INVESTIGATION OF ELECTRIC DICHROISM OF CETYLPYRIDINIUM BROMIDE BY SPECTROELECTROCHEMISTRY WITH A LONG OPTICAL-PATH LENGTH THIN-LAYER CELL

In this paper, the electric dichroism of cetylpyridinium bromide (CPB) has been found and studied by spectroelectrochemistry with a long optical path length thin-layer cell (LOPTLC) for the first time. The CPB molecule with a long carbon chain and a polar pyridinium ring is anisotropic in molecular configuration or in polarizability. In the electric field of a thin-layer cell, the CPB molecule reorientates along the direction of the electric field and exhibits electric dichroism, which results in the increase of absorbance of CPB in the UV-vis range. By use of in situ measurement of spectroelectrochemistry, the order parameters of long molecular axis (S = 0.845) and short molecular axis (D = 0.155) and the angle between the long axis direction of the CPB molecule and the direction normal to the electrode surface (theta = 18-degrees 44') have been determined. These data were used to describe the state of arrangement of the molecules in the solution. The reorientation of CPB molecules is the result of the interaction between the anisotropic molecules and electric field. The effects of the concentration of CPB and of the applied electric field on the electric dichroism have been investigated.

ANISOTROPY OF OPTICAL-CONSTANTS OF YBCO

Otto configuration attenuated total reflection (ATR) measurements of the excitation of surface plasmons in the infrared have been carried out on YBCO films deposited on MgO (100) substrates. The dielectric constants for YBCO at 3.392 mu m are determined to be -10 + 15i for c-axis material. The anisotropic nature of the cuprate is seen from films with other orientations: nearly a-axis material has constants of 4.0 + 7.0i. It is thus not metallic in its optical response along the c-axis which lies parallel to the substrate plane. Ellipsometric measurements in the visible on c-axis material point to a maximum surface plasmon energy of 1 eV.

Far infrared reflectance and optical properties of organic superconductor (TMTSF)2ClO4 /

Polarized reflectance measurements of the quasi I-D charge-transfer salt (TMTSFh CI04 were carried out using a Martin-Puplett-type polarizing interferometer and a 3He refrigerator cryostat, at several temperatures between 0.45 K and 26 K, in the far infrared, in the 10 to 70 cm- 1 frequency range. Bis-tetramethyl-tetraselena-fulvalene perchlorate crystals, grown electrochemically and supplied by K. Behnia, of dimensions 2 to 4 by 0.4 by 0.2 mm, were assembled on a flat surface to form a mosaic of 1.5 by 3 mm. The needle shaped crystals were positioned parallel to each other along their long axis, which is the stacking direction of the planar TMTSF cations, exposing the ab plane face (parallel to which the sheets of CI04 anions are positioned). Reflectance measurements were performed with radiation polarized along the stacking direction in the sample. Measurements were carried out following either a fast (15-20 K per minute) or slow (0.1 K per minute) cooling of the sample. Slow cooling permits the anions to order near 24 K, and the sample is expected to be superconducting below 1.2 K, while fast cooling yields an insulating state at low temperatures. Upon the slow cooling the reflectance shows dependence with temperature and exhibits the 28 cm- 1 feature reported previously [1]. Thermoreflectance for both the 'slow' and 'fast' cooling of the sample calculated relative to the 26 K reflectance data indicates that the reflectance is temperature dependent, for the slow cooling case only. A low frequency edge in the absolute reflectance is assigned an electronic origin given its strong temperature dependence in the relaxed state. We attribute the peak in the absolute reflectance near 30 cm-1 to a phonon coupled to the electronic background. Both the low frequency edge and the 30 cm-1 feature are noted te shift towards higher frequcncy, upon cntering the superconducting state, by an amount of the order of the expected superconducting energy gap. Kramers-Kronig analysis was carried out to determine the optical conductivity for the slowly cooled sample from the measured reflectance. In order to do so the low frequency data was extrapolated to zero frequency using a Hagen-Ru bens behaviour, and the high frequency data was extended with the data of Cao et al. [2], and Kikuchi et al. [3]. The real part of the optical conductivity exhibits an asymmetric peak at 35 cm-1, and its background at lower frequencies seems to be losing spectral weight with lowering of the temperature, leading us to presume that a narrow peak is forming at even lower frequencies.

