Field Diffraction Pattern Research Articles

A study of the effects of Gaussian distribution of coherence length of source on the diffraction of partial temporal coherence beam from multi slits: Theory and simulation

First, we have generalized the notion of Franhoufer diffraction of temporal coherent light from a single slit to the case of arbitrary n-slits. The diffraction pattern is investigated for different values of recently (Koushki and Alavi, 2019) introduced parameter η “decoherence parameter”. It is shown that for multi-slits, the temporal decoherence effects appear for η≥1 i.e., the coherence length is shorter that the size of the slits. Results of our study reproduce the previous studies for perfect temporal case, when coherence length tends to infinity. Then to bring the problem closer to reality, we do not fix the coherence length and consider a Gaussian distribution function for it. Numerical study of the effects of coherence parameters of Gaussian distribution on far field diffraction pattern is performed.

High Frequency MEMS Capacitive Mirror for Space Applications.

Free space optics laser communication using modulating retroreflectors (MR) is a challenging application for an active mirror, due to the high frequencies (>100 kHz) required to enable sufficient data transfer. Micro Electromechanical (MEMS) mirrors are a promising option for high-frequency applications, given the very small moving mass typical of such devices. Capacitive MEMS mirrors are presented here for free space communications, based on a novel fabrication sequence that introduces a single-layer thin film aluminum mirror structure with an underlying silicon oxide sacrificial layer. The use of aluminum instead of gold as a mirror layer diminishes the heating generated by the absorption of the sun's radiation once the mirrors exit the earth's atmosphere. Thanks to the novel fabrication sequence, the presented mirror devices have a full range actuation voltage of less than 40 V, and a high operational frequency with an eigenfrequency above 2 MHz. The devices were manufactured and characterized, and their main parameters were obtained from experimental data combined with finite element analysis, thus enabling future design optimization of the reported MEMS technology. By optical characterization of the far field diffraction pattern, good mirror performance was demonstrated.

Angle Resolved Scattering Measurement of Multiple Spherical Particles by Fourier Transform

In this paper, we report that the far field diffraction pattern of a specimen which is consisting of an array of spherical particles enables the determination of the size and refractive index of each scattering sphere. The far field 2D angular resolved diffraction pattern, of which the diffraction angle reaches tens of degrees, is measured by CCD camera. On one hand, the diffraction pattern distorted obviously at high angles is corrected for curvature. The amplitude and phase images of the specimen are reconstructed by difference map iterative algorithm. The size of each scattering microsphere is calculated according to its pixel numbers and the image resolution. On the other hand, the diffraction pattern without curvature correction is used to reconstruct the amplitude and phase images of the specimen by HIO algorithm. The amplitude and phase images of each sphere are isolated. Then the angular resolved scattering signals of the individual spheres are quantitatively indicated by Fourier transform. Finally, the refractive index of each microsphere is obtained by fitting the experimental results using Mie theory.

Far-field diffraction pattern of cube corner retroreflector at oblique incidence

<sec>Corner cube retroreflector (CCR) as a main optical component of laser ranging retroreflector array plays a key role in satellite laser ranging (SLR) to cooperative targets. To accurately estimate the echo energy of SLR, it is necessary to precompute photons’ distribution in the distance of SLR station by calculating the Far field diffraction pattern (FFDP) of CCR under various conditions. In this paper, the analysis of the effective reflection area and optical reflectivity of CCR for arbitrary incidence angle are carried out, in which a method to calculate the CCR effective reflection area with a wider applicability is used, and the difference between optical reflectivity of metal-coated CCR and uncoated (total internal reflection) CCR is also discussed. On this basis, combined with optical diffraction theory, a simulation program for CCR FFDP calculation is established, thereby producing FFDPs of CCR for a variety of incidence angles under different coating conditions. The results show that the FFDP of metal-coated CCR is almost unrelated to the azimuth angle of incident light or polarization, but is determined only by elevation angle of incident light. The pattern is always like Airy spot or its tensile deformation. Relatively, uncoated CCR’s FFDP has a more complex figure, its reflected energy is divided into several lobes whose size, number and position are all influenced by elevation and azimuth angle of incidence, and also by the polarization. Generally, the incidence direction which has a large total intensity of far optical field is to an extent the same as that of large effective reflection area and optical reflectivity. Furthermore, simulation results with uncoated CCR presents a higher relevance of incidence direction and FFDP.</sec><sec>To verify the reliability and correctness of these simulation results, a diffraction optical experimental system at a wavelength of 1550 nm is set up to conduct laboratory confirmation, including laser, camera, beam expander, rotating platform and other essential optics. A silver-coated CCR and an uncoated CCR (both made of fuse silica, each has different dihedral angle offset) are chosen to measure their FFDPs with random polarization directions at several random incidence angles. All the measurement results are in good agreement with the simulations of FFDPs.</sec>

