Intensity control of the focal spot by vectorial beam shaping

A vectorial beam shaping algorithm is presented for the design of a phase-only diffractive optical element to achieve a given target intensity profile in the focal plane under tight focusing conditions. The underlying iterative optimization scheme is based on the Richards-Wolf vectorial diffraction theory and the Gerchberg-Saxton method, and is suitable for an arbitrary incoming polarization distribution, since only the magnitudes of the field vectors in the focal plane are reshaped. The efficiency of the method is numerically demonstrated for flat-top beam shaping examples of linear and circular incoming beam polarizations and square and circular flat-top region shape. A diffraction efficiency of 97.1% and a uniformity error of 4.8% were achieved in the case of focusing a Gaussian input beam onto a 50λ × 50λ square flat-top region with a 1.4-NA lens.     

An approximate analysis of the diffraction losses in corner reflectors

The fundamental mechanism of energy loss from a Gaussian beam scattered by the edge of a corner reflector is considered. An independent calculation is performed to estimate the relative losses for different polarizations with allowance for the Goos-Hanchen shift effect. For the angle of incidence α = π/4, the relative energy losses by waves polarized along the reflector’s edge and normally to this direction are estimated at (W _dif/W _inc)_E ? 7.03(λ₀/a) and (W _dif/W _inc)_H ? 3.82(λ₀/a), respectively, where λ₀ is the wavelength in free space and a is the effective radius of the beam.     

“Temperature oscillation” as a real-time monitoring of the growth of 3C-SiC on Si substrate

Pyrometric interferometry has been observed during gas-source molecular beam epitaxy (GSMBE) of 3C-SiC on Si substrate using monomethyl silane. The period of the “temperature oscillation” is shown to correspond to λ/2n, with the λ and n being the wavelength used in the monochromatic optical pyrometry and the refractive index of the grown film, respectively. As is the case for other heteroepitaxies, pyrometric interferometry may provide a feasible real-time monitoring method for the growth of 3C-SiC film on Si substrates.     

Talbot interferometer with computer generated gratings

In a Talbot interferometer the self image of a periodic pattern, such as a Ronchi ruling of period d, illuminated by a monochromatic plane wavefront of wavelength λ, is formed at distances which are integral multiples of 2d²/λ. A refracting object placed in front of the Ronchi ruling distorts the self image. A computer generated pattern can be designed, such that, when placed in a self imaging plane, a uniform intensity or a distinct moire pattern characterising a standard object is obtained. A method of computing the required patterns and experimental results for some aspherical objects are described.     

The thermal–optical effect due to varying the angle of incidence used for designing a tunable filter in photonic crystals

Tunable devices based on photonic-crystal (PhC) structures are employed in optical sources, detectors, and filters. We present the design and optimization of a wavelength-selective tunable filter with potential applications to the wavelength-division-multiplexing (WDM) systems. We analyze the design of a 1D tunable photonic-crystal filter, where tunability is achieved either by changing the temperature or the angle of incidence. The device is designed in a multilayered structure of silicon/silica (Si/SiO₂) with a defect in the middle. Based on the induced variation of optical parameters introduced by an external change of temperature, we analyze the effects of these changes in temperature on the transmission of the optical filter at different angles of incidence. We show that the position of the resonance peak has a linear dependence on temperature and the square of the angle of incidence. A linear regression provides a slope of d??/dT?=?+0.06?nm/°C and d??/d?? ²?=??0.104?nm/degree² around the transmission wavelength ???=?1.55???m. We obtain the corresponding field patterns and the transmission spectra using the transfer-matrix-method (TMM) simulations. We show the ability to tune the optical properties of the photonic-crystal filter elaborated by changing two parameters: the angle of incidence for selecting the wavelength and the temperature for fine tuning of the wavelength, which can be applied in integrated optics.     

1 × N add-drop filter structures using one dense wavelength division multiplexing thin-film filter

This paper proposes 1 × N add-drop filter structures in which only one thin-film filter (TF) is used. Our key idea is based on a combination of an angle-multiplexing concept and the flexibility of the optical fiber to allow a multiwavelength optical beam hit the TF several times, each time at a different angle but same position. Due to the TF angle sensitivity, the desired wavelength optical beam corresponding to the incident angle is therefore spatially isolated from the main optical beam. Our first TF-based 1 × N add-drop filter structure is arranged in a reflective design in which N wavelength optical beams can be dropped out from the main channel. For our transmissive architecture, N − 2 channels are directed to their associated output terminals while the remaining λ_N−1 and λ_N wavelength optical beams are sent out at the same port. Experimental proof of concept for our reflective TF-based 1 × 3 add-drop filter using one off-the-shelf TF, a triple fiber-optic collimator, and an optical circulator separates two wavelength optical beams with their channel spacing of 0.8 nm from the main channel. In this case, measured optical losses of 0.67 dB, 1.66 dB, and 2.59 dB are obtained for the first, the second, and the remaining dropped wavelength optical beams, respectively. Optical crosstalk and polarization dependent loss of <−18 dB and <0.08 dB are also investigated, respectively.     

