Radiative transfer in static and spherically symmetric distording media: from the effective geometry to a kinetic theory

In numerous new media (superfluids, Bose-Einstein condensates, nonlinear dielectrics,…) and multiple settings (accretion flows onto compact objects, optics EIT, stellar collapses, supernovae expanding envelopes, relativistic vortex flow, early Universe…) matter appears to light as an effective curved spacetime. These media that we call ‘distording media’ induce spatial modifications on the phases functions of the electromagnetic fields so that light paths become curved lines. This nonlinear optical behavior gives birth to singular effects (confinement of light, black hole effect…) which confer in the same time a local and a non-local dimension to the radiative transfer. We develop a general phenomenological theory of radiative transfer inside any static and spherically symmetric distorting media. We especially prove that the curvature of the effective spacetime plays a fundamental role in the specific intensity balance.     

Radiative absorption in an infinitely long hollow cylinder with Fresnel surfaces

Radiation absorption in an infinitely long hollow cylinder with Fresnel surfaces is studied using the ray tracing method. It is found that the inner boundary can be modeled as a total reflective surface for the infinitely long hollow cylinder. Radiative absorption of hollow cylinders with Fresnel surfaces is compared to diffusive surfaces predicted by the finite volume method. Effects of refractive index, optical thickness and hole size on radiative absorption are studied. Abrupt changes in radiative absorption near τ_r/τ_Ro=1/n are observed for hollow cylinders with Fresnel surfaces. It is because the Fresnel relation predicts a critical angle at . This trend is not observed in diffusive surfaces. Refractive index and optical thickness are two competing factors that govern the radiative absorption. Higher refractive index drives higher absorption close to the inner surface, while higher optical thickness yields higher absorption near the outer surface. The results of this study can also serve as benchmark solutions for modeling radiative heat transfer in hollow cylinders with Fresnel surfaces. It is also found that the directional or hemispherical emittance can be calculated without solving the radiative transfer equation in the media when the temperature variation in the media is small.     

Retardation and nonstationarity effects on the generation of terahertz radiation by the e-h plasma in a semiconductor

Radiative processes in a nonequilibrium e-h plasma are theoretically studied using a self-consistent solution of the kinetic equation and Maxwell’s equations. The terahertz emission from a finite-thickness semiconductor sample is due to the retardation and nonstationarity of the electromagnetic interaction of the photocurrent in the e-h plasma and the radiation field. The duplex waveform of the terahertz electromagnetic pulse for an arbitrary ratio of the radiation formation length and the plate thickness originates due to coherent radiative processes accompanying the generation of the e-h plasma at the input boundary and its extinction at the output boundary of a semiconductor plate through which a weakly absorbed ultrashort laser pulse propagates. The theoretical conclusions show analogies with the radiative phenomena accompanying the start-stop motion of external currents (Tamm problem) and the nonlinear interaction of optical waves in a finite-thickness medium.     

Topological and morphological transformations of developing singular paraxial vector light fields

The paper is devoted to establishment of the real-time topological and morphological dynamics of generic developing paraxial elliptic speckle fields generated and driven by the system ‘laser beam + photorefractive crystal LiNbO₃:Fe’. Generic space-time development of full gamut of polarization ellipse parameters (ellipticity, azimuth, morphology of C points, optical diabolos and handedness) and their combination in fixed beam cross-section was measured in details by the elaborated quick-action real-time Stokes-polarimetry. Whole field irreversible evolution is fulfilled through totality of random space/time C point pair nucleation/annihilation. The ‘life-story’ of C point and optical diabolo pairs is realized through ‘local topological/morphological transition’ with fully reversible scenario. It starts from smooth fragment of speckle field by formation of pre-nucleation local structure and finishes by after-annihilation local structure which decays to another smooth structure. Scenarios of star-monstar pair nucleation/annihilation and monstar  ↔  lemon transformation were established. Measured statistics of C point and diabolo morphological forms was in excellent agreement with theory predictions. All allowed scenarios of diabolo pair ‘life-story’ started/finished as star-hyperbolic monstar-hyperbolic pair were measured. Evolution of polarization ellipses handedness is implemented through L contours movement and reconnection with a saddle as the catalyst. Reconnection of L contour peninsula leads to birth of closed L contour delimiting island of fixed handedness ellipses with/without C points. Elaborated approach and presented results start the dynamic singular optics of time-dependent vector light fields.     

