Crystal Length Research Articles

Intracavity frequency-doubled external-cavity surface-emitting blue laser with high conversion efficiency

Blue laser with high power and high beam quality has many applications such as in laser display, underwater communication and imaging, and non-ferrous metal processing. Optically pumped external-cavity surface-emitting laser combines the advantages of both surface-emitting semiconductor lasers and solid-state disk lasers, and can produce high output power and good beam quality simultaneously. Its high intracavity circulating power is more conducive to intracavity frequency doubling, achieving high-power and high beam quality blue light through fundamental laser in the near-infrared waveband. This paper reports an efficient intracavity frequency doubled 490 nm high power blue light by using a 980 nm fundamental laser in an external-cavity surface-emitting laser. The V-type resonant cavity is formed by the high reflectivity distributed Bragg reflector (DBR) at the bottom of gain chip, a folded flat concave mirror (high reflectivity coated for 980 nm and anti-reflectivity coated for 490 nm), and a flat concave end mirror (high reflectivity coated for 980 nm and 490 nm). By inserting a nonlinear crystal LBO into the cavity at the beam waist formed by the folded mirror and end mirror, and employing a birefringent filter (BRF) to polarize the fundamental laser and narrow the linewidth of the laser, a high power and high beam quality blue laser with high conversion efficiency is obtained. The effects of different factors including the length of nonlinear crystal, the linewidth of fundamental laser, and the compensation of walk off angle on the output power of the blue laser are studied experimentally. The length of the nonlinear crystal is optimized based on the size of the fundamental laser beam waist at the position of the crystal in the resonant cavity. Under the type-I phase matching condition of LBO, over 6 W output power at 491 nm wavelength is obtained when the crystal length is 5 mm and the BRF thickness is 1 mm. The beam quality <i>M</i><sup>2</sup> factor in the <i>x</i> direction and the <i>y</i> direction are both 1.08, and the conversion efficiency of frequency doubling is 63%. The experimental results also show that symmetrically placed nonlinear crystals can compensate for the walk-off angle during frequency doubling to a certain extent, thereby clearly improving the conversion efficiency of the frequency doubled blue laser.

Theoretical study of Dy<sup>3+</sup>,Na<sup>+</sup>: PbGa<sub>2</sub>S<sub>4</sub> mid-infrared laser based on experimental parameters

Based on the absorption spectra of Dy<sup>3+</sup>, Na<sup>+</sup>:PbGa<sub>2</sub>S<sub>4</sub> crystal elements, as well as the theoretical calculation data obtained from Judd-Ofelt analysis, we have derived partial fluorescence absorption and emission cross sections. For energy levels that cannot be directly measured, we have employed the reciprocal method to calculate their respective absorption and emission cross-sections. Combing both experimental measurements and calculated data, a numerical simulation is conducted to investigate the experimental setup for generating a 4.3 μm mid-infrared laser through direct pumping of dysprosium and Dy<sup>3+</sup>, Na<sup>+</sup>:PbGa<sub>2</sub>S<sub>4</sub> crystals using 1.3 μm and 1.7 μm diode lasers pumping. The simulation calculates spatial distributions of laser power, gain coefficient, and absorption coefficient within the crystal. Furthermore, we analyze the effects of pumping power, crystal length, and output mirror reflectance on laser performance. The model introduces 2.9 μm laser oscillation and observes the change of output power before and after introduction. Our findings demonstrate that the incorporation of 2.9 μm laser oscillation effectively facilitates the population transfer from the <sup>6</sup>H<sub>13/2</sub> level to the ground state 6H15/2, thereby mitigating the self-terminating phenomenon during the transition between the <sup>6</sup>H<sub>11/2</sub> and <sup>6</sup>H<sub>13/2</sub> levels, consequently enhancing both output power and slope efficiency of the laser system. Numerical results indicate that maximum output powers for the 1.3 μm diode laser pumping are achieved at 103 mW with a pumping threshold of 12 mW and a slope efficiency of 2.8%, while for the 1.7μm diode laser pumping, they reach up to 315 mW with a pumping threshold of 46 mW and a slope efficiency of 8%. Additionally, the optimal crystal lengths are determined as 17 mm for the 1.3 μm diode laser pumping and 32 mm for the 1.7 μm diode laser pumping. Finally, the best reflectance value for the output mirror is 0.92. These numerical results have important guiding significance for crystal processing and the selection of optical path structure parameters.

