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BCS theory describes a superconducting instability caused by attractive interactions between opposite-momentum fermions near a Fermi surface.

John Bardeen, Leon Neil Cooper and John Robert Schrieffer developed BCS theory in 1957, using attraction mediated by phonons.^[ref]

Weak-coupling Cooper pairs overlap. The Cooper instability reorganizes an unpaired Fermi surface; it is not Bose-Einstein condensation of compact, pre-existing molecules. The original paper explicitly distinguishes these pictures.^[ref]

Two complementary clues made the microscopic problem concrete. The superconducting isotope effect connected the transition to phonons.^[ref]

A 1957 transmission experiment used thin lead and tin films as samples in far-infrared and millimeter-microwave measurements. The measured transmission was converted to complex electrical conductivity, normalized to the normal-state value. Comparing film thickness, resistance, annealing and the two metals tested the response's reproducibility. Weak low-photon-energy absorption followed by an onset supported a superconducting energy gap; its extraction required a thin-film electrodynamic model.^[ref]

The later Giaever superconducting tunnelling experiment provided another way to resolve the superconducting energy gap through quantum tunnelling.^[ref] The derivations below explain what the model predicts, including the distinction between a single quasiparticle's minimum energy and the threshold for making two of them.

The eight-operation molecular point group of an ideal square pyramid. Its polar-vector components transform as $A_1$ for the principal-axis coordinate and $E$ for the transverse pair. Symmetric quadratic functions also contain $B_1$ and $B_2$, allowing Raman spectroscopy activity beyond the infrared modes.

Carbon dioxide is $\mathrm{C}{\mathrm{O}}_2$, a linear molecule with two carbon-oxygen double bonds. The individual bonds are polar, but their dipoles cancel in the symmetric equilibrium geometry. Some vibrations change the molecular dipole and therefore absorb infrared radiation.

Carbon dioxide is a product of many oxidation and combustion processes and a substrate for photosynthetic carbon fixation. Dissolved carbon dioxide participates in carbonate acid-base equilibria, so adding it to water can change pH without directly adding a strong acid.

A carbon dioxide laser, or CO2 laser, uses excited carbon dioxide molecules as its laser gain medium. Its characteristic emission lies in the infrared, with important lines near $10.6\mu \mathrm{m}$. The emitting transitions change the molecule's vibrational and rotational states. This connects laser action with molecular vibration and molecular rotation, rather than with a requirement to break the molecule into its constituent atoms.

Energy supplied to the gas creates an appropriate excited-state distribution. Stimulated emission amplifies light on a selected transition; an optical cavity returns it through the medium, and a partly transmitting output element extracts useful radiant power. The laser threshold depends on complete round-trip gain and loss. The presence of carbon dioxide alone does not establish population inversion or select a unique oscillating line.

A primary experimental landmark is C. K. N. Patel's 1964 report from Bell Telephone Laboratories. It identified continuous-wave laser action on several rotational lines of two vibrational bands, with the strongest reported vacuum wavelength $10.6324\mu \mathrm{m}$ and continuous output around $1\mathrm{mW}$. The same transitions were observed under pulsed-discharge excitation, and time-dependent output was studied. These are properties of that reported experiment, not universal power or wavelength limits for every CO2 laser.^[ref]

The molecular line structure explains why a quoted wavelength is only part of the specification. Several allowed transitions can supply gain, while the optical cavity favours its own normal modes. A device need not emit every line of a rovibrational spectrum, nor is its line selected merely by saying that the medium contains carbon dioxide. A spectral measurement can test which transitions actually oscillate.

An original calculation connects the reported wavelength with the size of an energy quantum. Using the Planck constant $h$ and the speed of light $c$,For a stipulated monochromatic $1\mathrm{mW}$ beam at that wavelength, the rate of emitted photons isThe individual photon energy is small even when the collective beam carries measurable power. This bookkeeping does not establish how efficiently the electrical input becomes output radiation; that comparison requires separate input and output measurements.