Optical properties of organic superconductor K-(BETS)2FeBr4 /

/c-(BETS)2FeBr4 is the first antiferromagnetic organic superconductor with successive antiferromagnetic and superconducting transitions at Ta^=2.5K and Tc=l.lK respectively at ambient pressure. Polarized reflectance measurements were performed on three single crystalsamples of this material using a Briiker IFS66V/S Interferometer, and a Bolometer detector or an MCT detector, at seven temperatures between 4K and 300K, in both the far-infrared and mid-infrared frequency range. After the reflectance results were obtained, the Kramers-Kronig dispersion relation was apphed to determine the optical conductivity of /c-(BETS)2FeBr4 at these seven temperatures. Additionally, the optical conductivity spectra were fitted with a Drude/Lorentz Oscillator model in order to study the evolution of the optical conductivity with temperature along the a-axis and c-axis. The resistivities calculated from the Drude model parameters along the a-axis and c-axis agreed reasonably with previous transport measurements.

Optical properties of organic superconductor K-(BETS)2FeBr4 /

K-(BETS)2FeBr4 is a quasi-2D charge transfer organic metal with interesting electronic and magnetic properties. It undergoes a transition to an antiferromagnetic (AF) state at ambient pressure at the Neel temperature (T^^) = 2.5 K, as well as to a superconducting (SC) state at 1.1 K [1]. The temperature dependence of the electrical resistivity shows a small decrease at T;v indicating the resistivity drops as a result of the onset of the ordering of Fe'*''" spins. A sharp drop in the resistivity at 1.1 K is due to its superconducting transition. The temperature dependence of the susceptibility indicates an antiferromagnetic spin structure with the easy axis parallel to the a-axis. The specific heat at zero-field shows a large peak at about 2.4 K, which corresponds to the antiferromagnetic transition temperature (Tat) and no anomaly is observed around the superconducting transition temperature (1.1 K) demonstrating that the magnetically ordered state is not destroyed by the appearance of another phase transition (the superconducting transition) in the 7r-electron layers [1], [2]. This work presents an investigation of how the low frequency electromagnetic response is affected by the antiferromagnetic and superconducting states, as well as the onset of strong correlation. The location of the easy axis of three samples was determined and polarized thermal reflectance measurements of these «-(BETS)2FeBr4 samples oriented with their vertical axis along the a- and c axes were then carried out using a *He refrigerator cryostat and a Martin-Puplett type polarizing interferometer at various temperatures (T = 0.5 K, 1.4 K. 1.9 K, 2.8 K) above and below the superconducting state and/or antiferromagnetic state. Comparison of the SC state to the normal state along the o- and c-axes indicates a rising thermal reflectance at low frequencies (below 10 cm"' ) which may be a manifestation of the superconducting energy gap. A dip-Hke feature is detected at low frequencies (below 15 cm"') in the thermal reflectance plots which probe the antiferromagnetic state along the two axes, and may be due to the opening of a gap in the excitation spectrum as a result of the antiferromagnetism. In another set of experiments, thermal reflectance measurements carried out along the a- and c-axes at higher temperatures (10 K-80 K) show that the reflectivity decreases with increasing temperature to 60 K (the coherence temperature) above which it increases again. Comparison of the thermal reflectance plots along the a- and c-axes at higher temperatures reveals an anisotropy between these two axes. The Hagen-Rubens thermal reflectance plots corresponding to an average over the ac-plane were calculated using experimental hterature resistivity values. Comparison of the Hagen-Rubens plots with the experimental thermal reflectance along the a- and c-axes indicates that both exhibit the general trend of a decrease in thermal reflectance with increasing frequency, however the calculated Hagen-Rubens thermal reflectance at different temperatures is much lower than the experimental curves.

