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Short Pulse equation derived by Schafer and Wayne is a nonlinear partial differential equation that describes ultra short laser propagation in a dispersive optical medium such as optical fibers. Some properties of this equation e.g. traveling wave solution and its soliton structure and some of its conserved quantities were investigated. Conserved quantities were obtained by mass conservation law, lax pair method and transformation between Sine-Gordon and short pulse equation. As a result, loop soliton characteristic and six conserved quantities were found.

In this thesis, I have developed a tunable two-color two-stage ultrafast Yb:fiber chirped pulse amplifier for the generation of short-pulse mid-infrared (MIR) radiation in the long-wavelength side of the "molecular fingerprint" (2.5-25 μm) using difference frequency generation (DFG) technique. The two colors called blue and red are in the wavelengths 1.03-1.11 μm and are amplified simultaneously in the same Yb-doped fiber amplifier (YDFA) stages in order to reduce the induced environmental noise on the phase difference of the pulses and to minimize the complexity and system cost. I will present numerical simulations on the two-stage YDFA system to amplify a two-color spectrum in the wavelengths 1.03-1.11 μm. The first and second YDFA called preamplifier and main amplifier are single-clad, single-mode and double-clad, single-mode YDFA respectively. From numerical simulations, the optimal length of the preamplifier to have equal power at two colors centered at 1043 nm and 1105 nm are in agreement with experimental results. It is well known that the power of MIR radiation generated by difference frequency mixing of two wavelengths scales up with the product of mixing powers in a fixed-field approximation. Furthermore, for the gain narrowing effect on the short-wavelength side of the YDFA gain profile, the spectral bandwidth of the blue color decreases resulting in pulse broadening. In addition, for the two colors separated largely, the amplified spontaneous emission is intensified. Considering the cited factors, I will present the modeling results on the two-color, two-stage YDFA system that the product of the power of the two colors is maximized for a maximized wavelength separation between the two mixing colors and a minimized gain narrowing on the blue color in order to build an as broadly tunable and powerful as possible ultrafast mid-infrared source by difference frequency mixing of the two colors. In this research, I achieved a wavelength separation as broad as 71 nm between pulses centered at 1038 nm and 1109 nm from the two-color ultrafast YDFA system. I achieved combined average powers of 2.7 W just after the main amplifier and 1.5 W after compressing the two-color pulses centered at 1041 nm and 1103 nm to nearly Fourier transform limited pulses. From autocorrelation measurements, the full width at half maximum (FWHM) of the compressed two-color pulses with the peak wavelengths of 1041 nm and 1103 nm was ~500 fs. By mixing the tunable two-color pulses in a 1-mm-thick GaSe crystal using DFG technique, I achieved tunable short-pulse MIR radiation. In this research, I achieved short-pulse MIR radiation tunable in the wavelengths 16-20 μm. The MIR tuning range from the lower side was limited to the 16 μm because of the 71-nm limitation on the two-color separation and from the upper side was limited to the 20 μm because of the 20-μm cutoff absorption wavelength of GaSe. Based on measured MIR spectra, the MIR pulses have a picosecond pulse duration in the wavelengths 16-20 μm. The FWHM of measured spectra of the MIR pulses increases from 0.3 μm to 0.8 μm as the MIR wavelength increases from 16 μm to 20 μm. According to Fourier transform theory, the FWHM of the MIR spectra corresponds to the bandwidth of picosecond MIR pulses assuming that the MIR pulses are perfectly Fourier-transform-limited Gaussian pulses. In this research, I achieved a maximum average power of 1.5 mW on short-pulse MIR radiation at the wavelength 18.5 μm corresponding to the difference frequency of the 500-fs two-color pulses with the peak wavelengths of 1041 nm and 1103 nm and average powers of 1350 mW and 80 mW respectively. Considering the gain bandwidth, Ti:sapphire is a main competitor to the YDFA to be used in the two-color ultrafast laser systems. In the past, the broad gain bandwidth of Ti:sapphire crystal has resulted in synchronized two-color pulses with a wavelength separation up to 120 nm. Apart from its bulkiness and high cost, Ti:sapphire laser system is limited to a watt-level output average power at room temperature mainly due to Kerr lensing problem that occurs at high pumping powers. In comparison, YDFA as a laser amplifier has a narrower gain bandwidth but it is superior in terms of average power. Optical parametric generation (OPG) and optical parametric amplification (OPA) techniques are two competitors to DFG technique for the generation of short-pulse long-wavelength MIR radiation. Although OPG offers a tunability range as broad as DFG, the MIR output power is lower because of the absence of input signal pulses. From the OPA technique, the tunability range is not as broad as the DFG technique due to limitations with the spectral bandwidth of the optical elements. Currently, quantum cascade lasers (QCLs) are the state-of-art MIR laser sources. At the present time, the tunability range of a single MIR QCL is not as abroad as that achieved from the DFG technique. More, mode-locked MIR QCLs are not abundant mainly because of the fast gain recovery time. Thus, the generation of widely tunable short-pulse MIR radiation from DFG technique such as that developed in this thesis remains as a persistent technological solution. The application of the system developed in this thesis is twofold: on one hand, the tunable two-color ultrashort pulses will find applications for example in pump-probe ultrafast spectroscopy, short-pulse MIR generation, and optical frequency combs generation. On the other hand, the short-pulse MIR radiation will find applications for example in time-resolved MIR spectroscopy to study dynamical behavior of large molecules such as organic and biological molecules.

