Hand-considered hypotheses, 701–800

Photons as sources, as carriers, as signals and as clocks. One hundred entries, each written on its own terms, and each labelled with the form of its argument rather than its topic: a claim that a quantity has been misattributed, a bound, an inversion, a counting argument, a degeneracy, an artefact that impersonates an effect. The forms repeat on purpose so that the repetition is visible; the sentences do not. Nothing here has been measured, and where a number appears it is an order-of-magnitude estimate marked as such. None has been tested.

Sources and gain media

Misattribution
H701. The excess linewidth of a diode-pumped solid-state laser above its Schawlow–Townes value is usually charged to acoustic vibration, yet in a monolithic cavity a few millimetres long the leading term is pump intensity noise converted to frequency through the gain medium's slow thermal response. That conversion has a corner at the medium's thermal diffusion time, so the noise spectrum acquires a shelf that a vibration spectrum never shows. Quieting the pump with a separate intensity servo, while leaving the bench untouched, should collapse the shelf and leave the vibration lines standing.
Hidden term
H702. Every slope efficiency quoted for a laser amplifier omits the amplified spontaneous emission leaving through the output aperture, and the omission is not a constant: it grows with the product of small-signal gain and collection solid angle, so a thin disk and a long fibre quoted at the same efficiency have not been quoted at the same quantity. Because the term rises with gain while the signal rises faster, the omission is invisible along the linear part of the curve and largest near roll-over. Blocking the signal beam at the same pump level measures the term directly.
Threshold
H703. Stable mode locking demands a saturable absorber that recovers within a fixed fraction of the round-trip time, and that fraction is set by the absorber's modulation depth rather than by the gain. When recovery is slower the absorber cannot re-bleach before the pulse returns, so successive pulses meet different losses and the train looks noisy without ever failing outright. Two absorbers of different recovery times, with modulation depth equalised by adjusting fluence, should differ in train stability while their autocorrelations remain identical.
Inversion of standard practice
H704. A cladding-pumped fibre amplifier is normally designed for the largest core-to-clad ratio the pump can fill, since that maximises absorption per unit length. For pulsed operation the better choice is a smaller ratio: the same absorbed power in a smaller core raises peak intensity faster than it shortens the fibre, so the nonlinear phase accumulated before the pulse exits grows. Comparing two amplifiers at equal output energy and equal B-integral should show the larger clad winning despite its weaker absorption.
Rank argument
H705. A pulse's spectral phase across N resolved bands has N−1 independent coefficients, so a shaper with N pixels cannot set more than N−1 of them whatever its mask resolution. Claims of arbitrary waveform synthesis are therefore claims about N, and N usually goes unreported because the shaper's pixel count is mistaken for the pulse's information content. The test is to request two target waveforms whose difference lies in the null space of the shaper's response matrix and observe that the outputs are indistinguishable.
Reversal
H706. Which polarization a vertical-cavity laser prefers at threshold says nothing about which it prefers at operating current, because gain anisotropy and cavity birefringence favour different axes. As current rises the gain anisotropy saturates first, so emission switches to the axis the birefringence sets, and the switch current is the ratio of the two. A polarization-resolved current sweep on one device locates the crossing and yields both anisotropies from a single run.
Selection effect
H707. Efficiency records are champion devices drawn from populations that are never reported, so the difference between two laboratories' best results measures how many devices each was willing to discard. The arithmetic is not fraud but extremes: the more devices measured, the higher the best, and the apparent variance between records shrinks as the populations grow even when the populations are identical. Requesting the wafer map with all devices and computing the median converts a record into a measurement.
Scale argument
H708. In a fibre laser the nonlinear phase per unit output power is almost independent of core diameter once the mode is confined, because intensity falls with area while the interaction length falls with the same area through the doping density. Enlarging the core therefore buys power handling only until bend loss and mode coupling intervene, and the practical ceiling is set by the coating's index contrast rather than by the glass's nonlinearity. Two fibres of different core diameter, compared at equal output and equal bend length, should broaden identically.
Identity
H709. The relaxation-oscillation peak in a laser's intensity noise and the corresponding peak in its frequency noise are one resonance, coupled by the linewidth enhancement factor, not two mechanisms that happen to share a frequency. Their amplitude ratio at the peak is therefore a direct reading of that factor, needing no modulation and no separate experiment. A simultaneous amplitude-and-phase noise measurement at two bias currents should return the same factor from both.
Unit trap
H710. Brightness is quoted as power per unit area per unit solid angle, but the same figure is often presented as power per unit area with the solid angle buried in a beam parameter product, and the two conventions differ by the fourth power of M². A source called ten times brighter may only be ten times further along that exponent, and the conversion is rarely printed. Asking for watts, square centimetres, steradians and M² separately settles it, since four stated quantities cannot conceal a factor among them.
Artefact mimicking effect
H711. The low-frequency excess reported as 1/f intensity noise in a diode laser is often the thermal resistance–capacitance product of its submount rather than a property of the gain medium. Its corner frequency tracks the submount's thickness and solder voids, so two lasers from one wafer on different submounts will display different "1/f" spectra. Mounting a single laser on two submounts of different thickness, changing nothing else, separates the two.
Bound
H712. No cavity delivers a linewidth below the Schawlow–Townes value set by its outcoupling rate and its intracavity photon number, and at low power that bound, not the servo, is what limits a laser locked to a high-finesse reference. The bound falls with power and with length, so longer and lower-loss is the only route, and any sub-hertz claim should be checked against the photon number it implies (estimate: a few milliwatts in a metre-long cavity sits near the hertz level). Measuring the same laser at two output powers tests it, because the bound scales inversely with power while technical noise does not.
Derived quantity
H713. Wall-plug efficiency is derived: it multiplies optical efficiency by the driver's and the cooler's, and for a device pumped far from its optimum the cooler's coefficient of performance dominates the product. Comparisons across wavelengths therefore compare thermal management rather than photon conversion, and rankings invert when the same devices are quoted at the laser output instead. Reporting the three factors separately removes the ambiguity, because each has its own units and the product is then reconstructible.
Sign argument
H714. The correlation between a laser's amplitude noise and its frequency noise carries the sign of the linewidth enhancement factor, so an anticorrelation at low frequency measures that factor and says nothing about the noise source. Above the relaxation frequency the sign reverses, because the carrier and photon reservoirs exchange roles, and a spectrum that fails to reverse has been measured through a limiter. One cross-spectrum between the two detectors, swept across the relaxation frequency, tests both statements together.
Degeneracy
H715. A light-in versus light-out curve fixes the product of gain and outcoupling and the difference between gain and loss, but not the internal loss separately; those two parameters are degenerate in that curve alone. This is why two lasers from one wafer can be assigned different internal losses by careful fitting and still behave identically. Inserting a known extra loss into one cavity and refitting breaks the degeneracy and reveals how much of the reported loss belonged to the fit.
Hysteresis
H716. The threshold of a laser that has been running sits below its cold-start threshold, because the gain medium's temperature profile and the mode's thermal alignment carry the previous run's imprint. The gap exceeds shot-to-shot jitter, so a threshold quoted without a thermal history is not a material property. Measuring a cold start and then an hour at full power, with the mount held at fixed temperature, sizes the history term.

