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The structure and properties of mixed monolayer or LB film of 5,10,15,20-tetra-4-oxy(2-stearic acid)phenyl porphyrin/C60 were studied. π-A isotherms and small angle X-ray diffraction (SAXD) results show that C60 molecules were incorporated into the cavities of porphyrin molecules in mixed monolayer and LB film. UV-vis spectra of mixed LB films show that the absorption intensity of porphyrin varied compared with pure porphyrin film, probably arising from the interactions between C60 and porphyrin ring. C60 molecules in mixed systems are well-dispersed. The TPP(CO2H)/C60 mixed LB film is a kind of two-dimensional host-guest system.

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length xi and the roughness exponent alpha, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with alpha = 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.

Starting from the electromagnetic wave equations and boundary conditions and using Green's integral theorem, we implement the rigorous numerical solutions of the speckle field produced by scattering of dielectric random surfaces in the optical near-field. The average sizes of speckle granules are enlarged very quickly with the increase of the distance in the range less than a wavelength. It is found that the speckle contrast in the near-field and in the neighbourhood region is inversely proportional to the square of lateral correlation length at its large values and linearly decreases with the roughness exponent.

The growth front evolution of ZrO2 thin films deposited by electronic beam evaporation has been studied with atomic force microscopy. The dynamic scaling characteristics are observed during the deposition process. After numerical correlation analysis, the roughness exponent α = 0.80±0.005 and the growth exponent β = 0.141 are all obtained. Based on these results, we suggest that the growth of ZrO2 thin films can be described by the combination of the Edwards-Wilkinson equation, the Mullins diffusion equation and the shadowing effect.

A method for the extracting the correlation functions of random surfaces is proposed by using the image speckle intensity. Theoretically, we analyse the integral expression of average intensity of the image speckles, and compare it with the pair of Fourier-Bessel-transform-and-the-inversion of the exponential function of the height-height correlation function of the random surfaces. Then the algorithm is proposed numerically to complement the lacking Bessel function factor in the expression of the average speckle intensity, which changes the intensity data into the pair of the Fourier-Bessel-transform. Experimentally, we measure the average image speckle intensities versus the radius of the filtering aperture in the 4f system and extract the height-height correlation function by using the proposed algorithm. The results of the practical measurements for three surface samples and the comparison with those by atomic force microscopy validate the feasibility of this method.

We study the evolution of (2+1)-dimensional surface morphology in the Kuramoto-Sivashinsky (K-S) model by using the numerical simulation approach. The results show that the surface morphology has the self-affine fractal properties and exhibits cellular structure after long time growth. With numerical correlation analysis, we explicitly observe the dynamic scaling characteristics and obtain the roughness exponent to be 0.77±0.07, the growth exponent to be 0.28 and 0.43, and the dynamic exponents 0.31 and 0.46, for the early times and later times. The simulating results are consistent with the theoretical values in the K-S model.

We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces. We use the mathematical decay function to approximate the duple negative exponent function in the rigorous theory of scattering, by letting them have the same maximum value and half-width, and the expression for the half-widths of the intensity profiles in the whole range of the perpendicular wave vector component is obtained. The previous results in the two extreme cases are included in the results of this paper. In the simulational verification, we propose a method for the generation of self-affine fractal random surfaces, using the square-root of Fourier transform of the correlation function of the surface height. The simulated results conform well with the theory.

Properties of movement and the boiling of dynamic partially coherent speckles are investigated. Theoretical analysis of the correlation functions shows that in front of and behind the Fraunhofer plane, the directions of the movement of the dynamics partially coherent speckles are the same and opposite to that of the object, respectively. The boiling occurs according to a parabolic factor with respect to time separation τ. These properties are observed experimentally by using an elaborately chosen extended source to meet the requirement of intensity and coherence. The boiling of the speckles is measured with the photon counting system, which is refitted for the automatic data acquisition, and the experimental results are confirmed by the theory.