The film-activation apparatus in laser capture microdissection supplies a distinct application: a carbon dioxide laser pulse activates a thermoplastic film locally to collect selected tissue. Its use there depends on the material's response and the spatial delivery of energy, rather than the name of the laser alone.^[ref]

C. Kumar N. Patel developed the carbon dioxide laser at Bell Laboratories. His National Inventors Hall of Fame record identifies the contribution and records his birth in 1938, education in India and at Stanford, and induction in 2012.^[ref] UCLA's faculty record uses the Kumar form and lists a Stanford doctorate in 1961; its publication list preserves the C.K.N. Patel byline.^[ref]

His 1964 experiment showed continuous laser action on rotational transitions within molecular vibrational bands of carbon dioxide, rather than only on atomic transitions. The strongest reported line was $10.6324\mu \mathrm{m}$ in vacuum, with about $1\mathrm{mW}$ continuous output.^[ref] Molecular vibration and molecular rotation therefore provide the energy-level structure behind the observed infrared lines.

The apparatus made those invisible lines measurable. The paper describes a five-metre quartz tube with an electrical discharge, a nearly confocal optical cavity formed by silicon mirrors with aluminium coatings, and output coupled through an uncoated central mirror aperture. A copper-doped germanium photoconductor cooled to $4.2\mathrm{K}$ detected the radiation; a thermopile checked power, and a scanning grating spectrometer measured wavelengths.^[ref] Electrical excitation, resonator feedback and infrared detection play separate roles in that observation.

An original calculation connects the recorded wavelength to familiar quantum scales. Using the Planck constant and vacuum speed of light,Treating a $1\mathrm{mW}$ output as monochromatic at that line gives $P/E_{\gamma }\simeq 5.35\times 10^{16}$ photons per second. This is a derived scale estimate, not a photon-count measurement from the paper. Photon energy and total radiant flux are different quantities.

The Hall of Fame records the later importance of carbon dioxide lasers for industrial cutting, welding, engraving and drilling.^[ref] That engineering reach explains why a small early molecular-laser demonstration became historically significant.

Difference-frequency generation produces a wave at the positive difference ${\omega }_i={\omega }_p-{\omega }_s$ of two incident angular frequencies, through a second-order nonlinear optical susceptibility. The product of two oscillating electric fields contains both sum and difference frequencies, and the corresponding polarization density drives the generated wave.

For plane waves in a uniform medium, coherent buildup is favored by ${\mathbf{k}}_p={\mathbf{k}}_s+{\mathbf{k}}_i$, the relevant phase matching condition. Two shorter-wavelength inputs can thereby generate longer-wavelength infrared radiation. Collecting the output after removing both incident frequencies distinguishes frequency generation from scattered pump light.^[ref]

Emissivity compares thermal emission from a surface with emission from an ideal blackbody at the same absolute temperature, using the same wavelength and angular averaging convention. For ordinary passive surfaces in the far field at local thermal equilibrium, the ratio lies between zero and one. A blackbody has emissivity one. Unless a spectral or directional qualification is given, the $ϵ$ in $M=ϵ\sigma T^4$ is total hemispherical emissivity: a ratio of emitted radiant exitances, not of all outgoing radiant flux including reflected radiation.^[ref]

Emissivity belongs to a specified surface state, not just a bulk material name. Coating, oxidation and surface finish can change it; wavelength, viewing direction and temperature also matter. A surface that looks white in visible light need not have low infrared emissivity. This distinction is useful when choosing a radiator coating or interpreting a radiation-based temperature measurement: a narrow-band detector needs the appropriate spectral emissivity, and its signal can include reflected surrounding radiation. The grey body and diffuse thermal emitter assumptions are separate simplifications, addressing wavelength and direction respectively.

