Stokes Components Research Articles

SPARTA – Solver for Polarized Atmospheric Radiative Transfer Applications: Introduction and application to Saharan dust fields

Non-spherical particles in the atmosphere absorb and scatter solar radiation. They change the polarization state of solar radiation depending on their shape, size, chemical composition and orientation. To quantify polarization effects, a new three-dimensional (3D) vector radiative transfer model, SPARTA (Solver for Polarized Atmospheric Radiative Transfer Applications) is introduced and validated against benchmark results. SPARTA employs the statistical forward Monte Carlo technique for efficient column-response pixel-based radiance calculations including polarization for 3D inhomogeneous cloudless and cloudy atmospheres. A sensitivity study has been carried out and exemplarily results are presented for two lidar-based mineral dust fields. The scattering and absorption properties of the dust particles have been computed for spheroids and irregular shaped particles. Polarized radiance fields in two-dimensional (2D) and one-dimensional (1D) inhomogeneous Saharan dust fields have been calculated at 532nm wavelength. The domain-averaged results of the normalized reflected radiance are almost identical for the 1D and 2D modes. In the areas with large spatial gradient in optical thickness with expected significant horizontal photon transport, the radiance fields of the 2D mode differ by about ±12% for the first Stokes component (radiance, I) and ±8% for the second Stokes component (linear polarization, Q) from the fields of the 1D mode.

Photon lifetime correlated increase of Raman scattering and third-harmonic generation in silicon nanowire arrays

Light propagation in silicon nanowire layers is studied via Raman scattering, third-harmonic generation and cross-correlation function measurements. The studied silicon nanowire arrays are characterized by a wire diameter of 50–100 nm and a layer thickness ranging from 0.2–16 μm. These structures are mesoscopic for light in the visible and near infrared ranges. The Raman signal increases monotonically with layer thickness increases at a 1.064 μm pump wavelength. The Stokes component for silicon nanowire arrays with a thickness larger than 2 μm exceeds that for crystalline silicon by more than an order. At the mentioned thicknesses, an increase is also registered for the third-harmonic signal, one that is up to fourfold greater than that for crystalline silicon for a 1.25 μm pump wavelength. Measurements of cross-correlation functions for the scattered photons evidence the significant photon lifetime increase in the silicon nanowire layers at their thickness increase. This fact can be connected with multiple scattering inside the studied mesoscopic structures and the increase of the interaction length for the Raman and third-harmonic generation processes.

Lidar Measurements of Ozone in the Upper Troposphere – Lower Stratosphere at Siberian Lidar Station in Tomsk

The paper presents the results of DIAL measurements of the vertical ozone distribution at the Siberian lidar station. Sensing is performed according to the method of differential absorption and scattering at wavelength pair of 299/341 nm, which are, respectively, the first and second Stokes components of SRS conversion of 4th harmonic of Nd:YAG laser (266 nm) in hydrogen. Lidar with receiving mirror 0.5 m in diameter is used to implement sensing of vertical ozone distribution in altitude range of 6-16 km. The temperature correction of zone absorption coefficients is introduced in the software to reduce the retrieval errors.

An efficient and long-time accurate third-order algorithm for the Stokes–Darcy system

A third-order in time numerical IMEX-type algorithm for the Stokes---Darcy system for flows in fluid saturated karst aquifers is proposed and analyzed. A novel third-order Adams---Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams---Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. The scheme is efficient in the sense that one needs to solve, at each time step, decoupled Stokes and Darcy problems. Therefore, legacy Stokes and Darcy solvers can be applied in parallel. The scheme is also unconditionally stable and, with a mild time-step restriction, long-time accurate in the sense that the error is bounded uniformly in time. Numerical experiments are used to illustrate the theoretical results. To the authors' knowledge, the novel algorithm is the first third-order accurate numerical scheme for the Stokes---Darcy system possessing its favorable efficiency, stability, and accuracy properties.