Area scalable and period manipulable three-dimensional optically induced photorefractive photonic periodic crystal or aperiodic quasicrystal

Abstract We experimentally investigate the formation of area-scalable three-dimensional (3D) photonic periodic crystal and aperiodic quasicrystal in an iron doped lithium niobate photorefractive material by multi-wedge prisms assisted compact and versatile single step optical induction approach. The induced large-area lattice microstructures are analyzed and verified by plane wave guiding, Brillouin-zone spectroscopy, far field diffraction pattern imaging, angle-dependent transmission spectra. Our technique can be easily expanded for the larger area of photonic periodic crystal or aperiodic quasicrystal microstructures. We also demonstrate experimentally and theoretically the manipulation to the period of 3D photorefractive photonic lattices by engineered vertex angle of multi-wedge prisms. The intensity analyses of interference light fields show that (1) the 3D photonic lattice has not only different Z-axis longitudinal structure, but also different X–Y front structure to the corresponding 2D photonic lattice, and (2) there exist three sets of sub-lattices which are mutually nested to form the 3D triangle photonic crystal.

Experimental observation of the far field diffraction patterns of functionalization single and multi-walled carbon nanotubes using nonlinear diffraction technique

Nonlinear diffraction pattern can be induced by focusing CWlaser into a thin quartzes cuvette containing nanofluid. The numberof revealed pattern rings indicates to the nonlinear behavior of fluid.Here, the nonlinear refractive index of each of functionalized singlewall carbon nanotube (F-SWCNTs) suspention and multi wall carbonnanotube (F-MWCNTs) suspention have been investigatedexperimentally .Each of CNTs suspention was at volume fraction of13×10−5 and 6×10−5. Moreover the laser source at wavelength of473 nm was used. The results show that SWCNTs suspentionpossesses higher nonlinearty than other at the same volume fraction

椭偏高斯光束经过非线性介质后的远场衍射图样

椭偏高斯光束经过非线性介质后的远场衍射图样

Development of a 170-mm hollow corner cube retroreflector for the future lunar laser ranging**Project supported by the National Natural Science Foundation of China (Grant Nos. 11655001 and 11605065).

Over the past 50 years, lunar laser ranging has made great contributions to the understanding of the Earth–Moon system and the tests of general relativity. However, because of the lunar libration, the Apollo and Lunokhod corner-cube retroreflector (CCR) arrays placed on the Moon currently limit the ranging precision to a few centimeters for a single photon received. Therefore, it is necessary to deploy a new retroreflector with a single and large aperture to improve the ranging precision by at least one order of magnitude. Here we present a hollow retroreflector with a 170-mm aperture fabricated using hydroxide-catalysis bonding technology. The precisions of the two dihedral angles are achieved by the mirror processing with a sub-arc-second precision perpendicularity, and the remaining one is adjusted utilizing an auxiliary optical configuration including two autocollimators. The achieved precisions of the three dihedral angles are 0.10 arc-second, 0.30 arc-second, and 0.24 arc-second, indicating the 68.5% return signal intensity of ideal Apollo 11/14 based on the far field diffraction pattern simulation. We anticipate that this hollow CCR can be applied in the new generation of lunar laser ranging.