Escape factors for laser-plasmas

A method of parameterizing escape factors (transmission factors and net radiative brackets) for conditions typical of laser-produced plasmas is introduced. The assumptions of planar geometry, exponentially decreasing emissivity and absorption coefficient with distance with a step rise at a particular point, and spatially constant Doppler broadened line profiles have been made. The effect of velocity gradients in spectrally shifting the absorption and emission line profiles relative to each other is taken into account assuming linear velocity gradients with distance. A parameter R representing the ratio of the spatial scale-length of the absorption coefficient to the Doppler decoupling length is introduced. Fitting formulae for transmission factors and net radiative brackets are given which are valid for all R and all optical depths. In the limit of small R (large Doppler decoupling length), the escape factors asymptotically approach formulae developed originally by, for example, Holstein assuming negligible plasma velocities. For large R (small Doppler decoupling length), the escape factors have been shown to asymptotically approach the Sobolev approximation. The parameterized net radiative bracket has been used in the hydrodynamic and atomic physics code ‘EHYBRID’ for the calculation of the effect of radiation trapping on population densities in laser-produced plasmas. The output of the modified EHYBRID code has then been post processed using the parameterised transmission factors to simulate 123 Ne-like and 399 F-like germanium resonance line intensities emitted in typical X-ray laser experiments. We obtain an agreement between the simulated and experimental spectra.     

Time shift and superposition method for solving transient radiative transfer equation

Due to the long-time transient response of pulse irradiation, the computational time required for solving transient radiative transfer (TRT) is often very long, especially for the case in which the boundary is subjected to continuous pulse train and the geometry is complicated. In addition, sometimes, before actual experiments are carried out, a suitable pulse shape or type often needs to be selected by numerical simulation and comparison. Because the numerical solution of TRT needs to be repeated many times, the selection processes is very time-consuming. In this paper, by considering that the TRT equation and its initial and boundary conditions are linear, a time shift and superposition method is developed for solving TRT equation in non-emitting media, in which only the transient response of a short square pulse needs to be solved, and the solution of TRT under any pulse shape can be constructed by time shift and then superposition using the basis solution of the short square pulse. Three numerical examples are studied to illustrate the peformance of the superposition method in solving TRT problems. The results show that the superposition is effective, accurate and very suitable for solving TRT in the medium subjected to a series of pulse train.     

Analysis of the linear stability of stationary solutions in a circular laser containing a saturable absorber “LSA” for inhomogeneous broadening

In this present paper, the optical bistability in a circular laser containing a saturable absorber LSA for inhomogeneous broadening is studied. A simple mathematical model was developed to describe the action of this type of laser in a circular resonator under two conditions, when the spontaneous emission is neglected or included in the cavity. For both of these two cases, the coefficient of saturation was considered to be equal or different to unity (ζ=1 or ζ≠1). The photons intensities Q_j were determined as function of the pumping rate σ₀ of the active medium and analyzed the linear stability of the stationary solutions obtained in a circular laser containing a saturable absorber “LSA” for inhomogeneous broadening.     

Ion-acoustic shock waves with negative ions in presence of dust particulates

Dust acoustics shock waves have been investigated experimentally in a homogeneous unmagnetized dusty plasma device containing negative ions. When the negative ion density larger than a critical concentration ‘rc’ negative shock waves were observed instead of positive shock waves. Again when it is nearly equal to ‘rc’ both positive and negative shock waves propagate. The experimental findings are compared with modified KdV-Burgers equation. The velocity of the shock waves are also measured and compared with the numerical integration of modified KdV-Burgers equation.     

Investigation of nonstationary models of laser pulse propagation through a homogeneous scattering layer

Using three nonstationary models of radiation transfer in two versions (diffusion-based and axial), the absorption and scattering coefficients of homogeneous scattering media are found from experimental temporal distributions of an ultrashort laser pulse transmitted through the scattering layer of different thickness. These optical characteristics are found to be dependent on the scattering layer thickness, which contradicts physical considerations. The reason for the discovered effect is related to incomplete taking into account of the properties of the scattering indicatrix in the used approximate models. The validity of this interpretation is supported by a Monte Carlo simulation, which yielded similar dependences. Recommendations on the correct use of the approximate radiation transfer models are given.     

Measurement of nonlinear optical coefficients by the z-scan technique: Correctness of the technique and investigation of a new compound-lutetium diphthalocyanine complex

Correctness of z-scan measurements of nonlinear refractive indices for optical media is considered. It is shown that accuracy of these measurements is greatly affected by the thickness of the nonlinear medium layer (as compared with the diffraction length of the laser beam). Nonlinear refractive indices of nitrobenzene are measured at different laser pulse durations (7 ns and 350 ps); the nonlinearity mechanism is discussed. It is shown that at the pulse duration 350 ps the orientation mechanism of nonlinearity is less effective than at the pulse duration 7 ns due to its time lag. Nonlinear refractive indices are measured for the solution of a new synthesized compound-hexadecabutyl-substituted lutetium diphthalocyanine.     

