific characteristics of the DUT. First, a combined metaheuristic gradient solution based on Role-Playing Game Theory has been developed. The advantage of this method is that it is able to search the optimum globally and is independent of the initial phase. In the second method, the optimization of the crest factor was realized based on a transformation by the generalized sigmoid function to limit the signal to the linear range, followed by clipping to eliminate the remaining peaks. Compared to common methods that rely solely on clipping, the sigmoid function offers a significant advantage. It acts as a variable multiplier, emphasizing values closer to the peaks while keeping the signal within the linear range. The third method uses a two-phase optimization approach. The first phase minimizes the peaks of battery charge variation to improve stability during the measurement. However, this can increase the crest factor of the excitation signal. The second phase minimizes the crest factor of the signal. Moreover, a stabilization method is proposed for electrochemical systems with strong transient behavior. This method involves including a dummy injection interval and considering multiple periods of the excitation signal. The determination of suitable stabilization time and the number of periods has been achieved through the use of the rLKK. The experimental validation was conducted on a lithium-ion battery cell and on bioimpedance spectroscopy, employing the Cole-Cole model. In the case of lithium-ion battery cells, it was demonstrated that the proposed excitation signals enable accurate and stable impedance measurement of the charge transfer and diffusion processes, which are critical for determining battery state of health and state of charge. With a signal duration of 100 s, six frequencies per decade, and a frequency range of 10 mHz to 1 kHz, the resulting impedance spectrum demonstrates an RMS rLKK deviation of 216 ppm. Compared to traditional sine sweep methods, it exhibits an RMS deviation of 0.02% in impedance spectra, which is a tenfold improvement over the 0.28% deviation reported in the literature. This approach achieves measurements from 3 to 9 times faster than conventional techniques with comparable accuracy. The addition of the proposed stabilization minimizes the rLKK deviation to 84 ppm, but adds 200 s to the measurement time. In the case of bioimpedance spectroscopy for measurements at six frequencies per decade in the frequency range 5 kHz to 500 kHz, the signal duration is 0.39 ms, and the total measurement time on an STM32 microcontroller is 1.53 seconds, with a maximum impedance deviation of 0.56 percent. This is at least 19 times faster than previous works and 2.67 times more accurate, as well as more robust to noise. / Für konsistente elektrochemische Impedanzspektroskopie (EIS) messungen müssen einige wichtige Bedingungen erfüllt sein. Die Messungen sollten in einem linearen Bereich der Kennlinie des Device-Under-Tests (DUT) durchgeführt werden, der kausal und über die Messzeit hinweg stabil gehalten werden sollte. Ein Verstoß gegen diese Bedingungen erfordert eine umfangreiche spezielle Signalverarbeitung oder kann die gesamte Messung ungültig machen. Das Messverfahren besteht darin, ein Anregungssignal anzulegen und das Antwortsignal zu messen. Daher spielt das Anregungssignal eine entscheidende Rolle für die Qualität der Messung. Es muss eine kleine Amplitude haben, um die Linearitäts- und Stabilitätsbedingungen zu erfüllen, und gleichzeitig ein ausreichendes Signal-Rausch-Verhältnis aufweisen. Dies ist besonders wichtig für elektrochemische Systeme, die ihren Zustand während langen Messzeiten und insbesondere bei niedrigen Frequenzen ändern. Mehrfrequenzsignale, wie z. B. Multisinus-Signale, erfüllen diese Bedingungen besser als Sinus-Sweep-Signale, da sie mehrere Frequenzen gleichzeitig in einem Signal kombinieren und dadurch die Messzeit erheblich verkürzen können. Diese Signale müssen optimiert werden, um sicherzustellen, dass die Amplitude innerhalb des Linearitätsbereichs bleibt und die Signalleistungsdichte pro Frequenz