Detectors and photon counting

Misattribution
H717. A silicon photodiode's responsivity deficit at short wavelength is usually assigned to surface recombination, yet much of it comes from carriers generated in the neutral region beneath the junction, which must diffuse to the depletion edge and arrive late or not at all. That deficit depends on depletion width and therefore on bias, which surface recombination does not. One wavelength at two reverse biases separates them, since widening the depletion region recovers the diffusing carriers and leaves the surface loss unchanged.
Hidden term
H718. A transimpedance measurement accounts for the feedback resistor's thermal noise and the amplifier's current noise, and habitually drops the photodiode's own shunt-conductance noise, which has the same spectral form as the first and dominates for large-area devices. At high shunt resistance the dropped term is negligible, so calibrations performed on small diodes do not transfer. Two diodes of one material and different area, read through the same amplifier, should differ in that term by exactly the area ratio.
Threshold
H719. Below some field an avalanche photodiode's multiplication is carried by one carrier type, so the excess noise factor approaches unity and the device multiplies almost silently, at a gain too small to be useful. The field at which the second carrier begins to ionize is a material constant, and it fixes the gain beyond which the noise factor climbs. Illuminating the thin side of the junction to inject electrons only, and sweeping gain, exposes the knee.
Reversal
H720. Photodiode bandwidth does not rise monotonically with reverse bias: at low bias the response is diffusion-limited, and widening the depletion region shortens the diffusion tail while lengthening the transit time. The two trends cross, so bandwidth peaks at a bias and falls beyond it. A frequency-response sweep at five biases on one device shows the maximum, and its position should move with wavelength if transit rather than RC sets the roll-off.
Count
H721. A photon-number-resolving detector built from N on-off elements returns at most N+1 distinguishable outcomes, so it can report no more than N+1 photon numbers whatever its quantum efficiency. Reports of resolving far more photons than there are elements are reports about a fit, and the fit's prior does the resolving. Feeding the detector a source whose statistics are deliberately flat over the first N+2 numbers, and watching where the reported distribution stops changing, tests it.
Artefact mimicking effect
H722. An afterpulse arriving a few nanoseconds after a real detection imitates a photon-bunching correlation at short delay, and at high count rates it can manufacture the very antibunching a quantum-optics demonstration is trying to show. The artefact scales with count rate and with detector temperature; a genuine field correlation does not. Changing repetition rate at fixed mean count, and warming the detector by ten kelvin, moves one and not the other.
Scale argument
H723. Timing jitter in a large-area detector with a uniform field grows as the square root of area, because the transit-time spread scales with the distance carriers must cross while the field is pinned by the bias. A jitter quoted for a small device therefore does not transfer to a large one, and the two numbers cannot be compared without the areas. Three diameters of one design, measured with one amplifier and one source, either show the square-root law or refute it.
Unit trap
H724. Noise-equivalent power in watts per root hertz and responsivity in volts per watt are compatible only when load resistance and bandwidth convention are stated, and a 50-ohm load turns an ampere-per-watt responsivity into a volt-per-watt one by a factor of fifty. Two data sheets quoting the same NEP can differ by exactly that factor with neither being wrong. Converting both to electrons per root hertz at a stated wavelength disposes of the ambiguity, because charge is the one unit neither convention can absorb.
Derived quantity
H725. Photon-counting efficiency is derived — quantum efficiency times collection times threshold acceptance — and it is normally fitted from a Poisson assumption about the source. If the source is not Poisson the fit buries the difference in the efficiency, which is how values slightly above the separately measured quantum efficiency appear. Calibrating against a source whose statistics are known independently, an attenuated mode-locked train with a measured photon-number distribution, tests the decomposition.
Inversion of standard practice
H726. Cooling a single-photon avalanche diode is standard for suppressing dark counts, but below the temperature at which trap emission slows, afterpulsing rises faster than the dark count falls, because traps hold charge longer and release it inside the next gate. The count-rate ceiling drops while the dark-count figure improves, so a specification written around dark counts picks the wrong operating point. Measuring afterpulsing and dark count at four temperatures and fixed excess bias locates the crossing.
Cancellation limit
H727. Common-mode rejection in a balanced homodyne detector cannot exceed the responsivity mismatch of its two photodiodes, and that mismatch drifts with temperature at a rate set by the two dies' unequal thermal coupling to the mount. A rejection figure quoted at one temperature therefore overstates rejection during a long run, and the drift surfaces as low-frequency excess noise. Swapping the two diodes' positions in the mount reverses the sign of the drift contribution and separates it from the electronics' own imbalance.
Identity
H728. Thermally generated counts and optically generated counts leave a single-photon detector identically: same amplitude, same shape, same time tag. Only the arrival-time distribution against a known optical gate separates them, so a dark-count figure taken in continuous light measures both populations under a name that promises one. Gating the source and histogramming arrival times relative to the gate recovers the split without touching the detector.
Selection effect
H729. Quantum efficiencies are reported for devices chosen because they are high, and the choice is invisible because the rejected devices are never counted as rejections. Process yield and best-device efficiency thereby become one number, and a "reproducible" ninety per cent can be a forty per cent yield. Measuring every device on one wafer and reporting median with maximum is the only test that distinguishes them.
Symmetry
H730. A photodiode's response to a fixed polarization is symmetric under a 180-degree rotation of that polarization only if the device is isotropic in its plane, so a departure from two-fold symmetry at normal incidence indicates stress rather than a coating. Stress birefringence in the chip folds the response into a pattern whose axes align with the die flat. Rotating a polarizer through a full turn on one device, then repeating with the die turned 45 degrees, separates the die's axes from the mount's.
Hysteresis
H731. A photodiode's responsivity at a fixed wavelength depends on its irradiation history, because ultraviolet exposure alters the passivation's charge and with it the surface recombination velocity. Two calibrations of the same device, before and after a high-flux exposure, can differ by more than the calibration uncertainty while dark current stays put. An unexposed monitor diode in the same beam separates a drifting source from a changing device.
Rate ceiling
H732. With dead time tau no counter can report a rate above 1/tau, so a linearity specification reaching high rates is a statement about tau and not about the detector's speed. The correction extending the apparent range is a model, and it fails first at the top where the model's assumption about pulse shape bites hardest. Sending one source through two neutral-density filters of different ratio, then comparing corrected rates, shows where the correction gives out.