Self-pumped SBS effect of high-power super-Gaussian-shaped laser pulses

AbstractMost of the high-energy laser systems deliver temporally super-Gaussian-shaped laser pulses. The propagation properties of this kind of pulses in a nonlinear medium are studied in this paper. There is Stokes component in the sideband spectrum of super-Gaussian-shaped pulses, and the frequency difference between the Stokes component and the center frequency is equals to the Brillouin frequency of the nonlinear medium. When the laser is reflected by optical elements in the light path, Stokes component in the reflected light can be amplified by the subsequent part of the laser pulse and excite stimulated Brillouin scattering (self-pumped SBS). The self-pumped SBS is studied theoretically and experimentally, and the experimental results agreed well with the calculated results. The simulation results show that lower-order super-Gaussian-shaped pulses are more suitable for suppressing the self-pumped SBS and of great benefit to the energy delivering of the high-power laser pulses. To the best of our knowledge, this is the first time to experimentally demonstrate the self-pumped SBS of high-power super-Gaussian-shaped laser pulses.

Raman diagnostics of photoinduced heating of silicon nanowires prepared by metal-assisted chemical etching

Raman spectroscopy was applied to investigate laser-induced heating of silicon nanowires (SiNWs) formed by metal-assisted chemical etching of lightly boron-doped crystalline silicon (c-Si) wafers. Low-frequency shift of the Raman peak from 520.5 cm−1 to about 517 cm−1 for SiNWs with length of 40–65 µm under laser irradiation with wavelengths of 632.8 or 488 nm was observed, and it was explained by an increase in the average temperature of SiNWs on about 150 K for the laser intensity about 1 kW/cm2. The same photoinduced heating was confirmed by analyzing the ratio between the Stokes and anti-Stokes components of the Raman scattering. The obtained experimental data allow us to estimate the thermal conductivity coefficient of SiNW array ~0.1 W/(m K), which is three orders of magnitude smaller than that of c-Si. Furthermore, the Raman spectra of SiNWs under excitation with intensity above 0.2–0.5 kW/cm2 consisted of an additional low-frequency peak, which is related to an overheated subsystem of well spatially separated fine SiNWs up to 600–700 K. The observed strong photoinduced heating can be used for local laser-induced treatment of SiNWs and biomedical applications.

Frozen ZnS Aqueous Suspension Nonlinear Optical Properties

The study of nonlinear effects, caused by nanosecond laser pulses’ impact on the frozen ZnS nanoparticles’ suspension, is presented. Laser pulses excite strong nanoparticles’ coherent vibrations in the near-terahertz range which lead to different nonlinear effects: X-ray emission, stimulated low-frequency Raman scattering, and luminescence. X-ray emission was observed as bright spots on the special X-ray film. This provides evidence that an X-ray propagates with narrow beams. Stimulated low-frequency Raman scattering is a result of light scattering by acoustic vibrations of nanoparticles. Its frequency shift corresponds to the nanoparticles’ eigenvibration frequencies and depends on the sample material and particle’s dimension. It was measured with the help of a Fabri-Perot interferometer in the range of dispersion $$16.67\,\hbox {cm}^{-1}$$ . For ZnS, the first Stokes component frequency shift is equal to 465 GHz. Under excitation by 20 ns ruby laser pulses, the luminescence of the frozen ZnS nanoparticles’ suspension was observed in two bands located at 480 nm and 510 nm. Its duration was more than 3 s.

Low-threshold collinear parametric Raman comb generation in calcite under 532 and 1064 nm picosecond laser pumping

Optimal conditions of low-threshold collinear parametric Raman comb generation in calcite (CaCO3) are experimentally investigated under 20 ps laser pulse excitation, in agreement with the theoretical study. The collinear parametric Raman generation of the highest number of Raman components in the short calcite crystals corresponding to the optimal condition of Stokes–anti-Stokes coupling was achieved. At the excitation wavelength of 1064 nm, using the optimum-length crystal resulted in the effective multi-octave frequency Raman comb generation containing up to five anti-Stokes and more than four Stokes components (from 674 nm to 1978 nm). The 532 nm pumping resulted in the frequency Raman comb generation from the 477 nm 2nd anti-Stokes up to the 692 nm 4th Stokes component. Using the crystal with a non-optimal length leads to the Stokes components generation only with higher thresholds because of the cascade-like stimulated Raman scattering with suppressed parametric coupling.