An analysis of the rotational, fine and hyperfine effects in the (0, 0) band of the AΠ-XΣ transition of manganese monohydride, MnH

High-resolution (±0.003 cm⁻¹), laser induced fluorescence (LIF) spectra of a supersonic molecular beam sample of manganese monohydride, MnH, have been recorded in the 17500-17800 cm⁻¹ region of the (0, 0) band of the A⁷Π-X⁷Σ ⁺ system. The low-N branch features were modeled successfully by inclusion of the magnetic hyperfine mixings of spin components within a given low-N rotational level using a traditional ‘effective’ Hamiltonian approach. An improved set of spectroscopic constants has been extracted and compared with those from previous analyses. The optimum optical features for future optical Stark and Zeeman measurements are identified.     

Relevance of the subgrid-scales for large eddy simulations of turbulence-radiation interactions in a turbulent plane jet

An a priori study based on direct numerical simulation (DNS) of a non-isothermal turbulent plane jet has been carried out in order to analyse the role of the small-scales of turbulence on thermal radiation. Filtered DNS and large eddy simulation (LES) without subgrid-scale (SGS) model have been estimated for the radiative heat transfer. The comparison of the results highlights the subgrid-scale influence over the filtered radiation quantities, such as the radiative intensity and the radiative emission. The influence of the optical thickness is also studied. It is shown that the subgrid-scales are not significant near the centerline of the jet, where the radiative heat transfer is more important, and therefore that the SGS can be neglected in this configuration. However, when the optical thickness increases, the SGS become relevant and SGS modeling may be needed.     

Simultaneous solution of Kompaneets equation and radiative transfer equation in the photon energy range 1-125 keV

Radiative transfer equation in plane parallel geometry and Kompaneets equation is solved simultaneously to obtain theoretical spectrum of 1-125 keV photon energy range. Diffuse radiation field are calculated using time-independent radiative transfer equation in plane parallel geometry, which is developed using discrete space theory (DST) of radiative transfer in a homogeneous medium for different optical depths. We assumed free-free emission and absorption and emission due to electron gas to be operating in the medium. The three terms n, n² and (∂n/∂x_k) where n is photon phase density and x_k=(hν/kT_e), in Kompaneets equation and those due to free-free emission are utilized to calculate the change in the photon phase density in a hot electron gas. Two types of incident radiation are considered: (1) isotropic radiation with the modified black body radiation I^MB[1] and (2) anisotropic radiation which is angle dependent. The emergent radiation at τ=0 and reflected radiation τ=τ_max are calculated by using the diffuse radiation from the medium. The emergent and reflected radiation contain the free-free emission and emission from the hot electron gas. Kompaneets equation gives the changes in photon phase densities in different types of media. Although the initial spectrum is angle dependent, the Kompaneets equation gives a spectrum which is angle independent after several Compton scattering times.     

Coupled radiative and conductive heat transfer in a non-grey absorbing and emitting semitransparent media under collimated radiation

This paper deals with heat transfer in non-grey semitransparent two-dimensional sample. Considering an homogeneous purely absorbing medium, we calculated the temperature field and heat fluxes of a material irradiated under a specific direction. Coupled radiative and conductive heat transfer were considered. The radiative heat transfer equation (RTE) was solved using a S₈ quadrature and a discrete ordinate method. Reflection and absorption coefficients of the medium were calculated with the silica optical properties. The conduction inside the medium was linked to the RTE through the energy conservation. Validation of the model and two original cases are also presented.     

‘Superluminal paradox’ in wave packet propagation and its quantum mechanical resolution

We analyse in detail the reshaping mechanism leading to apparently ‘superluminal’ advancement of a wave packet traversing a classically forbidden region. In the coordinate representation, a barrier is shown to act as an effective beamsplitter, recombining envelopes of the freely propagating pulse with various spacial shifts. Causality ensures that none of the constituent envelopes are advanced with respect to free propagation, yet the resulting pulse is advanced due to a peculiar interference effect, similar to the one responsible for ‘anomalous’ values which occur in Aharonov’s ‘weak measurements’. In the momentum space, the effect is understood as a bandwidth phenomenon, where the incident pulse probes local, rather than global, analytical properties of the transmission amplitude T(p)$T\left(p\right)$. The advancement is achieved when T(p)$T\left(p\right)$ mimics locally an exponential behaviour, similar to the one occurring in Berry’s ‘superoscillations’. Seen in a broader quantum mechanical context, the ‘paradox’ is but a consequence of an attempt to obtain ‘which way?’ information without destroying the interference between the pathways of interest. This explains, to a large extent, the failure to adequately describe tunnelling in terms of a single ‘tunnelling time’.     