Waveguides and fibres

Misattribution
H733. Bend loss in a high-contrast waveguide is routinely attributed to curvature, but for tight bends in a thin buried oxide the dominant channel is leakage into the silicon substrate rather than radiative loss at the outer cladding. The two mechanisms differ in how they respond to the substrate's distance and to the wavelength, and only one of them is improved by a deeper trench. The same bend measured on two chips with different oxide thicknesses decides it, since curvature is identical and the substrate path is not.
Hidden term
H734. Every propagation loss measured by cutback contains the coupling loss of the measurement's own transitions, and the subtraction is valid only if the transition is identical at every length. When the facet is repolished or a new chip is cleaved between points, the changing transition enters with the wrong sign and can yield a negative loss. Measuring the same length three times with the input realigned independently, and reporting the spread, exposes how much of the loss belongs to the launch.
Threshold
H735. There is an index step below which a waveguide bend loses light by tunnelling through the outer barrier and above which the loss is dominated by scattering from sidewall roughness. The regimes scale differently with wavelength — one exponentially, one approximately as the inverse third power — so a single bend measured at two wavelengths assigns the loss without any simulation. The crossover step is the design point, and it moves with the roughness the process actually delivers.
Reversal
H736. Dispersion in a silicon waveguide passes through zero at a width fixed by the mode's confinement, not by the material's own dispersion, and the width at which it crosses depends on the cladding above the core. Consequently the same nominal waveguide on two chips with different upper claddings has zero-dispersion points separated by more than the fabrication tolerance. Three widths on two claddings locate both crossings and show which of the two variables sets them.
Count
H737. A grating written with N independently addressed phase steps has N independent spectral degrees of freedom, so a sensor claiming more independent measurands from one grating is reporting cross-terms of the same N. The extra apparent channels come from the fitting, which can rotate the basis but cannot enlarge it. Requesting a measurement that perturbs two of the N steps in a known pattern shows whether the reported channels respond independently.
Artefact mimicking effect
H738. A group index far above the material's in a photonic-crystal waveguide is often read as slow light, but a Fano interference between a guided mode and a low-Q resonance produces the same delay signature with no reduction of the mode's group velocity anywhere. The discriminator is loss: true slow light loses in proportion to the group index, while a Fano feature loses in proportion to the resonance's width and can even show gain. Measuring insertion loss and delay on the same device across the feature separates them.
Invariance argument
H739. The nonlinear coefficient of a waveguide scales as the inverse mode area, but so do the two-photon absorption penalty and the free-carrier density generated per unit power, so a figure of merit for wavelength conversion is set by the bandgap and not by the confinement. This is why shrinking a converter improves efficiency in the low-power limit and changes nothing at the power where two-photon absorption saturates, and why reports of record efficiency cluster at low power. Measuring conversion efficiency against input power on two mode areas should produce curves that cross rather than separate.
Inversion of standard practice
H740. Maximising confinement is the reflex for a low-loss waveguide, yet when the loss is dominated by sidewall roughness the lower-loss design is one deliberately operated at weaker confinement, because the mode overlaps the sidewall less even as bend loss rises. The optimum sits where the roughness term has fallen below the bend term, and it is not the design that minimises either alone. A series of widths on one chip, with bend loss measured separately on each, locates it without changing the process.
Selection effect
H741. Propagation losses are quoted for the best waveguide on a chip, which converts a distribution into a single number that no device in production will achieve. Because the reported statistic is a minimum, improving the process's uniformity can make the quoted figure worse while every device gets better. Publishing the median and the worst case alongside the best is the test, and it costs nothing but the honesty of the table.
Unit trap
H742. Loss in decibels per centimetre and in decibels per millimetre differ by ten, and a "3 dB device" quoted for a one-centimetre chip may be a propagation figure or an insertion figure including two couplings that each cost more than the waveguide. The two are separated only by a length series, and without one the number cannot be used in a link budget. Recomputing a reported loss as dB per unit length with the coupling stated explicitly exposes the ambiguity.
Derived quantity
H743. The effective index extracted from a fringe spacing is a derived quantity that presumes a single mode, and in a multimode waveguide it is an average over the modes that the launch happened to excite. Changing the input alignment then changes the "material" index without any change to the device, and the change is largest near a mode crossing. Launching through two different fibres into the same waveguide, and comparing extracted indices, tests the presumption.
Degeneracy
H744. A ring's free spectral range constrains only the product of group index and radius, so a fit reporting both from one transmission spectrum is reporting a ratio it assumed. The degeneracy breaks only when a second, independent length is measured on the same chip, or when the ring is measured at two wavelengths far enough apart that the group index's dispersion matters. Two rings of different radius in series provide that second length at no extra alignment cost.
Sign argument
H745. Silicon's thermo-optic coefficient is positive, yet a silicon waveguide's effective index can fall with temperature near a photonic band edge, because the mode's confinement in the high-index material weakens as the index rises. The sign of the measured thermo-optic response therefore reports which side of the band edge the device operates on, and a heater calibrated on the wrong side will run away. Sweeping temperature on a waveguide at two wavelengths on either side of the edge shows the sign flip.
Hysteresis
H746. Photosensitivity in a germanosilicate fibre is not erased by annealing at the writing temperature, because part of the index change is frozen into the distribution of oxygen-deficient centres and depends on the writing sequence rather than on the final exposure. Two gratings written to the same total fluence but with different sequences therefore anneal to different strengths. Writing the pair, annealing both together and comparing their Bragg shifts isolates the history term.
Identity
H747. Polarization-dependent loss and birefringence are reported as separate defects, but they are two projections of one random perturbation tensor along the fibre, so a component with large birefringence and small PDL is one whose perturbation happens to be aligned. Twisting the fibre rotates the projection and should trade one for the other at fixed total perturbation. A twist series with both quantities measured at each angle tests the identity directly.
Conservation argument
H748. A phase-insensitive amplifier fed with a coherent input and measuring only one quadrature cannot have a noise figure below 3 dB, because the unmeasured quadrature's vacuum enters through the same inversion that provides the gain. Any report of a lower figure for such an amplifier has assigned part of the input coupling loss to the gain, or has measured a phase-sensitive configuration under a phase-insensitive name. Blocking the input and comparing the output noise with the shot-noise reference exposes which accounting was used.
Transform-pair bound
H749. The bandwidth of a grating coupler is tied to its length by a Fourier relation, so a design quoting both wide bandwidth and high efficiency at the same wavelength has usually paid in one of them somewhere unstated. Apodisation reshapes the trade but cannot remove it, and the product of bandwidth and coupling strength is the quantity that is actually conserved. Measuring efficiency against wavelength on two lengths of the same apodised design shows the product holding.
No-go
H750. A passive, linear, reciprocal element is unitary, so it cannot turn a mixture of two modes into a single pure mode without sending the orthogonal component somewhere, and reports of lossless mode purification are reports about a port the setup did not monitor. The discarded component leaves as an equal and opposite signal in another port, not as heat, so a power meter on the output alone cannot see it. Terminating every port and summing transmission while the input's mode mixture is scanned tests it: the sum cannot exceed unity, and any excess in one port is balanced in another.