Optical Properties of Sb2Te3, and Dilute Magnetic Semiconductors Sb1.97 VO.03 Te3 and Sb1.94 CrO.06 Te3

This thesis reports on the optical properties of the dilute magnetic semiconductors, Sb1.97 V 0.03 Te3 and Sb1.94Cr0.06Te3, along with the parent compound Sb2Te3' These materials develop a ferromagnetic state at low temperature with Curie temperatures of 22 K and 16 K respectively. All three samples were oriented such that the electric field vector of the light was perpendicular to the c-axis. The reflectance profile of these samples in the mid-infrared (500 to 3000 cm-1) shows a pronounced plasma edge which retracts with decreasing temperature. The far-infrared region of these samples exhibits a phonon at ~ 60 cm-1 which softens as temperature decreases. Kramers-Kronig analysis and a Drude-Lorentz model were employed to determine the optical constants of the bulk samples. The real part of the optical conductivity is shown to consist of intraband contributions at frequencies below the energy gap (~0.26 eV) and interband contributions at frequencies above the energy gap. The temperature dependence of the scattering rate show that a mix of phonon and impurity scattering are present, while the signature of traditional spin disorder (magnetic) scattering was difficult to confirm.

HI aperture synthesis and optical observations of the pair of galaxies NGC 6907 and 6908

NGC 6908, an S0 galaxy situated in the direction of NGC 6907, was only recently recognized as a distinct galaxy, instead of only a part of NGC 6907. We present 21-cm radio synthesis observations obtained with the Giant Metrewave Radio Telescope (GMRT) and optical images and spectroscopy obtained with the Gemini-North telescope of this pair of interacting galaxies. From the radio observations, we obtained the velocity field and the H I column density map of the whole region containing the NGC 6907/8 pair, and by means of the Gemini multi-object spectroscopy we obtained high-quality photometric images and 5 angstrom resolution spectra sampling the two galaxies. By comparing the rotation curve of NGC 6907 obtained from the two opposite sides around the main kinematic axis, we were able to distinguish the normal rotational velocity field from the velocity components produced by the interaction between the two galaxies. Taking into account the rotational velocity of NGC 6907 and the velocity derived from the absorption lines for NGC 6908, we verified that the relative velocity between these systems is lower than 60 km s(-1). The emission lines observed in the direction of NGC 6908, not typical of S0 galaxies, have the same velocity expected for the NGC 6907 rotation curve. Some emission lines are superimposed on a broader absorption profile, which suggests that they were not formed in NGC 6908. Finally, the H I profile exhibits details of the interaction, showing three components: one for NGC 6908, another for the excited gas in the NGC 6907 disc and a last one for the gas with higher relative velocities left behind NGC 6908 by dynamical friction, used to estimate the time when the interaction started in (3.4 +/- 0.6) x 10(7) yr ago.

DFT study of the electronic, vibrational, and optical properties of SnO(2)

We report results on the electronic, vibrational, and optical properties of SnO(2) obtained using first-principles calculations performed within the density functional theory. All the calculated phonon frequencies, real and imaginary parts of complex dielectric function, the energy-loss spectrum, the refractive index, the extinction, and the absorption coefficients show good agreement with experimental results. Based on our calculations, the SnO(2) electron and hole effective masses were found to be strongly anisotropic. The lattice contribution to the low-frequency region of the SnO(2) dielectric function arising from optical phonons was also determined resulting the values of E > (1aSyen) (latt) (0) = 14.6 and E > (1ayen) (latt) (0) = 10.7 for directions perpendicular and parallel to the tetragonal c-axis, respectively. This is in excellent agreement with the available experimental data. After adding the electronic contribution to the lattice contribution, a total average value of E >(1)(0) = 18.2 is predicted for the static permittivity constant of SnO(2).