maximiert wird. Bisher wurden Signaloptimierungsverfahren hauptsächlich für die Anforderungen spezifischer Anwendungen durchgeführt, so dass keine verallgemeinerte Methodik vorgeschlagen werden konnte. In dieser Arbeit wird zum ersten Mal eine neuartige Methodik für den Entwurf von Multisinus-Signalen vorgeschlagen, die die Messzeit reduzieren, die Signalleistungsdichte des Anregungssignals maximieren, den Linearitätsbereich beibehälten und damit die Systemstabilität auch bei niedrigen Frequenzen im mHz-Bereich gewährleisteten. In einem umfassenden Ansatz berücksichtigen wir mehrere Aspekte, wie die Optimierung der Frequenzauswahl, die Verringerung der Signaldauer und die Einhaltung des Linearitätsbereichs. Um die Konsistenz der gemessenen Impedanzspektren zu bewerten, schlagen wir eine neuartige Methode vor, die auf der regularisierten linearen Kramers-Kronig-Methode (rLKK) basiert und gegenüber Verzerrungen und Rauschen robust ist. Es wurden drei neuartige Phasenoptimierungsverfahren entwickelt, die auf die gewünschte Frequenzdichte bei niedrigen Frequenzen und die spezifischen Eigenschaften des DUT zugeschnitten sind. Zunächst wurde eine kombinierte metaheuristische Gradientenlösung auf der Grundlage der Rollenspieltheorie entwickelt. Der Vorteil dieser Methode ist, dass sie in der Lage ist, das Optimum global zu suchen, und dass sie unabhängig von der Anfangsphase ist. In der zweiten Methode wurde die Crest-Faktor-Optimierung auf der Grundlage einer Transformation durch die verallgemeinerte Sigmoid-Funktion realisiert, um das Signal auf den linearen Bereich zu begrenzen, gefolgt von Clipping, um die verbleibenden Peaks zu eliminieren. Im Vergleich zu herkömmlichen Methoden, die ausschließlich auf Clipping beruhen, bietet die Sigmoidfunktion einen wesentlichen Vorteil. Sie wirkt wie ein variabler Multiplikator, der die Werte in der Nähe der Spitzenwerte hervorhebt, während das Signal innerhalb des linearen Bereichs bleibt. Die dritte Methode verwendet einen zweiphasigen Optimierungsansatz. In der ersten Phase werden die Spitzen der Batterieladungsschwankungen minimiert, um die Stabilität der Messung zu verbessern. Dies kann jedoch den Crest-Faktor des Anregungssignals erhöhen. In der zweiten Phase wird der Crest-Faktor des Signals minimiert. Darüber hinaus wird für elektrochemische Systeme mit starkem Einschwingverhalten eine Stabilisierungsmethode vorgeschlagen, die ein Dummy-Injektionsintervall einschließt und mehrere Perioden des Anregungssignals berücksichtigt. Zur Bestimmung der geeigneten Stabilisierungszeit und der Anzahl der Perioden wurde die rLKK verwendet. Die experimentelle Validierung wurde an einer Lithium-Ionen-Batteriezelle und an der Bioimpedanzspektroskopie unter Verwendung des Cole-Cole-Modells durchgeführt. Im Fall von Lithium-Ionen-Batteriezellen wurde gezeigt, dass die vorgeschlagenen Anregungssignale eine genaue und stabile Impedanzmessung der Ladungstransfer- und Diffusionsprozesse ermöglichen, die für die Bestimmung des Batteriegesundheits- und Ladezustands entscheidend sind. Bei einer Signaldauer von 100 s, sechs Frequenzen pro Dekade und einem Frequenzbereich von 10 mHz bis 1 kHz weist das resultierende Impedanzspektrum eine RMS rLKK-Abweichung von 216 ppm auf. Im Vergleich zu herkömmlichen Sinus-Sweep-Methoden weist es eine RMS-Abweichung von 0,02% in Impedanzspektren auf, was eine zehnfache Verbesserung gegenüber der in der Literatur angegebenen Abweichung von 0,28% darstellt. Mit diesem Ansatz lassen sich Messungen 3 bis 9 Mal schneller als mit herkömmlichen Techniken durchführen, bei vergleichbarer Genauigkeit. Der Zusatz der vorgeschlagenen Stabilisierung minimiert die rLKK-Abweichung auf 84 ppm, verlängert aber die Messzeit um 200 s. Im Falle der Bei der Bioimpedanzspektroskopie für Messungen bei sechs Frequenzen pro Dekade im Frequenzbereich von 5 kHz bis 500 kHz beträgt die Signaldauer 0,39 ms, und die Gesamtmesszeit auf dem STM32 betrug 1,53 Sekunden, bei einer maximalen Impedanzabweichung von 0,56 Prozent. Dies ist mindestens 19-mal schneller als frühere Arbeiten und 2,67-mal genauer sowie robuster gegenüber Rauschen.

