Blackbody Limit Research Articles

Overcoming the black body limit in plasmonic and graphene near-field thermophotovoltaic systems

Near-field thermophotovoltaic (TPV) systems with carefully tailored emitter-PV properties show large promise for a new temperature range (600 – 1200K) solid state energy conversion, where conventional thermoelectric (TE) devices cannot operate due to high temperatures and far-field TPV schemes suffer from low efficiency and power density. We present a detailed theoretical study of several different implementations of thermal emitters using plasmonic materials and graphene. We find that optimal improvements over the black body limit are achieved for low bandgap semiconductors and properly matched plasmonic frequencies. For a pure plasmonic emitter, theoretically predicted generated power density of 14 W/cm2 and efficiency of 36% can be achieved at 600K (hot-side), for 0.17eV bandgap (InSb). Developing insightful approximations, we argue that large plasmonic losses can, contrary to intuition, be helpful in enhancing the overall near-field transfer. We discuss and quantify the properties of an optimal near-field photovoltaic (PV) diode. In addition, we study plasmons in graphene and show that doping can be used to tune the plasmonic dispersion relation to match the PV cell bangap. In case of graphene, theoretically predicted generated power density of 6(120) W/cm2 and efficiency of 35(40)% can be achieved at 600(1200)K, for 0.17eV bandgap. With the ability to operate in intermediate temperature range, as well as high efficiency and power density, near-field TPV systems have the potential to complement conventional TE and TPV solid state heat-to-electricity conversion devices.

Neutrino and anti-neutrino transport in accretion disks

We numerically solve the one dimensional Boltzmann equation of the neutrino and anti-neutrino transport in accretion disks and obtain the fully energy dependent and direction dependent neutrino and anti-neutrino emitting spectra, under condition that the distribution of the mass density,temperature and chemical components are given. Then, we apply the resulting neutrino and anti-neutrino emitting spectra to calculate the corresponding annihilation rate of neutrino pairs above the neutrino dominated accretion disk and find that the released energy resulting from the annihilation of neutrino pairs can not provide sufficient energy for the most energetic short gamma ray bursts whose isotropic luminosity can be as high as $10^{52}$ ergs/s unless the high temperature zone where the temperature is beyond 10 MeV can stretch over 200 km in the disk. We also compare the resulting luminosity of neutrinos and anti-neutrinos with the results from the two commonly used approximate treatment of the neutrino and anti-neutrino luminosity: the Fermi-Dirac black body limit and a simplified model of neutrino transport, i.e., the gray body model, and find that both of them overestimate the neutrino/anti-neutrino luminosity and their annihilation rate greatly. Additionally, as did in Sawyer (2003), we also check the validity of the two stream approximation, and find that it is a good approximation to high accuracy.

Numerically exact calculation of electromagnetic heat transfer between a dielectric sphere and plate

Near-field electromagnetic heat transfer holds great potential for the advancement of nanotechnology. Whereas far-field electromagnetic heat transfer is constrained by Planck's blackbody limit, the increased density of states in the near-field enhances heat transfer rates by orders of magnitude relative to the conventional limit. Such enhancement opens new possibilities in numerous applications, including thermal-photo-voltaics, nano-patterning, and imaging. The advancement in this area, however, has been hampered by the lack of rigorous theoretical treatment, especially for geometries that are of direct experimental relevance. Here we introduce an efficient computational strategy, and present the first rigorous calculation of electromagnetic heat transfer in a sphere-plate geometry, the only geometry where transfer rate beyond blackbody limit has been quantitatively probed at room temperature. Our approach results in a definitive picture unifying various approximations previously used to treat this problem, and provides new physical insights for designing experiments aiming to explore enhanced thermal transfer.