Rainer Schödel, Reinhard Genzel and collaborators combined NTT imaging with VLT adaptive-optics infrared observations. Silicon-monoxide masers registered stellar images to the radio position of Sagittarius A*. Their 2002 observations included S2's closest approach; a fitted Kepler orbit constrained a concentrated central mass. Rejecting a particular extended cluster also required its density and survival assumptions.^[ref]

Andrea Ghez and collaborators combined Keck speckle imaging and laser-guide-star adaptive optics with infrared spectra. Image fitting supplied angular positions; spectral lines supplied velocities. The 2008 analysis treated optical distortion, coordinate alignment and blended sources: a shifting photocentre can imitate motion. Joint angular and spectral fitting constrained both distance and mass, with assumptions about central radial motion affecting the result. Apparatus calibration and confusion tests are therefore part of the dynamical inference.^[ref]

Galactic multiwavelength astronomy compares observations of the Milky Way in different parts of the electromagnetic spectrum to distinguish its overlapping physical components. The neutral-hydrogen 21-centimeter line traces neutral atomic gas, carbon monoxide spectral lines trace molecular clouds, and infrared emission reveals warm interstellar dust and stars hidden at visible wavelengths. Radio waves from synchrotron radiation trace energetic electrons in magnetic fields, while X-rays reveal hot plasma and compact sources. Maps of the same sky region can therefore test whether a feature is a stellar concentration, an obscuring cloud or shocked gas. Comparing them also requires attention to differing angular resolution and foreground absorption.^[ref]

Keep the same bond force constant $k$ and approximate the nuclear masses of ${}^1\mathrm{H}$, ${}^2\mathrm{H}$, and ${}^{35}\mathrm{Cl}$ by $1u$, $2u$, and $35u$, respectively. Here $u$ is the unified atomic mass unit, and $\mathrm{D}$ denotes deuterium. These are chosen mass number approximations, not measured atomic masses or natural-abundance averages. With the same chlorine isotope in both molecules,This is the isotope scaling of diatomic vibration prediction. Doubling the light partner's mass nearly doubles the reduced mass, lowering the frequency by about $28.3\%$. The factor differs from $1/\sqrt{2}$ because the chlorine partner also moves.

For the same small initial stretch $A$ and zero velocity, both models start with the same internal mechanical energy $k{A}^2/2$, but the DCl oscillation period is longer by $\sqrt{72/37}\approx 1.394972$. In the centre of mass frame, $u_{\mathrm{H}}=-35q/36$ and $u_{\mathrm{Cl}}=q/36$ for HCl; $u_{\mathrm{D}}=-35q/37$ and $u_{\mathrm{Cl}}=2q/37$ for DCl. These ratios explain which partner moves and are separate from the change in frequency.

The common-$k$ assumption belongs to the leading Born-Oppenheimer approximation: fixed nuclear positions and electric charges determine the electronic potential energy, while nuclear masses govern motion on that curve. Quantitative comparison requires actual atomic masses, departures from that approximation, and separation of anharmonicity and molecular rotation from the measured band. Even with common $k$, the quantum harmonic oscillator predicts a different zero-point energy for each isotope.^[ref]

Heather A. Knutson mapped the thermal emission of the exoplanet HD 189733 b from its changing infrared brightness over part of an orbit. Different viewing phases expose different fractions of the hot dayside and cooler nightside.

The measured phase dependence constrained the longitudinal brightness distribution rather than producing a spatially resolved photograph. The relatively modest day–night contrast implied efficient redistribution of absorbed stellar energy, while the displaced brightness maximum supplied evidence about atmospheric transport. Inferred brightness temperatures apply to the observing band and adopted emission model.^[ref]

Indium antimonide is a narrow-gap semiconductor made of indium and antimony, with chemical formula $\mathrm{InSb}$. Its small band gap permits absorption of comparatively low-energy infrared photons, making it useful in infrared detection.

For an ideal interband threshold, $hc/\lambda$ must reach the gap; actual detector response also depends on optical coupling, carrier collection and temperature. Thermal excitation across a small band gap can supply unwanted carriers, so an operating detector's dark current is an essential measurement alongside quantum efficiency. ^[ref]

Infrared is electromagnetic radiation with wavelengths longer than the red end of ordinarily visible light. A useful named convention is the CIE range $780\mathrm{nm}$ to $1\mathrm{mm}$; the approximate visible range $400$–$700\mathrm{nm}$ used in some teaching texts puts the boundary nearer $700\mathrm{nm}$. ^[ref]. Neither number is a sharp physical cutoff of human vision. The CIE divisions IR-A, IR-B and IR-C are respectively $0.78$–$1.4\mu \mathrm{m}$, $1.4$–$3\mu \mathrm{m}$ and $3$–$1000\mu \mathrm{m}$; the boundaries of near-, middle- and far-infrared vary between applications. ^[ref].

