Thesis (MSc (Physics))--University of Stellenbosch, 2009. / The role fulfilled by theoretical models is rapidly increasing due to lasers becoming appli- cation driven to satisfy certain criteria and demands. Construction of high precision lasers requires good theoretical models and consequently good approximations of the parameters that such models are based upon. Despite the di erent model formalisms, most share a com- mon set of input parameters, including fibre waveguiding properties, input powers, transition cross-sections and overlaps between guided modes and the dopand distribution. Experimental and numerical work which was aimed at obtaining the wide-band emission and absorption cross-sections of fibre indirectly by means of the Giles parameters was done. The Giles parameters were used rather than the well known ionic cross-sections primarily because of the convenient encapsulation of the cumbersome overlap factors and the ionic cross-sections within the Giles parameters. The wide band spectral characteristics of the Giles parameters are indispensable in the design of fibre lasers and amplifiers, as they form the key parameters for laser models. These parameters are normally obtained utilizing absorption spectroscopy to obtain the absorption cross-sections and models such as the Fuchtbauer Ladenberg relation, the Mc- Cumber relation or uorescence spectroscopy to obtain the emission cross-sections. Recent research however indicates that these methods are inaccurate in certain spectral regions. An investigation was launched to extract the Giles parameters from measurements of the ampli- fied spontaneous emission (ASE) and pump absorption in ytterbium-doped fibre for several lengths of fibre and subsequent computer simulations, utilizing an ampli fier model. The Giles parameters are extracted with a fitting algorithm that adjusts the relevant numerical values to minimize the least square difference between the numerical data obtained from the amplifier model and the measured data. Using the model devised in this project on literature data, the Giles parameters were extracted and compared to the Giles parameters extracted in literature on the same data. This comparison conforms the extraction of the Giles parameters, utilizing the model devised in this project, as successful. Subsequently the model devised in this project was applied to extract the Giles parameters from experimental data measured at Stellenbosch, using a double cladding ytterbium-doped fibre. Finally a fibre laser was built utilizing the double cladding ytterbium-doped fibre and the output was measured. The Giles parameters extracted were then used in a fibre laser model to calculate the output and compare it to the measurements taken. This served as suffcient verification that the Giles parameters extracted can be used to model a fibre laser effciently.

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.

Cette thèse traite des dégradations induites par la pompe (photo-noircissement) et les radiations ionisantes externes (radio-noircissement) dans les fibres optiques en silice dopées ytterbium (FDY) utilisées en environnement sévère. Au travers de caractérisations expérimentales et de modélisations inédites, elle analyse leur interaction et en tire les conséquences quant à la tenue des FDY aux radiations sous pompe. La première partie porte sur l’identification des défauts induits (centres colorés) et leurs mécanismes de formation/guérison. Elle s’appuie sur un ensemble de caractérisations post-irradiation (RPE, ARI, TL) réalisées sur des échantillons de préformes et sur leur corrélation originale (guérison thermique, couplage TL et ARI). L’étude systématique en fonction de la composition met en évidence l’influence des co-dopants (Al, Ce) sur la capture des charges libérées lors des processus d’ionisation. La seconde partie analyse le noircissement se développant sous l’effet simultané de la pompe et de l’irradiation ionisante. A partir d’un banc de mesures autorisant le suivi de la dégradation en temps réel, on montre que photo- et radio-noircissements résultent des mêmes centres colorés blanchis par la pompe. Ce résultat, ajouté aux mécanismes préalablement identifiés, permet de proposer un modèle physique local de la dégradation photo-radio-induite. La confrontation des simulations issues de ce modèle à une large variété d’observations originales faites « en ligne » conduit à sa validation. Il est ainsi démontré que, pour des débits de dose inférieurs à une valeur critique, la dégradation des FDY pompées et irradiées ne peut excéder leur niveau de photo-noircissement. / This thesis deals with the degradation induced by the pump (photodarkening, PN) and ionizing radiations (radiodarkening, RN) in ytterbium-doped optical fiber (YDF) used in harsh environments. Through original experimental characterizations and modeling, it analyses the interplay between PN and RN and reveals important and novel properties of the radiation resistance of pumped YDF. The first part investigates induced defects (color centers) together with their creation/recovery mechanisms. It used a set of post-irradiation characterizations (ESR, RIA, TSL) conducted on preform samples and benefited from their original correlation (thermal recovery protocols coupling TSL and RIA). A systematic study as a function of composition reveals the influence of co-dopants (Al, Ce) on the trapping of carrier freed during ionization processes. The second part examines the darkening build-up under the simultaneous action of the pump and an ionizing irradiation. By using a measurement bench that allowed us to follow the real-time “on line” degradation of fiber samples, we showed that photo- and radio-darkening both arise from the same color centers that can be bleached by the pump. On the basis of this finding and of the preceding identified mechanisms, we propose a local physical model of the photo-radio-induced darkening. The latter is thoroughly validated by further successful comparisons of simulated degradation with a wide variety of “on line” original observations. Then, we notably demonstrate that for dose rates lying below a critical value (explicited by our theory), the degradation of pumped and irradiated YDF never exceeds the photo-darkening level.