Magnetic field induced changes in linear and nonlinear optical properties of Ti incorporated Cr2O3 nanostructured thin film

We report the magnetic field effect on the linear and nonlinear optical properties of pulse laser ablated Ti-incorporated Cr2O3 nanostructured thin film. Optical properties have been experimentally analyzed under Voigt geometry by performing ultraviolet-visible spectroscopy and closed aperture Z-scan technique using a continuous wave He–Ne laser source. Nonlinear optical response reveals a single peak-valley feature in the far field diffraction pattern in absence of magnetic field (B=0) confirming self-defocussing effect. This feature switches to a valley-peak configuration for B=5000G, suggesting self-focusing effect. For B≤750G, oscillations were observed revealing the occurrence of higher order nonlinearity. Origin of nonlinearity is attributed to the near resonant d-d transitions observed from the broad peak occurring around 2 eV. These transitions are of magnetic origin and get modified under the application of external magnetic field. Our results suggest that magnetic field can be used as an effective tool to monitor the sign of optical nonlinearity and hence the thermal expansion in Ti-incorporated Cr2O3 nanostructured thin film.

Performance analysis of next-generation lunar laser retroreflectors

Starting from 1969, Lunar Laser Ranging (LLR) to the Apollo and Lunokhod Cube Corner Retroreflectors (CCRs) provided several tests of General Relativity (GR). When deployed, the Apollo/Lunokhod CCRs design contributed only a negligible fraction of the ranging error budget. Today the improvement over the years in the laser ground stations makes the lunar libration contribution relevant. So the libration now dominates the error budget limiting the precision of the experimental tests of gravitational theories. The MoonLIGHT-2 project (Moon Laser Instrumentation for General relativity High-accuracy Tests – Phase 2) is a next-generation LLR payload developed by the Satellite/lunar/GNSS laser ranging/altimetry and Cube/microsat Characterization Facilities Laboratory (SCF_Lab) at the INFN-LNF in collaboration with the University of Maryland. With its unique design consisting of a single large CCR unaffected by librations, MoonLIGHT-2 can significantly reduce error contribution of the reflectors to the measurement of the lunar geodetic precession and other GR tests compared to Apollo/Lunokhod CCRs. This paper treats only this specific next-generation lunar laser retroreflector (MoonLIGHT-2) and it is by no means intended to address other contributions to the global LLR error budget. MoonLIGHT-2 is approved to be launched with the Moon Express 1(MEX-1) mission and will be deployed on the Moon surface in 2018. To validate/optimize MoonLIGHT-2, the SCF_Lab is carrying out a unique experimental test called SCF-Test: the concurrent measurement of the optical Far Field Diffraction Pattern (FFDP) and the temperature distribution of the CCR under thermal conditions produced with a close-match solar simulator and simulated space environment. The focus of this paper is to describe the SCF_Lab specialized characterization of the performance of our next-generation LLR payload. While this payload will improve the contribution of the error budget of the space segment (MoonLIGHT-2) to GR tests and to constraints on new gravitational theories (like non-minimally coupled gravity and spacetime torsion), the description of the associated physics analysis and global LLR error budget is outside of the chosen scope of present paper. We note that, according to Reasenberg et al. (2016), software models used for LLR physics and lunar science cannot process residuals with an accuracy better than few centimeters and that, in order to process millimeter ranging data (or better) coming from (not only) future reflectors, it is necessary to update and improve the respective models inside the software package. The work presented here on results of the SCF-test thermal and optical analysis shows that a good performance is expected by MoonLIGHT-2 after its deployment on the Moon. This in turn will stimulate improvements in LLR ground segment hardware and help refine the LLR software code and models. Without a significant improvement of the LLR space segment, the acquisition of improved ground LLR hardware and challenging LLR software refinements may languish for lack of motivation, since the librations of the old generation LLR payloads largely dominate the global LLR error budget.

Thermo-optical vacuum testing of IRNSS laser retroreflector array qualification model

