Propagation characteristics of flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture

The approximate analytical formula for flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture was derived by the extended Huygens–Fresnel principle. Some numerical simulations are illustrated to the effects on the propagation of flattened Gaussian beams by the misaligned annular aperture. To compare the difference between annular apertured system and circular apertured system, the circular apertured system is also studied. The results show that angle misalignments and lateral displacements of aperture create asymmetrical average intensity distribution at receiving plane z = 500. The effects on intensity distribution by angle misalignments of annular aperture were small. In annular aperture case, the smooth of intensity distribution was worse with escalating obscure ratio ? in near-field; the side-lobes increased and the central lobe decreased with escalating obscure ratio ? in far-field. At receiving plane z = 500: for circular aperture, the side-lobes decreased, even to be neglected, with the increasing of truncation parameter δ; for annular aperture, the side-lobes increased with the increasing of truncation parameter δ. In addition, it is found that the aligned thin lens can fix asymmetry of intensity distribution which was caused by the misaligned annular aperture.     

Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel

We analyze the orbital angular momentum (OAM) crosstalk of single photons propagation through low-order atmospheric turbulence. The probability models of the orbital angular momentum crosstalk for single photons propagation in the channel with the non-Kolmogorov turbulence tilt, coma, and astigmatism and defocus aberration have been established. It is found, for α = 11/3, that the turbulent tilt is the dominant aberration which causes the orbital angular momentum crosstalk, the coma is second and the astigmatism is third, but the defocus aberration has no impact on OAM. The results also indicate that the regularities of orbital angular momentum crosstalk caused by the tilt, the coma and the astigmatism are almost the same, respectively. The crosstalk probability of the orbital angular momentum increases as the azimuth mode index p of Laguerre-Gaussian (LG) beam increases, the turbulent strength C_n² enhances, the orbital angular momentum quantum number rises, the diameter of circular sampling aperture D and the channel zenith angle θ increase.     

Effect of the open roof on low frequency acoustic propagation in street canyons

This paper presents an experimental, numerical and analytical study of the open roof effect on acoustic propagation along a 3D urban canyon. The experimental study is led by means of a street scale model. The numerical results are performed with a 2D-Finite Difference in Time Domain approach adapted to take into account the acoustic radiation losses due to the street open roof. An analytical model, based on the modal decomposition of the pressure field in the street width mixed with a 2D image sources model including the reflection by the open roof, is also presented. Results are given for several frequencies in the low frequency domain. The comparison of these approaches shows a quite good agreement until f = 100 Hz at full scale. For higher frequency, experimental results show that the leakage, due to the street open roof, is not anymore uniformly distributed on all modes of the street. The notion of leaky modes must be introduced to model the acoustic propagation in a street canyon.     

Nonlinear change of on-axis pressure and intensity maxima positions and its relation with the linear focal shift effect

A comprehensive experimental, analytical and numerical study of the true focal region drift relative to the geometrical focus (focal shift effect) in acoustic focused beams and its nonlinear evolution is presented. For this aim, the concept of Fresnel number, proportional to the linear gain, is introduced as a convenient parameter for characterizing focused sources. It is shown that the magnitude of the shift is strongly dependent on the Fresnel number of the source, being larger for weakly focused systems where a large initial shift occurs. Analytical expressions for axial pressure distributions in linear regime are presented for the general case of truncated Gaussian beams. The main new contribution of this work is the examination of the connection between the linear and nonlinear stages of the focal shift effect, and its use for the estimation of the more complicated nonlinear stage. Experiments were carried out using a continuous-wave ultrasonic beam in water, radiated by a focused source with nominal frequency f = 1 MHz, aperture radius a = 1.5 cm and geometrical focal distance R = 11.7 cm, corresponding to a Fresnel number N_F = 1.28. The maximum measured shifts for peak pressure and intensity were 4.4 and 1.1 cm, respectively. The evolution of the different maxima with the source amplitude, and the disparity in their axial positions, is interpreted in terms of the dynamics of the nonlinear distortion process. Analytical results for the particular case of a sound beam with initial Gaussian distribution are also presented, demonstrating that the motion of peak pressure and peak intensity may occur in opposite directions.     