Imaging, contrast and gating

Misattribution
H751. The bright halo that surrounds a phase object in phase-contrast microscopy is usually read as a real redistribution of light around the object, but it is the transfer function's response to the phase ring's finite width, and it changes when the ring's absorption changes while the object does not. Its radius therefore encodes the condenser annulus, not the specimen. Imaging the same object with two rings of different absorption, matched in everything else, tests whether the halo follows the object or the aperture.
Hidden term
H752. Every intensity in a fluorescence image includes the medium's own emission, and for a sample thinner than the mean free path that term is spatially flat while for a thicker one it is not, so the same background-subtraction rule cannot serve both. The flat case hides the term inside a scalar offset; the thick case folds it into the object's apparent shape. Imaging a blank region of the same preparation at the same depth, and comparing with a region of known thickness, splits the two.
Threshold
H753. Coherence gating reaches a depth at which the ballistic fraction has fallen below the shot-noise floor, and because that fraction decays exponentially while the floor falls only as the square root of integration time, doubling the dynamic range buys a fixed increment of depth and not a proportional one. The increment is the transport mean free path times the logarithm of the range ratio — a scale, not a factor. Measuring the same sample at two detector gains, one decade apart, should move the maximum useful depth by a fixed amount, which is the prediction.
Reversal
H754. In dark-field illumination the collected signal falls when the illumination numerical aperture is raised past the collection aperture, because the geometry that excludes the specular beam also excludes part of the scattered light. Below that point the signal rises with aperture; above it, it falls. Sweeping one aperture while holding the other, on a fixed scatterer, should show the maximum and thereby measure the geometry rather than the scatterer.
Identity
H755. The stripes that light-sheet microscopists call shadowing and the stripes they call bleaching are the same observation viewed at two time scales, since both are the sample's absorption removing excitation before it reaches the focal plane. The separator is not intensity but motion: a shadow moves with the sheet, a bleached band stays with the sample. Translating the sheet while the sample is fixed, in one acquisition, discriminates them without changing any optics.
Artefact mimicking effect
H756. A circular-dichroism signal from a thin film on a substrate can be linear dichroism that a birefringent substrate has rotated into the circular channel, and the two are indistinguishable in a single spectrum. The artefact follows the substrate's axes while the true signal follows the film's, so rotating the sample about the beam axis moves one and not the other. Measuring at four rotation angles, with the substrate's orientation logged, is enough to assign the signal.
Scale argument
H757. Edge enhancement in propagation-based phase contrast has a width that grows as the square root of the propagation distance times the wavelength, so an image taken at one distance carries a contrast that depends on the apparatus and not only on the object. Two distances invert the relation and remove the artefact, which is why a single-distance phase image should not be quoted as a material contrast. The test is to predict the second distance's image from the first and compare.
Inversion of standard practice
H758. Deep imaging is usually pushed toward the highest numerical aperture available, but past a certain depth the ballistic signal falls faster with aperture than resolution improves, so the information rate peaks at a lower aperture. The optimum is where the derivative of collected signal with respect to aperture equals the derivative of the resolved volume, and it moves shallower as scattering rises. Imaging the same volume at three apertures end stops the argument: the deepest plane's contrast should be best at the middle aperture, not the largest.
Selection effect
H759. A demonstration that reports the best ten seconds of a ten-minute acquisition is a selection effect whose size can be measured by asking for the full recording and its frame-rejection log. The reported image quality is then a maximum over frames, and comparing two methods by their maxima says which had a luckier outlier rather than which is better on average. Reporting the tenth percentile of frame quality, alongside the maximum, costs one number and removes the ambiguity.
Unit trap
H760. Fluorescence brightness quoted per pixel, per molecule and per second differ by the binning, the exposure and the camera's conversion gain, so three papers can report the same sample and disagree by an order of magnitude without error. The unit that travels is photons per molecule per second at the sample, and it requires a calibration of the detection path. Converting a reported figure into that unit, and checking whether the conversion needs a number the paper does not give, tests the reporting rather than the sample.
Derived quantity
H761. Contrast-to-noise ratio is derived from a chosen signal region and a chosen background region, and moving the background annulus outward by one object width changes it by more than the difference between the two methods it is being used to rank. The number is therefore a property of the region of interest as much as of the image. Recomputing a published figure with three annular radii, all stated, shows the sensitivity without any new data.
Degeneracy
H762. In time-of-flight depth imaging a surface's albedo and its distance are degenerate in the returned intensity whenever the pulse shape is unknown, because a dimmer return can be a darker surface or a longer path with the same loss. Only the pulse's shape, measured on a reference surface at a known distance, breaks the degeneracy. Imaging a target with two known reflectivities at one distance and then at a second distance tests whether the system separates them or merely fits them.
Sign argument
H763. The sign of a quantitative phase image depends on the Fourier convention and on the propagation direction assumed in the reconstruction, so two published phase maps of the same cell can differ by a sign with neither being arithmetically wrong. The sign matters the moment it is read as a refractive index, because a positive and a negative index shift imply opposite compositions. Reconstructing one hologram under both conventions, and checking which reproduces a known-thickness reference, fixes the convention for that paper.
Reciprocity
H764. An imaging system whose illumination aperture differs from its collection aperture is not reciprocal, so its response is not the product of the two apertures' responses and cannot be inferred from either alone. This is why a system optimised by shaping the illumination can show a resolution that no symmetric system with the same collection optics reproduces. Interchanging the two apertures on the same hardware, and comparing the two images, measures the non-reciprocity directly.
Hysteresis
H765. A fluorescent sample's second image is not its first, because bleaching depends on the local oxygen concentration and the first exposure has already consumed it, so the bleaching time constant lengthens between frames. Ratio measurements that assume a constant bleaching rate therefore drift in a way that mimics a real change in the sample. An unexposed reference region in the same field, and a repeat acquisition after a pause, separate the drift from the change.
Photon accounting
H766. Emitted photons cannot exceed absorbed ones, so a measured fluorescence quantum yield above unity is a calibration error and almost always one of two: absorptance measured on a scattering film in transmission, or a reference dye whose spectrum was assumed rather than measured. Both inflate the denominator's complement. Integrating sphere measurements of absorptance and emission on the same film, in the same geometry, close the budget and expose the error.