Midwave thermal infrared detection using semiconductor selective absorption

The performance of thermal detectors is derived for devices incorporating materials with non-uniform spectral absorption. A detector designed to have low absorption in the primary thermal emission band at a given temperature will have a background-limited radiation noise well below that of a blackbody absorber, which is the condition typically assessed for ultimate thermal detector performance. Specific examples of mid-wave infrared (ʎ ∼ 3-5 μm) devices are described using lead selenide as a primary absorber with optical cavity layers that maximize coupling. An analysis of all significant noise sources is presented for two example room-temperature devices designed to have detectivities up to 4.37 × 10(10) cm Hz(1/2) W(-1), which is a factor 3.1 greater than the traditional blackbody limit. An alternative method of fabricating spectrally selective devices by patterning a plasmonic structure in silver is also considered.

Quantum-coupled single-electron thermal to electric conversion scheme

Thermal to electric energy conversion with thermophotovoltaics relies on radiation emitted by a hot body, which limits the power per unit area to that of a blackbody. Microgap thermophotovoltaics take advantage of evanescent waves to obtain higher throughput, with the power per unit area limited by the internal blackbody, which is n2 higher. We propose that even higher power per unit area can be achieved by taking advantage of thermal fluctuations in the near-surface electric fields. For this, we require a converter that couples to dipoles on the hot side, transferring excitation to promote carriers on the cold side which can be used to drive an electrical load. We analyze the simplest implementation of the scheme, in which excitation transfer occurs between matched quantum dots. Next, we examine thermal to electric conversion with a lossy dielectric (aluminum oxide) hot-side surface layer. We show that the throughput power per unit active area can exceed the n2 blackbody limit with this kind of converter. With the use of small quantum dots, the scheme becomes very efficient theoretically, but will require advances in technology to fabricate.

Breakdown of the Planck blackbody radiation law at nanoscale gaps

The Planck theory of blackbody radiation imposes a limit on the maximum radiative transfer between two objects at given temperatures. When the two objects are close enough, near-field effects due to tunneling of evanescent waves lead to enhancement of radiative transfer above the Planck limit. When the objects can support electromagnetic surface polaritons, the enhancement can be a few orders-of-magnitude larger than the blackbody limit. In this paper, we summarize our recent measurements of radiative transfer between two parallel silica surfaces and between a silica microsphere and a flat silica surface that show unambiguous evidence of enhancement of radiative transfer due to near-field effects above the Planck limit.

Thermal radiation in photonic crystals

We analyze the properties of thermal radiation in photonic crystals and show that the spectral energy density, the spectral intensity, and the spectral hemispherical power are only limited by the total number of available photonic states and their propagation characteristics. In addition, we show that the central quantity that determines these thermal radiation characteristics is the area of the isofrequency surfaces and not the photonic density of states as it is generally assumed. Through the presence of partial or complete photonic band gaps and the associated spectral and angular redistribution of photonic states, it is possible to have spectral regions over which the thermal radiation intensity is enhanced relative to the free space blackbody limit and propagation directions along which thermal photon focusing effects appear.

Proton–nucleus scattering and cross section fluctuations at RHIC and LHC

We consider high-energy proton–heavy nucleus scattering within the framework of the Glauber–Gribov approximation and taking into account cross section fluctuations. Fixing parameters of the model for cross section fluctuations by the available data, we make predictions for the total, elastic and coherent diffractive dissociation proton–nucleus cross sections for the RHIC and LHC energy range. We predict a strong change of the A-dependence of diffraction dissociation from A0.42 at RHIC energies to A0.27 at LHC energies. Based on the obtained results, we discuss the approach of the interactions to the black body (unitarity) limit. We estimate the electromagnetic contribution to coherent pA diffraction and find that it dominates the coherent diffractive cross section on heavy nuclear targets in the LHC kinematics.