We describe the activities performed by SCF_Lab (Satellite/lunar/GNSS laser ranging/altimetry and cube/microsat Characterization Facilities Laboratory) of INFN-LNF for the thermo-optical vacuum testing activity of a IRNSS (Indian Regional Navigation Satellite System) LRA (Laser Retroreflector Array), under contract for ISRO-LEOS. To our knowledge, this is the first publication on the characterization of the optical performance of an LRA operating at about 36,000km altitude (typical of regional GNSS segments, namely QZSS, COMPASS-G) executed in fully representative, carefully lab-simulated space conditions. In particular, this is the only such publication concerning IRNSS. Since laser ranging to its altitude is more challenging than to GNSS altitudes (from about 19,100km for GLONASS to about 23,200km for Galileo), comparative measurements were long awaited by ILRS (International Laser Ranging Service) and we present measurements of the absolute laser return to ground stations of the ILRS in terms of lidar OCS (Optical Cross Section) at the IRNSS relevant value of velocity aberration, in turn derived from measurements of the full FFDP (Far Field Diffraction Pattern) over a very large range of velocity aberrations. These measurements were acquired: (i) on a full-size qualification model of a IRNSS CCR (Cube Corner Retroreflector) LRA that ISRO-LEOS provided to INFN-LNF; (ii) during the lab-simulation of a 1/4 orbit segment, in which the LRA CCRs are exposed to the perturbation of the sun heat at varying angles, from grazing incidence (90° with respect to the direction perpendicular to the plane of array), up to the perpendicular to the LRA, with a same time variation consistent with the actual space orbit. In this 1/4 orbit condition, the LRA experiences potentially large thermal degradations of the OCS, depending on the detailed thermal and mechanical design of the LRA. Since all GNSS constellations have different LRA designs or configurations, this is another reason of the interest in the laboratory optical performance of the IRNSS designs. In fact, we tested two different IRNSS LRA configurations, without and with an auxiliary cover. The latter of the configurations is designed to give a somewhat increased performance. We also measured FFDPs and OCS: (1) in-air isothermal conditions (thus obtaining the LRA nominal performance); (2) in space conditions at a low, stationary value of the LRA bulk temperature; (3) in space conditions at a high, stationary value of the LRA bulk temperature (Figs. S1–S18, available in the online supplementary material for this paper). In all these three cases, we measured FFDPs and OCS at the following laser incidence angles: (a) normal to the LRA plane; (b) +9° to the normal to the LRA plane; (c) −9° to the normal to the LRA plane. This is the first time, to our knowledge, that the measurements (not simulations) at ±9° (values requested by ISRO-LEOS) are published for GNSS LRAs. Finally, we point out that we measured full-FFDP and OCS of single CCRs, for maximum diagnostic value and performance validation at subelement level. For all these reasons, the articulate and variate set of tests of the IRNSS LRA reported in this paper is unique.

Impact of different stochastic line edge roughness patterns on measurements in scatterometry - A simulation study

Abstract The impact of line edge roughness (LER) on measured light diffraction pattern of photo masks is investigated. This is relevant for scatterometry as an accurate, indirect method in wafer metrology to determine geometry parameters of periodic surface structures from scattered light intensities. The sensitivity to roughness increases the smaller the wavelength of the incident light is. For EUV scatterometry at 13.5 nm, the efficiencies of many higher diffraction orders can be measured. In the nanometer range they are sensitive to deviations from the ideal periodic straight line structure such as LER. Applying the Fraunhofer approximation, we calculate the far field diffraction pattern of an illuminated 2D aperture plane composed of many rough slits by its 2D-Fourier transform. The rough edges of the aperture gaps are created by means of power spectrum density (PSD) functions used with a random complex exponential phase term. A simple theory neglecting correlation in the roughness profile predicts for the intensities an exponential decrease with the diffraction order and the standard deviation of the roughness amplitude which can be tested by our numerical solutions. The calculated light intensities for a rough aperture are compared with the ones found for an ideal periodic aperture whose edges are straight lines. Ensembles of rough apertures with different values for the imposed standard deviation of the roughness amplitude σ , the linear correlation length ξ , and the roughness exponent α were examined. The validity of the exponential decrease was investigated for correlation lengths ξ from 5 nm up to 1000 nm and roughness exponents α from 0.3 to 1.0. It was found that the results for the exponential correction factor deviate substantially from the mentioned theoretical value for large correlation lengths and small roughness exponents.

Structured beam diffraction.

We report on the observation of a modulated pattern induced by a single laser beam in a polymeric film. In spite of the simple geometrical configuration, the analysis of the far field diffraction pattern allows a sensitive retrieving of the wavelength of the recording beam and of its incidence angle, pointing out the high information content of the recorded spot. A theoretical model is presented which satisfactorily explains the observed behavior. It takes into account the interaction of structured light with structured matter with the same symmetries and spatial modulation frequencies close to each other. This result shows a feature of the interaction between structured light and structured matter which has not been explored yet.

