This thesis focuses on research I have done on ytterbium-doped femtosecond fiber lasers. These lasers operate in the near infrared region, lasing at 1030 nm. This wavelength is particularly important in biomedical applications, which includes but is not limited to confocal microscopy and ablation for surgical incisions. Furthermore, fiber lasers are advantageous compared to solid state lasers in terms of their cost, form factor, and ease of use. Solid state lasers still dominate the market due to their comparatively high energy pulses. High energy pulse generation in fiber lasers is hindered by either optical wave breaking or by multipulsing. One of the main challenges for fiber lasers is to overcome these limitations to achieve high energy pulses. The motivation for the work done in this thesis is increasing the output pulse peak power and energy. The main idea of the work is that decreasing the nonlinearity that acts on the pulse inside the cavity will prevent optical wave breaking, and thus will generate higher energy pulses. By increasing the output energy, ytterbium-doped femtosecond fiber lasers can be competitive with solid state lasers which are used commonly in research. Although fiber lasers tend to lack the wavelength tuning ability of solid state lasers, many biomedical applications take advantage of the 1030 µm central wavelength of ytterbium-doped fiber lasers, so the major limiting factor of fiber lasers in this field is simply the output power. By increasing the output energy without resorting to external amplification, the cavity is optimized and cost can remain low and economical. During verification of the main idea, the cavity was examined for possible back-reflections and for components with narrow spectral bandwidths which may have contributed to the presence of multipulsing. Distinct cases of multipulsing, bound pulse and harmonic mode-locking, were observed and recorded as they may be of more interest in the future. The third-order dispersion contribution from the diffraction gratings inside the laser cavity was studied, as it was also considered to be an energy-limiting factor. No significant effect was found as a result of third-order dispersion; however, a region of operation was observed where two different pulse regimes were found at the same values of net cavity group velocity dispersion. Results verify the main idea and indicate that a long length of low-doped gain fiber is preferable to a shorter, more highly doped one. The low-doped fiber in an otherwise equivalent cavity allows the nonlinear phase shift to grow at a slower rate, which results in the pulse achieving a higher peak power before reaching the nonlinear phase shift threshold at which optical wave breaking occurs. For a range of net cavity group velocity dispersion values, the final result is that the low doped fiber generates pulses of approximately twice the value of energy of the highly-doped gain fiber. Two techniques of mode-locking cavities were investigated to achieve this result. The first cavity used NPE mode-locking which masked the results, and the second used a SESAM for mode-locking which gave clear results supporting the hypothesis.

High Harmonic Generation (HHG) enables the production of bursts of coherent soft x-rays with attosecond pulse duration. This process arrises from the nonlinear interaction between intense infrared laser pulses and an ionizing gas medium. Soft x-ray photons are used for spectroscopy of inner-shell electron correlation and exchange processes, and the availability of attosecond pulse durations will enable these processes to be resolved on their natural time scales. The maximum or cutoff photon energy in HHG increases with both the intensity as well as the wavelength of the driving laser. It is highly desirable to increase the harmonic cutoff as this will allow for the generation of shorter attosecond pulses, as well as HHG spectroscopy of increasingly energetic electronic transitions. While the harmonic cutoff increases with laser wavelength, there is a corresponding decrease in harmonic yield. The first part of this thesis describes the experimental measurement of the wavelength scaling of HHG efficiency, which we report as lambda^(-6.3) in xenon, and lambda^(-6.5) in krypton. To increase the HHG cutoff, we have developed a 1.8 um source, with stable carrier envelope phase and a pulse duration of <2 optical cycles. The 1.8 um wavelength allowed for a significant increase in the harmonic cutoff compared to equivalent 800 nm sources, while still maintaing reasonable harmonic yield. By focusing this source into neon we have produced 400 eV harmonics that extend into the x-ray water window. In addition to providing a source of photons for a secondary target, the HHG spectrum caries the signature of the electronic structure of the generating medium. In krypton we observed a Cooper minimum at 85 eV, showing that photoionization cross sections can be measured with HHG. Measurements in xenon lead to the first clear observation of electron correlation effects during HHG, which manifest as a broad peak in the HHG spectrum centred at 100 eV. This thesis also describes several improvements to the HHG experiment including the development of an ionization detector for measuring laser intensity, as well as an investigation into the role of laser mode quality on HHG phase matching and efficiency.