Nonlinear optics

Misattribution
H767. Second-harmonic generation from a nominally centrosymmetric film is credited to the surface, but in a strained film a flexoelectric field breaks inversion symmetry throughout the thickness and the bulk contribution can exceed the interface's. The two are separated by their dependence on thickness: interface terms saturate, strain terms grow, and the crossover thickness is set by the strain gradient. Depositing the same film on two substrates that strain it in opposite senses inverts the sign of the bulk term while leaving the surface term fixed.
Hidden term
H768. A z-scan of a thin film on a substrate carries the substrate's nonlinearity and the free carriers that two-photon absorption generates, and neither is in the model that produces the quoted nonlinear index. The carrier term's sign is opposite to the Kerr term and its magnitude depends on pulse repetition rate, so the apparent nonlinearity of the same film changes when the laser's repetition rate changes. Repeating the scan at two repetition rates, with pulse energy and fluence held equal, separates the instantaneous from the accumulated contribution.
Threshold
H769. Self-focusing overtakes diffraction at a critical power that depends on the material and the wavelength but not on the beam's width, so a measured threshold that scales with beam size is not self-focusing at all but damage or impurity breakdown wearing its name. The invariance is the test, and it is cheap: the same material at two beam sizes. A threshold that moves with the size has already answered the question.
Reversal
H770. The sign of a semiconductor's nonlinear refraction reverses below the band edge, where two-photon absorption fills the bands and the resulting carrier plasma defocuses faster than the bound-electronic Kerr effect focuses. The reversal wavelength is therefore a direct readout of the ratio between the two, not a materials curiosity. A wavelength scan across the edge, at fixed fluence below damage, shows the sign change and locates it without any assumption about either coefficient.
Count
H771. N pump frequencies generate at most N(N−1) distinct products of the form two-of-one-minus-another, so a measured spectrum containing more lines than that count has recorded cascaded products and is not a single mixing event. The count is a diagnostic that costs nothing and is rarely applied, which is why spectra with unexplained extra lines are sometimes read as new processes. Reducing the input to two pumps and counting the output lines tests whether the extra structure is cascade.
Artefact mimicking effect
H772. A pulse that appears to advance through a gain medium by more than its length allows is showing waveform rearrangement, not superluminal propagation, and the discriminator is scaling: a true propagation advance grows with the medium's length, while rearrangement saturates once the medium is longer than the pulse's coherence. Two lengths of the same medium, with the advance measured at both, decides it. An advance that stops growing with length has already been explained by the pulse's own shape.
Scale argument
H773. Filamentation clamps the peak intensity at a value set by the balance between Kerr self-focusing and plasma defocusing, so the clamped value is a property of the gas and hardly of the pulse. A reported filament intensity above that value is therefore a measurement of the input's spatial chirp or of the focusing aperture, both of which alter the measured spectrum without altering the clamp. Varying only the aperture, at fixed pulse energy, should leave the clamp fixed and move only the spectrum's width.
Inversion of standard practice
H774. Efficient parametric conversion is conventionally pursued with a long periodically poled crystal and the narrowest phase-matching bandwidth the application allows, but for a broadband pump the better device is a short chirped crystal, because acceptance bandwidth and conversion efficiency trade and the pump's own spectrum sets which end of the trade matters. The optimum length is where the pump's coherence time is fully accepted, not where the efficiency peaks for a monochromatic pump. Measuring conversion against crystal length with the real pump, and again with a filtered narrow-line pump, shows the two optima differing.
Bound
H775. An optical parametric amplifier's conversion cannot rise indefinitely with length, because once the pump depletes the process back-converts and the signal falls again, so "longer crystal, more gain" has a maximum that the small-signal theory does not show. The optimum length is the one at which pump transmission is fully exhausted, which is measurable directly on the same setup. Reporting pump transmission alongside gain would make the maximum visible in every published curve.
