Photon Number Density Research Articles

Dynamical model of non-chain pulsed DF laser

Based on the reaction mechanism of non-chain pulsed DF laser and taking into consideration the deactivation of the stimulated DF molecules by ground state DF molecules, D2 molecules, D atoms, F atoms, the dynamical model for non-chain pulsed DF laser is established using the rate equation theory. Through solving this model with Runge-Kutta method, the dependence of species concentration in the gain area on time is obtained. Then the effects of the working gas ratio and the reflectance of output mirror on photon number density, single pulse energy, pulse width and output power are studied in light of this model. The optimum parameters of the working gas ratio and the reflectance of output mirror are attained based on the theoretical calculation. The pulse waveform and single pulse energy of non-chain pulsed DF laser calculated by using the rate equations theory agree well with experimental data based on electric-discharge. These results would provide a theoretical support for the optimization of non-chain pulsed DF laser.

Evolution of ultrashort laser pulse in large amplitude plasma waves

The propagation and evolution of an ultrashort laser pulse in a large amplitude plasma wave are investigated based on the photon kinetic theory. The photon number distribution function for a laser pulse in the phase space is analytically obtained by solving the photon kinetic equation in the background plasma wave. And then, the behavior of the laser pulse can be described by combining the single photon dynamics and the photon number distribution function. The evolutions of the photon number density in the coordinate and frequency domain space are discussed, and broadening or compressing of the laser pulse is also displayed in this paper. In particular, the frequency shift of the entire laser pulse is analyzed, which reflects a way of energy transformation between the laser pulse and the plasma wave.

Quantum optical correlation through metamaterials

Based on the quantization scheme of the radiation fields in the dispersive and absorptive magnetic media, the normally ordered correlation functions of the outgoing field through a metamaterial plate are obtained. Then the relative photon-number densities of the transmitted field, the reflected field and the absorbed field are gotten through the correlation functions. Furthermore, the contributions of the relative permittivity and permeability of the metamaterials to the transmission are analyzed. Our results show that the permittivity and permeability reinforce the transmission for frequencies that are big compared with the magnetic resonance frequency.

Quantum properties of optical images in coupled nondegenerate parametric processes

Quantum properties of parametric amplification and frequency conversion of an optical image in coupled parametric interactions are analyzed for the case of a remote object. The coupled-wave interaction consists of a traditional process of parametric amplification in the high-frequency pump field accompanied by the frequency mixing of generated and pump waves. The photon number density and signal-to-noise ratio at the interacting frequencies are studied in the image plane at the output of the nonlinear frequency converter in the fixed pump field approximation. The degree of entanglement of optical images at frequencies above and below the pump frequency is investigated.

Simultaneous parametric generation and up-conversion of entangled optical images

A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.

HIGH-FREQUENCY-PEAKED BL LACERTAE OBJECTS AS SPECTRAL CANDLES TO MEASURE THE EXTRAGALACTIC BACKGROUND LIGHT IN THE FERMI AND AIR CHERENKOV TELESCOPES ERA

The Extragalactic Background Light (EBL) is the integrated light from all the stars that have ever formed, and spans the IR-UV range. The interaction of very-high-energy (VHE: E>100 GeV) gamma-rays, emitted by sources located at cosmological distances, with the intervening EBL results in electron-positron pair production that leads to energy-dependent attenuation of the observed VHE flux. This introduces a fundamental ambiguity in the interpretation of measured VHE gamma-ray spectra: neither the intrinsic spectrum, nor the EBL, are separately known -- only their combination is. In this paper we propose a method to measure the EBL photon number density. It relies on using simultaneous observations of BL Lac objects in the optical, X-ray, high-energy (HE: E>100 MeV) gamma-ray (from the Fermi telescope), and VHE gamma-ray (from Cherenkov telescopes) bands. For each source, the method involves best-fitting the spectral energy distribution (SED) from optical through HE gamma-rays (the latter being largely unaffected by EBL attenuation as long as z<1) with a Synchrotron Self-Compton (SSC) model. We extrapolate such best-fitting models into the VHE regime, and assume they represent the BL Lacs' intrinsic emission. Contrasting measured versus intrinsic emission leads to a determination of the photon-photon opacity to VHE photons. Using, for each given source, different states of emission will only improve the accuracy of the proposed method. We demonstrate this method using recent simultaneous multi-frequency observations of the high-frequency-peaked BL Lac object PKS 2155-304 and discuss how similar observations can more accurately probe the EBL.

