Blackbody Radiation Spectrum Research Articles

Scheme for Quantum-Logic Based Transfer of Accuracy in Polarizability Measurement for Trapped Ions Using a Moving Optical Lattice.

Optical atomic clocks based on trapped ions suffer from systematic frequency shifts of the clock transition due to interaction with blackbody radiation from the environment. These shifts can be compensated if the blackbody radiation spectrum and the differential dynamic polarizability is known to a sufficient precision. Here, we present a new measurement scheme, based on quantum logic that allows a direct transfer of precision for polarizability measurements from one species to the other. This measurement circumvents the necessity of calibrating laser power below the percent level, which is the limitation for state-of-the-art polarizability measurements in trapped ions. Furthermore, the presented technique allows one to reference the polarizability transfer to hydrogenlike ions for which the polarizability can be calculated with high precision.

Does the Blackbody Radiation Spectrum Suggest an Intrinsic Structure of Photons?

Photons are considered to be elementary bosons in the Standard Model. The assumption that photons are not elementary particles is assessed from an outlook of computational statistical mechanics. A prediction of variations in the shape of the blackbody radiation spectrum with polarization is made. A better understanding of the origins of quantum statistics could be crucial for theories beyond the Standard Model.

Adiabatic invariance and its application to Wien's complete displacement law of blackbody radiation

We derive the “complete” or “strong” version of Wien's displacement law from two adiabatic invariants: one of a thermodynamic system composed of a finite-sized segment of frequencies taken from the spectrum of blackbody radiation and one of the individual electromagnetic waves that compose this system. By exploiting the algebra of these invariants, we shift the calculational burden of deriving Wien's displacement law toward the methods of classical thermodynamics. These methods also produce a class of displacement laws that constrain both the particles of a classical ideal gas and the acoustic waves of the Debye model of a solid.

Some Interesting Facts About Planck’s Law of Blackbody Radiation

Introductory textbooks of Modern and Thermal Physics discuss the Planck radiation law as a backbone of the blackbody radiation spectrum. This law is used to explain the intensity of blackbody radiation as a function of either frequency or wavelength at a given temperature. In the introductory coursework, the Planck’s formula is also used to study other blackbody radiation laws such as Stefans–Boltzmann law, Wien’s Displacement law, Rayleigh–Jeans Law and Wien’s Distribution law. In this work, we highlight some interesting facts related to the total energy density, photon number density and average energy of photon of blackbody radiation. The main objective of this work is to focus on the lesser known features associated with physics of blackbody radiation. We believe that these simple analytic calculations may give very useful and interesting information about the Planck radiation law to the undergraduate students.

Novel high-flux indoor solar simulator for high temperature thermal processes

A novel 32 kWe high flux solar simulator compound of eight xenon arc lamps coupled with a truncated paraboloid mirror and a secondary paraboloid mirror was designed, built, and tested. Collimated rays from a set of xenon arc lamps emulating outdoor solar radiation were reflected by a secondary set of paraboloid mirrors to a common system focus. Relative irradiance measurements were performed to obtain the xenon arc lamp radiation spectrum. Thermal power delivered by each lamp was evaluated by using a heat flux gauge mounted at the system focus. Concentrated thermal power was estimated by the heat superposition method, which allowed us to quantify both the total and the concentrated peak power along with the heat flux mapping. A 10.2% energy conversion efficiency was achieved. Experimental results determined a 3.0 kW total concentrated power on a 100 mm spot diameter resulting in a 1028 kWm−2 peak flux at the center; a lamp total thermal radiant power average of 615 W was achieved, and the lamp spectrum was compared with the 6200 K blackbody radiation spectrum.

Generalized Unruh effect: A potential resolution to the black hole information paradox

We generalize the vacuum-Unruh effect to arbitrary excited states in the Fock space and find that the Unruh mode at the horizon induces coherent excitation on the canonical background ensemble measured by an accelerated observer. When there is only one type of Unruh mode in the system, for example, the ones outgoing from a black hole horizon, the mapping from an arbitrary density matrix on the maximal foliation to a vector space spanned by the pseudo-thermal density matrix on the partitioned spacetime wedge is one-to-one. Hence we propose that the information of the particles that are inside a collapsing shell, thus inside the asymptotic black hole horizon is at least partially retrievable by measuring the deviation of the Hawking radiation from the black body radiation spectrum. This work shows that the long-standing black hole information confusion might come from overlooking the possibility that the information could be preserved much better than we have expected in a seemingly non-unitary process when the partitions of the system are strongly entangled.