Derived quantity
H776. A nonlinear refractive index extracted from a z-scan is derived using an assumed transverse profile, and re-fitting the same data with a top-hat instead of a Gaussian changes the quoted value by tens of per cent. Because the profile is rarely stated, two values in the literature can differ by exactly that factor with neither measurement wrong. Fitting one dataset under both profile assumptions and reporting both numbers tests the sensitivity and costs a line in a table.
Selection effect
H777. A high-harmonic cutoff is quoted from the shots with the best phase matching, which is a maximum over an unreported ensemble and therefore partly a measurement of how long the laser was left running. The cutoff from a single-shot ensemble's median is lower, and the gap between the two is the size of the selection. Recording single-shot spectra instead of an accumulated grating spectrum exposes the distribution in one experiment.
Unit trap
H778. Second-order coefficients appear as picometres per volt and as electrostatic units, and the conversion absorbs a factor of the speed of light and of four pi, so a factor-of-ten disagreement between two papers is often a units disagreement. Worse, some conventions write the polarisation with a factor of two in front of the nonlinear term and some do not, which changes d by two without changing anything physical. Converting a reported value into both conventions, and checking which reproduces the measured conversion efficiency, identifies the convention actually used.
Symmetry
H779. The polar pattern of second-harmonic generation from a thin film has the rotational symmetry of the susceptibility tensor contracted with the two fundamental fields, so a pattern with the wrong fold count means the signal is not coming from the film's bulk symmetry at all. Interface generation, strain, and misalignment each break the pattern differently, and the fold count alone can rule out two of the three. Rotating a half-wave plate in front of the sample while recording the harmonic efficiency, at fixed incidence, gives the pattern directly.
Hysteresis
H780. Two-beam coupling gain in a photorefractive crystal depends on the sequence of illuminations and not only on the intensities, because the space-charge field retains a grating from the previous configuration that the new one must overwrite. A gain coefficient measured after a strong exposure can therefore differ from the same coefficient measured on a virgin region of the same crystal. Translating the crystal to a fresh region between measurements, and repeating with the beams crossed in the opposite order, separates the history from the response.
Identity
H781. Self-phase modulation and cross-phase modulation are one third-order process seen with one field and with two, so an experiment that "separates" them by using different colours is measuring the ratio of tensor elements and not two mechanisms. The practical consequence is that a cross-phase coefficient quoted without the tensor ratio cannot be compared with a self-phase one. Using two colours whose tensor ratio is known from a four-wave-mixing measurement on the same sample closes the comparison.
No-go
H782. A single-pass frequency converter cannot be both broadband and efficient without chirping the medium, because acceptance bandwidth and gain are Fourier conjugates through the interaction length. Designs claiming both at once have usually narrowed the pump and called the result broadband, or have measured efficiency at one wavelength and bandwidth at another. Measuring both on the same alignment, and stating the pump's linewidth, settles it.
Sign argument
H783. The cascaded second-order contribution to the effective third-order nonlinearity takes the sign of the phase mismatch, so a crystal that self-focuses can be made to self-defocus by a temperature change of a few kelvin, without any change of material. The effect is large enough near a phase-matching resonance to dominate the intrinsic Kerr term, which is why temperature tuning appears to change a material constant. Scanning temperature across a phase-matching peak, at fixed intensity, shows the effective nonlinearity pass through zero and change sign.
Conservation argument
H784. In a parametric process the photon number flows from pump to signal and idler in a ratio fixed by the three frequencies, so an efficiency quoted for the idler that exceeds that ratio means either the idler's frequency was mis-measured or the pump's depletion was left out of the accounting. The bookkeeping is exact and requires no model beyond energy conservation. Summing the measured photon fluxes at all three wavelengths, and comparing with the input pump's, tests any efficiency claim in one measurement.