On the universality of cross sections of hadron–hadron (nuclei) collisions at superhigh energies

We analyze the interplay of the hard and soft interaction dynamics in the onset of the black body limit in the high energy hadron–hadron and hadron–nucleus collisions. We demonstrate that hard interactions of large x partons with the strong small x gluon fields result in a faster increase of the range of the impact parameters where interaction reaches the unitarity limit. At superhigh energies, far above the Greizen–Zatsepin–Kuzmin limit, the radius of hadronic interactions, proportional to ln(s/s0), significantly exceeds static radii of the interacting hadrons (nuclei) and the dependence of the high energy elastic hadron–hadron scattering cross section on the impact parameter b becomes universal leading to the ratios of total cross sections of hadron–hadron, hadron–nucleus, nucleus–nucleus collisions becoming equal to one. The same universality is also expected for the ratio of structure functions: F2A(x,Q2)/F2N(x,Q2)→1 at very small x. We analyze how increase of the interaction radii with energy changes the energy dependence of total, absorption and inelastic cross sections, and the distribution over the number of wounded nucleons in proton–nucleus collisions.

A Compact Starburst Core in the Dusty Lyman Break Galaxy Westphal-MD11

Using the IRAM Plateau de Bure Interferometer, we have searched for CO (3-2) emission from the dusty Lyman break galaxy Westphal-MD11 at z = 2.98. Our sensitive upper limit is surprisingly low relative to the system's 850 μm flux density and implies a far-IR/CO luminosity ratio as elevated as those seen in local ultraluminous mergers. We conclude that the observed dust emission must originate in a compact structure radiating near its blackbody limit and that a relatively modest molecular gas reservoir must be fueling an intense nuclear starburst (and/or deeply buried active nucleus) that may have been triggered by a major merger. In this regard, Westphal-MD11 contrasts strikingly with the lensed Lyman break galaxy MS 1512-cB58, which is being observed apparently midway through an extended episode of more quiescent disk star formation.

Determining the proximity ofγ*Nscattering to the black body limit using deep inelastic scattering andJ/ψproduction

We use information about DIS and $J/ \psi$ production on hydrogen to model the $t$-dependence of the $\gamma^{\ast} N$ scattering amplitude. We investigate the profile function for elastic scattering of hadronic components of the virtual photon off both a nucleon and heavy nuclear target, and we estimate the value of the impact parameter where the black body limit is reached. We also estimate the fraction of the cross section that is due to hadronic configurations in the virtual photon wave function that approach the unitarity limit. We extract, from these considerations, approximate lower limits on the values of $x$ where the leading twist approximation in DIS is violated. We observe that the black body limit may be approached within HERA kinematics with $Q^{2}$ equal to a few GeV$^2$ and $x \sim 10^{-4}$. Comparisons are made with earlier predictions by Munier {\it et al.}, and the longitudinal structure function is compared with preliminary HERA data. The principle advantage of our method is that we do not rely solely on the $t$-dependence of $\rho$-meson production data. This allows us to extend our analysis down to very small impact parameters and dipole sizes. Finally, we perform a similar calculation with a $^{208}$Pb target, and we demonstrate that the black body limit is already approached at $Q^{2} \sim 20$ GeV$^{2}$ and $x \sim 10^{-4}$.

Photon emission from dense quark matter

Thermal emission rates and mean free paths of photons in a color-flavor locked (CFL) phase of quark matter at high densities and moderate temperatures are evaluated. Our calculations are based on a low-energy effective theory for CFL matter describing Goldstone boson excitations and their electromagnetic as well as strong interactions. In-medium coupling strengths of vector mesons are estimated to be smaller than in vacuum. As a consequence of in-medium modified pion dispersion relations, novel processes such as π + π −→ γ and γ→ π + π − become possible. The total photon emissivity is found to be very large, exceeding contributions from thermal e + e − annihilation above temperatures of about 5 MeV. At the same time, the corresponding mean free paths become very small. Our results imply that the photon flux from the surface of a (hypothetical) CFL star in its early hot stages saturates the black-body limit. Schematic estimates for the early thermal evolution of the star are also presented.