GRB 200829A: External-shock Origin of the Very Early Prompt Emission?

Long-duration GRB 200829A was detected by Fermi-GBM and Swift-BAT/XRT, and then rapidly observed by other ground-based telescopes. It has a weak γ-ray emission in the very early phase and is followed by a bright spiky γ-ray emission pulse. The radiation spectrum of the very early emission is best fitted by a power-law function with index ∼−1.7. However, the bright spiky γ-ray pulse, especially the time around the peak, exhibits a distinct two-component radiation spectrum, i.e., Band function combined with a blackbody radiation spectrum. We infer the photospheric properties and reveal a medium magnetization at a photospheric position by adopting the initial size of the outflow as r 0 = 109 cm. It implies that the Band component in this pulse may be formed during the dissipation of the magnetic field. The power-law radiation spectra found in the very early prompt emission may imply the external-shock origination of this phase. Then, we perform the Markov Chain Monte Carlo method fitting on the light curves of this burst, where the jet corresponding to the γ-ray pulse at around 20 s is used to refresh the external shock. It is shown that the light curves of the very early phase and X-ray afterglow after 40 s, involving the X-ray bump at around 100 s, can be well modeled in the external-shock scenario. For the obtained initial outflow, we estimate the minimum magnetization factor of the jet based on the fact that the photospheric emission of this jet is missed in the very early phase.

Sustainable Energy and the Second Law of Thermodynamics: An Introduction to the Special Issue

At the end of the 19th century, the field of physics was considered nearly complete, encouraging triumphal statements by some of the most eminent physicists of the day, for instance, "There is nothing new to be discovered in physics now. All that remains is more and more precise measurement (William Thompson, Baron Kelvin of Largs). Only a few random clouds troubled this bright horizon, for instance, the vexing negative result of the Michelson-Morley experiment, some puzzling aspects to the photoelectric effect, and a the lack of a coherent explanation for the blackbody radiation spectrum. Nothing terribly serious, nothing that wouldn’t be mopped up eventually. In fact, the first would soon be key to Einstein’s revolutionary special theory of relativity, the second would win him the Nobel prize in physics, and the third, in the able hands of Max Planck, would crack open the door to the paradigm-shattering quantum world. Indeed, every moment is the end of physics or its beginning-–depending on one’s curiosity. Viewed through the lens of Thomas Kuhn’s The Structure of Scientific Revolutions, physics’ sudden turnabout was to be expected. Whenever experts consider a field complete, beware and be amused, for it will likely erupt in revolution. This is because the nature of knowledge itself guarantees scientific paradigms will invariably germinate the seeds of their own destructions. They must. When a paradigm is established, it is encumbent upon scientists to explore it as fully as possible, to extend its domain to the fullest possible extent.