Plasmonics: Absorption and scattering of light of non-straight ordered array of Au rings

In this paper, Au nanorings in a SiO₂ substrate have been utilized to design a plasmonic waveguide with lower losses and perfect energy coupling. Our recommended structure consists of a chain of dozen Au nanorings with a given intercenter space between them going on resonance, if a beam with specific wavelength is launched in the input area of the waveguide. Nanoring has an extra degree of freedom in its geometry and have a preferable tunability in comparison to other shapes of nanoparticles (e.g. nanospheres). It is shown that a modified plasmon waveguide structure can be utilized at optical communication band (λ = 1550 nm), in optical integrated devices. Red-shifted of localized surface plasmon resonance (LSPR) has been considered as a fundamental condition to have a maximum of optical response at λ = 1550 nm. Cross-sectional depictions of field propagation through the structure are displayed in order to show the absorption and scattering of light by particles. Ultimately, transmitted power ratio is computed for the structure to clear-cutting its characteristics.     

Geometrical theory of energy launching and pulse distortion in dielectric optical waveguides

In this paper the geometrical theory of pulse distortion and energy launching into multimode optical fibres is generalized when skew rays are taken into account. To this purpose, within the geometrical theory of skew rays, we firstly obtained a new expression for the numerical aperture. From this expression we derived an extensive analysis of the energy launched and the pulse response of a multimode optical fibre. A better launching efficiency and a different pulse form at the output of the fibre together with a larger broadening are obtained in comparison with the results derived from theories only for meridional rays. The theory is also applied to sources having planar geometry (such as LED) and linear geometry (such as semiconductor lasers), and the response to some rectangular-shaped pulses is investigated. Finally some considerations concerning scattering effects are described.     

Planar quarter wave stacks prepared from chalcogenide Ge-Se and polymer polystyrene thin films

Planar quarter wave stacks based on amorphous chalcogenide Ge-Se alternating with polymer polystyrene (PS) thin films are reported as Bragg reflectors for near-infrared region. Chalcogenide films were prepared using a thermal evaporation (TE) while polymer films were deposited using a spin-coating technique. The film thicknesses, d∼165 nm for Ge₂₅Se₇₅ (n=2.35) and d∼250 nm for polymer film (n=1.53), were calculated to center the reflection band round 1550 nm, whose wavelengths are used in telecommunication. Optical properties of prepared multilayer stacks were determined in the range 400-2200 nm using spectral ellipsometry, optical transmission and reflection measurements. Total reflection for normal incidence of unpolarized light was observed from 1530 to 1740 nm for 8 Ge-Se+7 PS thin film stacks prepared on silicon wafer. In addition to total reflection of light with normal incidence, the omnidirectional total reflection of TE-polarized light from 8 Ge-Se+7 PS thin film stacks was observed. Reflection band maxima shifted with varying incident angles, i.e., 1420-1680 nm for 45° deflection from the normal and 1300-1630 nm for 70° deflection from the normal.     

Trapping Rayleigh particles using highly focused higher-order radially polarized beams

The optical trapping characteristics of highly focused higher-order radially polarized beams (R-TEM_p1*) acting on a Rayleigh particle are studied theoretically. Numerical results show that as the order p of beam increases and the numerical aperture NA_o of the objective decreases, the axial trap distance increases but the trap depth and maximum restoring force decreases. In a limit of NA_o = 1, three higher-order R-TEM_p1* beams of p = 1, 2, 3, like the fundamental lowest-order radially polarized beam of p = 0, can three-dimensionally trap a particle to the focus but the axial trap stiffness decreases with the increase of p. When NA_o = 0.95, the focus is still a stable trap point for the two beams of p = 0 and 1 but it becomes an unstable trap point for the two beams of p = 2 and 3. The trap stability is also discussed for higher-order radially polarized beam illumination.     