In this thesis, I have developed a tunable two-color two-stage ultrafast Yb:fiber chirped pulse amplifier for the generation of short-pulse mid-infrared (MIR) radiation in the long-wavelength side of the "molecular fingerprint" (2.5-25 μm) using difference frequency generation (DFG) technique. The two colors called blue and red are in the wavelengths 1.03-1.11 μm and are amplified simultaneously in the same Yb-doped fiber amplifier (YDFA) stages in order to reduce the induced environmental noise on the phase difference of the pulses and to minimize the complexity and system cost. I will present numerical simulations on the two-stage YDFA system to amplify a two-color spectrum in the wavelengths 1.03-1.11 μm. The first and second YDFA called preamplifier and main amplifier are single-clad, single-mode and double-clad, single-mode YDFA respectively. From numerical simulations, the optimal length of the preamplifier to have equal power at two colors centered at 1043 nm and 1105 nm are in agreement with experimental results. It is well known that the power of MIR radiation generated by difference frequency mixing of two wavelengths scales up with the product of mixing powers in a fixed-field approximation. Furthermore, for the gain narrowing effect on the short-wavelength side of the YDFA gain profile, the spectral bandwidth of the blue color decreases resulting in pulse broadening. In addition, for the two colors separated largely, the amplified spontaneous emission is intensified. Considering the cited factors, I will present the modeling results on the two-color, two-stage YDFA system that the product of the power of the two colors is maximized for a maximized wavelength separation between the two mixing colors and a minimized gain narrowing on the blue color in order to build an as broadly tunable and powerful as possible ultrafast mid-infrared source by difference frequency mixing of the two colors. In this research, I achieved a wavelength separation as broad as 71 nm between pulses centered at 1038 nm and 1109 nm from the two-color ultrafast YDFA system. I achieved combined average powers of 2.7 W just after the main amplifier and 1.5 W after compressing the two-color pulses centered at 1041 nm and 1103 nm to nearly Fourier transform limited pulses. From autocorrelation measurements, the full width at half maximum (FWHM) of the compressed two-color pulses with the peak wavelengths of 1041 nm and 1103 nm was ~500 fs. By mixing the tunable two-color pulses in a 1-mm-thick GaSe crystal using DFG technique, I achieved tunable short-pulse MIR radiation. In this research, I achieved short-pulse MIR radiation tunable in the wavelengths 16-20 μm. The MIR tuning range from the lower side was limited to the 16 μm because of the 71-nm limitation on the two-color separation and from the upper side was limited to the 20 μm because of the 20-μm cutoff absorption wavelength of GaSe. Based on measured MIR spectra, the MIR pulses have a picosecond pulse duration in the wavelengths 16-20 μm. The FWHM of measured spectra of the MIR pulses increases from 0.3 μm to 0.8 μm as the MIR wavelength increases from 16 μm to 20 μm. According to Fourier transform theory, the FWHM of the MIR spectra corresponds to the bandwidth of picosecond MIR pulses assuming that the MIR pulses are perfectly Fourier-transform-limited Gaussian pulses. In this research, I achieved a maximum average power of 1.5 mW on short-pulse MIR radiation at the wavelength 18.5 μm corresponding to the difference frequency of the 500-fs two-color pulses with the peak wavelengths of 1041 nm and 1103 nm and average powers of 1350 mW and 80 mW respectively. Considering the gain bandwidth, Ti:sapphire is a main competitor to the YDFA to be used in the two-color ultrafast laser systems. In the past, the broad gain bandwidth of Ti:sapphire crystal has resulted in synchronized two-color pulses with a wavelength separation up to 120 nm. Apart from its bulkiness and high cost, Ti:sapphire laser system is limited to a watt-level output average power at room temperature mainly due to Kerr lensing problem that occurs at high pumping powers. In comparison, YDFA as a laser amplifier has a narrower gain bandwidth but it is superior in terms of average power. Optical parametric generation (OPG) and optical parametric amplification (OPA) techniques are two competitors to DFG technique for the generation of short-pulse long-wavelength MIR radiation. Although OPG offers a tunability range as broad as DFG, the MIR output power is lower because of the absence of input signal pulses. From the OPA technique, the tunability range is not as broad as the DFG technique due to limitations with the spectral bandwidth of the optical elements. Currently, quantum cascade lasers (QCLs) are the state-of-art MIR laser sources. At the present time, the tunability range of a single MIR QCL is not as abroad as that achieved from the DFG technique. More, mode-locked MIR QCLs are not abundant mainly because of the fast gain recovery time. Thus, the generation of widely tunable short-pulse MIR radiation from DFG technique such as that developed in this thesis remains as a persistent technological solution. The application of the system developed in this thesis is twofold: on one hand, the tunable two-color ultrashort pulses will find applications for example in pump-probe ultrafast spectroscopy, short-pulse MIR generation, and optical frequency combs generation. On the other hand, the short-pulse MIR radiation will find applications for example in time-resolved MIR spectroscopy to study dynamical behavior of large molecules such as organic and biological molecules.