Revisiting the Boltzmann Derivation of the Stefan Law

The Stefan–Boltzmann (SB) law relates the radiant emittance of an ideal black-body cavity at thermal equilibrium to the fourth power of the absolute temperature [Formula: see text] as [Formula: see text], with [Formula: see text][Formula: see text]W[Formula: see text]m[Formula: see text][Formula: see text]K[Formula: see text] the SB constant, first estimated by Stefan to within [Formula: see text] of the present theoretical value. The law is an important achievement of modern physics since, following Planck [Ueber das Gesetz der Energieverteilung im Normalspectrum [On the law of distribution of energy in the normal spectrum], Ann. Phys. 4 (1901) 553–563], its microscopic derivation implies the quantization of the energy related to the electromagnetic field spectrum. Somewhat astonishing, Boltzmann presented his derivation in 1878 making use only of electrodynamic and thermodynamic classical concepts, apparently without introducing any quantum hypothesis (here called first Boltzmann paradox). By contrast, the Boltzmann derivation implies two assumptions not justified within a classical approach, namely: (i) the zero value of the chemical potential and (ii) the internal energy of the black body with a finite value and dependent from both temperature and volume. By using Planck [Ueber das Gesetz der Energieverteilung im Normalspectrum [On the law of distribution of energy in the normal spectrum], Ann. Phys. 4 (1901) 553–563] quantization of the radiation field in terms of a gas of photons, the SB law received a microscopic interpretation free from the above assumptions that also provides the value of the SB constant on the basis of a set of universal constants including the quantum action constant [Formula: see text]. However, the successive consideration by Planck [Uber die Begründung des Gesetzes der schwarzen Strahlung [On the grounds of the law of black body radiation], Ann. Phys. 6 (1912) 642–656] concerning the zero-point energy contribution was found to be responsible of another divergence of the internal energy for the single photon mode at high frequencies. This divergence is of pure quantum origin and is responsible for a vacuum-catastrophe, to keep the analogy with the well-known ultraviolet catastrophe of the classical black-body radiation spectrum, given by the Rayleigh–Jeans law in 1900. As a consequence, from a rigorous quantum-mechanical derivation we would expect the divergence of the SB law (here called second Boltzmann paradox). Here, both the Boltzmann paradoxes are revised by accounting for both the quantum-relativistic photon gas properties, and the Casimir force.

Relativity, scaling, and electromagnetic radiation equilibrium for circular orbits

The radiation emitted by a charged particle moving in a circular orbit requires that the orbital speed of the particle is less than the speed of light in vacuum. This crucial relativistic restriction is lost in any treatment which combines nonrelativistic mechanics with classical electrodynamics through the nonrelativistic Larmor radiation formula or the dipole approximation, which approximations correspond to taking only the lowest power of velocity. A notable example of the resulting failure involves the derivation of the blackbody radiation spectrum within classical physics. Nature contains a smallest electric charge e and a largest speed c. Both these fundamental constants should appear in a classical theory of nature. We connect the assumptions regarding fundamental constants to the scaling aspects of classical theories. Nonrelativistic mechanics exhibits scaling which is entirely different from that found in relativistic classical electrodynamics where only Coulomb potentials are allowed and the constants e and c both appear. The scaling aspects are reflected in the radiation spectra which different theories predict for thermal radiation equilibrium. The Rayleigh–Jeans spectrum reflects the scaling aspects of nonrelativistic classical mechanics whereas the classical electromagnetic zero-point spectrum and the Planck spectrum share the scaling aspects of relativistic classical electrodynamics which includes both e and c.

Infrared scene projector (IRSP) for cryogenic environments based on a light-driven blackbody micro cavity array (BMCA)

An infrared scene projector (IRSP) that can operate at an ambient temperature lower than 190 K is developed for the hardware-in-the-loop (HIL) simulation of space-borne IR detection systems. The IRSP is composed of a visible scene generator (VSG), a visible to IR converter, and an IR projection system optimized for cryogenic environments. The core component of the IRSP is a light-driven blackbody micro cavity array (BMCA). The BMCA is a photothermal conversion device. It can transform visible light images into IR images. The BMCA can operate properly in an ultralow temperature environment, and the temperature of the BMCA is the same as the ambient temperature. This property allows the BMCA to generate IR scenes with a pure low temperature background, which is crucial for the ground testing of space-borne IR detection systems. The performance of the IRSP was tested in a vacuum cold chamber. In the cryogenic environment with an ambient temperature of 187.75K, the observed highest temperature of the generated IR scene was 426.15 K, the lowest temperature was 187.75 K, the dynamic range of the IR scene was 38.69 db, and the frame rate of the IR scene reached 76 Hz. The average visible to IR conversion efficiency of BMCA was about 10.6%∼3.1% under different ambient temperatures. The radiation spectrum of the IRSP is close to the standard blackbody radiation spectrum both in the MWIR band and the LWIR band. The IRSP has been applied in a HIL simulation test of a space-borne IR detection system.