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Abnormal electromagnetic wave propagation characterized by negative group velocity and consequently negative group delay (NGD) has been observed in certain materials as well as in artificially built structures. Within finite frequency intervals where an NGD phenomenon is observed, higher frequency components of the applied waveform are propagated with phase advancement, not delay, relative to the lower frequency components. These media have found use in many applications that require positive delay compensation and an engineered phase characteristic, such as eliminating phase variation with frequency in phase shifters, beam-squint minimization in phased array antenna systems, size reduction of feed-forward amplifiers and others. The three principal questions this thesis addresses are: can a generic formulation for artificial NGD structures based on electric circuit resonators be developed; is it possible to derive a quantitative functional relationship (asymptotic limit) between the maximum achievable NGD and the identified trade-off quantity (out-of-band gain); and, can a microwave circuit exhibiting a fully loss-compensated NGD propagation in both directions be designed and implemented? A generic frequency-domain formulation of artificial NGD structures based on electric circuit resonators is developed and characterized by three parameters, namely center frequency, bandwidth and the out-of-band gain. The developed formulation is validated through several topologies reported in the literature. The trade-off relationship between the achievable NGD on one hand, and the out-of-band gain on the other, is identified. The out-of-band gain is shown to be proportional to transient amplitudes when waveforms with defined “turn on/off” times are propagated through an NGD medium. An asymptotic limit for achievable NGD as a function of the out-of-band gain is derived for multi-stage resonator-based NGD circuits as well as for an optimally engineered linear causal NGD medium. Passive NGD media exhibit loss which can be compensated for via active elements. However, active elements are unilateral in nature and therefore do not allow propagation in both directions. A bilateral gain-compensated circuit is designed and implemented, which overcomes this problem by employing a dual-amplifier configuration while preserving the overall circuit stability.

Abnormal electromagnetic wave propagation characterized by negative group velocity and consequently negative group delay (NGD) has been observed in certain materials as well as in artificially built structures. Within finite frequency intervals where an NGD phenomenon is observed, higher frequency components of the applied waveform are propagated with phase advancement, not delay, relative to the lower frequency components. These media have found use in many applications that require positive delay compensation and an engineered phase characteristic, such as eliminating phase variation with frequency in phase shifters, beam-squint minimization in phased array antenna systems, size reduction of feed-forward amplifiers and others. The three principal questions this thesis addresses are: can a generic formulation for artificial NGD structures based on electric circuit resonators be developed; is it possible to derive a quantitative functional relationship (asymptotic limit) between the maximum achievable NGD and the identified trade-off quantity (out-of-band gain); and, can a microwave circuit exhibiting a fully loss-compensated NGD propagation in both directions be designed and implemented? A generic frequency-domain formulation of artificial NGD structures based on electric circuit resonators is developed and characterized by three parameters, namely center frequency, bandwidth and the out-of-band gain. The developed formulation is validated through several topologies reported in the literature. The trade-off relationship between the achievable NGD on one hand, and the out-of-band gain on the other, is identified. The out-of-band gain is shown to be proportional to transient amplitudes when waveforms with defined “turn on/off” times are propagated through an NGD medium. An asymptotic limit for achievable NGD as a function of the out-of-band gain is derived for multi-stage resonator-based NGD circuits as well as for an optimally engineered linear causal NGD medium. Passive NGD media exhibit loss which can be compensated for via active elements. However, active elements are unilateral in nature and therefore do not allow propagation in both directions. A bilateral gain-compensated circuit is designed and implemented, which overcomes this problem by employing a dual-amplifier configuration while preserving the overall circuit stability.