Theoretical analysis shows that the deviation roughness w and the lateral correlation length ξ of a weak scattering object determine the different properties of the contrast of the speckles in the image plane of a 4f system. Experimentally, we have measured the data of the speckle contrast versus the radius R of the variable filtering aperture. By fitting the theoretical results to these data, we extract the parameters w and ξ of the random surfaces with Gaussian correlation. This method can determine the two parameters simultaneously and independently, and pre-calibrations are not needed.

A shock-accelerated flying foil is diagnosed with a chirped pulse spectral interferometry. The shock is pumped by a 1.2 ps chirped laser pulse with a power of ~1014 W/cm2 at 785 nm irradiating on a 500 nm aluminium film and detected by a probe pulse split from the pump based on a Michelson spectral interferometry. A flying foil of ~5.595×10-6 g in ~400 µm diameter was accelerated to ~165 nm away from the initial target rear surface at ~1.83 km/s before ablation.

We propose a method for the generation of self-affine fractal random surfaces, in which we use Fourier transform and its inversion in the algorithm. The light scattering of surfaces of this kind is simulated at different incident angles of illumination. The variation of the full width at half maximum (FWHM) of the intensity profile versus the perpendicular component k⊥ of the wave-vector shows clearly the characteristics of the surfaces parameters. The simulation demonstrates how the value of FWHM at k2⊥w2 >1 region are used, respectively, to extract the lateral correlation length ξ and the roughness exponent α.

Based on the interference patterns of the speckle field and the reference beam recorded by the charge-coupled device, and the digital Fourier transform technique, the complex amplitudes and phases of speckle field produced at different scattering angles are extracted. The phase distribution and the statistical properties at the singular point, such as the angle between two zero-contour lines of real part and imaginary part of the complex amplitude, the eccentricity of the intensity contours, etc. are studied. We find that there are some special properties of phase singularity when the scattering angle is large enough. With the increase of the scattering angle, great changes have taken place in the spatial distributions of the amplitude and the phase, and the probability of the angle between two zero-contour lines of real part and imaginary part is close to a smaller value, and the average eccentricity of the intensity contours around the phase singularity gradually increase. Moreover, the most interesting thing is that the eccentricity is probably greater than 1 in large anger scattering. The phase singular line as a new kind of phase singularity is found at a large scattering angle; the phase mutation rules and the vortex distribution characteristics of the phase on both sides of the phase singular line are investigated, and the hyperbolic or parabolic shape intensity contour around the phase singular line is found.

The near-field distribution of a light wave in a metal-coated optical fiber probe under the illumination of femtosecond laser pulses is numerically simulated. By choosing the maximum of the calculated light field data and the time when the light field reaches the maximum in a time period of one light wave cycle at each spatial point, we obtain the amplitude and phase distributions of the light field near the probe. We find that the output amplitude distribution of y-polarization has roughly a circled-cross-like pattern with two arc-like zero-amplitude zones. The zeros of light intensity are the phase singularities at which the phase is undefined. By analyzing the output phase distribution of y-polarization, we obtain the temporal evolution of the phase singularities and their characteristics

Based on the coherent superposition principle of direct-transmited light with the Gaussian speckle field, and also with the Kirchhoff approximation, the speckle in the deep Fresnel diffraction region is investigated. Expressions of speckle field in the deep Fresnel diffraction region, and the probability density of intensity, and contrast are obtained. In the deep Fresnel diffraction region of different scattering distance the variation of speckles is simulated with the height distribution data of random scattering surface measured by atomic force microscopy, and the curves of these two statistic functions are drawn. Combining the theory with the simulation, characteristics of these two statistic functions, the effect of the fraction of the direct transmit light intensity as well as their variations with the scattering distance are discussed.