Metrology and frequency

Misattribution
H785. The low-frequency floor of a short-arm interferometer is usually charged to seismic noise, yet in an instrument whose two arms differ in length the laser's own frequency noise enters multiplied by that imbalance and can be the larger term at a few hertz. The signature is that the floor falls when the arms are equalised, which no amount of isolation achieves. Building one arm with a removable delay of a few centimetres, and comparing the floors with and without it, measures the laser's contribution against the seismic one.
Hidden term
H786. Every heterodyne phase measurement includes the acousto-optic modulator's drive phase, and that drive's temperature coefficient enters the result as a scale error rather than an offset, so it survives a zeroing procedure. The term is proportional to the drive's electrical length and therefore to the cable as much as to the crystal. Swapping two drive cables of different lengths, at fixed frequency and power, changes the measured scale by an amount that identifies the term.
Threshold
H787. Below some received signal a time-of-flight rangefinder's depth error stops being set by noise and starts being set by the walk of the leading-edge discriminator, and the transition shows as a change of slope in error against amplitude. Above the transition, averaging helps as the square root of N; below it, averaging does nothing because the error is deterministic. Plotting error against received amplitude, with N averaging as a second axis, shows the corner in one figure.
Reversal
H788. In a Pound–Drever–Hall lock the residual frequency noise falls as modulation frequency rises, because the discriminant steepens, until the modulation sidebands leave the cavity linewidth, after which the discriminant flattens and noise rises again. The optimum is therefore at a modulation frequency comparable to the cavity's half width, and it is a property of the cavity rather than of the laser. Sweeping modulation frequency on one locked laser, and measuring the in-loop error signal's spectrum at each point, shows the minimum.
Count
H789. A comb with N teeth across a span gives N optical frequencies but only N−1 independent differences, so a dual-comb spectrometer reporting more independent spectral points than it has teeth is interpolating, and its resolution is the tooth spacing rather than the reported point spacing. The interpolation is legitimate only when a line's width exceeds the spacing. Measuring a known two-line source at two comb spans shows whether extra points resolve anything.
Artefact mimicking effect
H790. Anomalous dispersion inferred from a resonator's transient response can be the mount's thermal or mechanical settling occurring on the same timescale as the sweep, and the two produce the same asymmetric line shape. The artefact scales with the mount's mass and with the sweep's speed; a genuine dispersive response does not. Repeating the sweep on two mounts of different mass, at fixed optical power, moves one and not the other.
Scale argument
H791. The fractional frequency instability of a comparison improves as the inverse square root of averaging time only until the laser's frequency noise becomes a random walk, after which the average diverges and more averaging makes the answer worse. Stability values quoted at one second and at ten thousand seconds therefore describe different noise processes and cannot be compared as one number. Computing the modified Allan deviation, which separates the two regimes, on a published dataset settles which was being quoted.
Inversion of standard practice
H792. Longer averaging is free and therefore always taken, but past the point where the local oscillator's noise is a random walk each additional factor of two in time adds variance rather than removing it, so the best estimate is at a finite averaging time that can be computed from the noise type. An experiment that averages to the end of the run reports a number worse than one it had an hour earlier and does not know it. Plotting the Allan deviation of an existing record shows the minimum, and the record already contains it.
Selection effect
H793. Inter-laboratory clock comparisons publish the campaigns that ran to completion, and the campaigns abandoned because of unexplained drifts are exactly the evidence about systematic uncertainty that the published ones lack. The reported agreement is then a maximum over attempts, in the same way a best-of-N efficiency is. Asking for the campaign log, including aborted runs, converts the comparison into a measurement of the systems rather than of their good days.
Unit trap