Use vacuum wavelength $\lambda$ when comparing these ranges. With frequency $\nu$, speed of light $c$, Planck constant $h$ and photon energy $E$,Thus the CIE infrared interval corresponds approximately to $3.00\times 10^{11}$–$3.84\times 10^{14}\mathrm{Hz}$ and $1.99\times 10^{-22}$–$2.55\times 10^{-19}\mathrm{J}$ per photon, with the smaller energy at the longer wavelength. A $940\mathrm{nm}$ infrared photon has $E\simeq 2.11\times 10^{-19}\mathrm{J}$, whereas a $254\mathrm{nm}$ ultraviolet photon has $E\simeq 7.82\times 10^{-19}\mathrm{J}$. These are calculations from $hc/\lambda$, not measurements of a particular source. A television remote is a familiar approximately $940\mathrm{nm}$ source; its information is carried by variations in the emitted radiant flux. ^[ref].

Detection and visual perception answer different questions. A photodetector can respond to infrared even when an observer perceives no light; a thermometer detects an increase in temperature after photon absorption. Conversely, a small readout can reflect a small spectral responsivity, rather than absence of incident electromagnetic radiation. Images made from infrared readouts use display colors chosen by the imaging system; those colors are not the colors of the incoming infrared.

The important microscopic mechanisms also differ. In infrared spectroscopy, photon absorption often increases the energy of a normal mode in which chemical bonds stretch or bend. The corresponding optical spectrum helps distinguish molecules by their motions. For the usual electric dipole mechanism, the motion must change the electric dipole moment; matching the frequency alone is not sufficient. ^[ref]. Electronic processes can also emit or absorb infrared, so it is not exclusively radiation from molecular motion. ^[ref]; ^[ref].

Infrared is especially useful for observing thermal radiation from objects near everyday temperatures. For an ideal $300\mathrm{K}$ blackbody, Wien's displacement law gives a wavelength peak near $9.66\mu \mathrm{m}$. A thermal camera's readout nevertheless depends on emissivity, reflected surroundings and transmission along the path, as well as temperature. ^[ref]. A source emitting infrared need not be hot: an infrared remote is useful precisely because a photodetector can distinguish its signal from a background. Visible light and ultraviolet can also cause heating when absorbed; “infrared” names a wavelength range, not a unique form of heat.

Herschel's 1800 discovery made the distinction between sight and detection experimentally concrete. His report describes a optical prism spreading sunlight across a white, ruled receiving surface, with three thermometers at different positions near the end of the visible optical spectrum. He observed heating beyond the red edge where no visible color appeared. The result established that sunlight contained invisible radiation less strongly refracted by that optical prism than the visible red; it did not measure a photon energy or establish today's infrared boundaries. ^[ref]; ^[ref].

A documented modern version by Caltech/IPAC uses a glass optical prism, white paper in a shaded box and three blackened liquid-filled thermometers. Initial readings in shade provide each thermometer's baseline; subsequent readings compare blue, yellow and just beyond red after the bulbs have had time to warm. The measured quantity is the rise in temperature, not a “temperature of a color”. The lesson reports the expected largest rise beyond visible red and specifically discusses matching the bulb coatings and thermometer calibration. Clouds and changes in the projected optical spectrum affect the comparison. ^[ref].

For a stronger modern interpretation, an additional shaded thermometer would monitor ambient drift, exchanging bulbs between positions would test differences between thermometers, and blocking the incident beam would distinguish beam-dependent heating from warmed supports or air. These are suggested controls, not claims about Herschel's historical procedure. Thermal conduction through the mounting and convection can change the readout. A broad bulb also samples a range of wavelengths; the optical prism's transmission and optical dispersion, the bulb's absorption and heat loss all affect the position of the largest rise. In particular, the result does not show that an infrared photon carries more energy than a visible photon.