Coherence effects in diffractive electroproduction from nuclei

We argue that study of the cross section of coherent photo(electro) production of $\rho,\rho^{\prime}, ...$-mesons provides an effective method to probe onset of black body limit(BBL) in the soft and hard QCD interactions. We illustrate the expected features of the onset of BBL using generalized vector dominance model(GVDM). We show that this model describes very well $\rho$-meson coherent photoproduction at $6 \leq E_{\gamma} \leq 10$ GeV. The advantages of the process of coherent dijet production and hard diffractive processes in general for probing the onset of BBL and measuring the light-cone wave function of the photon in a hard scattering regime where decomposition over twists becomes inapplicable are explained. We argue also that the regime of color fluctuations manifests itself at intermediate energies in exclusive and semiexclusive photoproduction of vector mesons and that the color transparency(CT) should reveal itself in these processes at $Q^2$ of the order of a few GeV$^2$.

Signals for black body limit in coherent ultraperipheral heavy ion collisions

We argue that study of total cross section of photoabsorption and coherent photoproduction of ρ, ρ′-mesons in ultraperipheral heavy ion collisions (UPC) is effective method to probe onset of black body limit (BBL) in the soft and hard QCD interactions. We illustrate the expected features of the onset of BBL using generalized vector dominance model. We show that this model describes very well ρ-meson coherent photoproduction at 6⩽ E γ ⩽10 GeV. In the case of ρ-meson production we find a UPC cross section which is a factor ∼1.5 larger than the one found by Klein and Nystrand. The advantages of the process of coherent dijet production to probe onset of BBL in hard scattering regime where decomposition over the twists becomes inapplicable are explained and relative importance of the γ+pomeron and γ+ γ mechanisms is estimated.

Phenomenological models of the quark-gluon plasma equation of state

Two phenomenological models describing an SU( N) quark-gluon plasma are presented. The first is obtained from high temperature expansions of the free energy of a massive gluon, while the second is derived by demanding color neutrality over a certain length scale. Each model has a single free parameter, exhibits behavior similar to lattice simulations over the range T d – 5 T d , and has the correct blackbody behavior for large temperatures. The N = 2 deconfinement transition is second order in both models, while N = 3,4, and 5 are first order. Both models appear to have a smooth large- N limit. In both models, the confined phase is characterized by a mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop expectation value zero. In the deconfined phase, the rotation of the eigenvalues in the complex plane towards 1 is responsible for the approach to the blackbody limit over the range T d – 5 T d . The addition of quarks in SU(3) breaks Z(3) symmetry weakly and eliminates the deconfining phase transition for sufficiently light quarks.

Phenomenological equations of state for the quark-gluon plasma

Two phenomenological models describing an $\mathrm{SU}(N)$ quark-gluon plasma are presented. The first is obtained from high temperature expansions of the free energy of a massive gluon, while the second is derived by demanding color neutrality over a certain length scale. Each model has a single free parameter, exhibits behavior similar to lattice simulations over the range ${T}_{d}\ensuremath{-}{5T}_{d},$ and has the correct blackbody behavior for large temperatures. The $N=2$ deconfinement transition is second order in both models, while $N=3, 4,$ and $5$ are first order. Both models appear to have a smooth large-N limit. For $N>~4,$ it is shown that the trace of the Polyakov loop is insufficient to characterize the phase structure; the free energy is best described using the eigenvalues of the Polyakov loop. In both models, the confined phase is characterized by a mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop expectation value zero. In the deconfined phase, the rotation of the eigenvalues in the complex plane towards $1$ is responsible for the approach to the blackbody limit over the range ${T}_{d}\ensuremath{-}{5T}_{d}.$ The addition of massless quarks in $\mathrm{SU}(3)$ breaks $Z(3)$ symmetry weakly and eliminates the deconfining phase transition. In contrast, a first-order phase transition persists with sufficiently heavy quarks.

Revealing the black-body regime of small-x deep-inelastic scattering through final-state signals.

We derive the major characteristics of inclusive and diffractive final states in deep-inelastic scattering off heavy nuclei for the high-energy (small-x) kinematics in which the limit of complete absorption is reached for the dominant hadronic fluctuations in the virtual photon (the black-body limit of the process). Both the longitudinal and transverse distributions of the leading hadrons are found to be strikingly different from the corresponding ones within the leading-twist approximation, and hence provide unambiguous signals for the onset of the black-body limit.