The Structural Basis of DL0410, a Novel Multi-Target Candidate Drug for the Treatment of Alzheimer’s Disease

Alzheimer’s disease (AD) is a complicated disease for which there are still no ideal one-target drugs, while multi-target drugs are closer to ideal drugs and will provide new solutions for the clinical treatment of AD. DL0410 is a promising multi-target drug candidate for AD treatment that is not only a significant inhibitor against both acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE) but also an antagonist of histamine H3 receptor (H3R), and its therapeutic efficacy in treating cognitive dysfunction has been validated in a series of AD-related animal models, including scopolamine-induced mice, D-galactose-induced and Aβ-induced mice, and APP/PS1 and SAMP8 mice. Although the structure of DL0410 has been analyzed using various detection techniques, such as MS and NMR, its three-dimensional crystal structure still requires further confirmation. In this study, the crystal of DL0410 was grown in aqueous solution, and its structure was detected using the X-ray diffraction method. The crystal data, atomic coordinates, bond lengths, angles, and hydrogen bonds of DL0410 were obtained. Its stability was proven by differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). Based on this study, the molecular docking of DL0410 with AChE, BuChE, and H3R was performed to uncover their interaction mechanisms and explain their bioactivities. This study provides important information for new multi-target drug design and the research and development of new drugs for AD treatment.

Dual-donor organic solar cells with 19.13% efficiency through optimized active layer crystallization behavior

D18:D18-Cl:L8-BO ternary organic solar cells (TSCs) with dual-donor are fabricated, and the highest power conversion efficiency (PCE) of 19.13% is achieved. The open circuit voltage of D18:D18-Cl:L8-BO TSCs is 0.915 V, the short circuit current density is 26.22 mA cm−2, and the fill-factor is 79.75%. D18 and D18-Cl form alloys in ternary films due to their similar chemical structures. The D18-Cl acts as a morphology modulator, enhancing the crystallization behavior of the active layer besides shortening the π-π and intermolecular stacking distances and augmenting the crystal coherence lengths. Moreover, adding D18-Cl can make the morphology of the active layer smoother and form a nanofiber structure. These factors collectively promoted charge extraction, transport, and collection. Furthermore, D18:D18-Cl:L8-BO TSCs exhibit excellent long-term stability, maintaining over 84% of the initials PCE after stored in N2-filled glove box for 4000 h. The work shows that it is feasible to prepare TSCs with high PCE and high stability using dual-donor with similar molecular structure.

Proton-beam energy diagnostics by color-center photoluminescence imaging in LiF crystals: Implementation of multiple Coulomb scattering into an analytical Bragg-curve model

Lithium fluoride crystals are used to assess proton-beam energy spectra. Proton irradiation induces laser-active color centers in the crystal, whose density correlates with the absorbed dose. The spatial distribution of photoluminescence emitted by these color centers is exploited to estimate the proton-beam energy spectrum using an analytical Bragg-curve model. This study integrates the effects of multiple Coulomb scattering (MCS) into the model. At high enough energies, MCS leads to proton leakage through the crystal faces with a reduction in absorbed dose along the crystal length. The model incorporates MCS using an empirical approach based on Monte Carlo simulations.

Zero-optical-distance mini-LED backlight with light-guiding microstructure lens for extra-thin, large-area notebook LCDs.

Mini-light-emitting diode (Mini-LED) backlight units (BLUs) in combination with high dynamic range technology can reduce energy and ensure high contrast and luminance. However, the number of LEDs used in mini-LED BLUs is considerably larger than the number of partitions in local dimming, resulting in low cost effectiveness. We proposed a design combining edge-light mini-LEDs and light-guiding microstructure lenses to reduce the number of light sources required in displays considerably. A 16-inch prototype was produced for experiments. The length, width, and thickness of the liquid crystal display module were 351.87, 225.75, and 1.709 mm, respectively. For edge-light mini-LEDs with a pitch of 8.6 mm, the average luminance was 18,836 nits for an input power of 22.5 watts, the uniformity was 85%, the uniformity merit function was 10.13, and the contrast ratio was 60,000:1. Thus, a zero-optical-distance (ZOD) mini-LED backlight for extra-thin, large-area notebook LCDs was produced.