Tandem pumping technique are traditionally adopted to develop > 3-kW continuous-wave (cw) Yb3+-doped fiber lasers, which are usually pumped by other fiber lasers at shorter wavelengths (1018 nm e.g.). Fiber lasers directly pumped by laser diodes have higher wall-plug efficiency and are more compact. Here we report two high brightness monolithic cw fiber laser sources at 1080 nm. Both lasers consist of a cw fiber laser oscillator and one laser-diode pumped double cladding fiber amplifier in the master oscillator-power amplifier configuration. One laser, using 30-mu m-core Yb3+-doped fiber as the gain medium, can produce > 5-kW average laser power with near diffraction-limited beam quality (M-2<1.8). The slope efficiency of the fiber amplifier with respect to the launched pump power reached 86.5%. The other laser utilized 50-mu m-core Yb3+-doped fiber as the gain medium and produced > 8-kW average laser power with high beam quality (M-2: similar to 4). The slope efficiency of the fiber amplifier with respect to the launched pump power reach 83%. To the best of our knowledge, this is the first detailed report for > 5-kW near-diffraction-limited and > 8-kW high-brightness monolithic fiber lasers directly pumped by laser diodes.

Fiber lasers represent the state-of-the-art in laser technology and hold great promise for a wide range of applications because they have a minimum of exposed optical interfaces, very high efficiency, and are capable of exceptional beam quality. In the near future, the most important markets such as micromachining, automotive, biomedical and military applications will begin to use this technology. The scope of this thesis is to design and develop a short picosecond pulsed fiber laser using rare-earth doped fiber as a gain medium. The proposed master oscillator power amplifier (MOPA) will be used to generate pulses with high repetition rates. In this study, first we explain the basic theoretical background of nonlinear optics and fiber laser. Then, the numerical simulation will be introduced to explain how the laser system design and optimization. The simulation is based on nonlinear Schr&ouml / dinger equation with the method of split-step evaluation. The brief theoretical background and simulation results of the laser system will be shown. Finally, the experimental study of the developmental fiber laser system that comprises an oscillator, preamplifier and power amplifier will be discussed.