Tight focusing of circularly polarized beam over high NA lens axicon with a diffractive optical element

We propose to use diffractive optical element in combination with high NA lens axicon to achieve a high depth of focus when illuminated by a circularly polarized beam. With this kind of system, the focal depth is increased to 12.816λ and the magnetic spot size is reduced to 0.3764λ. However, in the conventional lens with same NA, the FWHM of the magnetic spot is found to be 0.4308λ and its corresponding magnetization depth is only 0.888λ. The author expects that such a high focal depth strong longitudinal magnetic field with large magnetization depth can be widely used in high density magneto optic recording, laser machining, laser cutting and the scanning near-field magnetic microscope.     

On the shape consistency in the deformed shell-model approach

We show that the shape inconsistency (β^V_λ ? β^ρ_λ) between the average potential and the corresponding nucleonic density is generally small (～? 5%) for λ = 2, 3, 4 in both Nilsson and Woods-Saxon models. The properties of (β^V_λ ? β^?_λ) are analysed in detail and understood in terms of the extended Thomas-Fermi model. Approximate formulas β^ρ_λ = β^ρ_λ(β^V) are given and the microscopic reasons for the shape inconsistency discussed.     

The origin of the super-resolution via a nonlinear thin film

In laser applications, resolutions beyond the diffraction limit can be obtained with a thin film of strong optical nonlinear effect. The optical index of the silicon thin film is modified with the incident laser beam as a function of the local field intensity n(r)∼E²(r). For ultrathin films of thickness d?λ, the transmitted light through the film forms a profile of annular rings. Therefore, the device can be related to the realization of super-resolution with annular pupils. Theoretical analysis shows that the focused light spot appears significantly reduced in comparison with the diffraction limit that is determined by the laser wavelength and the numerical aperture of the converging lens. Analysis on the additional optical transfer function due to the thin film confirms that the resolving power is improved in the high spatial frequency region.     

Die optischen Konstanten des Cäsiums im Wellenlängenbereich von 0,3 bis 2,5 μ und ihre Abhängigkeit von Temperatur und Aggregatzustand

The optical constants of the alkali metal cesium have been measured in the wavelength region from 0.3 to 2.5 μ in the solid and liquid state at temperatures between 90 and 302 K, by analysing intensity and polarisation of the monochromatic radiations reflected by the surface of the metal. These mirrorlike surfaces, free of any contamination and not distorted by any treatment, were prepared and measured in ultrahigh vacuum. The purity of the metal was checked by measuring the residual resistance at liquid helium temperatures. The values thus obtained forn,k, ?₁=n ²-k ² and ?₂=2nk, listed in tables, and their temperature dependence permit to separate quantitatively the absorption due to different absorption mechanisms and to determine some of the quantities describing the behaviour of the free electrons.     

Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case

Consider ?Δ + λV with V short range at a value λ₀ where some eigenvalue e(λ) → 0 as λ ↓ λ₀. We analyze two questions: (i) What is the leading order of e(λ), i.e., for what α does e(λ) ～ c(λ ? λ₀)^α? (ii) Is e(λ) analytic at λ = λ₀ and, if not, what is the natural expansion parameter? The results are highly dimension dependent.     

Hyperfeinstrukturuntersuchungen mit einem sphärischen Fabry-Perot-Interferometer mit internem Absorptionsatomstrahl im Tm I- und Eu I-Spektrum

A spherical Fabry-Perot spectrometer with an absorbing atomic beam passing the interior of the interferometer is described. By use of the internal beam it is possible to reduce the amount of material needed for the atomic beam source to a few milligrams per hour. The set-up is especially suitable for hyperfine structure and isotope shift investigations. For the photoelectric recording of the signal the geometrical distance between the spherical mirrors was changed using the piezoelectric effect. In order to reduce the influence of the intensity distribution of the light sourceI ₀(λ) the ratio [I ₀(λ)-I(λ)]/I ₀(λ) was measured, whereI ₀(λ)=I ₀(λ) exp (—V·k(λ)·d) is the observed intensity with absorbing atoms between the mirrors, andV the increase of the absorption signal due to the multiple reflections of the light through the atomic beam (V≈75). For an accurate and easy evaluation of the data this ratio was measured by a digital voltmeter and punched into paper tape. The small line width of the absorption profile obtained in the experiments with Tm and Eu enabled us to measure hyperfine distances of the order of 5 · 10^?3 cm^?1 to 20 · 10^?3 cm^?1 with an error not exceeding 0.1 · 10^?3 cm^?1 in some cases. From the measurements theA-factors for five levels of the configurations 4f ¹³6s 6p and 4f ¹²5d 6s ² in Tm I and theA- andB-factors of the stable Eu isotopes of the 4f ⁷ 6s 6p y ⁸ P _5/2level in Eu I were determined.     