Structural, optical, photocatalytic, and magnetic properties of new hydrothermal synthesized Cd1–xSnxFe2O4 nanocomposites

Herein, structural, surface area, optical, photocatalytic, and magnetic properties of a new Cd1–xSnxFe2O4 nanocomposites (1 ≥ x ≥ 0), synthesized by the hydrothermal approach were investigated. The nanocomposite formation is confirmed by X-ray diffraction analysis (XRD), Transmission electron microscopes (TEM), Fourier transform infrared (FTIR), Inductively coupled plasma (ICP), and Energy dispersive X-ray (EDX) analyses. The XRD findings reveal the formation of Fe2O3 at x = 0, 0.2, 0.4, and 1, while the Fe3O4 phase at x = 1 besides the spinel CdFe2O4 phase for x = 0.6 and 0.8, and rutile SnO2 phase for x ≥ 0.8. The crystal structure, e.g., lattice parameters, bond length, cell volume, theoretical density, crystallite size, dislocation density, and microstrain are remarkably influenced by elemental ratios. The average crystallite size of composites declined to 15.2 ± 4 nm as x increased to 0.4, then grew to 40.5 ± 4 nm at x = 0.6, and then decreased to 21 ± 10 nm at x = 1. The particle morphologies were deduced, and crystal structures were confirmed by analyzing field-emission scanning electron microscope (FE-SEM), and TEM micrographs. FTIR confirmed the presence of metal oxide bands for all nanocomposites. The surface area was calculated via the Brunauer–Emmett–Teller (BET) and Barrett-Joyner-Halenda (BJH) theories to the N2 adsorption–desorption isotherm and equals 10.5, 20.3, 17.1, and 25.2 m2/g at x = 0, 0.4, 0.6, and 1, respectively. The magnetic properties of the Cd1–xSnxFe2O4 nanocomposites were studied by vibrating-sample magnetometry (VSM) technique, which displayed their ferromagnetic behaviors. The addition of Sn2+ into the composite improved the magnetic saturation from 0.42 to 34.7 emu/g by changing x from 0 to 0.4 then was reduced to 5.9 emu/g at x = 1 which well matched with the behavior of total pore volume. Furthermore, the indirect optical band gap (Egin) was increased, e.g., Egin equals 1.22, 1.82, 1.88, and 2.08 eV for x = 0, 0.4, 0.6, and 1, respectively. Methylene blue photocatalytic performance was investigated, and the maximumdegradation efficiency of 44.33 %was detected using Cd1–xSnxFe2O4 at x = 0.8 under UV–visible irradiation for 160 min.

Silatranes: Relationship between the experimental Si ← N dative bond length and its calculated energy according to AIM analysis data

X-ray structures of a number of silatranes with Si ← N dative bonds of various lengths were analyzed using the AIM analysis method. The features of the effect of substituents at the silicon atom and in the silatranyl core on the length of the Si ← N dative bond have been established. The relationship between optimazed in the crystal length of the Si ← N dative bond and its calculated energy with a high correlation coefficient is obtained. A similar dependence was obtained for the electron density at the bond critical point of the Si ← N dative contact. The calculated value of the positive charge on silicon atoms is determined by the electronegative properties of the axial substituent.

Broadband Hybridly Polarized Vector Vortex Raman Microchip Laser

AbstractHybridly polarized (HP) vector vortex Raman lasers dramatically extend their applications on optical microscopy, optical communication, and quantum information. Spatial light modulators and waveplates are widely used for generating HP vector vortex lasers, however, the performance and beam quality of HP vector vortex lasers are restricted by diffraction loss and low damage threshold of these optical elements. Here, HP vector vortex Raman microchip lasers constructed with Yb3+:Y3Al5O12 (Yb:YAG) and vanadate (YVO4) crystals is demonstrated. The states of polarization (SoP) of HP vector vortex lasers are combination of radial and anti‐radial polarizations (RP‐ARP), azimuthal and anti‐azimuthal polarizations (AP‐AAP). The SoP of HP vector vortex lasers can be controlled by adjusting the length of YVO4 crystal and applying pump power. Maximum output powers are 456 and 586 mW with optical efficiency of 7.1% and 9.2% for HP vector vortex lasers with SoP of RP‐ARP and AP‐AAP. The HP vector vortex Raman lasers with SoP of RP‐ARP and AP‐AAP oscillate ≈1076 nm with bandwidths of 11.4 and 10.8 nm. High beam quality is achieved for HP vector vortex lasers with measured M2 nearly equal to theoretical value. The broadband HP vector vortex Raman lasers with high beam quality extend applications on optical trapping, and quantum information processing.

