Theoretical and numerical study of the laser-plasma ion acceleration

The laser driven ion acceleration is a burgeoning field of resarch and is attracting a growing number of scientists since the first results reported in 2000 obtained irradiating thin solid foils by high power laser pulses. The growing interest is driven by the peculiar characteristics of the produced bunches, the compactness of the whole accelerating system and the very short accelerating length of this all-optical accelerators. A fervent theoretical and experimental work has been done since then. An important part of the theoretical study is done by means of numerical simulations and the most widely used technique exploits PIC codes (“Particle In Cell'”). In this thesis the PIC code AlaDyn, developed by our research group considering innovative algorithms, is described. My work has been devoted to the developement of the code and the investigation of the laser driven ion acceleration for different target configurations. Two target configurations for the proton acceleration are presented together with the results of the 2D and 3D numerical investigation. One target configuration consists of a solid foil with a low density layer attached on the irradiated side. The nearly critical plasma of the foam layer allows a very high energy absorption by the target and an increase of the proton energy up to a factor 3, when compared to the ``pure'' TNSA configuration. The differences of the regime with respect to the standard TNSA are described The case of nearly critical density targets has been investigated with 3D simulations. In this case the laser travels throughout the plasma and exits on the rear side. During the propagation, the laser drills a channel and induce a magnetic vortex that expanding on the rear side of the targer is source of a very intense electric field. The protons of the plasma are strongly accelerated up to energies of 100 MeV using a 200PW laser.

Grazing incidence pumped Zr x-ray laser for spectroscopy on Li-like ions

X-ray laser fluorescence spectroscopy of the 2s-2p transition in Li-like ions is promising to become a widely applicable tool to provide information on the nuclear charge radii of stable and radioactive isotopes. For performing such experiments at the Experimental Storage Ring ESR, and the future NESR within the FAIR Project, a grazing incidence pumped (GRIP) x-ray laser (XRL) was set up at GSI Darmstadt using PHELIX (Petawatt High Energy Laser for heavy Ions eXperiments). The experiments demonstrated that lasing using the GRIP geometry could be achieved with relatively low pump energy, a prerequisite for higher repetition rate. In the first chapter the need of a plasma XRL is motivated and a short history of the plasma XRL is presented. The distinctive characteristic of the GRIP method is the controlled deposition of the pump laser energy into the desired plasma density region. While up to now the analysis performed were mostly concerned with the plasma density at the turning point of the main pump pulse, in this thesis it is demonstrated that also the energy deposition is significantly modified for the GRIP method, being sensitive in different ways to a large number of parameters. In the second chapter, the theoretical description of the plasma evolution, active medium and XRL emission properties are reviewed. In addition an innovative analysis of the laser absorption in plasma which includes an inverse Bremsstrahlung (IB) correction factor is presented. The third chapter gives an overview of the experimental set-up and diagnostics, providing an analytical formula for the average and instantaneous traveling wave speed generated with a tilted, on-axis spherical mirror, the only focusing system used up to now in GRIP XRL. The fourth chapter describes the experimental optimization and results. The emphasis is on the effect of the incidence angle of the main pump pulse on the absorption in plasma and on output and gain in different lasing lines. This is compared to the theoretical results for two different incidence angles. Significant corrections for the temperature evolution during the main pump pulse due to the incidence angle are demonstrated in comparison to a simple analytical model which does not take into account the pumping geometry. A much better agreement is reached by the model developed in this thesis. An interesting result is also the appearance of a central dip in the spatially resolved keV emission which was observed in the XRL experiments for the first time and correlates well with previous near field imaging and plasma density profile measurements. In the conclusion also an outlook to the generation of shorter wavelength XRL’s is given.