Thermo-optical vacuum testing of Galileo In-Orbit Validation laser retroreflectors

The Galileo constellation is a space research and development program of the European Union to help navigate users all over the world. The Galileo IOV (In-Orbit Validation) are the first test satellites of the Galileo constellation and carry satellite laser retroreflectors as part of their payload systems for precision orbit determination and performance assessment. INFN-LNF SCF_Lab (Satellite/lunar/GNSS laser ranging/altimetry and Cube/microsat Characterization Facilities Laboratory) has been performing tests on a sample of the laser array segment under the Thermo-optical vacuum testing of Galileo IOV laser retro-reflectors of Galileo IOV LRA project, as defined in ESA-INFN Contract No. 4000108617/13/NL/PA. We will present the results of FFDP (Far Field Diffraction Pattern) and thermal relaxation times measurements in relevant space conditions of Galileo IOV CCRs (Cube Corner Retroreflectors) provided by ESA-ESTEC. A reference for the performance of laser ranging on Galileo satellites is the FFDP of a retroreflector in its design specifications and a Galileo retroreflector, in air and isothermal conditions, should have a minimum return intensity within the range [0.55×106m2–2.14×106m2] (ESA-INFN, 2013). Measurements, performed in SCF_Lab facility, demonstrated that the 7 Galileo IOV laser retroreflectors under test were compliant with design performance expectations (Porcelli et al., 2015). The kind of tests carried out for this activity are the first performed on spare Galileo IOV hardware, made available after the launch of the four Galileo IOV satellites (2011 and 2012), which were the operational core of the constellation. The characterisation of the retroreflectors against their design requirements is important because LRAs (Laser Retroreflector Arrays) will be flown on all Galileo satellites.

Microstructure characterisation of in situ TiC particulates reinforced Fe-based composites

Iron-based composites were reinforced with TiC particulates by in situ synthesis. The microstructure was characterised by transmission electron microscope. The bright field image, dark field image and diffraction pattern of reinforcing particulates and graphite harmful phase were obtained. Meanwhile, the interface between reinforcing particulates and matrix of TiCp/Fe composite material was also observed by scanning electron microscope and transmission electron microscope. The results showed that the calculated lattice constant of reinforcing TiC particulates was 0·41 nm and the calculated lattice constants of graphite were a = 0·282 nm and c = 0·459 nm. The TiC particulates had quadrilateral morphology, and were chemically wetted in Fe matrix without distinct interface product. There was no transition layer at the interface, avoiding pollution of reinforcing particulates. This study provided some details for understanding the bonding interface of in situ metal matrix composites.

Self-induced diffraction patterns in nonlinear Fabry-Perot interferometer on lithium niobate

The effects of self-action of light fields within Fabry-Perot interferometers based on photorefractive lithium niobate plates both, of X- and Z- cuts are experimentally investigated. Formation of one-dimensional practically regular diffractive elements within the interferometers with slightly non-parallel input and output surfaces has been demonstrated at laser light wavelength of 532 nm. It has been found that these diffractive elements are formed due to the photorefractive response of the crystal to the steady-state optical interference patterns appeared within the interferometer at multiple reflections of light beam. From the Raman-Nath far field diffraction patterns the ordinary refractive index change within the interferometer on Z-cut crystal has been estimated.

Babinet’s principle for scalar complex objects in the far field

Babinet’s principle is briefly reviewed, especially regarding the zeroth diffraction order of the far field diffraction pattern associated with a given aperture. The pattern is basically described by the squared modulus of the Fourier transform of its amplitude distribution (scalar case). In this paper, complementary objects are defined with respect to complex values and not only with respect to unity in order to include phase objects and phase modulation. It is shown that the difference in complementary patterns can be sometimes a bright spot at the zero order location as is widely known, but also, it can be a gray spot or even a dark one. Conditions of occurrence for each case are given as well as some numerical and experimental examples.