Since blood pressure is a significant parameter to examine people's physical attributes and it is useful to indicate cardiovascular diseases, the measurement/estimation of blood pressure has gained increasing attention. The continuous, cuff-less and non-invasive blood pressure estimation is required for the daily health monitoring. In recent years, studies have been focusing on the ways of blood pressure estimation based on other physiological parameters. It is widely accepted that the pulse transit time (PTT) is related to arterial stiffness, and can be used to estimate blood pressure.<p> A promising signal processing technology, Hilbert-Huang Transform (HHT), is introduced to analyze both ECG and PPG data, which are applied to calculate PTT. The relationship between blood pressure and PTT is illustrated, and the problems of calibration and re-calibration are also discussed. The proposed algorithm is tested based on the continuous data from MIMIC database. To verify the algorithm, the HHT algorithm is compared with other used processing technique (wavelet transform). The accuracy is calculated to validate the method. Furthermore, we collect data using our own developed system and test our algorithm.

Since blood pressure is a significant parameter to examine people's physical attributes and it is useful to indicate cardiovascular diseases, the measurement/estimation of blood pressure has gained increasing attention. The continuous, cuff-less and non-invasive blood pressure estimation is required for the daily health monitoring. In recent years, studies have been focusing on the ways of blood pressure estimation based on other physiological parameters. It is widely accepted that the pulse transit time (PTT) is related to arterial stiffness, and can be used to estimate blood pressure.<p> A promising signal processing technology, Hilbert-Huang Transform (HHT), is introduced to analyze both ECG and PPG data, which are applied to calculate PTT. The relationship between blood pressure and PTT is illustrated, and the problems of calibration and re-calibration are also discussed. The proposed algorithm is tested based on the continuous data from MIMIC database. To verify the algorithm, the HHT algorithm is compared with other used processing technique (wavelet transform). The accuracy is calculated to validate the method. Furthermore, we collect data using our own developed system and test our algorithm.

The ultrafast optical regime is defined, as it applies to laser pulses, along with a brief introduction to pulse generation and characterisation technologies. A more extensive description of our particular amplified pulse generation and SPIDER characterisation systems follows. Data verifying the correct operation of the characterisation system is presented and interpreted. Our laser system is then characterised in two different configurations. In each case, the data describing the system is presented and analyzed. Conclusions are made regarding the performance of both the characterisation and laser systems, along with suggested improvements for each.

The goal of this thesis is developing a two-color Ytterbium (Yb) fiber amplifier system that can be used for generation of mid-infrared radiation. Previously, our group reported generating 20 µW of average power, at a wavelength of 18µm. This was accomplished through the amplification of a two color-seed with peaks at 1040nm and 1110nm, through a two stage amplification without any compression. The mid-infrared radiation (MIR) was generated with a 4.5 ps pulse duration by the method of difference-frequency mixing, using 300 mW of average power from the two-color Yb-fiber amplifier. Because there was no limitation by two-photon absorption, MIR output power could be scaled by increasing the amplifier power. The current project aims to increase the peak power of the laser pulses to improve the efficiency of the nonlinear mixing. The two-colour seed is generated by continuum generation in a photonic crystal fibre, pumped by 200 mW of average power from a mode-locked Yb:fibre laser. In order to efficiently increase the energy of the two wavelengths, the 4.6 mW seed pulse is now pre-amplified up to 21 mW in a 2.7 m length single mode, single core Yb:fibre . The pre-amplifier used a double-ended pumping scheme with two single mode diode lasers at 976 nm each having 150 mW maximum pump power. A notch filter was placed in the output beam to eliminate any Amplified Spontaneous Emission. After further amplification in a 7 m length of double clad, Yb-fibre, a maximum average power of 727 mW was achieved for two colours peaked at 1035 nm and 1105 nm wavelengths. The pump power for this stage was 6 W. A grating stretcher is now used to select the two-colour input along with stretching the pulses. A three grating compressor is used to compress the output pulses to 466 fs pulse duration. After compression the average power of the two colours is 350 and 110 mW for wavelengths at 1035 and 1105nm, respectively. These higher power pulses are planned to be used to increase the mid-infrared generation efficiency.