Characterization and optimization of an x-ray laser for the spectroscopy of Li-like heavy-ions

Recent developments in the theory of plasma-based collisionally excited x-ray lasers (XRL) have shown an optimization potential based on the dependence of the absorption region of the pumping laser on its angle of incidence on the plasma. For the experimental proof of this idea, a number of diagnostic schemes were developed, tested, qualified and applied. A high-resolution imaging system, yielding the keV emission profile perpendicular to the target surface, provided positions of the hottest plasma regions, interesting for the benchmarking of plasma simulation codes. The implementation of a highly efficient spectrometer for the plasma emission made it possible to gain information about the abundance of the ionization states necessary for the laser action in the plasma. The intensity distribution and deflection angle of the pump laser beam could be imaged for single XRL shots, giving access to its refraction process within the plasma. During a European collaboration campaign at the Lund Laser Center, Sweden, the optimization of the pumping laser incidence angle resulted in a reduction of the required pumping energy for a Ni-like Mo XRL, which enabled the operation at a repetition rate of 10 Hz. Using the experiences gained there, the XRL performance at the PHELIX facility, GSI Darmstadt with respect to achievable repetition rate and at wavelengths below 20 nm was significantly improved, and also important information for the development towards multi-100 eV plasma XRLs was acquired. Due to the setup improvements achieved during the work for this thesis, the PHELIX XRL system now has reached a degree of reproducibility and versatility which is sufficient for demanding applications like the XRL spectroscopy of heavy ions. In addition, a European research campaign, aiming towards plasma XRLs approaching the water-window (wavelengths below 5 nm) was initiated.

Towards a new test of time dilation: Laser spectroscopy on lithium ions stored at a velocity of 33.8 % of the speed of light

The subject of the presented thesis is the accurate measurement of time dilation, aiming at a quantitative test of special relativity. By means of laser spectroscopy, the relativistic Doppler shifts of a clock transition in the metastable triplet spectrum of ^7Li^+ are simultaneously measured with and against the direction of motion of the ions. By employing saturation or optical double resonance spectroscopy, the Doppler broadening as caused by the ions' velocity distribution is eliminated. From these shifts both time dilation as well as the ion velocity can be extracted with high accuracy allowing for a test of the predictions of special relativity. A diode laser and a frequency-doubled titanium sapphire laser were set up for antiparallel and parallel excitation of the ions, respectively. To achieve a robust control of the laser frequencies required for the beam times, a redundant system of frequency standards consisting of a rubidium spectrometer, an iodine spectrometer, and a frequency comb was developed. At the experimental section of the ESR, an automated laser beam guiding system for exact control of polarisation, beam profile, and overlap with the ion beam, as well as a fluorescence detection system were built up. During the first experiments, the production, acceleration and lifetime of the metastable ions at the GSI heavy ion facility were investigated for the first time. The characterisation of the ion beam allowed for the first time to measure its velocity directly via the Doppler effect, which resulted in a new improved calibration of the electron cooler. In the following step the first sub-Doppler spectroscopy signals from an ion beam at 33.8 %c could be recorded. The unprecedented accuracy in such experiments allowed to derive a new upper bound for possible higher-order deviations from special relativity. Moreover future measurements with the experimental setup developed in this thesis have the potential to improve the sensitivity to low-order deviations by at least one order of magnitude compared to previous experiments; and will thus lead to a further contribution to the test of the standard model.

Construction and commissioning of a collinear laser spectroscopy setup at TRIGA Mainz and laser spectroscopy of magnesium isotopes at ISOLDE (CERN)

Collinear laser spectroscopy has been used as a tool for nuclear physics for more than 30 years. The unique possibility to extract nuclear properties like spins, radii and nuclear moments in a model-independent manner leads to important physics results to test the predictive power of existing nuclear models. rnThis work presents the construction and the commissioning of a new collinear laser spectroscopy experiment TRIGA-LASER as a part of the TRIGA-SPEC facility at the TRIGA research reactor at the University of Mainz. The goal of the experiment is to study the nuclear structure of radioactive isotopes which will be produced by neutron-induced fission near the reactor core and transported to an ion source by a gas jet system. rnThe versatility of the collinear laser spectroscopy technique will be exploited in the second part of this thesis. The nuclear spin and the magnetic moment of the neutron-deficient isotope Mg-21 will be presented, which were measured by the detection of the beta-decay asymmetry induced by nuclear polarization after optical pumping. A combination of this detection method with the classical fluorescence detection is then used to determine the isotope shifts of the neutron-rich magnesium isotopes from Mg-24 through Mg-32 to study the transition to the ''island of inversion''.