A Monte-Carlo simulation study for design of brain dedicated TOF-PET

Brain positron emission tomography (PET) has several advantages, including improved sensitivity and spatial resolution compared to whole-body PET, which provides a more accurate diagnosis and observation of metabolic activity in the brain. However, the small diameter and design parameter result in a high parallax error and a random count rate, leading to a deteriorated imaging performance. We designed and evaluated brain PET with various design parameters and applied time-of-flight (TOF) technology to overcome the above problems. The aim of the study was to design an optimal structure of the brain dedicated TOF-PET that provides excellent image quality. This study investigated effects of ring diameter, crystal length, and TOF capability on the performance of brain TOF-PET using a Monte-Carlo simulation. Two brain PET were designed and evaluated, consisting of a commercially available brain PET ring diameter (357 mm) and a smaller ring diameter (257 mm) to verify the effect of ring diameter on the performance of the brain PET. Three brain TOF-PET with different crystal thicknesses (10 mm, 15 mm, and 20 mm) and TOF capacities (180 ps, 220 ps, and 260 ps) were assessed and their performances were compared. An optimization study was also performed to design the optimal structure based on the two simulation results. This study determined the optimal structure of brain-dedicated TOF-PET based on trade-offs and performance differences depending on the parameters of brain PET. As a result, we propose a brain-dedicated TOF-PET with a 15 mm crystal length and 257 mm diameter as the optimal structure. The results of this paper could be used to design PET systems for the brain and other specific organs.

A Physics-Assisted Data-Driven Framework for Predicting Crystal Chord Length Distributions under Arbitrary Experimental Conditions

A Physics-Assisted Data-Driven Framework for Predicting Crystal Chord Length Distributions under Arbitrary Experimental Conditions

Modulating Polymer Ultrathin Film Crystalline Fraction and Orientation with Nanoscale Curvature.

We investigated the effect of nanoscale curvature on the structure of thermally equilibrated poly-3-hexylthiophene (P3HT) ultrathin films. The curvature-induced effects were investigated with synchrotron grazing incidence X-ray diffraction (GIXRD) and atomic force microscopy (AFM). Our results demonstrate that nanoscale curvature reduces the polymer crystalline fraction and the crystal length. The first effect is strongest for the lowest curvature and results in a decrease in the out-of-plane thickness of the polymer crystals. On the other hand, the crystal in-plane length decreases with the increase in substrate curvature. Finally, the semi-quantitative analysis of crystal anisotropy shows a marked dependence on the substrate curvature characterized by a minimum at curvatures between 0.00851 nm-1 and 0.0140 nm-1. The results are discussed in terms of a curvature-dependent polymer fraction, which fills the interstices between neighboring particles and cannot crystallize due to extreme space confinement. This fraction, whose thickness is highest at the lowest curvatures, inhibits the crystal nucleation and the out-of-plane crystal growth. Moreover, because of the adhesion to the curved portion of the substrates, crystals adopt a random orientation. By increasing the substrate curvature, the amorphous fraction is reduced, leading to polymer films with higher crystallinity. Finally, when the thickness of the film exceeds the particle diameter, the curvature no longer affects the crystal orientation, which, similarly to the flat case, is predominantly edge on.

Prediction of the Structural Color of Liquid Crystals via Machine Learning

Materials that generate structural color may be promising alternatives to dyes and pigments due to their relative long-term stability and environmentally benign properties. Liquid crystal (LC) mixtures of cholesteryl esters demonstrate structural color due to light reflected from the helical structure of the self-assembled molecules. The apparent color depends on the pitch length of the liquid crystal. While a wide range of colors have been achieved with such LC formulations, the nature of the pitch–concentration relationship has been difficult to define. In this work, various machine learning approaches to predict the reflected wavelength, i.e., the position of the selective reflection band, based on LC composition are compared to a Scheffe cubic model. The neural network regression model had a higher root mean squared error (RMSE) than the Scheffe cubic model with improved predictions for formulations not included in the dataset. Decision tree regression provided the best overall performance with the lowest RMSE and predicted position of the selective reflection band within 0.8% of the measured values for LC formulations not included in the dataset. The predicted values using the decision tree were over two-fold more accurate than the Scheffe cubic model. These results demonstrate the utility of machine learning models for predicting physical properties of LC formulations.