UV optical absorption spectra analysis of beryl crystals from Brazil

The spectral decomposition analysis was applied to the optical absorption spectra of green and colorless beryl crystals from the Brazilian Eastern Pegmatitic province in the natural state, Submitted to heat treatment and irradiated with UV light The attributions of the lines were made taking into account highly accurate quantum mechanical calculations The deconvolution of the green beryl spectra revealed four lines, two of them around 12,000 cm(-1) (1 5eV) and two of them around 34,000 cm(-1) (4.2 eV) attributed to Fe(2+) and Fe(3+), respectively The deconvolution of the colorless beryl spectra without any treatment, after heating and for the same heat treatment followed by UV light irradiation revealed five lines The analysis of ratio relations showed that the lines at 36,400 cm(-1) (4.5 eV) and 41,400 cm(-1) (5 1 eV) belongs to a single defect attributed to a silicon dangling bond defect (=Si). Discussions and comparison with reported defects in quartz have supported the allocation of the lines at 61,000 cm(-1) (7.6 eV) and 43,800 cm(-1) (5 4 eV) to diamagnetic oxygen vacancy defect ( Si-Si ) and unrelaxed ( Si Si ) defect, respectively Finally, the line at 39.100 cm(-1) (4.8 eV), quite polarized along the c-axis, was attributed to a (Fe(2+) OH(-)) defect in the structural channels (C) 2009 Elsevier B V All rights reserved

The optical absorption edge of nanocrystalline Ga(1-x)Mn(x)N films deposited by reactive sputtering

We have focused on the optical absorption edge of nanocrystalline Ga(1-x)Mn(x)N (0.00 <= x <= 0.18) films deposited by reactive RF magnetron sputtering. The films obtained are nanocrystalline with grain sizes of about 25 nm, having wurtzite structure and strong orientation texture in the c-axis direction. The optical characterizations of the absorption edges were obtained in the 190-2600 nm spectral range. The increase of the Mn content causes an increase of the absorption coefficient which can be clearly noticed at low energies, and a quasi-linear decrease of the optical gap. Broad absorption bands observed around similar to 1.3 and similar to 2.2 eV were associated with transitions between the Mn acceptor level and the valence and conduction bands, respectively. The observed changes in the optical properties due to the Mn incorporation observed in these nanocrystalline films are similar to those reported for ferromagnetic GaMnN single-crystal films.

Structural electrical and optical properties of undoped and indium doped ZnO thin films prepared by the pyrosol process at different temperatures

The influence of the substrate temperature on the structural features and opto-electrical properties of undoped and indium-doped ZnO thin films deposited by pyrosol process was investigated. The addition of indium induces a drastic decrease (by a factor approximate to 10(10) for samples deposited at 300 degreesC) in the electrical resistivity of films, the lowest electrical resistivity (6 mOmega-cm) being observed for the film deposited at 450 degreesC. Films are highly transparent (>80%) in the Vis-NIR ranges, and the optical band gap exhibits a blue shift (from 3.29 to 3.33 eV) for the In-doped films deposited at increasing temperature. Preferential orientation of the ZnO crystallites with the c-axis perpendicular to the substrate surface and an anisotropic morphology of the nanoporous structure was observed for films growth at 300 and 350 degreesC. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Beyond the diffraction limit of optical/IR interferometers I. Angular diameter and rotation parameters of Achernar from differential phases