Ce travail de thèse concerne le développement de sources femtoseconde de forte puissance moyenne ou de forte énergie avec des matériaux pompés par diodes laser, dopés à l’ytterbium. Plus particulièrement au cours de cette thèse deux types de matrices ont été utilisés, le CALGO (CaGdAlO4) et les fluorures, possédant le potentiel de générer des impulsions courtes (100aine de femtoseconde). Les caractéristiques spectroscopiques et thermiques du CALGO dopés à l’ytterbium permettent d’envisager le développement d’oscillateur femtoseconde court de forte puissance moyenne. Dans ce contexte, la technologie des disques minces permet d’obtenir avec d’autres matrices, des résultats très intéressants. C’est pourquoi durant cette thèse le choix de maitriser cette nouvelle technologie, avec l’utilisation de ce cristal, a été fait. Dans ce cadre, des résultats très prometteurs ont été obtenus. L’oscillateur femtoseconde Yb :CALGO de plus forte puissance moyenne a en effet été développé (28 W), pour une énergie non négligeable, supérieure au µJ et une durée d’impulsions de 300 fs. Des améliorations sont à prévoir avec l’utilisation de nouveaux cristaux plus dopés et plus fins, mais d’hors et déjà les résultats obtenus sont au niveau de l’état de l’art des oscillateurs femtoseconde de forte puissance moyenne.Le cristal de CaF2 quant à lui, possède un grand intérêt pour le développement d’amplificateurs énergétiques courts, puisqu’il a la capacité de stocker beaucoup d’énergie. Deux types d’amplificateurs ont alors été développés, avec des objectifs bien différents. Le premier permet d’obtenir un fort gain (~106), avec une énergie extraite proche du mJ (amplificateur régénératif), alors que le second a pour but d’extraire le maximum d’énergie (amplificateur multipassage), dans notre cas jusqu’à 160 mJ, avec un gain plus faible (~10).Le potentiel de ces matériaux pour la génération d’impulsions courtes et/ou de forte puissance moyenne a alors été démontré. / This work concerns the development of high average power or high energy laser with diode-pumped ytterbium-doped materials. Two host matrices were studied, CALGO (CaGdAlO4) and fluoride, which permit the generation of ultra-short pulses. Spectroscopic and thermal properties of ytterbium doped CALGO crystals are adapted for the development of high average power oscillator. In this area, thin disk technology seems to be particularly interesting for the development of such oscillator. That’s why we choose to master this technology with ytterbium-doped CALGO crystals. Thus, Yb:CALGO oscillator with the highest average power was developed (28 W), with more than µJ energy and pulse duration of 300 fs. Using more doped and thinner crystals should permit to improve our performances, however they are already at the state of the art of high average power oscillator.Ytterbium doped CaF2 has a great interest for short-pulse high energy amplifier, thanks to its capacity to store energy. Two types of amplifier were developed. A regenerative amplifier with high gain (~106), mJ energy level, and a multipass amplifier with lower gain (~10) but permitting to extract really high energy (up to 160 mJ).Potential of these materials for the development of short pulse high average power and/or high energy system was demonstrated.

The use of supercontinuum light sources in different optical measurement methods, like microscopy or optical coherence tomography, has increased significantly compared to classical wideband light sources. The development of various optical measurement techniques benefits from the high brightness and bandwidth, as well as the spatial coherence of these sources. For some applications, only a portion of the broad spectral range can be used. Therefore, an increase of the spectral power density in limited spectral regions would provide a clear advantage over spectral filtering. This study describes a method to increase the spectral power density of supercontinuum sources by amplifying the excitation wavelength inside a nonlinear photonic crystal fiber (PCF). An ytterbium doped photonic crystal fiber was manufactured by a nanopowder process (drawn by the company fiberware) and used in a fiber amplifier setup as the nonlinear fiber medium. In order to characterize the fiber’s optimum operational characteristics, group-velocity dispersion (GVD) measurements were performed on the fiber during the amplification process. For this purpose, a notch-pass mirror was used to launch the radiation of a stabilized laser diode at 976 nm into the fiber sample for pumping. The performance of the fiber was compared with a conventional PCF. Finally, the system as a whole was characterized in reference to common solid state-laser-based photonic supercontinuum light sources. An improvement of the power density up to 7.2 times was observed between 1100 nm to 1380 nm wavelengths.