Propagation regimes of intense circularly polarized laser beam in magnetoactive plasma

This paper presents an analytical and numerical investigation of an intense circularly polarized wave propagating along the static magnetic field parallel to oscillating magnetic field in magnetoactive plasma. In the relativistic regime such a magnetic field is created by pulse itself. The authors have studied different regimes of propagation with relativistic electron mass effect for magnetized plasma. An appropriate expression for dielectric tensor in relativistic magnetoactive plasma has been evaluated under paraxial theory. Two modes of propagation as extraordinary and ordinary exist; because of the relativistic effect, ultra-strong magnetic fields are generated which significantly influence the propagation of laser beam in plasma. The nature of propagation is characterized through the critical-divider curves in the normalized beam width with power plane For given values of normalized density (ω_p/ω) and magnetic field (ω_c/ω) the regions are namely steady divergence (SD), oscillatory divergence (OD) and self-focusing (SF). Numerical computations are performed for typical parameters of relativistic laser-plasma interaction: magnetic field B = 10-100 MG; intensity I = 10¹⁶ to 10²⁰ W/cm²; laser frequency ω = 1.1 × 10¹⁵ s⁻¹; cyclotron frequency ω_c = 1.7 × 10¹³ s⁻¹; electron density n_e = 2.18 × 10²⁰ cm⁻³. From the calculations, we confirm that a circularly polarized wave can propagate in different regimes for both the modes, and explicitly indicating enhancement in wave propagation, beam focusing/self-guiding and penetration of E-mode in presence of magnetic field.     

Broadband second-harmonic generation in a double-tapered gallium arsenide slab using total internal reflection quasiphase matching

This article analytically describes broadband second-harmonic generation in a double-tapered gallium arsenide (GaAs) slab using total internal reflection quasi-phase matching technique. This double-tapered configuration ensures a combination of increasing and then decreasing bounce lengths which provides an extremely wide 3 dB bandwidth of 573.6 nm with a conversion efficiency of 1.929%, after considering reflection and absorption losses. Effect of varying the slab dimensions, viz., length and tapering angles, as well as the operating temperature on the performance parameters has also been incorporated in the analysis.     

Electro-optic Q-switched intracavity optical parametric oscillator at 1.53 μm based on KTiOAsO4

An eye-safe, high peak power optical parameter oscillator (OPO) intracavity pumped by electro-optic Q-switched Nd:YAG laser is presented. This OPO is based on a 20 mm length KTiOAsO₄ crystal with non-critical phase matching (θ = 90°, ?=0°) cut. An aperture ∅3 mm acted as limiting diaphragm to get good beam quality of pumping laser. The output energy of 25 mJ at the signal wavelength 1.53 μm was obtained with repetition rate of 1 Hz. The highest peak power intensity was up to 88 MW/cm² with pulse width of 4 ns. Without diaphragm, the maximum output energy of 90 mJ was achieved with area of light spot (∅6 mm) four times larger, but the peak power intensity was lower.     

Enhancement effect in photon-stimulated ion desorption for benzene adsorbed on silicon surfaces observed using angle-dependent technique

We have investigated photon-stimulated ion desorption from deuterated benzene (C₆D₆) adsorbed on Si(1 0 0) and Si(1 1 1) surfaces following C 1s core excitation. Using time-of-flight mass spectrometry combined with angle-dependent technique, we measured the dependences of mass-spectra of desorption ions on photon energies and on incident angle (θ) of synchrotron beam. We have found the ion yields for adsorbate-derived fragments of CD⁺ and CD₂⁺ are enhanced in very small angles of incident X-rays. Moreover, molecular orientation effect appeared in excitation energy dependences of D⁺ ions from the Si(1 0 0) and Si(1 1 1) surfaces; that is, ion yield spectra measured at θ = 10° are different from that at θ = 65°. Furthermore, it was found that desorption ion yields increase greatly with decreasing incident angles. The angular dependences are consistently similar for all ion species, excitation energies, and indexes of substrates. Possible desorption processes are described on the basis of the observations.     