Synchronously pumped picosecond all-fibre Raman laser based on phosphorus-doped silica fibre.

Reported for the first time is picosecond-range pulse generation in an all-fibre Raman laser based on P₂O₅-doped silica fibre. Employment of phosphor-silicate fibre made possible single-cascade spectral transformation of pumping pulses at 1084 nm into 270-ps long Raman laser pulses at 1270 nm. The highest observed fraction of the Stokes component radiation at 1270 nm in the total output of the Raman laser amounted to 30%. The identified optimal duration of the input pulses at which the amount of Stokes component radiation in a ~16-m long phosphorus-based Raman fibre converter reaches its maximum was 140-180 ps.

Compact Diode-Side-Pumped Stimulated Raman Laser Based on a KGW:Nd Crystal

We have studied an all solid-state diode-side-pumped laser which lases in the nominally eye-safe spectral range of ~1.5–1.6 μm. The optical configuration of the laser is based on using a potassium gadolinium tungstate crystal doped with neodymium ions, in which lasing occurs at a wavelength of λ = 1.351 μm and stimulated Raman selfconversion occurs to the first Stokes component (λ = 1.538 μm). The maximum output pulse energy was 17 mJ and 7 mJ for repetition frequencies of respectively 1 Hz and 10 Hz.

Ripplon spectroscopic study on multilayered liquid surface

Ripplon spectroscopy was used to observe the propagation modes of surface waves on a layered structure. We experimentally prepared a water surface covered with an oil layer of µm-order thickness, on which two surface modes, bending and squeezing, were theoretically predicted to stand independently. Thermally excited capillary waves, called ripplons, propagating on the layered surface were observed with an optical beating light-scattering system developed by us and two modes were clearly observed as the doublet peaks of the Stokes and anti-Stokes components, respectively. The dispersion and the damping constant of ripplons of the two modes as well as their intensity ratio agreed well with the theoretical calculations. The dispersion of the mechanically excited surface waves, which is attributed to the bending mode, was also measured to examine the mode assignment in the light-scattering experiment.

SO(3) matrix transformation for rapid polarization search and coding in a three-plate polarizer

A SO(3) transformer of a three-plate polarizer is adopted to rapidly achieve the transformation of the polarized state. The polarization coding based on Stokes components S 2 and S 3 is analyzed and demonstrated. Tabu search algorithm is used to accelerate the transformation of the polarized state by utilizing Mueller matrix roots decomposition to decompose the SO(3) matrix, and substituting first order Taylor series approximations for the trigonometric functions in the SO(3) matrix. The results show that bias voltage is less than 120 V in the coding zone. The search speed of our algorithm is faster than the one without first order Taylor series approximations by 4 times.

Polarization imaging over sea surface - a method for measurements of Stokes components angular distribution

This article describes a method for determining the angular distribution of light polarization over a roughened surface of the sea. Our method relies on measurements of the Stokes vector elements using a polarization imaging camera that operates using the Division of Focal Plane (DoFP) method. It uses special monochrome CCD array in which the neighbouring cells, instead of recording different colours (red green and blue), are equipped with micropolarizers of four directions (0, 45, 90 and 135 degrees). We combined the camera with a fish-eye lens of Field of View (FoV) > 180 deg. Such a large FoV allowed us to crop out the fragment of the frame along the circular horizon, showing a view covering all directions of the hemisphere. Because of complicated optical design of the fish-eye lens (light refraction on surfaces of parts of the lens) connected to the sensor we checked the accuracy of the measurement system. A method to determine the accuracy of measured polarization is based on comparison of the experimentally obtained rotation matrix with its theoretical form. Such a comparison showed that the maximum error of Stokes vector elements depended on zenith angle and reached as much as 24% for light coming from just above the horizon, but decreased rapidly with decreasing zenith angle to the value of 12% for the angles 10° off the edge of FoV. Moreover we present the preliminary results prepared over rough sea surface. These results include total intensity of light, Degree of Linear Polarization (DoLP) and their standard deviations. The results have been averaged over one thousand frames of a movie. These results indicate that the maximum polarization is observed near the reflection of the sun, and the signal coming from below the surface may be observed at zenith angles far from the vertical direction.