We study the light scattering of an orthogonal anisotropic rough surface with secondary most probable slope distribution. It is found that the scattered intensity profiles have obvious secondary maxima, and in the direction perpendicular to the plane of incidence, the secondary maxima are oriented in a curve on the observation plane, which is called the orientation curve. By numerical calculation of the scattering wave fields with the height data of the sample, it is validated that the secondary maxima are induced by the side face element, which constitutes the prismoid structure of the anisotropic surface. We derive the equation of the quadratic orientation curve. Experimentally, we construct the system for light scattering measurement using a CCD. The scattered intensity profiles are extracted from the images at different angles of incidence along the orientation curves. The experimental results conform to the theory.

Using the interference of speckle and the spherical reference wave, we extract the real and the imaginary parts of the complex amplitudes of the speckle in large angle scattering. By calculating the spatial correlation functions of intensity, we find that the speckle has a property of regional fractality, i.e. the fractal exponent equals 1 in a small spatial region and it becomes less than 1 in a bigger region. The empirical analytic expression of the intensity correlation function is gained. The probability density distributions of the intensities and the complex amplitudes show that the regional fractal speckle still obeys zero-mean circular complex Gaussian statistics.

We calculate the light field in metal-coated optical fiber probes under illumination of femtosecond laser pulses with the three-dimensional finite-difference time-domain method. By choosing the maximum of the calculated light field data in the time period of one light wave cycle at each spatial point, we obtain the amplitude distributions instead of the conventional light field distribution of a time instant. It is found that with an incident plane wave pulse of y-polarization, the output amplitude distributions of y-polarization have roughly a circled-cross-like pattern with two arc-like zero-amplitude zones. By analyzing the y-polarized waveforms versus time at the points near the arc-like zero-amplitude zones, we find that waveform distortions appear at points in the neighborhood of the zero amplitude lines and in the time intervals when two wave-packets overlap.

The intensity distribution and phase vortices of the speckle fields generated by multi-aperture random scattering screens are simulated, and it is found that the vortices exhibit layer-like structures and the dislocation phenomena occur in the local phase patterns produced by the two-pinhole aperture, whose phase distributions appear as striped structures. For three- or four-pinhole aperture, there are many circular bright spots appearing in the speckle grains, and there is one vortex between the neighboring circular bright spots. The positive and negative phase vortex lattices appear in the phase distributions, and the regions circled by the isothetic phase lines form irregular quadrilaterals or hexagons. Moreover, the relative positions of the vortices or bright spots can be adjusted by changing those of the pinhole apertures.

The phase and the zero-contour of the real part and the imaginary part of the interference field on a far-field plane generated by multi-aperture diffraction screen are simulated. It is found that when the orbital angular momentum quantum number of incident beam is equal to zero, at the center of interference field the zero-lines cannot cross each other, therefore, thereby the phase vortices cannot form. When the orbital angular momentum quantum numbers of incident beam are opposite to each other in sign, namely -1 and +1 at the center of interference field the zero-lines are perpendicular to and cross each other, the signs of the phase vortices at the corresponding positions in interference fields are also opposite to each other. When the orbital angular momentum quantum numbers of incident beam are equal to ±2 and ±3, there are four zero-lines that cross each other at the center of interference fields, where the topological charge values of phase vortices are just equal to the orbital angular momentum quantum numbers of the Laguerre-Gaussian beam. Therefore, these results can be used to measure the orbital angular momentum of optical vortex beam.

A method for simultaneously extracting the parameters of self-affine fractal surfaces from a single experimental profile of scattered intensity data is proposed. The Levenberg–Marquardt algorithm is introduced to fit the theoretical equation for the scattering intensity profile to the experimental data. A precision system is designed for acquisition of scattering intensity data using the Boxcar integration technique. The surface parameters extracted (root-mean-square roughness ω, lateral correlation length ξ, and roughness exponent α) are compared to those obtained using atomic force microscopy.