Laser driven proton acceleration and beam shaping

In the race to obtain protons with higher energies, using more compact systems at the same time, laser-driven plasma accelerators are becoming an interesting possibility. But for now, only beams with extremely broad energy spectra and high divergence have been produced. The driving line of this PhD thesis was the study and design of a compact system to extract a high quality beam out of the initial bunch of protons produced by the interaction of a laser pulse with a thin solid target, using experimentally reliable technologies in order to be able to test such a system as soon as possible. In this thesis, different transport lines are analyzed. The first is based on a high field pulsed solenoid, some collimators and, for perfect filtering and post-acceleration, a high field high frequency compact linear accelerator, originally designed to accelerate a 30 MeV beam extracted from a cyclotron. The second one is based on a quadruplet of permanent magnetic quadrupoles: thanks to its greater simplicity and reliability, it has great interest for experiments, but the effectiveness is lower than the one based on the solenoid; in fact, the final beam intensity drops by an order of magnitude. An additional sensible decrease in intensity is verified in the third case, where the energy selection is achieved using a chicane, because of its very low efficiency for off-axis protons. The proposed schemes have all been analyzed with 3D simulations and all the significant results are presented. Future experimental work based on the outcome of this thesis can be planned and is being discussed now.

Geomorphological and statistical analysis on Ravenna dune fields changes, based on Terrestrial Laser Technology

Coastal sand dunes represent a richness first of all in terms of defense from the sea storms waves and the saltwater ingression; moreover these morphological elements constitute an unique ecosystem of transition between the sea and the land environment. The research about dune system is a strong part of the coastal sciences, since the last century. Nowadays this branch have assumed even more importance for two reasons: on one side the born of brand new technologies, especially related to the Remote Sensing, have increased the researcher possibilities; on the other side the intense urbanization of these days have strongly limited the dune possibilities of development and fragmented what was remaining from the last century. This is particularly true in the Ravenna area, where the industrialization united to the touristic economy and an intense subsidence, have left only few dune ridges residual still active. In this work three different foredune ridges, along the Ravenna coast, have been studied with Laser Scanner technology. This research didn’t limit to analyze volume or spatial difference, but try also to find new ways and new features to monitor this environment. Moreover the author planned a series of test to validate data from Terrestrial Laser Scanner (TLS), with the additional aim of finalize a methodology to test 3D survey accuracy. Data acquired by TLS were then applied on one hand to test some brand new applications, such as Digital Shore Line Analysis System (DSAS) and Computational Fluid Dynamics (CFD), to prove their efficacy in this field; on the other hand the author used TLS data to find any correlation with meteorological indexes (Forcing Factors), linked to sea and wind (Fryberger's method) applying statistical tools, such as the Principal Component Analysis (PCA).