Planck Spectroscopy (Laser Photonics Rev. 15(10)/2021)

Planck Spectroscopy Existing spectrometers rely on wavelength-selective optical components such as gratings or prisms. As featured on the cover, a new spectroscopic technique–Planck spectroscopy–that does not require any wavelength-selective optical components is demonstrated in article number 2100121 by Mikhail A. Kats and co-workers. The technique relies on the fundamental relationship that relates temperature to the spectrum of blackbody radiation and can be implemented using only a heater, photodetector, and computational algorithm.[Image credit: X. Zou]

Cryogenic background infrared scene generation method based on a light-driven blackbody micro cavity array

We propose a cryogenic background infrared scene (CBIRS) generation method based on a light-driven blackbody micro cavity array (BMCA). The BMCA is a passive converter which is driven by visible light. It can transform visible light images into infrared (IR) images. The micro structure of the BMCA is fabricated using MEMS technology. A temperature rise of 223.5 K was observed on the surface of the BMCA when the input visible light power density was 833 W/m2 and the ambient temperature was 96.7 K. The radiation spectrum of the BMCA is close to the blackbody radiation spectrum, which covers both the mid-wave infrared (MWIR) of 3 ~ 5 μm and the longwave infrared (LWIR) of 8 ~ 12 μm. The transient temperature response of the BMCA was experimentally tested. The thermal rising time was 4.16 ms and the thermal falling time was 2.63 ms. The BMCA is efficient for generating dynamic IR scene. The refreshing frame rate of the IR scene can reach more than 100 Hz.

New Higher-Order Generalized Uncertainty Principle: Applications

Recently Chung and Hassanabadi proposed a higher order general uncertainty principle (GUP∗) that predicts a minimal length as well as possesses a upper bound momentum limit. In this article, we have discussed an ideal gas system and its thermal properties using that deformed canonical algebra introduced by them. Moreover, we examined blackbody radiation spectrum and the cosmological constant in the presence of the GUP∗. After a comparison with the existing literature, we concluded that the given formalism of Chung and Hassanabadi yields more accurate results.

Procedimiento didáctico para el estudio de la fórmula de Planck en carreras de ingeniería

En este artículo se analiza la ley de distribución de energía en el espectro de la radiación del cuerpo negro, y la fórmula de Planck que la sintetiza, un descubrimiento revolucionario, que marca el nacimiento de la teoría cuántica. Se propone un procedimiento didáctico para el estudio de la fórmula de Planck en carreras de ingeniería, siguiendo la secuencia del ciclo de la creación científica: Hechos → Modelo-hipótesis → Consecuencias → Verificación experimental. Se ejemplifican los pasos metodológicos y los elementos esenciales de la idea básica de la cuantización de la energía, con notas históricas que facilitan la comprensión del fenómeno estudiado y el papel que jugaron los científicos en su determinación. Se consideran hechos iniciales: Las leyes de Kirchhoff, Stefan-Boltzmann y Wien, además de la fórmula de Rayleigh-Jeans y se desarrollan las ideas fundamentales que permitieron a Planck encontrar la solución teórica, que culmina en 1900 con la propuesta del cuanto de acción, expresado por la constante h que lleva su nombre. De la fórmula de Planck, se deducen las leyes antecedentes y se obtienen otras relaciones de importancia para la física y la química. Para cerrar el ciclo de la creación científica, se realiza la verificación experimental, con la medición de la radiación de fondo cósmico, que se comporta como la radiación de un cuerpo negro a una temperatura de 2,73 K. Se concluye con ejemplos de aplicaciones de la radiación térmica, que involucran algunos conceptos básicos de la elaboración teórica de Planck: Energía solar, recubrimientos térmicos y pirometría.

Correlation-Like Demodulation of Fiber Fabry–Perot Sensor Based on Blackbody Radiation Light Source

The blackbody radiation can provide light source for the fiber Fabry-Perot sensor system, but the output signal is difficult to demodulate. Because the signal of Fabry-Perot sensor is modulated by spectrum of blackbody radiation and SNR of signal is low. In this paper, the characteristics of the fiber Fabry-Perot sensor signal based on the blackbody light source were investigated. Effect of spectrum of blackbody radiation and low SNR on demodulation was analyzed. Strain experimental results show that correlation-like algorithm can accurately demodulate the signal when the temperature of the blackbody light source is equal to or higher than 800 °C. The maximum mean square error is $8.375~\mu \varepsilon $ after separating influence of temperature by the relationship between center wavelength of blackbody radiation and temperature. Higher the temperature, higher the demodulation accuracy.