Context. Spectrally resolved long-baseline optical/IR interferometry of rotating stars opens perspectives to investigate their fundamental parameters and the physical mechanisms that govern their interior, photosphere, and circumstellar envelope structures. Aims. Based on the signatures of stellar rotation on observed interferometric wavelength-differential phases, we aim to measure angular diameters, rotation velocities, and orientation of stellar rotation axes. Methods. We used the AMBER focal instrument at ESO-VLTI in its high-spectral resolution mode to record interferometric data on the fast rotator Achernar. Differential phases centered on the hydrogen Br gamma line (K band) were obtained during four almost consecutive nights with a continuous Earth-rotation synthesis during similar to 5h/night, corresponding to similar to 60 degrees position angle coverage per baseline. These observations were interpreted with our numerical code dedicated to long-baseline interferometry of rotating stars. Results. By fitting our model to Achernar's differential phases from AMBER, we could measure its equatorial radius R-eq = 11.6 +/- 0.3 R-circle dot, equatorial rotation velocity V-eq = 298 +/- 9 km s(-1), rotation axis inclination angle i = 101.5 +/- 5.2 degrees, and rotation axis position angle (from North to East) PA(rot) = 34.9 +/- 1.6 degrees. From these parameters and the stellar distance, the equatorial angular diameter circle divide(eq) of Achernar is found to be 2.45 +/- 0.09 mas, which is compatible with previous values derived from the commonly used visibility amplitude. In particular, circle divide(eq) and PA(rot) measured in this work with VLTI/AMBER are compatible with the values previously obtained with VLTI/VINCI. Conclusions. The present paper, based on real data, demonstrates the super-resolution potential of differential interferometry for measuring sizes, rotation velocities, and orientation of rotating stars in cases where visibility amplitudes are unavailable and/or when the star is partially or poorly resolved. In particular, we showed that differential phases allow the measurement of sizes up to similar to 4 times smaller than the diffraction-limited angular resolution of the interferometer.

Retrieval of trace gases vertical profile in the lower atmosphere combining. Differential Optical Absorption Spectroscopy with radiative transfer models

The motivation for the work presented in this thesis is to retrieve profile information for the atmospheric trace constituents nitrogen dioxide (NO2) and ozone (O3) in the lower troposphere from remote sensing measurements. The remote sensing technique used, referred to as Multiple AXis Differential Optical Absorption Spectroscopy (MAX-DOAS), is a recent technique that represents a significant advance on the well-established DOAS, especially for what it concerns the study of tropospheric trace consituents. NO2 is an important trace gas in the lower troposphere due to the fact that it is involved in the production of tropospheric ozone; ozone and nitrogen dioxide are key factors in determining the quality of air with consequences, for example, on human health and the growth of vegetation. To understand the NO2 and ozone chemistry in more detail not only the concentrations at ground but also the acquisition of the vertical distribution is necessary. In fact, the budget of nitrogen oxides and ozone in the atmosphere is determined both by local emissions and non-local chemical and dynamical processes (i.e. diffusion and transport at various scales) that greatly impact on their vertical and temporal distribution: thus a tool to resolve the vertical profile information is really important. Useful measurement techniques for atmospheric trace species should fulfill at least two main requirements. First, they must be sufficiently sensitive to detect the species under consideration at their ambient concentration levels. Second, they must be specific, which means that the results of the measurement of a particular species must be neither positively nor negatively influenced by any other trace species simultaneously present in the probed volume of air. Air monitoring by spectroscopic techniques has proven to be a very useful tool to fulfill these desirable requirements as well as a number of other important properties. During the last decades, many such instruments have been developed which are based on the absorption properties of the constituents in various regions of the electromagnetic spectrum, ranging from the far infrared to the ultraviolet. Among them, Differential Optical Absorption Spectroscopy (DOAS) has played an important role. DOAS is an established remote sensing technique for atmospheric trace gases probing, which identifies and quantifies the trace gases in the atmosphere taking advantage of their molecular absorption structures in the near UV and visible wavelengths of the electromagnetic spectrum (from 0.25 μm to 0.75 μm). Passive DOAS, in particular, can detect the presence of a trace gas in terms of its integrated concentration over the atmospheric path from the sun to the receiver (the so called slant column density). The receiver can be located at ground, as well as on board an aircraft or a satellite platform. Passive DOAS has, therefore, a flexible measurement configuration that allows multiple applications. The ability to properly interpret passive DOAS measurements of atmospheric constituents depends crucially on how well the optical path of light collected by the system is understood. This is because the final product of DOAS is the concentration of a particular species integrated along the path that radiation covers in the atmosphere. This path is not known a priori and can only be evaluated by Radiative Transfer Models (RTMs). These models are used to calculate the so called vertical column density of a given trace gas, which is obtained by dividing the measured slant column density to the so called air mass factor, which is used to quantify the enhancement of the light path length within the absorber layers. In the case of the standard DOAS set-up, in which radiation is collected along the vertical direction (zenith-sky DOAS), calculations of the air mass factor have been made using “simple” single scattering radiative transfer models. This configuration has its highest sensitivity in the stratosphere, in particular during twilight. This is the result of the large enhancement in stratospheric light path at dawn and dusk combined with a relatively short tropospheric path. In order to increase the sensitivity of the instrument towards tropospheric signals, measurements with the telescope pointing the horizon (offaxis DOAS) have to be performed. In this circumstances, the light path in the lower layers can become very long and necessitate the use of radiative transfer models including multiple scattering, the full treatment of atmospheric sphericity and refraction. In this thesis, a recent development in the well-established DOAS technique is described, referred to as Multiple AXis Differential Optical Absorption Spectroscopy (MAX-DOAS). The MAX-DOAS consists in the simultaneous use of several off-axis directions near the horizon: using this configuration, not only the sensitivity to tropospheric trace gases is greatly improved, but vertical profile information can also be retrieved by combining the simultaneous off-axis measurements with sophisticated RTM calculations and inversion techniques. In particular there is a need for a RTM which is capable of dealing with all the processes intervening along the light path, supporting all DOAS geometries used, and treating multiple scattering events with varying phase functions involved. To achieve these multiple goals a statistical approach based on the Monte Carlo technique should be used. A Monte Carlo RTM generates an ensemble of random photon paths between the light source and the detector, and uses these paths to reconstruct a remote sensing measurement. Within the present study, the Monte Carlo radiative transfer model PROMSAR (PROcessing of Multi-Scattered Atmospheric Radiation) has been developed and used to correctly interpret the slant column densities obtained from MAX-DOAS measurements. In order to derive the vertical concentration profile of a trace gas from its slant column measurement, the AMF is only one part in the quantitative retrieval process. One indispensable requirement is a robust approach to invert the measurements and obtain the unknown concentrations, the air mass factors being known. For this purpose, in the present thesis, we have used the Chahine relaxation method. Ground-based Multiple AXis DOAS, combined with appropriate radiative transfer models and inversion techniques, is a promising tool for atmospheric studies in the lower troposphere and boundary layer, including the retrieval of profile information with a good degree of vertical resolution. This thesis has presented an application of this powerful comprehensive tool for the study of a preserved natural Mediterranean area (the Castel Porziano Estate, located 20 km South-West of Rome) where pollution is transported from remote sources. Application of this tool in densely populated or industrial areas is beginning to look particularly fruitful and represents an important subject for future studies.

