Online text: farside.ph.utexas.edu/teaching/315/Waveshtml/node12.html

Cited passages: Richard Fitzpatrick, Damped Harmonic Oscillation, equations 2.19–2.22; his mν equals the coefficient b used here.

Online text: farside.ph.utexas.edu/teaching/315/Waves/node98.html

Cited passages: Richard Fitzpatrick, Two-Dimensional Fourier Optics, equations 10.78–10.87 and Table 10.1.

Cited passages: Fitzpatrick, §10.9, equations 10.70–10.74: path expansion and aperture superposition; Richard Fitzpatrick, University of Texas at Austin, Two-Dimensional Fourier Optics, circular-aperture first minimum; Richard Fitzpatrick, Wave Optics, §10.9: Two-dimensional Fourier optics.

Anharmonicity is departure from the motion of a harmonic oscillator, often caused by nonquadratic terms in a potential energy. It can make the oscillation frequency depend on amplitude and generate higher harmonics. A quartic oscillator has one such anharmonic potential energy.

By Yoshihiro Ohno.

Online text: www.nist.gov/publications/radiometry-and-photometry-review-vision-optics

Cited passages: Abstract: distinction between radiometry and photometry; Abstract: luminous flux in lumens and spectral weighting; Abstract: radiometric quantities and units; photometry weights radiation by the eye's spectral response.

Online text: openstax.org/books/organic-chemistry/pages/10-2-preparing-alkyl-halides-from-alkanes-radical-halogenation

Cited passages: Organic Chemistry by John McMurry, §10.2, Figure 10.2 and following paragraphs: radical combination terminates the chain; further substitution gives product mixtures.

Online text: openstax.org/books/organic-chemistry/pages/6-6-radical-reactions

Cited passages: Organic Chemistry by John McMurry, §6.6: chlorine photolysis and the two-step methane chlorination cycle.

Online text: openstax.org/books/organic-chemistry/pages/26-4-peptides-and-proteins

Online text: openstax.org/books/organic-chemistry/pages/26-2-amino-acids-and-the-henderson-hasselbalch-equation-isoelectric-points

Online text: openstax.org/books/organic-chemistry/pages/26-1-structures-of-amino-acids

Online text: openstax.org/books/organic-chemistry/pages/31-1-chain-growth-polymers

Cited passages: John McMurry, Organic Chemistry, §31.1: successive reactive intermediates and radical, cationic and anionic initiation; McMurry, Organic Chemistry, 31.1; McMurry, §31.1, initiating species and the first reactive intermediate.

A carboxylic acid contains the functional group $-\mathrm{C}(=\mathrm{O})\mathrm{OH}$. Loss of its hydroxyl proton gives a carboxylate ion, whose electronic structure distributes negative charge over two oxygen atoms.

Acetic acid is a small example; fatty acids combine the same group with a longer hydrocarbon chain. Formation and cleavage of esters connect carboxylic acids with both organic synthesis and lipid chemistry.^[ref]

A mitochondrion is an organelle with an outer mitochondrial membrane and an inner mitochondrial membrane. The latter encloses the mitochondrial matrix and folds into cristae; the intermembrane space lies on its opposite side. This architecture separates a chemical workspace from a membrane that couples electron transport to ATP formation.^[ref]

For an original location exercise, place soluble label A in the mitochondrial matrix and soluble label B in the interior of a crista. In the depicted geometry, B can reach the peripheral intermembrane space through the fold's opening without crossing a lipid bilayer. A must cross the inner mitochondrial membrane to reach either location. A fold projecting into the mitochondrial matrix therefore does not make its enclosed fluid part of the mitochondrial matrix. Following a continuous path through the colored regions proves the distinction; merely asking whether a label is “inside the mitochondrion” loses it.

The functional connection is equally spatial. The mitochondrial respiratory chain pumps protons from the mitochondrial matrix side across the inner mitochondrial membrane. Their return through ATP synthase can drive ATP formation. Oxidative phosphorylation develops the mechanism and chemiosmosis gives its free energy bookkeeping. Compartmentalization is useful because it lets a shared electrochemical gradient couple different proteins without direct transfer of a chemical intermediate between each pair.

Under aerobic conditions, mitochondria supply much of the ATP in many eukaryotic biological cells; the contribution varies with biological tissue, demand and oxygen supply. Glycolysis also makes ATP in the cytosol. Mature mammalian red blood cells lack mitochondria, and bacteria have no mitochondria at all. Neither all ATP production nor all biological cells fit the familiar mitochondrial picture.^[ref]

Mitochondria descend from a bacterial endosymbiosis and retain a genome and ribosomes, although many required proteins are encoded by nuclear genes. Endosymbiotic theory develops the ancestry argument; organelle protein import explains delivery of nuclear-encoded proteins. A functioning isolated mitochondrion demonstrates biochemical autonomy under supplied conditions, rather than independently establishing that ancestry.

A plastid is an organelle of the lineage that includes chloroplasts. A chloroplast is a photosynthetic plastid; the terms are not interchangeable because some plastids are nonphotosynthetic. Endosymbiotic theory connects plastid origins to cyanobacteria, while endosymbiotic gene transfer and organelle protein import explain genetic and functional integration with the host.

A laser generates amplified light through stimulated emission. Its name abbreviates “light amplification by stimulated emission of radiation”. Lasers supply the intense beams used in optical tweezers; optical coherence also makes them useful for wave interference measurements. ^[ref].

In the usual material picture, a gain medium stores energy supplied by pumping, for example by incident light or an electric current. Stimulated emission transfers that stored energy to a selected optical normal mode, while competing photon absorption removes light. Producing net optical gain requires a suitable population distribution, such as population inversion in the simple model below.

A familiar laser oscillator uses mirrors to return light through the gain medium. This optical feedback favours resonant normal modes; a partly transmitting mirror lets useful power escape. Feedback and mode selection have different implementations, including ring arrangements: every laser need not resemble the same two-mirror device. The laser threshold example treats just that device. ^{[ref] [ref]}.

The useful combination is concentrated power and controlled optical normal modes. It gives optical tweezers a localized source of force and wave interference measurements a source with useful optical coherence. A laser can nevertheless emit several frequencies; “laser” alone does not guarantee a single frequency. ^[ref].

An original experimental landmark is T. H. Maiman's 1960 report of stimulated optical radiation from optically pumped ruby at about $694.3\mathrm{nm}$. His paper describes both the pumping path and the observed emission, connecting stored material energy with amplified light. ^[ref].

Spectral pulse shaping changes an optical pulse by applying a complex amplitude-and-phase mask $M(\omega )$ to its frequency components. The output in time is the inverse Fourier transform of the masked spectrum. A passive device cannot amplify unavailable spectral components; finite bandwidth and spectral resolution constrain the realizable waveforms and time window.

A spatial light modulator applies an electronically controlled spatially varying optical phase, amplitude, or polarization change. In a 4f pulse shaper, frequency maps to transverse position, allowing the pixels to implement a calibrated spectral mask. A phase-only modulator generally needs additional polarization optics or another modulation stage for independent amplitude control.