The impact of Lyman series photons on the intergalactic medium during the Epoch of Reionization

The role of higher order Lyman series photons in the 21 cm absorption or emission signature of the intergalactic medium (IGM) against the background cosmic microwave background (CMB) during the Epoch of Reionization is examined. It is shown that, taking into account the diminishing resonance line scattering cross-section with increasing Lyman order, a non-negligible net scattering rate of higher order Lyman photons is expected. The resulting radiative cascades will substantially enhance the number density of Lyα photons near a radiation source. It is also shown that the higher order Lyman series photons are able to collisionally heat the IGM by amounts of tens to hundreds of degrees kelvin. The possibility that the Wouthuysen-Field effect may be suppressed by the presence of dust near a galaxy is discussed, and it is shown that the higher order Lyman series photons would still induce the effect, but with a somewhat reduced 21 cm radiation efficiency. It is also demonstrated that extended low surface brightness emission-line haloes will be produced from radiative cascades following the scattering of higher order Lyman series photons. These haloes would provide a unique means of confirming that reionization source candidates were surrounded by an IGM that was still largely neutral on large scales.

Primordial black holes and the observed Galactic 511 keV line

The observed 511 keV line from the Galactic Bulge is a real challenge for theoretical astrophysics: despite a lot of suggested mechanisms, there is still no convincing explanation and the origin of the annihilated positrons remains unknown. Here we discuss the possibility that a population of slowly evaporating primordial black holes with the mass around 1016–1017 g ejects (among other particles) low-energy positrons into the Galaxy. In addition to positrons, we have also calculated the spectrum and number density of photons and neutrinos produced by such black holes and found that the photons are potentially observable in the near future, while the neutrino flux is too weak and below the terrestrial and extra-terrestrial backgrounds. Depending on their mass distribution, such black holes could make a small fraction or the whole cosmological dark matter.

Inertial mechanism: Dynamical mass as a source of particle creation

A kinetic theory of vacuum particle creation under the action of an inertial mechanism is constructed within a nonperturbative dynamical approach. At the semi-phenomenological level, the inertial mechanism corresponds to quantum field theory with a time-dependent mass. At the microscopic level, such a dependence may be caused for different reasons: the non-stationary Higgs mechanism, the influence of a mean field or condensate, the presence of a conformal multiplier in the scalar-tensor gravitation theory, etc. In what follows, a kinetic theory in the collisionless approximation is developed for scalar, spinor, and massive vector fields in the framework of the oscillator representation, which is an effective tool for transition to the quasiparticle description and for derivation of non-Markovian kinetic equations. Properties of these equations and relevant observables (particle number and energy densities, pressure) are studied. The developed theory is applied here to describe the vacuum matter creation in conformal cosmological models and explain the observed number density of photons in the cosmic microwave background radiation. As another example, the self-consistent evolution of scalar fields with non-monotonic self-interaction potentials (the W-potential and Witten-Di Vecchia-Veneziano model) is considered. In particular, conditions for the appearance of tachyonic modes and the problem of the relevant definition of a vacuum state are discussed.

Lorentz-invariant photon number density

A Lorentz-invariant positive definite expression for photon number density is derived as the absolute square of the invariant scalar product of a polarization-sensitive position eigenvector and the photon wave function. It is found that this scalar product is independent of the form chosen for the wave function and that the normalized positive frequency vector potential--electric field pair is a convenient choice of wave function in the presence of matter. The number amplitude describing a localized state is a $\ensuremath{\delta}$ function at the instant at which localization and detection are seen as simultaneous.

Spectral formation in x-ray pulsars and associated identities involving the Laguerre polynomials

The partial differential equation governing the formation of the radiation spectrum in the shocked plasma accreting onto an x-ray pulsar is solved to obtain the associated Green’s function describing the scattering of monochromatic radiation injected into the plasma at a fixed altitude above the star. Collisions between the photons and the infalling electrons cause both the ordered and random components of the plasma energy to be transferred to the radiation, which escapes by diffusing through the walls of the accretion column. The analytical solution for the Green’s function provides important physical insight into the formation of the observed spectra in x-ray pulsars. Interesting mathematical aspects of the problem include the establishment of a new summation formula involving the Laguerre polynomials, based on the calculation of the photon number density via integration of Green’s function.