By recording the interference patterns of the speckle fields and the reference beam with the charge coupled device （CCD）, and by using the digital Fourier transform technique, the amplitude and the phase distribution of the speckle fields are experimentally extracted. We find that at the tangential points of the zero curves of the real and the imaginary parts, a new kind of speckle phase singularities may appear. Different from the conventional singularities at the zero crossings of the real and imaginary parts with the monotonically spiral change of phase, this new kind of singularities has the property that the phase undergoes an increase and then a decrease around the singular point with nearly a symmetric distribution. We introduce the concept of quasi twin phase vortices to explain the formation of the new kind of phase vortices. Based on a theoretical study of the longitudinal autocorrelation function of the speckle intensities, we experimentally observe the propagation of the phase vortices of speckles. It is found that in planes at different propagation distances but within a longitudinal correlation length, the real and the imaginary parts of the complex speckle field vary considerably, but the position of the phase vortices and the angle of the zero crossings of the real and imaginary parts remain unchanged.

Using the three-dimensional finite difference time domain （3D-FDTD） method, we calculate light field in metal-coated optical fiber probes with different taper angles and different lengths under illumination of femtosecond laser pulses. The transmission of temporal fields of the laser pulses propagating in the probes and the properties of their frequency spectrum and phases are studied. The influences of the taper angle and the length of the probe on these properties are analyzed. The calculation results show that the structure of probe leads to the broadening, amplitude oscillation and the spectrum splitting of the laser pulses. With the analysis of the spectrum and the phase variation, we give a preliminary explanation to the phenomena of the pulse broadening and the periodic variation of the pulse amplitude with time.

Using the interference patterns of speckle fields and the reference beam, we extract digitally the complex amplitudes, phases and intensities of speckles fields and then study experimentally their properties. The influences of noise on the measurement of statistical functions, especially on that of the probability density function, appearing in the conventional method is satisfactorily eliminated. The experimental studies of the statistical properties of the complex amplitude and the phases of the speckle fields were also performed. By the practical measurement of speckle fields scattered at different angles, we find that the speckles are laterally broadened gradually with increase of the scattering angle, and their average widths become anisotropic. Such anisotropy brings about no change in the probability density function of the speckle fields, which remain circularly Gaussian as in the case of the traditional small angle scattering.

The two-dimensional speckle field and the phase produced by the Gaussian correlation random surfaces on the Fraunhofer plane were simulated. It was found that the zero-contour of the real and imaginary parts can be in the tangent and superposition situations besides the traditional intersection situation. The tangential points and the superposition-lines can also form phase singularities, around which the phase distribution shows the characteristics of discontinuity and symmetry and differs from the spiral distribution around the traditional singular points formed by the zero crossings of the real and imaginary parts. With the propagation of the optical wave, the relative positions of the zero-contour of the real and imaginary parts change from tangent to superposition, and then to intersection on the different observation plane with the simultaneously changes of the the phase singularities.

We study the statistical properties of the image speckles produced by strongscattering objects in the 4f optical imaging system. Using the generic expression of the complex amplitude of speckles and the approximation of the doubleexponential function, we first obtain the ensemble average of the speckle intensity. Then we derive the variance of the speckle intensity based on the rotational transformation of the real and imaginary parts of the complex amplitude of speckles. We finally obtain the expression for the contrast of the speckles, which is explicitly related to the statistical parameters of random surface and to the parameters of the imaging system. Our results are an obvious improvement compared with those reported in the literature, where the relations including such implicit quantities as the average size of the scattering grains of the random surface and the number of scattering grains are usually used. The results of this paper would be helpful for the characterization of random surface by speckle contrast.