Ultra-long dual-sideband BOTDA with balanced detection

Abstract We experimentally study a dual-sideband Brillouin optical time-domain analyzer (BOTDA) with balanced detection. The amplification regime is simple (only bi-directional first-order Raman amplification); however, taking advantage of the balanced detection, 200 km fiber-loop sensing system is achieved (half of the whole length is used for sensing). Before the balanced detector, a FBG is used to separate the anti-Stokes and the Stokes components of the probe light, and the optical source׳s wavelength with regard to the given FBG׳s Bragg wavelength is shown to be highly relevant to the system׳s performance.

Method for Optimizing the Cavity Parameters of Pulsed Raman Lasers with Longitudinal External Pumping

A simple method is proposed for calculating the dependence of the Stokes radiation power of Raman lasers with external pulsed pumping on the cavity parameters. A relationship is obtained which defines the range of pump powers at which a laser system should generate only the first Stokes component. The dependence of this output on the reflectivity of the output window and on the pump power is obtained for fixed values of the other parameters.

The spectral dependence of SBS-induced noise in all-optical wavelength conversion

We demonstrate the effect of stimulated Brillouin scattering (SBS) on the conversion efficiency and the nature of noise transfer from the mixing frequencies to the generated frequencies during the wavelength conversion of 10 Gbps amplitude modulated signal using four-wave mixing in a highly nonlinear fiber. The impact of SBS is found to be different for the Stokes and anti-Stokes components.

High-efficiency cascaded Raman fiber laser with random distributed feedback.

Cascaded lasing provided by Raman gain (at 1115-nm pumping) and random distributed feedback (via Rayleigh backscattering) in a 1.65-km phosphosilicate fiber is studied. Output power for the second Stokes component (1398 nm) exceeds 5 W at pump power of 11 W. In contrast to conventional cascaded Raman laser with high-Q cavity for the intermediate first Stokes component, there is no cavity here and no cavity losses, correspondingly. Longitudinal power distribution is shown to be quite different also. As a result, the efficiency of pump to 2nd Stokes wave conversion is not influenced by the intermediate stage and depends only on the integral attenuation in the fiber. Herewith, the number of generated 2nd Stokes photons at the output may even exceed the absorbed pump photons due to the lower attenuation of Stokes waves.

Chirped pulse Raman amplification in Ba(NO3)2 crystals

Abstract In this study, 35.5% conversion efficiency is obtained at the first Stokes component frequency (873 nm) upon two-stage chirped pulse Raman amplification in a Ba(NO 3 ) 2 crystal by an 8 mJ, 620 ps, 800 nm pump laser. A maximum energy of 4.22 mJ with 3.82% rms stability at the first Stokes pulse can be obtained under 35 mJ pump energy. Moreover, the chirped first Stokes pulse can be compressed to 143 fs.

Zircon, ZrSiO4- A novel SRS-active crystal

The discovery of χ(3)-nonlinear lasing by stimulated Raman scattering (SRS) in natural crystals of zircon, ZrSiO4, is reported. All recorded Stokes and anti-Stokes Raman-induced lasing components are identified and attributed to the two occurring SRS-promoting phonon modes with ωSRS1 ≈ 1008 cm−1 and ωSRS2 ≈ 356 cm−1, which are related to the anti-symmetric stretching vibration B1g(ν3) and the bending mode Eg(ν4), respectively, of the crystal with symmetry . The study indicates the high potential of ZrSiO4 as an effective SRS crystal. Crystals of ZrSiO4, as used for sample preparation, together with a sample for SRS measurement.

Cascaded SRS of single- and double-scale fiber laser pulses in long extra-cavity fiber.

This work presents, for the first time, the results of studies of stimulated Raman scattering (SRS) in 1.2-km P2O5-doped silica fiber of radiation of single- and double-scale picosecond pulses generated in a fiber master oscillator and amplified in a one-stage fiber amplifier. Shown are differences in supercontinuum spectra composed of several Stokes components when pumped with pulses of different structure. More efficient Raman transformation of double-scale pulses was identified, leading to broader supercontinuum spectra.