The development of resistance measurement techniques is very important for characterization of future nanoelectronics. Pulsed IV measurement techniques are very useful for accurate resistance measurements on nanoscale samples because of the efficient removal of e.g. EMF errors. In the project we have designed a pulsed IV-setup based on a state-of-the art current source (6221) and nanovoltmeter (2182A) from Keithley, and used the setup for resistance measurements on ferromagnetic samples. Two different samples were investigated using the pulsed IV system – ferromagnetic wires with a central nanoconstriction and amorphous microwires. We have tested the pulse delta system with different pulse widths, duty cycles and voltage levels. The results show a successful integration of the setup. From the measurement results we confirm that the pulse delta system provides accurate measurements with a low noise of about 0.02Ω. The resistance of the samples increases approximately quadratically with bias which is interpreted as a heating effect due to the very high current density of about 107A∙cm-2.

The ultrafast optical regime is defined, as it applies to laser pulses, along with a brief introduction to pulse generation and characterisation technologies. A more extensive description of our particular amplified pulse generation and SPIDER characterisation systems follows. Data verifying the correct operation of the characterisation system is presented and interpreted. Our laser system is then characterised in two different configurations. In each case, the data describing the system is presented and analyzed. Conclusions are made regarding the performance of both the characterisation and laser systems, along with suggested improvements for each.

The goal of this thesis is developing a two-color Ytterbium (Yb) fiber amplifier system that can be used for generation of mid-infrared radiation. Previously, our group reported generating 20 µW of average power, at a wavelength of 18µm. This was accomplished through the amplification of a two color-seed with peaks at 1040nm and 1110nm, through a two stage amplification without any compression. The mid-infrared radiation (MIR) was generated with a 4.5 ps pulse duration by the method of difference-frequency mixing, using 300 mW of average power from the two-color Yb-fiber amplifier. Because there was no limitation by two-photon absorption, MIR output power could be scaled by increasing the amplifier power. The current project aims to increase the peak power of the laser pulses to improve the efficiency of the nonlinear mixing. The two-colour seed is generated by continuum generation in a photonic crystal fibre, pumped by 200 mW of average power from a mode-locked Yb:fibre laser. In order to efficiently increase the energy of the two wavelengths, the 4.6 mW seed pulse is now pre-amplified up to 21 mW in a 2.7 m length single mode, single core Yb:fibre . The pre-amplifier used a double-ended pumping scheme with two single mode diode lasers at 976 nm each having 150 mW maximum pump power. A notch filter was placed in the output beam to eliminate any Amplified Spontaneous Emission. After further amplification in a 7 m length of double clad, Yb-fibre, a maximum average power of 727 mW was achieved for two colours peaked at 1035 nm and 1105 nm wavelengths. The pump power for this stage was 6 W. A grating stretcher is now used to select the two-colour input along with stretching the pulses. A three grating compressor is used to compress the output pulses to 466 fs pulse duration. After compression the average power of the two colours is 350 and 110 mW for wavelengths at 1035 and 1105nm, respectively. These higher power pulses are planned to be used to increase the mid-infrared generation efficiency.

In this thesis we discuss deterministic compartmental epidemic models. We study the asymp- totic stability of the disease-free solution of models with pulse vaccination campaigns. The main contributions of this thesis are to extend the literature of pulse vaccination models with delay. We take results for ordinary differential equation models and extend them to models with delay differential equations. Model generalizations include the use of a general incidence term as an upper bound for the actual incidence, and the use of switch parameters to approximate time-varying parameters. In particular, we look at contact rate parameters which are piecewise constant or time-varying. We extend literature results for non-delay general incidence models to find uniform asymptotic stability of the disease-free solution which helps us to add delay. We find an upper bound for the susceptible population under pulse vaccination and use this bound to tighten results for eradication thresholds: that is, we use this upper bound to find sufficient conditions for the uniform asymptotic stability of the disease-free solution of delayed pulse vaccination models. We extend literature results for constant contact rate bilinear incidence delay models to models with periodic time-varying contact rate, and determine conditions under which the disease-free solution is uniformly asymptotically stable for small delay. We also find conditions for disease permanence in the corresponding non-delay, time-varying-parameter pulse vaccination model. For piecewise- constant contact rate bilinear incidence models we again find thresholds which guarantee uniform asymptotic stability under small delay. We additionally discuss the effects of time-varying total population on our results, through a change of variables to population fractions. The total population is commonly held constant in the literature, for analytical simplicity, so we survey the methods for time-varying total population and the effects of such variation on the pulse vaccination schemes. We retain thresholds for eradication by considering the compartment populations as fractions of the total, instead of population numbers. The result is also applied to constant-population delay systems. When changing from standard incidence to bilinear incidence in delay systems, we discuss a way to estimate the effect of time-varying N. We support our theory with simulation results.