A fast synthetic strategy for quick preparation and optimization of platelike MFI crystals

The demand for high aspect ratio zeolite crystals has been increasing dramatically for many applications, ranging from catalysis to membrane separations. However, manufacturing such platelike crystals usually requires energy-intensive and time-consuming synthesis procedures. Here, by employing a thin-wall tubular reactor, we report for the first time a fast synthetic strategy that yields preferentially-b-oriented platelike MFI crystals within minutes of hydrothermal treatment. Various synthesis conditions such as hydrolysis, precursor aging, chemical compositions, etc. can be quickly optimized within days. Such optimization resulted in highly crystalline platelike crystals with lateral dimensions up to ∼5 μm length in c-axis or ultra-thin crystals with ∼25 nm thickness. Meanwhile, non-platelike MFI crystals can even reach 135 μm lateral size in 24 h. This fast synthetic strategy can be further generalized for the preparation and optimization of diverse important materials including MOFs, COFs, and other zeolites, benefiting both fundamental research and practical applications.

Crystal type, chain length and polydispersity impact the resistant starch type 3 immunomodulatory capacity via Toll-like receptors

Food ingredients that can activate and improve immunological defense, against e.g., pathogens, have become a major field of research. Resistant starches (RSs) can resist enzymes in the upper gastrointestinal (GI) tract and induce health benefits. RS-3 physicochemical characteristics such as chain length (DP), A- or B-type crystal, and polydispersity index (PI) might be crucial for immunomodulation by activating human toll-like receptors (hTLRs). We hypothesize that crystal type, DP and PI, alone or in combination, impact the recognition of RS-3 preparations by hTLRs leading to different RS-3 immunomodulatory effects. We studied the activation of hTLR2, hTLR4, and hTLR5 by 0.5, 1 and 2 mg/mL of RS-3. We found strong activation of hTLR2-dependent NF-kB activation with PI <1.25, DP 18 as an A- or B-type crystal. At different doses, NF-kB activation was increased from 6.8 to 7.1 and 10-fold with A-type and 6.2 to 10.2 and 14.4-fold with B-type. This also resulted in higher cytokine production in monocytes. Molecular docking, using amylose-A and B, demonstrated that B-crystals bind hTLR2 promoting hTLR2-1 dimerization, supporting the stronger effects of B-type crystals. Immunomodulatory effects of RS-3 are predominantly hTLR2-dependent, and activation can be tailored by managing crystallinity, chain length, and PI.

Absorption coefficients and scattering losses of TGG, TGP, KTF, FS, and CeF3 magneto-optical crystals in the visible via cavity ring-down spectroscopy.

We demonstrate a method for determining small absorption coefficients and surface-scattering losses of crystals using cavity ring-down spectroscopy and perform measurements on magneto-optical crystals of terbium gallium garnet (TGG), terbium gallium phosphate (TGP), fused silica (FS), potassium terbium fluoride (KTF), and C e F 3 at 532 and 634nm. Surface scattering is distinguished from absorption losses by using crystals of different lengths. A figure of merit (FoM) for magneto-optical crystals is defined to evaluate their suitability as intracavity optics in optical cavity applications. It is found that TGP has the highest FoM for crystal lengths up to ∼10m m, whereas C e F 3 and FS potentially outperform TGP for longer crystals. Single-pass applications are also briefly discussed.

Dual-wavelength collaboratively pumping scheme for a 3.9 µm continuous-wave Ho:YLF laser

A dual-wavelength collaboratively pumping scheme is proposed to realize the efficient operation of a 3.9 µm continuous wave Ho:YLF laser. An 888 nm laser is used to excite ions from the 5I8 ground-state manifold to the 5I5 laser’s upper manifold. Another 2.1 µm laser is used to excite ions from the 5I6 laser’s lower manifold to the short-lived 5I4 manifold to eliminate the self-terminated effect of 3.9 µm laser oscillation. Numerical simulation of 3.9 µm laser output performances is carried out, based on the developed rate equations. Simulation results indicate that the dual-wavelength collaboratively pumping scheme is feasible to realize the highly efficient output of the 3.9 µm continuous wave Ho:YLF laser. The relationship between the pump power for 888 nm and 2.1 µm laser sources is analyzed to obtain the optimal output. Furthermore, the impacts of crystal doping concentration, crystal length, output mirror transmittance, and important energy-transfer processes on the laser output performances are also analyzed. The dual-wavelength collaboratively pumping scheme provides beneficial guidance for the generation of a 3.9 µm high-power continuous-wave laser in an Ho:YLF laser.