Efficient laser operation of diode-pumped Pr3+,Mg2+:SrAl12O19

We report on diode-pumped laser operation of Pr³⁺,Mg²⁺:SrAl₁₂O₁₉ at lasing wavelengths of λ _L = 724.4 nm, λ _L = 643.5 nm, and λ _L = 622.8 nm. Furthermore, the laser threshold could be reached in the green spectral range. By pumping the crystal longitudinally from each side with two polarization beam combined InGaN laser diodes, a total pump power of ≈4 W was available. In the deep red spectral range, a maximum output power of 564 mW was achieved with a maximum slope efficiency of 50 % with respect to the absorbed pump power. The maximum possible internal losses were estimated to ≈1 %. Beam quality factors M ² were in the range of 1.2–1.5.     

Efficient light confinement with nanostructured optical microfiber tips

Nanostructured optical microfiber tips are proposed and experimentally demonstrated to efficiently confine light beyond the diffraction limit at high powers. Focused ion beam milling was used for the nanostructuring of gold-coated optical microfiber tips with both single-ramp and wedge geometries. Small apertures were formed by flat cutting or hole drilling and optical spot sizes of ∼λ/10 with high transmission efficiency were achieved. Numerical simulations were carried out to optimize the device design with circularly polarized light. Enhanced transmission efficiencies (higher than 10⁻²) were recorded by optimizing the overall light throughput along the fiber tips. The tip thermal behavior was investigated by launching high powers into the device and recording the tip position in a scanning near-field optical microscopy set-up. This nanostructured optical microfiber tip has the potential for applications in optical recording, scanning near-field optical microscopy and lithography.     

Luminescent Sensor for Carbonate Ion Based on Lanthanide(III) Complexes of 1,4,7,10-Tetraazacyclododecane-1,4,7-Triacetic Acid (DO3A)

Lanthanide(III) complexes of 1,4,7,10-tetraazacyclododecane-1,4,7-triacetic acid (H₃DO3A) are suggested as sensors for sensitive luminescence-based determination of a carbonate anion. Thermodynamic study of association of [Eu(H₂O)₂(DO3A)] with bidentate anionic ligands using luminescence spectroscopy reveals an affinity order CO ₃ ^2? > oxalate^2? > picolinate^? > phthalate^2? ≈ citrate^3?; presumably as a consequence of an increasing chelate ring size. The ternary [Eu(DO3A)(picolinate)]^? and [Tb(DO3A)(picolinate)]^? complexes show improved photophysical properties due to the antenna effect of the picolinate anion. High quenching effect of carbonate anion and, to a lesser extent also oxalate, enables construction of a linear calibration plot utilizing optimized experimental conditions (e.g. c _LnL?=?0.1 mM, c _picolinate?=?2–5 mM, pH?=?7.4, λ _exc?=?286 nm, etc.) for carbonate determination in solution. Both sensors show a comparable sensitivity and the detection limit of about 0.4 mM. In order to improve the photophysical properties of Ln(III) sensor by shift of excitation wavelength about 40 nm to VIS range, the isoquinoline-3-carboxylic acid (IQCA) as antenna ligand was employed instead of picolinic acid. The analysis of commercial samples of European mineral waters was carried out and they were compared to the results obtained by capillary isotachophoresis to confirm there is no inherent (systematic) error to the present analysis. The Ln(III) sensor with IQCA is recommended since it has a better robustness than that with picolinate. The present analytical method is simple and rapid, and it is useful for sensitive determination of bicarbonate/carbonate concentration in water samples under aerobic conditions.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

Effect of thermal nonlinearity in high-absorption media on the parameters of the photoacoustic signal detected by the gas microphone method: The fundamental and second harmonics

