Optics fundamentals

The underlying wave and semiconductor physics: interference, polarization, Gaussian beams, dispersion, nonlinearity, and band structure.

2 articles · 90 glossary terms · 1 tool · 1 material

Tools

Optical coatings

AR Coating Thickness Calculator

Quarter-wave anti-reflection design: film thickness, ideal index, and residual reflectance with a live spectrum plot.

Articles

Jul 26, 2026Reference · Materials
Thermo-Optic Coefficients of Photonic Materials: Reference Table
dn/dT values for silicon, silicon nitride, silica, InP, GaAs, lithium niobate, and polymers at telecom wavelengths. Includes the resonator-shift formula, athermal design logic, and the caveats that make coefficients composition-dependent.
Jul 26, 2026Reference · Optical coatings
Anti-Reflection Coating Design: The Quarter-Wave Condition
How single-layer anti-reflection coatings work and how to design one: the quarter-wave thickness condition, the ideal-index rule, worked examples on glass and silicon, and when a single layer isn't enough.

Glossary

Aberrations: Departures from ideal image formation in real optical systems. The principal categories (spherical, coma, astigmatism, field curvature, distortion, and chromatic) are the main targets of lens design and correction.
Acceptance angle: The maximum incidence angle at which light can enter an optical fiber or waveguide and still be guided. Geometrically related to the numerical aperture.
Acceptance bandwidth: The range of input wavelengths, incidence angles, or polarization conditions over which a nonlinear or wavelength-selective optical process operates efficiently. Sets the wavelength tolerance of frequency conversion crystals, filters, and gratings.
Acousto-optic modulator (AOM): An optical device that diffracts and frequency-shifts light using an acoustic wave traveling through a transparent crystal. Used for laser intensity modulation, frequency shifting, beam deflection, and Q-switching.
Airy disk: The diffraction pattern formed in the focal plane of an ideal lens or telescope from a uniformly-illuminated circular aperture. A central bright disk surrounded by concentric rings of decreasing intensity, setting the resolution limit of imaging systems.
Anti-reflection coating (AR): A thin-film stack designed to reduce the reflectance of an optical surface by destructive interference between front- and back-surface reflections. The standard surface treatment for any high-performance optical element.
Auger recombination: A non-radiative carrier recombination process in which the energy of an electron–hole pair is transferred to a third carrier rather than emitted as a photon. The dominant non-radiative loss in long-wavelength III–V semiconductor lasers.
Bandgap (energy gap, E_g): The energy separation between the top of the valence band and the bottom of the conduction band in a semiconductor. Determines the longest wavelength a material can emit or absorb.
Beam waist (w_0): The minimum radius of a Gaussian laser beam along its propagation axis. Sets focused spot size, fiber coupling efficiency, and beam divergence.
Beer–Lambert law: Exponential decay of optical intensity through an absorbing medium. Foundational relation for absorption spectroscopy, fiber loss, and laser gain calculations.
Birefringence: The optical property of a material whose refractive index depends on the polarization of the propagating light. Produces polarization mode splitting in fibers and waveguides.
Bragg condition: The wavelength selection rule for a periodic refractive-index structure. Determines the wavelength of constructive backward reflection or out-of-plane diffraction in DFB lasers, fiber Bragg gratings, and grating couplers.
Brewster angle: The angle of incidence at which p-polarized light is fully transmitted (zero reflection) through a dielectric interface. Used to suppress reflection in laser cavities and clean polarization.
Brillouin scattering: Inelastic scattering of light from acoustic phonons or material density waves, producing a small frequency shift (10s of GHz). Used in distributed strain sensing and a power limit in narrow-linewidth fiber transmission.
Chromatic dispersion: The wavelength dependence of the group velocity in an optical medium. Causes pulse broadening and frequency-dependent phase shift in optical communication.
Coherence length: The propagation distance over which an optical wave maintains a fixed phase relationship with itself. Determined by the source linewidth via the Wiener-Khinchin theorem.
Coherent vs incoherent light: The fundamental distinction between light whose phase is well-defined (laser, single-mode sources) and light with random phase relationships (thermal sources, LEDs). Determines interference behavior, focusing limits, and detection schemes.
Critical angle: The minimum incidence angle for total internal reflection at the interface between two media of different refractive indices. The geometric basis of all dielectric optical waveguiding.