Simultaneous radiative and conductive heat transfer in non-gray media

Steady-state energy transfer through non-gray radiating and conducting media enclosed by black walls of unequal temperature is studied. A rectangular Milne-Eddington type relation is used to describe the frequency dependence of the absorption coefficient. Temperature distributions and total heat transfer results are presented for materials which absorb radiation (a) of low frequency, (b) of high frequency, (c) within a finite band width, and (d) of all frequencies (gray). The influence of optical thickness (τ₀) and conduction to a radiation interaction parameter (N) are examined and the results for non-gray materials are compared with those for a gray analysis. Exact results are compared with those determined by using the optically-thin and the optically-thick approximations, as well as with those evaluated for purely conductive and purely radiative transfer.     

Percolation picture for long wavelength phonons in zinc blende alloys: application to GaInAs

We propose a ‘one bond→two modes’ model for the long wavelength optical phonons in random zinc-blende A_xB_1−xC ternary alloys, based on the percolation site theory. Our model takes into account the ‘fractal→normal’ object transition, which goes with the ‘dispersion→continuum’ topology transition at the percolation thresholds of the A-C and B-C bonds. We first introduce the basics of our model in the case of Zn_1−xBe_x(Se,Te) mixed crystals, whose parent binaries display a high contrast in the bond stiffness, which enhances the percolation effects. We then focus our study on standard systems, which display a much weaker contrast in the bond stiffness. The multi-phonon behavior of GaInAs alloys is re-examined in the light of the percolation model, with much success.     

Specific features of the acoustic emission upon the optical breakdown in liquid induced by the radiation of Nd:YAG laser

The acoustic emission from the zone of the optical breakdown in liquid is experimentally studied. The spectral characteristics and energy of the acoustic wave that is generated in liquid due to expansion of the plasma formation initiated by the optical breakdown at a wavelength of 532 nm are analyzed. Two spectral peaks that characterize the acoustic emission and the low-frequency shift of the low-frequency peak owing to an increase in the laser pulse energy are demonstrated. In general, the linear dependence of the acoustic pressure on the laser pulse energy is observed. The acoustic data can be used to reconstruct function R(t) that is in agreement with dependences R(t) resulting from the optical data. This circumstance is important for the study of breakdown in opaque media.     

The quantum field as a quantum computer

It is supposed that at very small scales a quantum field is an infinite homogeneous quantum computer. On a quantum computer the information cannot propagate faster than c=a/τ, a and τ being the minimum space and time distances between gates, respectively. For one space dimension it is shown that the information flow satisfies a Dirac equation, with speed v=ζc and ζ=ζ(m) mass-dependent. For c the speed of light ζ−1 is a vacuum refraction index that increases monotonically from ζ−1(0)=1 to ζ−1(M)=∞, M being the Planck mass for 2a the Planck length. The Fermi anticommuting field can be entirely qubitized, i.e. it can be written in terms of local Pauli matrices and with the field interaction remaining local on qubits. Extensions to larger space dimensions are discussed.     

Radiation transfer in metallic powder beds used in laser processing

Two-dimensional radiation transfer in a powder layer backed with a substrate of the same material and normally irradiated with a narrow axially symmetric bell-like or the flat-top laser beam is numerically calculated. This corresponds to physical experiments with the powder layer of 50 μm thickness and the laser beam diameters 60–120 μm. The powder bed is treated as an equivalent homogeneous absorbing scattering medium, the radiative properties of which are estimated from the optical properties of the solid phase and the morphological parameters of the powder bed. The theoretical analysis shows that the absorptance of a semi-infinite powder bed of opaque particles is a universal function of the absorptivity of the solid phase being independent of the specific surface and the porosity. This is confirmed by literature experimental data. The radial transport of the radiative energy due to scattering of the incident laser beam in the powder layer can considerably reduce the deposited energy at the centre of the beam but the widening of the radial profile of the deposited energy is not pronounced. The fraction of laser energy deposited within the projection of the incident laser beam is evaluated. The efficiencies of laser heating the whole powder/substrate system and the substrate decrease with increasing the reflectivity of the material. More uniform heating of the powder layer can be attained at higher reflectivity.