No description available.

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Generation of high-peak power, microwave ultra-short pulses (USPs) is desirable for ultra-wideband communications and remote sensing. A variety of microwave USP generators exist today, or are described in the literature, and have benefits and limitations depending on application. A new class of pulse compressors for generating USPs using electromagnetic time reversal (TR) techniques have been developed in the last decade, and are the topic of this dissertation. This dissertation presents a compact TR microwave pulse-compression cavity that has ultra-wide bandwidth (5 GHz – 18 GHz), and employs waveguide feeds for high-peak power output over the entire band. The system uses a time-reversal-based pulse compression scheme with one-bit processing (OBTR) to achieve high compression gain. Results from full-wave simulations are presented as well as measurements showing compression gain exceeding 21.2 dB, 22% efficiency, and measured instantaneous peak output powers reaching 39.2 kW. These are all record results for this type of pulse compressor. Additionally presented is new analysis of variation in compression gain due to impulse response recording time and bandwidth variation, new experimental work on the effect of mode stirrer position on compression gain, and a novel RF switch-based technique for reducing time-sidelobes while using OBTR. Finally, a new technique is presented that uses a reverberant cavity with only one feed connected to an ultra-wideband circulator (6.5 GHz to 17 GHz) to perform TRPC. Prior to this work, TRPC has only been demonstrated in electromagnetics using two or more feeds and a reverberant cavity acting as the time-reversal mirror. This new 1-port technique is demonstrated in both simulation and measurement. The proposed system achieves up to a measured 3 dB increase in compression gain and increased efficiency. Also, a novel application of the random coupling model (RCM) to calculate compression gain is presented. The cavity eigenfrequencies are modeled after eigenvalues of random matrices satisfying the Gaussian orthogonal ensembles (GOE) condition. Cavity transfer functions are generated using Monte Carlo simulations, and used to compute the compression gains for many different cavity realizations. / Doctor of Philosophy / Generation of high-peak power, microwave ultra-short pulses (USPs) is desirable for ultra-wideband communications and remote sensing. A variety of microwave USP generators exist today, or are described in the literature, and have benefits and limitations depending on application. A new class of pulse compressors for generating USPs using electromagnetic time reversal (TR) techniques have been developed in the last decade, and are the topic of this dissertation. This dissertation presents a compact TR-based microwave pulse-compression cavity that has unique features that make it optimal for high-power operations, with results from simulations as well as measurements showing improved performance over other similar cavities published in the literature with a record demonstrated peak output power of 39.2 kW. Additionally, new analysis on the operation and optimization of this cavity for increased performance is also presented. Finally, a new technique is presented that uses a cavity with only one feed that acts as both the input and output. This 1-port technique is demonstrated in both simulation and measurement. The proposed system achieves a two-times increase in compression gain over its 2-port counterpart. In conjunction with these measurements and simulations, a novel technique for predicting the performance of these cavities using Monte Carlo simulation is also presented.