Development of a system measuring adhesion forces in powder collectives

Fine powders commonly have poor flowability and dispersibility due to interparticle adhesion that leads to formation of agglomerates. Knowing about adhesion in particle collectives is indispensable to gain a deeper fundamental understanding of particle behavior in powders. Especially in pharmaceutical industry a control of adhesion forces in powders is mandatory to improve the performance of inhalation products. Typically the size of inhalable particles is in the range of 1 - 5 µm. In this thesis, a new method was developed to measure adhesion forces of particles as an alternative to the established colloidal probe and centrifuge technique, which are both experimentally demanding, time consuming and of limited practical applicability. The new method is based on detachment of individual particles from a surface due to their inertia. The required acceleration in the order of 500 000 g is provided by a Hopkinson bar shock excitation system and measured via laser vibrometry. Particle detachment events are detected on-line by optical video microscopy. Subsequent automated data evaluation allows obtaining a statistical distribution of particle adhesion forces. To validate the new method, adhesion forces for ensembles of single polystyrene and silica microspheres on a polystyrene coated steel surface were measured under ambient conditions. It was possible to investigate more than 150 individual particles in one experiment and obtain adhesion values of particles in a diameter range of 3 - 13 µm. This enables a statistical evaluation while measuring effort and time are considerably lower compared to the established techniques. Measured adhesion forces of smaller particles agreed well with values from colloidal probe measurements and theoretical predictions. However, for the larger particles a stronger increase of adhesion with diameter was observed. This discrepancy might be induced by surface roughness and heterogeneity that influence small and large particles differently. By measuring adhesion forces of corrugated dextran particles with sizes down to 2 µm it was demonstrated that the Hopkinson bar method can be used to characterize more complex sample systems as well. Thus, the new device will be applicable to study a broad variety of different particle-surface combinations on a routine basis, including strongly cohesive powders like pharmaceutical drugs for inhalation.

Diffusion in heterogeneous systems studied by laser scanning confocal microscopy and fluorescence correlation spectroscopy

Understanding and controlling the mechanism of the diffusion of small molecules, macromolecules and nanoparticles in heterogeneous environments is of paramount fundamental and technological importance. The aim of the thesis is to show, how by studying the tracer diffusion in complex systems, one can obtain information about the tracer itself, and the system where the tracer is diffusing. rnIn the first part of my thesis I will introduce the Fluorescence Correlation Spectroscopy (FCS) which is a powerful tool to investigate the diffusion of fluorescent species in various environments. By using the main advantage of FCS namely the very small probing volume (<1µm3) I was able to track the kinetics of phase separation in polymer blends at late stages by looking on the molecular tracer diffusion in individual domains of the heterogeneous structure of the blend. The phase separation process at intermediate stages was monitored with laser scanning confocal microscopy (LSCM) in real time providing images of droplet coalescence and growth. rnIn a further project described in my thesis I will show that even when the length scale of the heterogeneities becomes smaller than the FCS probing volume one can still obtain important microscopic information by studying small tracer diffusion. To do so, I will introduce a system of star shaped polymer solutions and will demonstrate that the mobility of small molecular tracers on microscopic level is nearly not affected by the transition of the polymer system to a “glassy” macroscopic state. rnIn the last part of the thesis I will introduce and describe a new stimuli responsive system which I have developed, that combines two levels of nanoporosity. The system is based on poly-N-isopropylacrylamide (PNIPAM) and silica inverse opals (iOpals), and allows controlling the diffusion of tracer molecules. rn

Analyse der intrazellulären Freisetzung von Wirkstoffmodellen via konfokaler Laser-Raster-Mikroskopie