H794. Stability quoted as a fractional number and as an absolute frequency differ by the carrier, so ten to the minus fifteen at one second is a few hundred millihertz at a micrometre (estimate) and a few hertz at a telecom wavelength. Two clocks compared across wavelengths can appear to disagree by a factor of three when the comparison is exact in fractional terms. Converting both to hertz at their own carriers, and stating the carrier, exposes the arithmetic.
Derived quantity
H795. A linewidth from delayed self-heterodyne is derived on the assumption of a Lorentzian spectrum, and a laser whose noise is dominated by a slow drift has no constant linewidth at all: the fitted value depends on the delay and on the fitting window. Two delays on the same laser therefore return two "linewidths", both defensible. Fitting a noise model rather than a line shape, and reporting the model, is the only version of the number that transfers.
Degeneracy
H796. For a film thinner than roughly ten nanometres (estimate, and material-dependent), ellipsometric thickness and refractive index are degenerate, and a fit that reports both with small uncertainties has usually reported the correlation's diagonal while ignoring the correlation itself. The pair lies on a curve, and any point on it fits equally well. Measuring the same film at two angles of incidence, or in two ambient indices, breaks the degeneracy and shows how wide the valley was.
Sign argument
H797. The sign of a measured displacement in a heterodyne interferometer depends on whether the reference is taken from the upper or the lower sideband, so a laboratory that changes its driver's sideband reports the opposite sign with identical hardware. The convention is invisible until two datasets are compared. Reversing the sideband deliberately, and confirming that the magnitude is unchanged while the sign flips, documents the convention in one line and prevents the confusion.
Reciprocity
H798. A ring laser gyroscope's beat is reciprocal under rotation but not under the medium's dispersion, because the two counter-propagating waves see the discharge differently, so the lock-in bias and the rotation can be separated by reversing the discharge current rather than by shielding. The bias reverses with the current and the rotation does not, which makes the reversal a self-calibration. Performing it on a stationary table gives the bias directly, with no turntable required.
Hysteresis
H799. A piezoelectric actuator's displacement is not a function of its applied voltage: the loop is wide enough — of order ten per cent of the range in common stacks, an estimate — that a single calibration curve leaves a positioning error larger than the interferometer that calibrated it. The error is history, not noise, so no filter removes it. Closing the loop on a capacitive sensor, or driving a predictive hysteretic model and checking the residual against the interferometer, distinguishes the two.
Bound
H800. The stability of any two-clock comparison over a fibre link is bounded below by the link's own temperature coefficient, and for links of a few hundred kilometres that bound sits below the clocks' instability, so the comparison measures the link and not the clocks. The bound falls with active compensation only until the compensation's own delay becomes the limit. Comparing the same pair over two links of different length, and finding the agreement improves with the shorter one, identifies which term was being reported.

Status and plan

100 entries, H701–H800. Each was written separately and given its own logical form; the labels are printed so that a reader can check the forms differ structurally and not merely in subject. The subjects are physical mechanisms — sources, detectors, waveguides, imaging, nonlinear optics, metrology — and nothing here touches the derived-column, extreme-value or constant-fitting material of the earlier batches, nor the resolution, coherence-statistics, detector-calibration and computational-imaging leads of the photonics page.

Four entries carry an explicit estimate label, and every such number is an order-of-magnitude guess written into the sentence that holds it. None has been tested. A hypothesis list is worth the ideas in it; a test is worth something else, and the two should not be confused.

If one of these deserves an afternoon, it is H769: self-focusing's critical power does not depend on beam width, so a threshold that scales with the beam is damage wearing self-focusing's name. Two beam sizes and one sample settle it.

Incoprea Research · hand-considered hypotheses 701–800 · photonics and optical physics · 3 November 2026 · ~/Desktop/Nov3/