Metastability exchange optical pumping in 3 He gas up to 30 mT: Efficiency measurements and evidence of laser-induced nuclear relaxation

Advances in metastability exchange optical pumping (MEOP) of 3He at high laser powers, with its various applications, but also at high gas pressures p3 and high magnetic field strengths B, have provided strong motivation for revisiting the understanding and for investigating the limitations of this powerful technique. For this purpose, we present systematic experimental and theoretical studies of efficiency and of relaxation mechanisms in B≤30 mT and p3=0.63−2.45 mbar. 3He nuclear polarisation is measured by light absorption in longitudinal configuration where weak light beams at 1083 nm parallel to magnetic field and cell axis with opposite circular polarisations are used to probe the distribution of populations in the metastable state. This method is systematically tested to evaluate potential systematic biases and is shown to be reliable for the study of OP dynamics despite the redistribution of populations by OP light. Nuclear polarisation loss associated to the emission of polarised light by the plasma discharge used for MEOP is found to decrease above 10 mT, as expected, due to hyperfine decoupling in highly excited states. However, this does not lead to improved MEOP efficiency at high laser power. We find clear evidence of additional laser-induced relaxation instead. The strong OP-enhanced polarisation losses, currently limiting MEOP performances, are quantitatively investigated using an angular momentum budget approach and a recently developed comprehensive model that describes the combined effects of OP, ME and relaxation, validated by comparison to experimental results.

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.