Beyond the Formulations of the Fluctuation Dissipation Theorem Given by Callen and Welton (1951) and Expanded by Kubo (1966)

The quantum formula of the fluctuation dissipation theorem (FDT) was given by Callen and Welton in 1951 for the case of conductors, and then expanded by Kubo in 1966. The drawback of these quantum relations concerns with the appearance of a zero-point contribution, ${\hbar \omega}/{2}$ with $\hbar$ the reduced Planck constant and $\omega$ the angular frequency of the considered photon, which implies a divergence of the fluctuation spectrum at increasing frequencies. This divergence is responsible for a vacuum-catastrophe, to keep the analogy with the well-known ultraviolet catastrophe of the classical black-body radiation spectrum. As a consequence, the quantum formulation of the FDT as given by Callen-Welton and Kubo introduces a Field Grand Challenge associated with the existence or less of a vacuum-fluctuations catastrophe for the energy-density spectrum. Here we propose a solution to this challenge by taking into account of the Casimir energy that, in turns, is found to be responsible for a quantum correction of the Stefan-Boltzmann law.

Broadband Radiative Cooling and Decoration for Passively Dissipated Portable Electronic Devices by Aperiodic Photonic Multilayers

AbstractBroadband radiative cooling and decoration for passively dissipated portable electronic devices by an aperiodic photonic multilayer structure is proposed theoretically. The designed optical structure can strongly emit in the infrared region from 6.9 to 40 µm within the blackbody radiation spectrum of electronic devices. Its emission spectrum exhibits good uniformity across different incident angles, enhancing the cooling performance. At an ambient temperature of 20 °C, the designed broadband radiative cooler can produce a net cooling power of 46.88 W m−2, 65.95% higher than pure silica of the same thickness. At a typical junction temperature of 90 °C allowed by the microprocessor die, the net cooling power reaches 239.55 W m−2, still with an 18.21% improvement over pure silica glass. In the visible regime, the designed structure displays a low uniformity in the reflection spectrum, producing an elegant color shift from the translucent gray color of normal direction to the silver and highly reflective look at a grazing angle. These results can be useful in future exterior and thermal designs of portable electronic devices.

Spectra of Selective Radiation of Al2O3 : Ti3+ under Laser-Thermal Heating

In this Letter, we experimentally study the temperature dependence of the thermal radiation spectra of an Al2O3 : Ti3+ single crystal in the visible and near-infrared regions of the spectrum under laser-thermal heating. The thermal spectra of Al2O3 : Ti3+ in the temperature range of T = 330–900 K were found to differ significantly from the blackbody radiation spectrum and to be selective with a maximum at λ ≈ 1060 nm. The conversion of thermal energy into electrical energy due to the photovoltaic conversion of the selective radiation of a heated Al2O3 : Ti3+ single crystal by silicon photodiodes of the spectrometer receiving line was demonstrated. The possibility of applying the effect in thermovoltaic electric generators is discussed.

Спектры селективного излучения Al-=SUB=-2-=/SUB=-O-=SUB=-3-=/SUB=- : Ti-=SUP=-3+-=/SUP=- при лазерно-термическом нагреве

The temperature dependence of the thermal radiation spectra of the Al2O3:Ti3+ single crystal in the visible and near infrared spectral regions under laser thermal heating has been experimentally investigated. It was found that the thermal spectra of Al2O3:Ti3+ in the temperature range T=330-900 K differ significantly from the spectrum of blackbody radiation and are selective with a maximum at λ≈1060 nm. Conversion of thermal energy into electrical energy of a heated single crystal Al2O3:Ti3+ was demonstrated due to the photoelectric trnsformation of selective radiation by silicon photodiodes of the receiving line of the spectrometer. The possibility of application of this effect in thermophotoelectric generators is discussed.