In der vorliegenden Arbeit wurde gezeigt, wie man das Potential nanopartikulärer Systeme, die vorwiegend via Miniemulsion hergestellt wurden, im Hinblick auf „Drug Delivery“ ausnutzen könnte, indem ein Wirkstoffmodell auf unterschiedliche Art und Weise intrazellulär freigesetzt wurde. Dies wurde hauptsächlich mittels konfokaler Laser-Raster-Mikrokopie (CLSM) in Kombination mit dem Bildbearbeitungsprogramm Volocity® analysiert.rnPBCA-Nanokapseln eigneten sich besonders, um hydrophile Substanzen wie etwa Oligonukleotide zu verkapseln und sie so auf ihrem Transportweg in die Zellen vor einem etwaigen Abbau zu schützen. Es konnte eine Freisetzung der Oligonukleotide in den Zellen aufgrund der elektrostatischen Anziehung des mitochondrialen Membranpotentials nachgewiesen werden. Dabei war die Kombination aus Oligonukleotid und angebundenem Cyanin-Farbstoff (Cy5) an der 5‘-Position der Oligonukleotid-Sequenz ausschlaggebend. Durch quantitative Analysen mittels Volocity® konnte die vollständige Kolokalisation der freigesetzten Oligonukleotide an Mitochondrien bewiesen werden, was anhand der Kolokalisationskoeffizienten „Manders‘ Coefficients“ M1 und M2 diskutiert wurde. Es konnte ebenfalls aufgrund von FRET-Studien doppelt markierter Oligos gezeigt werden, dass die Oligonukleotide weder beim Transport noch bei der Freisetzung abgebaut wurden. Außerdem wurde aufgeklärt, dass nur der Inhalt der Nanokapseln, d. h. die Oligonukleotide, an Mitochondrien akkumulierte, das Kapselmaterial selbst jedoch in anderen intrazellulären Bereichen aufzufinden war. Eine Kombination aus Cyanin-Farbstoffen wie Cy5 mit einer Nukleotidsequenz oder einem Wirkstoff könnte also die Basis für einen gezielten Wirkstofftransport zu Mitochondrien liefern bzw. die Grundlage schaffen, eine Freisetzung aus Kapseln ins Zytoplasma zu gewährleisten.rnDer vielseitige Einsatz der Miniemulsion gestattete es, nicht nur Kapseln sondern auch Nanopartikel herzustellen, in welchen hydrophobe Substanzen im Partikelkern eingeschlossen werden konnten. Diese auf hydrophobe Wechselwirkungen beruhende „Verkapselung“ eines Wirkstoffmodells, in diesem Fall PMI, wurde bei PDLLA- bzw. PS-Nanopartikeln ausgenutzt, welche durch ein HPMA-basiertes Block-Copolymer stabilisiert wurden. Dabei konnte gezeigt werden, dass das hydrophobe Wirkstoffmodell PMI innerhalb kürzester Zeit in die Zellen freigesetzt wurde und sich in sogenannte „Lipid Droplets“ einlagerte, ohne dass die Nanopartikel selbst aufgenommen werden mussten. Daneben war ein intrazelluläres Ablösen des stabilisierenden Block-Copolymers zu verzeichnen, welches rn8 h nach Partikelaufnahme erfolgte und ebenfalls durch Analysen mittels Volocity® untermauert wurde. Dies hatte jedoch keinen Einfluss auf die eigentliche Partikelaufnahme oder die Freisetzung des Wirkstoffmodells. Ein großer Vorteil in der Verwendung des HPMA-basierten Block-Copolymers liegt darin begründet, dass auf zeitaufwendige Waschschritte wie etwa Dialyse nach der Partikelherstellung verzichtet werden konnte, da P(HPMA) ein biokompatibles Polymer ist. Auf der anderen Seite hat man aufgrund der Syntheseroute dieses Block-Copolymers vielfältige Möglichkeiten, Funktionalitäten wie etwa Fluoreszenzmarker einzubringen. Eine kovalente Anbindung eines Wirkstoffs ist ebenfalls denkbar, welcher intrazellulär z. B. aufgrund von enzymatischen Abbauprozessen langsam freigesetzt werden könnte. Somit bietet sich die Möglichkeit mit Nanopartikeln, die durch HPMA-basierte Block-Copolymere stabilisiert wurden, gleichzeitig zwei unterschiedliche Wirkstoffe in die Zellen zu bringen, wobei der eine schnell und der zweite über einen längeren Zeitraum hinweg (kontrolliert) freigesetzt werden könnte.rnNeben Nanokapseln sowie –partikeln, die durch inverse bzw. direkte Miniemulsion dargestellt wurden, sind auch Nanohydrogelpartikel untersucht worden, die sich aufgrund von Selbstorganisation eines amphiphilen Bock-Copolymers bildeten. Diese Nanohydrogelpartikel dienten der Komplexierung von siRNA und wurden hinsichtlich ihrer Anreicherung in Lysosomen untersucht. Aufgrund der Knockdown-Studien von Lutz Nuhn konnte ein Unterschied in der Knockdown-Effizienz festgestellt werden, je nach dem, ob 100 nm oder 40 nm große Nanohydrogelpartikel verwendet wurden. Es sollte festgestellt werden, ob eine größenbedingte, unterschiedlich schnelle Anreicherung dieser beiden Partikel in Lysosomen erfolgte, was die unterschiedliche Knockdown-Effizienz erklären könnte. CLSM-Studien und quantitative Kolokalisationsstudien gaben einen ersten Hinweis auf diese Größenabhängigkeit. rnBei allen verwendeten nanopartikulären Systemen konnte eine Freisetzung ihres Inhalts gezeigt werden. Somit bieten sie ein großes Potential als Wirkstoffträger für biomedizinische Anwendungen.rn