On the general relativistic symmetric hyperbolic moment system for matter and radiation: local rotational symmetry

For the one-dimensional, locally rotationally symmetric case, we employ the relativistic Boltzmann equations and the moment methods to derive a 6D causal evolution system of first-order symmetric hyperbolic form for a fluid-radiation mixture, i.e., a relativistic gas composed of material particles and photons. The material medium is assumed to be a nonbarotropic perfect gas and the evolution equations for this medium are obtained by using the local Jüttner equilibrium distribution function as seen by an observer with arbitrary 4-velocity. In order to derive the evolution equations for the photon gas, we develop the modified Grad-type method which consists of expanding the phase density (i.e., the number density of photons) about a local Planck equilibrium distribution function and including the trace-free anisotropic pressure in the expansion. In our approach, it is significant that the matter fluid's peculiar velocity and the radiative heat flux (relative to an arbitrary 4-velocity vector field) are incorporated into the model in a non-perturbative manner, thereby allowing arbitrarily large values for the two nonvanishing components of these dynamical variables. The additional difference about the treatment here as opposed to other treatments is that we do not neglect terms in the evolution equations which involve small first-order quantities multiplying the spatial frame derivatives of hydrodynamical variables.

FOUNDATION AND RESULTS OF A COSMOLOGY WITHOUT BIG BANG ON THE BASIS OF THE PROJECTIVE UNIFIED FIELD THEORY

After a short introduction into the Projective Unified Field Theory developed by the author during the last decades this theory is applied to a closed homogenous isotropic 2-component cosmos model, based on a mixture of a mechanical particle (urparticle) gas and a photon gas. The field equations lead to three nonlinear differential equations for the temporal course of the world radius, the scalaric world function and the mechanical energy density of the cosmos. These equations were solved numerically and evaluated in detail. The results are presented for a series of important cosmological quantities: world radius, world age, cosmological frequency shift and Hubble parameter, deceleration parameter, mechanical mass density, photon mass density, mechanical pressure, electromagnetic radiation pressure, kinetic particle temperature, electromagnetic radiation (microwave background) temperature, mechanical particle number density, photon number density, etc. Specific results of the theory are: explanation of the time dependence of the Newton gravitational constant, scalaric cosmological heat production in moving celestial bodies and the numerical value of the mass of an urparticle.

A SYMMETRIC HYPERBOLIC FORMULATION OF THE GENERAL RELATIVISTIC MOMENT EQUATIONS FOR MATTER AND RADIATION

For a fluid-radiation mixture, i.e. a relativistic gas consisting of material particles and photons, we derive a 14D causal evolution system of first-order symmetric hyperbolic form for a set of basic physical gas-state variables, which is defined relative to a network of observers with arbitrary 4-velocities. This system is obtained by taking moments of the relativistic Boltzmann equation (the so-called central moments) and by truncating and closing the resulting system of moment equations by means of an appropriate (5+9)-moment closure prescription. The material medium under consideration is assumed to be a nonbarotropic perfect gas described by a local Jüttner equilibrium distribution function. With regards to the photon gas, we employ the modified Grad-type approach, which begins by expanding the phase density (i.e. the number density of photons) about a local Planck equilibrium distribution and including the trace-free anisotropic pressure in the expansion. The main advantage of using the above (5+9)-moment closure prescription is that the matter fluid's peculiar velocity and the radiative heat flux are incorporated into the model in a non-perturbative manner, thereby allowing virtually arbitrarily large values for the individual components of these dynamical variables. Within the framework of a reduced 3 + 1 orthonormal frame formalism, we also explain how to choose the initially arbitrary 4-velocity vector field, as this is crucial for the determination of the full 38D causal matter-radiation-gravity system.

Spectral energy distribution of super-Eddington flows

Spectral properties of super-Eddington accretion flows are investigated by means of a parallel line-of-sight calculation. The subjacent model, taken from the two-dimensional radiation hydrodynamic simulations by Ohsuga et al. (2005), consists of a disc accretion region and an extended atmosphere with high-velocity outflows. The non-grey radiative transfer equation is solved, including relativistic effects, by applying the flux-limited diffusion approximation. The calculated spectrum is composed of a thermal, blackbody-like emission from the disc which depends sensitively on the inclination angle, and of high-energy X-ray and gamma-ray emission from the atmosphere. We find mild beaming effects in the thermal radiation for small inclination angles. If we compare the face-on case with the edge-on case, the average photon energy is larger by a factor of ∼1.7 due mainly to Doppler boosting, while the photon number density is larger by a factor of ∼3.7 due mainly to anisotropic matter distribution around the central black hole. This gives an explanation for the observed X-ray temperatures of ULXs which are too high to be explained in the framework of intermediate-mass black holes. While the main features of the thermal spectral component are consistent with more detailed calculations of slim accretion discs, the atmosphere induces major changes in the high-energy part, which cannot be reproduced by existing models. We also conclude that, in order to interpret the observational data properly, simple approaches like the Eddington–Barbier approximation cannot be applied.