Lesões dentais por erosão têm sido cada vez mais presentes na prática clínica. A restauração direta com resina composta é uma das opções de tratamento para lesões severas, em que há comprometimento estético/funcional. Com o aprimoramento da tecnologia, a utilização do laser para pré-tratamento da superfície dentinária, antes do condicionamento ácido, tem sido considerada como método alternativo para melhorar a adesão das resinas compostas às superfícies erodidas. Assim, o objetivo deste estudo in vitro foi avaliar a influência da irradiação com laser de Er:YAG (2,94 ?m), de pulso super-curto, na adesão da resina composta à superfície dentinária erodida. Quarenta e seis discos de dentina foram obtidos a partir de 46 dentes terceiros molares humanos. A dentina oclusal planificada de 40 molares humanos teve metade de sua face protegida com fita UPVC (dentina hígida), enquanto na outra metade foi produzida uma lesão de erosão através da ciclagem em ácido cítrico (0,05 M, pH 2,3, 10 minutos, 6x/dia) e solução supersaturada (pH 7,0, 60 minutos entre os ataques ácidos). Metade das amostras foi irradiada com o laser de Er:YAG (50 ?s, 2 Hz, 80 mJ, 12,6 J/cm2) e a outra não (grupo controle). Em cada grupo de tratamento (laser ou controle) (n=10), um sistema adesivo autocondicionante foi utilizado e, então, confeccionados 2 cilindros de resina composta, tanto do lado erodido como no hígido (total de 4 cilindros), os quais foram submetidos à avaliação da Resistência de União através do ensaio de microcisalhamento (1 mm/min), após armazenamento em saliva artificial por 24 h. A análise do padrão de fratura foi realizada em microscópio óptico (40x). Por meio da Microscopia Eletrônica de Varredura (MEV), a morfologia das superfícies dentinárias hígida e submetida ao desafio erosivo, antes e após o tratamento com laser de Er:YAG (n=3), foi avaliada. Os valores obtidos de resistência de união (MPa) foram submetidos ao teste ANOVA e de comparações múltiplas de Tukey (p<0,05) e as análises das eletromicrografias foram feitas de forma descritiva. A análise morfológica da superfície mostrou alterações significativas na dentina hígida irradiada e na submetida à ciclagem erosiva, irradiada ou não. Quanto à resistência de união, houve diferença entre os 4 substratos analisados, sendo: dentina hígida irradiada (12,77±5,09 A), dentina hígida não irradiada (9,76±3,39 B), dentina erodida irradiada (7,62±3,39 C) e dentina erodida não irradiada (5,12±1,72 D). Houve predominância de padrão de fratura do tipo adesiva. Com base nos resultados e nos parâmetros de irradiação utilizados neste estudo, pode-se concluir que a erosão reduz a adesão em dentina e que o tratamento da superfície dentinária com laser de Er:YAG de largura de pulso super curta aumenta a adesão no substrato erodido ou hígido. / Dental erosion injuries have been increasingly present in clinical practice. Direct restoration with composite resin is one of the treatment options for severe injuries, where there is aesthetic/functional impairment. With the improvement of technology, laser-irradiation for pre-treatment of dentin before surface etching has been considered as an alternative method to improve the adhesion of composite resins to eroded surfaces. The objective of this in vitro study was to evaluate the influence of the irradiation with a super-short pulse Er:YAG (2.94 ?m) laser to the adhesion of composite resin to eroded dentin surface. Forty six dentin discs were obtained from 46 third molars. Forty samples of planned occlusal dentine, obtained from human molars, had half of their surface protected with plastic tape (sound dentin), while the other half was submitted to erosive cycles, consisted on immersion on citric acid (0.05 M, pH 2.3, 10 minutes, 6x/day) and supersaturated solution (pH 7.0, 60 minutes of acid attacks). Half of the samples was irradiated with the Er:YAG laser (50 ?s, 2 Hz, 80 mJ, 12.6 J/cm2) and the other was kept as control. In each treatment group (n = 10), a self-etching adhesive system was used and then two cylinders of composite resin were prepared, on both eroded and sound dentin (total of 4 cylinders). Microshear bond strength test was performed (1 mm/min), after 24 hours storage in artificial saliva. The analysis of the fracture pattern was determined by optical microscopy (40x). The morphology of sound and eroded dentin, before and after treatment with the Er:YAG laser (n = 3) was evaluated under Scanning Electron Microscopy (SEM). Bond strength values (MPa) were subjected to ANOVA and Tukey multiple comparisons test (p<0.05). The analyses of electron micrographs were made descriptively. Morphological analysis of the surface showed significant changes in irradiated and sound dentin subjected to erosive cycling. As for the bond strength, there were differences among the groups, as follows: sound dentin submitted to irradiation (12.77 ± 5.09 A), non-irradiated sound dentin (9.76 ± 3.39 B), eroded dentin submitted to irradiation (7 62 ± 3.39 C) and non-irradiated eroded dentin (5.12 ± 1.72 D). There was a predominance for the adhesive mode of failure. It was concluded that the erosion reduces the adhesion to dentin and that treating the dentin surface with a super-short-pulse Er:YAG laser increases adhesion to both eroded or sound dentin.