Starting from the Helmholtz Equation, we obtain the integral equations of the light field at the medium interfaces by use of Green's theorem. Then the integral equations are discretized into a linear equation set, from which the values of the light field and its derivatives at the interface can be numerically solved. We also obtain the expression for the transmissive light waves from the Green's-function integral in the case of Kirchhoff's approximation. By an analogy to the derivation process of the autocorrelation functions of speckles in Frauhofer plane, we propose the method for the generation of random self-affine fractal surfaces and Fourier transformation method for the numerical derivative of random surfaces. Then we study the accuracy of Kirchhoff's approximation in the scattering of light field from the random self-affine fractal surface. We find that the accuracy of Kirchhoff's approximation is relatively high when the root-mean-square roughness w is small. for random surfaces with the same value of w but smaller values of roughness exponent α, the Kirchhoff's approximation gives higher accuracy in the calculation of scattered light fields. We believe that the results of this paper would be of significance in understanding the validity range of the Kirchhoff's approximation when it is applied to light scattering from self-affine random surfaces.

We have studied the properties of the dynamic partially coherent speckles in the Fresnel and Fraunhofer diffraction regions. We use the theory of propagation of the mutual intensity in partially coherent light, and derive the general form of the spatio-temporal cross-correlation functions of the dynamic speckle intensities produced by a moving diffusing object. Based on these theoretical expressions, the characteristics of the movement and the boiling of the dynamic partially coherent speckles are discussed. By choosing the proper extended incoherent light source and by adjusting the parameters of the optical setup, we have observed experimentally the partially coherent speckle in the Fresnel and Fraunhofer diffraction regions. Then we study qualitatively the movement and the boiling of the speckles. Using techniques of photon counting and automatic data acquisition, we have measured the temporal evolution of the speckle intensity in the Fraunhofer plane as the object moves, and thus measured the cross-correlation of the speckles versus the temporal increment. The experimental data are in agreement with the theoretical results.

Using the Gaussian correlation model of random surfaces, we conduct the theoretical derivation of the image-plane intensity produced by a weak scatterer in the 4f optical filtering system.Then the method is proposed for characterizing the square-root-mean deviation roughness and lateral correlation length.This method uses the derived theoretical expressions to fit the experimentally measured curve of image speckle intensity versus the radius of filtering aperture,and the two surface parameters can be extracted simultaneously.In the experiment,random surface samples are specially made and their surface parameters are measured. The results conforms with those obtained by atomic force microscopy,which shows that the method of this paper is of good accuracy.

Good adherent indium-tin oxide (ITO) (10wt% SnO2 impurity) films with a transmittance of about 80% in visible range and resistivity as low as 6.3×10-4Ωcm,were deposited on water-cooled PPA (Polypropylene adipate) substrate by bias r.f. magnetron sputtering.The transmittance in wavelength range of 300—550nm of these films was found to increase with the negative bias applied to the substrate.All these films have a preferred orientation of [222].The X-ray diffraction peaks of [200] decrease with increasing negative bias of the substrate.This means the number of crystal grains growing along [400] decreases.The grain sizes,as well as the conductivities of the films have a maximum value indicated by both AFM microscopy and XRD pattern in the range of -20—-40V of the bias applied to the substrate.The proper working pressure of argon is about 0.5—1Pa,and the proper impurity density of SnO2 is 7.5%—10%(w.t.).

The morphology of random screens with different surface roughness is studied with atomic force microscope and it is found that their height distributions have very obvious fractal characteristics in short range regions.For screens with larger and smaller roughness,the fractals exist in the forms of random height fluctuations and small grains without characteristic size respectively.The self-affine fractal surface model is introduced to the quantitative descriptions of randomscreens.The light scattering measurements show that:(1)the scattered intensity in off-axis region descends in negative power functions,and the theoretical analy sis based on self-affine fractal model indicates that it originates from the sho rt-range fractal of the screens;and(2)there is a halo ring in the scattered fiel ds in the paraxial region .This phenomenon cannot yet be explained on the basis of the self-affine fractal model.

The method for the simulational generation of Gaussian correlation random surfaces is proposed,and the computational simulation of the speckle field produced by this kind of surfaces on the Fraunhofer plane is performed.10000 speckle fieldsamples at each