Supercontinuum light sources provide a high power spectral density with a high spatial coherence. Coherent octavespanning supercontinuum can be generated in photonic crystal fibers (PCFs) by launching short pulses into the fiber. In the field of optical metrology, these light sources are very interesting. For most applications, only a small part of the entire spectrum can be utilized. In biological tissue scattering, absorption and fluorescence limits the usable spectral range. Therefore, an increase of the spectral power density in limited spectral regions would provide a clear advantage over spectral filtering. This study describes a method to increase the spectral power density of supercontinuum sources by amplifying the excitation wavelength inside a nonlinear photonic crystal fiber (PCF). An all-fiber-based setup enables higher output power and power stability. An ytterbium-doped photonic crystal fiber was manufactured by a nanopowder process (drawn by the fiberware GmbH, Germany) and used in a fiber amplifier setup as the nonlinear fiber medium. In order to characterize the fiber’s optimum operational characteristics, group-velocity dispersion (GVD) measurements were performed. The performance of the fiber-based setup was compared with a free space setup. Finally, the system as a whole was characterized in reference to common solid state-laser-based supercontinuum light sources. An improvement of the power density was observed in the spectral range between 1100 nm to 1400 nm.

Ce travail de thèse a eu pour but de développer des nouvelles sources lasers, oscillateurs et ampli?cateurs, construites autour des ?bres dopées aux ions ytterbium. Ces systèmes lasers génèrent des fortes puissances moyennes. L’oscillateur réalisé délivre des impulsions courtes (<10 ns) avec des énergies de l’ordre du milliJoule. Le système fonctionne à des cadences variables (10-100 kHz) avec un faisceau polarisé, monomode dont la largeur spectrale est inférieure à 0.1 nm. A?n d’avoir de plus fortes puissances crêtes et des impulsions courtes, deux types d’ampli?- cateurs ont été étudiés. Les résultats expérimentaux que nous avons obtenus sont en accord avec le modèle numérique développé. Le premier système ampli?e un microlaser émettant à 1064 nm dans une ?bre dopée ytterbium. Des puissances crêtes supérieures à 500 kW ont été obtenues avec des impulsions de l’ordre de la nanoseconde et une cadence comprise entre 1 kHz et 30 kHz. Le second ampli?cateur est construit autour d’un oscillateur à ?bre dopée ytterbium déclenché injecté dans une deuxième ?bre qui constitue l’ampli?cateur. L’originalité de ce système réside dans le cou- plage de deux cavités. Nous avons alors en sortie deux faisceaux cohérents, polarisés, monomode, indépendamment ajustables en énergie. En?n, nous avons utilisé les sources lasers développées, qui présentent des caractéristiques spec- trales, modales, énergétiques adéquats pour effectuer la conversion de fréquence. Des ef?cacités de l’ordre de 64 % et 38 % ont été atteintes respectivement en doublage et en triplage. Les faisceaux en sortie de ces systèmes possèdent des remarquables caractéristiques spatiales et temporelles. / This work presents the development of oscillators and ampli?ers build around new ytterbium rod type ?ber. These ?ber systems generate high average power generation. The oscillator makes it possible to deliver well linearly polarized, almost TEM 00 mode, and millijoule-level nanosecond pulses at a tunable repetition rate (10-100 kHz). The spectral bandwidth was shown to be less than 0.1 nm. To achieve higher peak power and shorter pulses, two types of ampli?ers have been developed and characterized. The experimental results we obtain, do well agree with the numerical simulations we developped. The ?rst system ampli?es in a rod type ?ber the nanosecond pulses yielded by a microlaser working at 1064 nm wavelength injected . Its provides pulses with a high peak power system (500 kW). Its repetition rate was tuned from 1 kHz to 30 kHz. The second ampli?er was built using a Q-switched ytterbium doped ?ber oscillator injected in a second ?ber which acts as ampli?er. In this original system the two cavities are coupled. It delivers two nanosecond pulses that are coherent, polarized, almost TEM00 single mode beams and that can have independently tunable pulse energies. We have shown that these oscillators and ampli?ers can be easily doubled and tripled in fre- quency. Very high ef?ciency of about 64 % and 38 % have been achieved respectively at 2? and 3?. These outputs have been to have remarquable spatial and temporal characteristics.