Vibrational Relaxation of N2O (v2) by Atomic Oxygen Measured by Tunable Diode Laser Absorption Spectroscopy

Through the use of Transient Diode Laser Absorption Spectroscopy (TDLAS), the rate coefficient for the vibrational relaxation of N2O (ν2) by O(3P) at room temperature (32 ºC)) was determined to be (1.51 ± 0.11)x10-12 cm3molecule-1sec-1. A Q-switched, frequency quadrupled (266 nm) Nd:YAG laser pulse was used as the pump for this experiment. This pulse caused the photodissociation of O3 into O2 and O atoms.Excited oxygen (O(1D)) was collisionally quenched to ground state (O(3P)) by Ar and/or Xe. Photodissociation also caused a temperature jump within the system, exciting the ν2 state of N2O molecules. Population in the ν2 state was monitored through a TDLASobservation of a ν3 transition. Data were fit using a Visual Fortran 6.0 Global Fitting program. Analysis of room temperature data taken using only Ar to quench O atoms to the ground state gave the same rate coefficient as analysis of data taken using an Ar/Xe mixture, suggesting Ar alone is a sufficient bath gas. Experimentation was alsoperformed at -27 ºC and -82 ºC for a temperature dependence analysis. A linear regression analysis gave a rate coefficient dependence on temperature of ... for the rate coefficient of the vibrational relaxation of N2O (ν2) by atomic oxygen.

Detection of approximal caries with a new laser fluorescence device

The laser device DIAGNOdent developed for the detection of occlusal caries has limited value on approximal surfaces. The aim of this study was to develop and to test a new laser fluorescence (LF) device for the detection of approximal caries. Light with a wavelength of 655 nm was transported to the approximal surface using two different sapphire fibre tips. Seventy-five teeth were selected from a pool of extracted permanent human molars, frozen at -20 degrees C until use. Before being measured, they were defrosted, cleaned and calculus was removed with a scaler. The molars were set in blocks simulating the contact area of adults. Bitewing radiographs were obtained using Kodak Insight films. After two independent assessments with the new LF device, the teeth were histologically prepared, and assessed for caries extension. Using the laser, specificity values for D1 threshold (outer half of enamel), D2 threshold (inner half of enamel), D3 threshold (dentine) ranged between 0.81 and 0.93, sensitivity between 0.84 and 0.92 with no difference between the two tips. Bitewing radiography showed an inferior performance compared to LF (p<0.05). Intraex aminer reproducibility was high (kappa>.74). The new LF system might be a useful additional tool in detecting approximal caries. Because of its good reproducibility, it could be used to monitor caries regression or progression on approximal surfaces.

[The study of apoptosis factors released from laser injured cartilage inducing apoptosis of chondrocyte]