Constraining gravitino dark matter with the cosmic microwave background

We consider super-gravity models in which the lightest supersymmetric particle (LSP) is a stable gravitino. The next-to-lightest supersymmetric particle (NLSP) freezes out with its thermal relic density and then decays after $(10^5-10^{10})$ sec, injecting high-energy photons into the cosmic plasma. These photons heat up the electron plasma which then thermalizes with the cosmic microwave background (CMB) via Compton scattering, bremsstrahlung and double-Compton scattering. Contrary to previous studies which assume instantaneous energy injection, we solve the full kinetic equation for the photon number density with a source term describing the decay of the NLSP. This source term is based on the requirement that the injected energy be almost instantaneously redistributed by Compton scattering, hence leading to a time-dependent chemical potential. We investigate the case of a stau NLSP and determine the constraints on the gravitino and stau masses from observations of the CMB spectrum by assuming that all gravitino LSPs come from stau NLSP decays. Unlike the analytical approximations, we find that there may be a stau mass below which the constraint from the CMB spectrum vanishes.

A two-dimensional electrodynamical outer gap model for -ray pulsars: -ray spectrum

A two-dimensional electrodynamical model is used to study particle acceleration in the outer magnetosphere of a pulsar. The charge depletion from the Goldreich-Julian charge density causes a large electric field along the magnetic field lines. The charge particles are accelerated by the electric field and emit γ-rays via the curvature process. Some of the emitted γ-rays may collide with X-ray photons to make new pairs, which are accelerated again on the different field lines in the gap and proceed similar processes. We simulate the pair creation cascade in the meridional plane using the pair creation mean-free path, in which the X-ray photon number density is proportional to inverse square of radial distance. With the space charge density determined by the pair creation simulation, we solve the electric structure of the outer gap in the meridional plane and calculate the curvature spectrum. We investigate in detail relation between the spectrum and total current, which is carried by the particles produced in the gap and/or injected at the boundaries of the gap. We demonstrate that the hardness of the spectrum is strongly controlled by the current carriers. Especially, the spectrum sharply softens if we assume a larger particle injection at the outer boundary of the outer gap. This is because the mean-free path of the pair creation of the inwardly propagating γ-ray photons is much shorter than the light radius so that the many pairs are produced in the gap to quench the outer gap.

Kinetic description of vacuum creation of massive vector bosons

In the simple model of massive vector field in a flat spacetime, we derive the kinetic equation of non-Markovian type describing the vacuum pair creation under action of external fields of different nature. We use for this aim the nonperturbative methods of kinetic theory in combination with a new element when the transition of the instantaneous quasiparticle representation is realized within the oscillator (holomorphic) representation. We study in detail the process of vacuum creation of vector bosons generated by a time-dependent boson mass in accordance with the framework of a conformal-invariant scalar-tensor gravitational theory and its cosmological application. It is indicated that the choice of the equation of state allows one to obtain a number density of vector bosons that is sufficient to explain the observed number density of photons in the cosmic microwave background radiation.

Relationship of quantum mechanics to classical electromagnetism and classical relativistic mechanics

Some connections between quantum mechanics and classical physics are explored. The Planck–Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the canonical commutation relations and the Maxwell–Lorentz equation may be understood in a simple way by comparing classical electromagnetism and the photonic description of light provided by classical relativistic kinematics. The method used may be described as ‘inverse correspondence’ since quantum phenomena become apparent on considering the low photon number density limit of classical electromagnetism. Generalization to massive particles leads to the Klein–Gordon and Schrödinger equations. The difference between the quantum wavefunction of the photon and a classical electromagnetic wave is discussed in some detail.

Identification of the boundary surface of an interstellar cloud from a measurement of the photon far‐field

AbstractWe study an inverse problem for photon transport in a host medium (e.g. an interstellar cloud), that occupies a bounded and strictly convex region Ω⊂R3. Under the assumption that the cross‐sections and the sources are known, we identify the boundary surface ∑ = ∂Ω(within a suitable family F of surfaces), provided that one value of the photon number density is measured at some given location far from Ω. Copyright © 2004 John Wiley &amp; Sons, Ltd.