Interaction of low-frequency axisymmetric ultrasonic guided waves with bends in pipes of arbitrary bend angle and general bend radius

The use of ultrasonic guided waves for the inspection of pipes with elbow and U-type bends has received much attention in recent years, but studies for more general bend angles which may also occur commonly, for example in cross-country pipes, are limited. Here, we address this topic considering a general bend angle φ, a more general mean bend radius R in terms of the wavelength of the mode studied and pipe thickness b. We use 3D Finite Element (FE) simulation to understand the propagation of fundamental axisymmetric L(0, 2) mode across bends of different angles φ. The effect of the ratio of the mean bend radius to the wavelength of the mode studied, on the transmission and reflection of incident wave is also considered. The studies show that as the bend angle is reduced, a progressively larger extent of mode-conversion affects the transmission and velocity characteristics of the L(0, 2) mode. However the overall message on the potential of guided waves for inspection and monitoring of bent pipes remains positive, as bends seem to impact mode transmission only to the extent of 20% even at low bend angles. The conclusions seem to be valid for different typical pipe thicknesses b and bend radii. The modeling approach is validated by experiments and discussed in light of physics of guided waves.     

Transverse superresolution with extended depth of focus using binary phase filters for optical storage system

This paper reports the study of superresolution and extension of depth of focus (DOF) of three-zone binary phase filters (BPFs) under high numerical aperture (NA) focusing. Two three-zone BPFs (BPF1 and BPF2) are specially designed to achieve transverse superresolution and extension of DOF simultaneously for the optical disc system with an objective lens of NA = 0.65. Numerical simulations based on the vectorial diffraction theory indicate that the transverse focal spot size of this system can be as small as that of NA = 0.85 and its DOF is as large as that of NA = 0.6 with acceptable Strehl ratios (> 0.4 for BPF1 and > 0.35 for BPF2) and low side-lobe intensity ratios (< 10%) by using these BPFs. It suggests that the storage capacity of this optical storage system may be improved to the same as that of a system with an objective lens of NA = 0.85. Moreover, the strict requirement of the focusing servo system caused by decreasing wavelength or employing higher NA objective lens can be mitigated. Therefore, these BPFs presented in this paper should be highly interesting for applications of high density optical data storage.     

Characterization of nanoparticles of organic carbon (NOC) produced in rich premixed flames by differential mobility analysis

Differential mobility analysis (DMA) is used to measure on-line the size distributions of inception particles in atmospheric pressure premixed ethylene air flames ranging from C/O = 0.61 to 0.69, just at the onset of soot formation. DMA is also used, in combination with electrospray, to measure the size distributions of suspended flame products captured in water samples. The DMA systems used for this work employ detectors sensitive to the full range of molecular clusters/nanoparticles in gas-to-particle conversion processes (as small as about 1 nm) and they have much larger sheath gas flow rates than is typically used to reduce losses and peak broadening by diffusion. The measured size distributions show that the first particles observed in flames have a size of 2 nm, consistent with previous in situ measurements by light scattering and extinction (LSE) and the off-line measurements of material captured in water samples from the same flames. For richer flames, the quantity of the 2 nm particles measured increases, and the width of its size distribution shifts asymmetrically toward larger sizes. A numerical coagulation model assuming size-dependent coagulation efficiency predicts well the experimentally measured size distributions in the flames examined. Similarly, the slightly larger size distributions measured by atomic force microscopy of inception particles deposited on surfaces can also be attributed to the size-dependent coagulation/adhesion efficiency. The results imply that the smaller nanoparticles formed in combustion processes have a longer lifetime than those larger than 6-7 nm and may play an important role in the formation of fine organic carbon particulate in the atmosphere.     

Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides

The propagation of electromagnetic energy via coupled surface plasmon polariton modes in a metal-insulator-metal heterostructure is analyzed analytically for a core material exhibiting optical gain. It is shown that a sufficiently large gain can completely compensate for the absorption losses due to energy dissipation in the metallic boundaries, enabling long-range transport with a confinement below the diffraction limit for on-chip switching and sensing applications. For a free-space wavelength of 1500 nm, lossless propagation in a gold-semiconductor-gold waveguide with a core size of 50 nm is predicted for a gain coefficient γ = 4830 cm⁻¹, comparable to that of semiconductor gain media. The gain requirements decrease with the use of low-index nanocrystal-doped glasses or polymers as core materials.     

Transmission analysis of ultrasonic Lamb mode conversion in a plate with partial-thickness notch

Mode conversions of Lamb waves can occur upon encountering damage or defect such as a notch, leading to newly-converted modes apart from wave reflection and transmission. In this paper, the transmission of the fundamental Lamb modes symmetrical S0 and anti-symmetrical A0 with anti-symmetrical notches were investigated in steel plates within the relatively short propagation distance. The group velocity and modal energy of the converted modes were analyzed using simulations and experiments. Two-dimensional finite difference time domain (2D-FDTD) method was employed to calculate the scattering field and extract numerical trends for simulation study and experimental confirmation. Both simulations and experiments revealed that the apparent group velocities of the converted modes in the transmitted signals subject to the notch positions. To describe the mode conversion degree and evaluate the notch severity, wave packets of the originally-transmitted modes and newly-converted modes were separated and corresponding mode energy percentages were analyzed at different notch severities. Frequency-sweeping measurements illustrated that the modal energy percentages varied monotonically over the notch-depth increase with a statistically consistency (R = 1.00, P < 0.0004).     

Quasi Bessel beam by Billet's N-split lens

This study utilizes the focal property of a classical Billet's split lens to create more focal points by splitting the lens. This approach distributes the focal points circularly on the focal plane. This study explores the characteristics of beam propagation and analytically derives the asymptotic characteristics of beam propagation based on the stationary phase approximation and the moment-free Filon-type method. Results show that the unique Billet's N-split lens can generate a quasi Bessel beam if the number of splitting N is large enough, e.g., N ≧ 24. This study also explores the diffraction efficiency of corresponding quasi Bessel beam and the influence of aperture size. The potential advantage of proposed split lens approach is that, unlike the classical means of annular aperture, this simple lens approach allows a much larger throughput in creating the Bessel beam and hence the Bessel beam could have more optical energy.     

Effect of the surface integral in the torque equation of the electromagnetic angular momentum on the Faraday rotation

A circularly polarized plane wave of infinite transverse extent (δ = ∞) has no spin angular momentum, while a realistic light does carry it. This paradox originates from the presence (δ = ∞) and absence (δ ≈ 0) of the surface integral in the total angular momentum J. The same holds for the torque equation of dJ/dt, so that δ is also connected with the relative Faraday rotation angle Θ_F/θ_F when a radius (a) of a cylindrical medium with optical activity is only a little larger than that (b) of light beam, where Θ_F is the Faraday rotation angle and θ_F is the intrinsic Faraday rotation angle of a medium. It is shown here that it is possible to estimate δ for a realistic light from the drastic variation in Θ_F/θ_F near b/a = 1.     

The focusing property of vector Bessel-Gauss beams by a high numerical aperture objective

The rich available transverse intensity structure of vector Bessel-Gauss beams make it important to probe into the focusing property by high numerical aperture objective. In this paper, we obtain the analytical expressions of azimuthally, radially and longitudinally polarized components in the focal area of the objective after tight focusing. Theoretical analysis and the numerical simulation show that, the transverse intensity distributions of the focused beams still have doughnut-like structure, two separate peak structure and circularly aligned array structure. The focused beam spots obtained by an objective with annular aperture usually have smaller spots than with circular aperture. The focused beam of the vector Bessel-Gauss beam with lowest mode number m = 0 is a radially and azimuthally polarized doughnut-like beam with no longitudinal component. These properties and results are useful in optical trapping and particle alignment.