A perturbation theory is put forward that describes the effect of thermal nonlinearity due to the temperature dependence of the thermophysical parameters of high-absorption systems with a low thermal conductivity on the parameters of the photoacoustic signal detected by the gas microphone technique. It is found that the dependence of the photoacoustic signal amplitude on incident beam intensity I ₀ stems from the dependence of the illuminated surface temperature on I ₀. This dependence is a complicated function instead of being a simple quadratic function as was expected. In the limiting cases (μ_sβ ? 1 and μ_sβ ? 1), this contribution to the photoacoustic signal amplitude is described by simple expressions, which are convenient for determining the thermal coefficients of the thermophysical parameters of the medium. It is found that the thermal nonlinearity significantly affects the photoacoustic signal phase in the frequency region meeting the condition μ_sβ ～ 1. In the above limiting cases, its effect is insignificant. A theory of generation of the photoacoustic signal second harmonic is proposed. The second harmonic is related to the temperature dependence of the thermophysical parameters of the buffer gas and sample. It is shown that the amplitude of the signal is a quadratic function of the incident beam intensity and varies with its frequency as ω^?3/2 for μ_sβ ? 1 and ω^?5/2 for μ_sβ ? 1.     

Measurement of azimuthal magnetic fields in a Z-pinch gas discharge using the faraday rotation of a probe beam

The Faraday rotation of the plane of polarisation of a probe beam by azimuthal magnetic fields in the presence of beam deflection caused by refractive index gradients is discussed for a plasma carrying an axial current. A method for calculation of the magnetic field profile from experimental data is described. Bθ can be found by Abel inversion if the electron density is known and if deflected rays can be collected by an optical system and focussed onto a detector. Typical Faraday rotations calculated for the Bennett pinch assuming small beam deflection are found to be proportional to the plasma current and to the angle of deflection. If the probe beam wavelength is chosen to satisfy the approximate relation N₀λ² ≈ 3.5 × 10¹³ m^-1, where N₀ is the electron density on the axis, measurement of Bθ with beam deflections less than 2 × 10^-2 radians should be possible in cases where small rotations can be detected in the mid-to-far infra-red part of the spectrum.     

The Excited Triplet State of Azoalkanes: Electron Spin Polarization and Magnetic Field Effects During Triplet-Sensitized Photolysis of trans-Azocumene in Solution

The triplet-sensitized photodecomposition of azocumene into nitrogen and cumyl radicals is investigated by time-resolved electron paramagnetic resonance and absorption spectroscopy. The radicals are found to be created spin polarized with a yield depending on the strength of the applied magnetic field. The phenomenon arises because in triplet azocumene, the decay into radicals competes with a fast triplet-sublevel selective intersystem crossing back to the azocumene ground state. The size of the initial spin polarization of the radicals and the magnetic field effect on their yield are determined in solvents of different viscosities. Data analysis yields rate constants for the intersystem crossing and the cleavage reaction of triplet azocumene as well as its zero-field splitting D _ZFS. At room temperature in nonpolar solvents, the most probable values are: k _x ?=?k _y ?=?1.2?×?10¹¹?s^?? and k _z ?=?1.9?×?10¹⁰?s^?? for the intersystem crossing from the energetically lower and upper triplet substates, respectively, k _p ?=?1.6?×?10⁹?s^?? for the cleavage reaction and for the zero-field splitting D _ZFS?=???.4?×?10^10?s^?? (0.18?cm^??).     

Effect of Fe2O3 nanoparticles on combustion of coal surrogate (Anisole): Enhanced ignition and formation of persistent free radicals

This contribution explores the effect of nanoparticles of iron (III) oxide (Fe₂O₃) on the combustion of coal surrogate, i.e., anisole, identifying the changes in ignition features as well as the occurrence of persistent organic pollutants in the initiation channels. The method applies packed-bed reactor coupled with Fourier transform infrared (FTIR) spectroscopy to quantitate the ignition temperature under typical fuel-rich conditions, in-situ electron paramagnetic resonance (EPR) to elucidate the formation of environmentally-persistent free radicals (EPFR), diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) to monitor the chemisorption of organic substrates on the nanoparticles, as well as X-ray diffraction for particles characterisation (PXRD). We employ cluster-based quantum mechanical calculation to map the reaction pathway within the scope of the density functional theory. The results of Fe₂O₃-mediated combustion of anisole depict an excessive reduction in ignition temperature from 500?°C around 220?°C at λ?=?0.8. As confirmed both from EPR and DRIFTS measurements, the chemisorption of anisole on α-Fe₂O₃ surfaces follows the direct dissociation of the O–CH₃ (and OCH₂–H), leading to the formation of surface-bound phenoxy radicals at temperatures as low as 25?°C and incurring an estimated energy barrier of E_a?=?18?kJ mol^?1 and a preexponential factor of A?=?2.7?×?10¹² M^?1 s^?1. This insight applies to free-radical chain reactions that induce spontaneous fires of coal, as coal comprises ferric oxide nanoparticles, and equally to coexistence of aromatic fuels with thermodynamically reactive Fe₂O₃ surface, e.g., in fly ash, at the cooled-down tail of combustion stacks.