On the Inability of Comptonization to Produce the Broad X‐Ray Iron Lines Observed in Seyfert Nuclei

It has recently been suggested that Compton downscattering may give rise to the broad iron lines seen in the X-ray spectra of Seyfert 1 galaxies. This challenges the standard model in which these lines originate from the innermost regions of the black hole accretion disk with Doppler shifts and gravitational redshifts giving rise to the broadened line profile. Here, we apply observational constraints to the Compton downscattering model for MCG-6-30-15 and NGC3516, the two best cases to date of Seyfert galaxies with relativistically broad lines. We show that the continuum source in MCG-6-30-15 required by the constrained model violates the black body limit. In the case of NGC3516, only a very small region of parameter space is compatible with the constraints. Hence, we conclude that the Comptonization model is not a viable one for the broad line seen in these two objects. The accretion disk model remains the best interpretation of these data.

Diffraction at HERA, Color Opacity and Nuclear Shadowing in DIS off nuclei

The QCD factorization theorem for diffractive processes in DIS is used to derive formulae for the leading twist contribution to the nuclear shadowing of parton distributions in the low thickness limit (due to the coherent projectile (photon) interactions with two nucleons). Based on the current analyzes of diffraction at HERA we find that the average strength of the interactions which govern diffraction in the gluon sector at x≤ 10−3, Q 0= 2 GeV is ∼50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q 0 in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N≥ 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q 2 dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G A(x,Q 0 2) /AG N(x,Q 0 2)|x ≤ 10−3∼ 0.25–0.4 is sensitive to the probability of the small size configurations within wave function of the gluon “partonometer” at the Q 0 scale. At this scale for A∼ 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4–5 at x≤ 10−3 unmasking PQCD physics in the gluon distribution of heavy nuclei. We point out that the shadowing of this magnitude would strongly modify the first stage of the heavy ion collisions at the LHC energies, and also would lead to large color opacity effects in eA collisions at HERA energies. In particular, the leading twist contribution to the cross section of the coherent J/ψ production off A≥ 12 nuclei at s −2≥ 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F 2A(x,Q 2) is extended to the case of the gluon distributions in nuclei and shown to be relevant for the HERA kinematics of eA collisions. Properties of the final states are also briefly discussed.

The Molecular Interstellar Medium in Ultraluminous Infrared Galaxies

We present CO observations of a large sample of ultraluminous IR galaxies out to z = 0.3. Most of the galaxies are interacting, but not completed mergers. All but one have high CO(1-0) luminosities, log(Lco [K-km/s-pc^2]) = 9.92 +/- 0.12. The dispersion in Lco is only 30%, less than that in the FIR luminosity. The integrated CO intensity correlates Strongly with the 100 micron flux density, as expected for a black body model in which the mid and far IR radiation are optically thick. We use this model to derive sizes of the FIR and CO emitting regions and the enclosed dynamical masses. Both the IR and CO emission originate in regions a few hundred parsecs in radius. The median value of Lfir/Lco = 160 Lsun/(K-km/s-pc^2), within a factor of two of the black body limit for the observed FIR temperatures. The entire ISM is a scaled up version of a normal galactic disk with densities a factor of 100 higher, making even the intercloud medium a molecular region. Using three different techniques of H2 mass estimation, we conclude that the ratio of gas mass to Lco is about a factor of four lower than for Galactic molecular clouds, but that the gas mass is a large fraction of the dynamical mass. Our analysis of CO emission reduces the H2 mass from previous estimates of 2-5e10 Msun to 0.4-1.5e10 Msun, which is in the range found for molecular gas rich spiral galaxies. A collision involving a molecular gas rich spiral could lead to an ultraluminous galaxy powered by central starbursts triggered by the compression of infalling preexisting GMC's.