A simple analytical illustration makes those limitations explicit. Let $\theta =T-T_{\mathrm{amb}}$ be the bulb's excess temperature, $C$ its heat capacity, $G$ its effective heat-loss coefficient in $\mathrm{W}{\mathrm{K}}^{-1}$, and $P_{\mathrm{abs}}$ the absorbed power. Assume one uniform bulb temperature, constant ambient temperature, constant $C,G$, and losses linear in $\theta$. Thenfor a beam switched on at $t=0$ with $\theta (0)=0$. After switching the beam off at $t=t_s$, $\theta (t)=\theta (t_s)e^{-(t-t_s)/\tau }$. The exponential function follows by solving this linear differential equation. The steady excess temperature measures $P_{\mathrm{abs}}/G$; it is not a direct measurement of the optical spectrum. With illustrative $C=0.020\mathrm{J}{\mathrm{K}}^{-1}$ and $G=0.0010\mathrm{W}{\mathrm{K}}^{-1}$, $\tau =20\mathrm{s}$. Absorbed powers of $1.0$ and $0.5\mathrm{mW}$ give steady rises of $1.0$ and $0.5\mathrm{K}$, regardless of which wavelengths supplied that absorbed power.

The upper schematic represents the logic of the optical prism experiment; its light ray positions are not a calibrated wavelength scale. The lower curves use the illustrative heat-balance model, with the beam blocked at $60\mathrm{s}$; they are not historical or modern measured data. The beauty of the experiment is that a simple change of detector extends observation beyond what the eye can perceive.

In a centrosymmetric molecule, a fundamental vibration cannot be both electric-dipole infrared active and ordinary Raman spectroscopy active. Dipole components are odd under inversion; polarizability components are even. This selection rule concerns modes, not accidental numerical equality of unrelated frequencies.

Application of infrared energy to produce a localized tissue effect, including in treatment of internal haemorrhoids. It differs from cutting away tissue or applying a mechanical ligature.

Infrared spectroscopy measures a sample's response to infrared electromagnetic radiation. Absorption associated with stretching or bending motions of chemical bonds helps identify groups and their environments. Peak positions are commonly reported as reciprocal wavelength, in $\mathrm{c}{\mathrm{m}}^{-1}$; a lower value means lower frequency. ^[ref]

I. P. Clark coauthored the 2005 spatially offset Raman spectroscopy paper. Its collection geometry changes the mixture of signals arriving from an obscuring surface and the material below it.^[ref]

The Research Complex at Harwell identifies Ian Clark as an Ultra instrument scientist and describes his work on a microbolometer array for measuring the focal size of infrared beams. Knowing a beam's size matters when comparing excitation conditions in time-resolved spectroscopy.^[ref]

For an original Gaussian beam example, suppose the pulse radiant exposure is $F(r)=F_0\exp (-2r^2/w^2)$, with total pulse energy $E$. Integration over the transverse plane gives $E=F_0\pi w^2/2$, so $F_0=2E/(\pi w^2)$. If the actual radius is $110\mu \mathrm{m}$ but the analysis assumes $100\mu \mathrm{m}$, it overestimates peak radiant exposure by $(110/100{)}^2=1.21$, or $21\%$. Measuring pulse energy alone therefore does not determine the excitation delivered per unit area. These values illustrate the dependence on spot size, not a measured error in Clark's apparatus.

Laser flash analysis measures thermal diffusivity by heating one face of a specimen briefly and recording the opposite face's temperature rise. The original 1961 experiment used a flash tube rather than a laser: a blackened thin metal specimen sat in an opaque ceramic holder, with thermocouple wires pressed against its rear face. An amplifier, oscilloscope and camera recorded the signal. Uniform front illumination and the black coating promoted uniform absorption; the opaque low-thermal conductivity holder blocked direct rear illumination and reduced edge losses. The delayed rear response reveals internal thermal conduction rather than direct heating of the sensor. ^[ref]