OBJECTIVE: To explore the role of pro-apoptotic signals following tissue injury and how these may promote a progression of further cell death. METHODS: Laser treated porcine articular cartilage disks were maintained in culture media. The collected media at various time periods (3, 6, 9, 12, 24 and 48 h), was called treated conditioned media (TCM). Non-laser treated cartilage disks were used to create control conditioned media (CCM). Each disk was subsequently maintained for 28 days and used in confocal microscopic assessment to document the progression of the damaged area. Isolated porcine chondrocytes were cultured in monolayer, and were exposed to TCM, CCM or normal culture medium (NM). As a positive inducer of apoptosis, the monolayer cells were exposed to UV radiation for 10 min and cultured in NM. Following 24 h exposure, the cells were harvested and stained with the appropriate combination of fluorescent dyes and processed via flow cytometry. RESULTS: All cultured cells exposed to TCM displayed a caspase-3 positive subpopulation, a loss of CMXRos, and with a reduced or lost NO signal. CCM exposure signals were comparable to the NM treatments with all having retained CMXRos, NO and without evidence of caspase-3 activity. UV treatment also induced a reduction in NO, but both CMXRos and caspase-3 positive, representing an earlier stage of apoptosis and suggesting that the mode of cell death via UV and TCM exposure are via different processes. The investigation of a dose (100%, 50%, 25% and 12.5%) and time (0.5, 1, 3, 9, 12 h) response to TCM exhibited that all treatments observed an increase in caspase-3 positive cells and a reduction in NO and CMXRos. CONCLUSION: The usefulness of FCM can be used in the study of cell viability and apoptosis. Such a system may be useful in the study of mechanisms of disease such as osteoarthritis, thus may be of practical use for the pharmaceutical industry for screening associated drugs.

Fading pdf of free-space optical communication system with pointing error

A free-space optical (FSO) laser communication system with perfect fast-tracking experiences random power fading due to atmospheric turbulence. For a FSO communication system without fast-tracking or with imperfect fast-tracking, the fading probability density function (pdf) is also affected by the pointing error. In this thesis, the overall fading pdfs of FSO communication system with pointing errors are calculated using an analytical method based on the fast-tracked on-axis and off-axis fading pdfs and the fast-tracked beam profile of a turbulence channel. The overall fading pdf is firstly studied for the FSO communication system with collimated laser beam. Large-scale numerical wave-optics simulations are performed to verify the analytically calculated fading pdf with collimated beam under various turbulence channels and pointing errors. The calculated overall fading pdfs are almost identical to the directly simulated fading pdfs. The calculated overall fading pdfs are also compared with the gamma-gamma (GG) and the log-normal (LN) fading pdf models. They fit better than both the GG and LN fading pdf models under different receiver aperture sizes in all the studied cases. Further, the analytical method is expanded to the FSO communication system with beam diverging angle case. It is shown that the gamma pdf model is still valid for the fast-tracked on-axis and off-axis fading pdfs with point-like receiver aperture when the laser beam is propagated with beam diverging angle. Large-scale numerical wave-optics simulations prove that the analytically calculated fading pdfs perfectly fit the overall fading pdfs for both focused and diverged beam cases. The influence of the fast-tracked on-axis and off-axis fading pdfs, the fast-tracked beam profile, and the pointing error on the overall fading pdf is also discussed. At last, the analytical method is compared with the previous heuristic fading pdf models proposed since 1970s. Although some of previously proposed fading pdf models provide close fit to the experiment and simulation data, these close fits only exist under particular conditions. Only analytical method shows accurate fit to the directly simulated fading pdfs under different turbulence strength, propagation distances, receiver aperture sizes and pointing errors.

Optimal beam forming for laser beam propagation through random media

Focusing optical beams on a target through random propagation media is very important in many applications such as free space optical communica- tions and laser weapons. Random media effects such as beam spread and scintillation can degrade the optical system's performance severely. Compensation schemes are needed in these applications to overcome these random media effcts. In this research, we investigated the optimal beams for two different optimization criteria: one is to maximize the concentrated received intensity and the other is to minimize the scintillation index at the target plane. In the study of the optimal beam to maximize the weighted integrated intensity, we derive a similarity relationship between pupil-plane phase screen and extended Huygens-Fresnel model, and demonstrate the limited utility of maximizing the average integrated intensity. In the study ofthe optimal beam to minimize the scintillation index, we derive the first- and second-order moments for the integrated intensity of multiple coherent modes. Hermite-Gaussian and Laguerre-Gaussian modes are used as the coherent modes to synthesize an optimal partially coherent beam. The optimal beams demonstrate evident reduction of scintillation index, and prove to be insensitive to the aperture averaging effect.