Sparse SiPM Pixel Arrangement for a TOF-PET Detector Design that Achieves 100 ps Coincidence Time Resolution

Coupling silicon photomultipliers (SiPMs) to the side of a long and narrow scintillation crystal elements offers near-complete light extraction efficiency, independent of 511 keV photon interaction depth, and reduced scintillation light transit time jitter in its path toward the photodetector. With these advantages, significant improvements in PET detector coincidence time resolution (CTR) can be achieved compared to the traditional scintillation light readout configuration where an SiPM is coupled on the narrow end of crystals. Moreover, the arrangement of photosensors along the crystal’s side intrinsically provides a three-dimensional position sensing detector. One consideration for the side readout approach is the increase in the number of SiPMs required to read each crystal element. In this work, we investigate the achievable CTR when the number of SiPM elements coupled to the side of crystals is parametrically varied, including different crystal lengths and reflector configurations. A simulation model for CTR was validated against measurements with 3-20 mm length crystals employing side readout of scintillation light. The validated simulation model was used to parametrically investigate twenty-seven configurations of SiPMs arranged along the side of crystal elements. Reflector and sensor placement was parametrically varied to find configurations that optimize light collection efficiency, energy resolution, and CTR. One configuration achieved 101±1 ps FWHM CTR, while maintaining high light collection efficiency and good energy performance with a 33% reduction in photosensor area.

Investigation of the acicular aragonite growth behavior in AOD stainless steel slag during slurry-phase carbonation

This study presents a novel method for producing acicular aragonite using argon oxygen decarburization (AOD) slag while controlling the reaction temperature, reaction time, stirring speed, and the magnesium-to‑calcium stoichiometric ratio. This approach provides steel plants with an opportunity to decrease their CO2 emissions and promote efficient resource utilization and CO2 storage through the production of high-quality value-added products. The experimental results showed that reaction temperature was the most significant factor affecting the carbonation efficiency of AOD slag, followed by reaction time, stirring speed, CO2 partial pressure, and the liquid-to-solid ratio (L/S). The study also found that elevated temperature and prolonged reaction duration favored the preferential precipitation of aragonite. Additionally, raising the temperature and the magnesium-to‑calcium stoichiometric ratio was shown to enhance the formation of aragonite, affecting its crystal growth orientation and dimensions. The optimal combination of reaction parameters for the preparation of acicular aragonite was found to be the reaction time of 8 h, the magnesium-to‑calcium stoichiometric ratio of 0.8, the reaction temperature of 120 °C, and the stirring speed of 200 r·min−1. Under these conditions, the resulting acicular aragonite exhibited excellent overall uniformity, a large aspect ratio, and a smooth crystal surface, with a content of 91.49 %, a single crystal length ranging from 9.86 to 32.6 μm, and a diameter ranging from 0.63 to 2.15 μm. This study provides valuable insights into the efficient production of acicular aragonite from steel slag while reducing CO2 emissions and promoting the sustainable use of resources.

Shape and polarization distribution of non-circular conical diffraction beams from conjugate cascades.

Peculiar non-circularly shaped vector type beams can be obtained naturally by the conical diffraction phenomenon if specific manipulations in wavevector space are performed between optically biaxial crystals arranged in a cascade. We analyze in detail this situation by focusing on the general shapes and the polarization distribution. Both are shown to be correlated to the values of structure parameters introduced in this work. These control parameters depend on the conical diffraction cone aperture angle, on the crystal lengths, and on the magnification values due to x- and y-oriented cylindrical lenses placed between the crystals and coupling common conjugate planes. The local polarization is found to be always linear with the exception of regions where structures composing the pattern intersect or overlap, where elliptical or circular polarization can occur. The way in which the obtained patterns depend on the orientation of individual crystal samples around the common optical axis and on an eventual polarization filtering at various stages of the cascade is discussed as well. Theoretical and experimental findings agree well, as verified for the case of a cascade of two crystals.