A modern version uses a laser or flash lamp, a specimen of measured thickness $L$, controlled initial temperature, and a rear-facing infrared detector with a synchronized recorder. The readout is a temperature rise versus time, starting from a pre-pulse baseline. Thermal conductivity additionally requires mass density and specific heat capacity; it is not obtained from timing alone. ^[ref]

Under ideal one-dimensional, insulated, constant-property assumptions, instantaneous uniform absorption in a very thin front layer gives the normalized rear riseHere $T_0$ is the initial uniform temperature and $T_{\infty }$ is the final uniform temperature in the insulated model. Fitting this curve estimates thermal diffusivity; each term has the same $\alpha K_n^2$ decay as the insulated-bar Fourier modes. Equivalently, the half-rise time $t_{1/2}$ solves $R(t_{1/2})=1/2$. Writing $s=\alpha t/L^2$, the series gives $s_{1/2}\approx 0.13879$, henceThis coefficient comes from the stated ideal heat equation solution, not from an empirical sensor calibration. It has been independently checked by solving the series equation. Absolute absorbed pulse energy cancels from the normalized curve; determining heat capacity from its absolute height needs additional information. ^[ref]

Parker and colleagues identify finite flash duration, heat loss, nonuniform illumination, recording bandwidth and electrical interference as practical limits. A specimen too thin responds during the pulse; one too thick allows losses before the rear rise finishes. They shielded the electrical chain and recorded a baseline; their reported tests were preliminary metal measurements near ambient and moderately elevated temperatures. ^[ref]

Useful additional controls are to measure thickness at several points, verify the recorder's time scale and detector response independently, record a no-pulse baseline, and repeat at different pulse energies while avoiding phase transitions. Compare different thicknesses of the same homogeneous material: ideal half-rise times scale as $L^2$. Failure of these checks can expose finite-pulse effects, sensor delay, optical transmission, coating storage or edge losses; a thickness error is especially consequential because the inferred thermal diffusivity depends on $L^2$. These are proposed diagnostic controls, not invented measurements. When the pulse is not short or the sample exchanges appreciable heat with its surroundings, fit a model that includes those effects instead of applying the ideal half-rise coefficient unchanged.

Light is electromagnetic radiation in the visible range; optics also studies neighboring infrared and ultraviolet radiation.

A microbolometer is a miniaturized bolometer in which absorbed electromagnetic radiation heats a thermally isolated sensing element and the readout detects the resulting change in electrical resistance. Arrays of microbolometers can form an infrared image without cryogenic detector cooling. A pixel commonly has an absorbing membrane suspended above its readout circuit on narrow supports.^[ref]

An elementary small-signal heat transfer model writesHere $C$ is the sensing element's heat capacity, $G$ its thermal conductance to a fixed-temperature substrate $T_b$, $P$ incident radiant power and $\eta$ its absorbed fraction. The model treats the element as having a single temperature and neglects changes in readout self-heating. A step to constant incident power $P_0$ givesThe thermal time constant therefore connects sensitivity to response speed. Lowering $G$ increases the steady temperature rise, but at fixed $C$ also lengthens the response.^[ref]

For an original example, choose $C=10^{-9}\mathrm{J}{\mathrm{K}}^{-1}$, $G=10^{-7}\mathrm{W}{\mathrm{K}}^{-1}$, $\eta =0.8$ and $P_0=1\mathrm{nW}$. Then $\tau =10\mathrm{ms}$ and the final sensing-element rise is $8\mathrm{mK}$; after $30\mathrm{ms}$ it has reached about $95\%$ of that rise. If the initial resistance is $100\mathrm{k\Omega }$ and the temperature coefficient of resistance is $\alpha =-0.02{\mathrm{K}}^{-1}$, the linear approximation $\Delta R\approx \alpha R\theta$ gives $\Delta R=-16\Omega$ at steady state. These stipulated values illustrate the model, not a particular camera's specification.

The sensing element's temperature rise is not the observed object's temperature rise. Inferring object temperature from the measured infrared signal additionally depends on emissivity, reflected radiation, the optical path and measurement calibration. “Uncooled” also permits temperature stabilization of the array; it describes the absence of required cryogenic operation, not the absence of thermal design.