Optimum beam steering of optical phased arrays using mixed weighting technique

In this paper, we present a novel technique for high precision optical beam steering of optical phased arrays (OPA) using mixed weighting method. Optimal OPA parameters are determined to obtain the best beam directivity by minimizing the main lobe width and eliminating grating lobes of the far field diffraction pattern. The quantitative analysis for a fibre-type optical phased array is given. The calculation results demonstrate that the grating lobe level can be distinctly reduced from 80% to 20% of the main lobe level. Thus, the mixed weighting technique proposed in this paper can substantially improve the beam steering efficiency and the beam quality.

Optically induced three-dimensional Penrose-type photonic quasicrystal lattices in iron-doped lithium niobate crystal

Three-dimensional Penrose-type photonic quasicrystal lattices are optically induced inside an iron-doped lithium niobate photorefractive crystal for the first time using a single multi-pinhole plate. The setup of this method is simple and compact dispense with complex optical adjustment system. Induced Penrose-type photonic quasicrystal lattices are analyzed and verified by plane wave guiding and far field diffraction pattern imaging. The quasicrystal microstructures can be maintained for a long time inside the crystal in a dark room. Other more complex three-dimensional photonic quasicrystal structures can be fabricated with this method by designing the multi-pinhole plate flexibly.

MOONLIGHT: A NEW LUNAR LASER RANGING RETROREFLECTOR AND THE LUNAR GEODETIC PRECESSION

Since the 1970s Lunar Laser Ranging (LLR) to the Apollo Cube Corner Retroreflector (CCR) arrays (developed by the University of Maryland, UMD) supplied almost all significant tests of General Relativity (Alley et al., 1970; Chang et al., 1971; Bender et al.,1973): possible changes in the gravitational constant, gravitational self-energy, weak equivalence principle, geodetic precession, inverse-square force-law. The LNF group, in fact, has just completed a new measurement of the lunar geodetic precession with Apollo array, with accuracy of 9 × 10−3, comparable to the best measurement to date. LLR has also provided significant information on the composition and origin of the moon. This is the only Apollo experiment still in operation. In the 1970s Apollo LLR arrays contributed a negligible fraction of the ranging error budget. Since the ranging capabilities of ground stations improved by more than two orders of magnitude, now, because of the lunar librations, Apollo CCR arrays dominate the error budget. With the project MoonLIGHT (Moon Laser Instrumentation for General relativity High-accuracy Tests), in 2006 INFN-LNF joined UMD in the development and test of a new-generation LLR payload made by a single, large CCR (100mm diameter) unaffected by the effect of librations. With MoonLIGHT CCRs the accuracy of the measurement of the lunar geodetic precession can be improved up to a factor 100 compared to Apollo arrays. From a technological point of view, INFN-LNF built and is operating a new experimental apparatus (Satellite/lunar laser ranging Characterization Facility, SCF) and created a new industry-standard test procedure (SCF-Test) to characterize and model the detailed thermal behavior and the optical performance of CCRs in accurately laboratory-simulated space conditions, for industrial and scientific applications. Our key experimental innovation is the concurrent measurement and modeling of the optical Far Field Diffraction Pattern (FFDP) and the temperature distribution of retroreflector payloads under thermal conditions produced with a close-match solar simulator. The apparatus includes infrared cameras for non-invasive thermometry, thermal control and real-time payload movement to simulate satellite orientation on orbit with respect to solar illumination and laser interrogation beams. These capabilities provide: unique pre-launch performance validation of the space segment of LLR/SLR (Satellite Laser Ranging); retroreflector design optimization to maximize ranging efficiency and signal-to-noise conditions in daylight. Results of the SCF-Test of our CCR payload will be presented. Negotiations are underway to propose our payload and SCF-Test services for precision gravity and lunar science measurements with next robotic lunar landing missions. In particular, a scientific collaboration agreement was signed on Jan. 30, 2012, by D. Currie, S. Dell’Agnello and the Japanese PI team of the LLR instrument of the proposed SELENE-2 mission by JAXA (Registered with INFN Protocol n. 0000242-03/Feb/2012). The agreement foresees that, under no exchange of funds, the Japanese single, large, hollow LLR reflector will be SCF-Tested and that MoonLIGHT will be considered as backup instrument.