Cross-phase modulation (XPM): Nonlinear phase shift induced on one optical wave by the intensity of a different co-propagating wave through the Kerr effect. A primary source of inter-channel impairment in WDM transmission.
Cube beamsplitter: A beam splitter formed by cementing two right-angle prisms along their hypotenuses, with the splitting coating embedded at the interface. The standard general-purpose beam-splitting element for visible and near-IR optical systems.
Decibel (dB, dBm): A logarithmic unit for expressing ratios of power, with dBm specifically denoting power referenced to 1 milliwatt. The standard unit for optical power and loss in photonics and telecommunications.
Density of states (DOS): The number of allowed quantum states per unit energy per unit volume in a semiconductor band. Determines carrier concentration, gain spectrum, absorption shape, and many other observable properties.
Depth of focus / depth of field: The longitudinal range over which an imaging system maintains acceptable focus. Depth of focus refers to image-side tolerance; depth of field refers to object-side tolerance.
Dichroic mirror: A thin-film interference filter that reflects one band of wavelengths while transmitting another. The standard wavelength-separation element in fluorescence microscopy, laser combining, and multi-wavelength optical systems.
Diffraction: The bending and spreading of waves around obstacles or through apertures, and the resulting interference pattern in the far field. The fundamental wave-optics phenomenon that sets the resolution limit of all optical systems.
Diffraction limit: The lower bound on the resolution or spot size of an optical system imposed by the wave nature of light. Roughly $\lambda/2$ in lateral resolution and $\lambda/\text{NA}^2$ in axial resolution.
Direct vs indirect bandgap: The two fundamental classes of semiconductor band structure, distinguished by whether the conduction-band minimum and valence-band maximum occur at the same crystal momentum. Determines whether efficient optical emission is possible.
Effective mass: The dynamical mass of electrons and holes near band extrema, $m^* = \hbar^2 / (d^2E/dk^2)$. Encodes the curvature of the band structure and determines mobility, density of states, and many other transport and optical properties.
Electro-optic effect (Pockels effect): A linear change in refractive index produced by an applied electric field in a non-centrosymmetric crystal. The underlying mechanism of fast electro-optic modulators.
Electroluminescence (EL): Light emission from a material driven by an injected electrical current. The fundamental emission process of LEDs and the sub-threshold output of semiconductor lasers.
Epitaxy (MBE and MOCVD): Growth of single-crystal layers in registry with a substrate, with composition and thickness controlled to the nanometer. The fabrication step where a laser's quantum wells are created and most of its performance is decided.
Etalon: An optical element consisting of two parallel partially-reflective surfaces, transmitting light only at discrete resonant wavelengths. Used as narrowband filter, wavelength reference, and laser cavity tuning element.
Evanescent wave: A non-propagating electromagnetic field that exponentially decays from a boundary, present in the lower-index medium during total internal reflection or outside a guided mode's confinement region. Underlies near-field optics, fiber sensors, and integrated photonic coupling.
Fabry–Pérot resonator (FP): An optical resonator formed by two parallel reflecting surfaces. The simplest and most fundamental resonator geometry; ubiquitous as laser cavities, optical filters, and spectroscopic reference standards.
Faraday effect: Rotation of the polarization of light propagating through a magnetically biased medium, with rotation sense set by the field direction rather than the propagation direction. The basis of optical isolators.
Fermi level: The energy at which the probability of electron occupation is 1/2 in thermal equilibrium. The reference energy that determines carrier concentrations, junction band-bending, and contact alignment in all semiconductor devices.
Fermi-Dirac distribution: The thermal occupation probability for fermions (electrons, holes), $f(E) = 1/[1 + \exp((E - E_F)/k_B T)]$. The fundamental statistical mechanics underlying all semiconductor carrier statistics.
Finesse: The ratio of the free spectral range to the FWHM linewidth of a single resonance. Quantifies resonator sharpness, set by round-trip losses.
Four-wave mixing (FWM): A third-order nonlinear process in which three input optical waves generate a fourth wave at a new frequency. The basis of wavelength conversion, parametric amplification, and a source of inter-channel crosstalk in WDM systems.
Free spectral range (FSR): The frequency or wavelength spacing between adjacent resonances of an optical cavity. Set by the round-trip group delay.
Free-space optics (FSO): Optical communication or measurement using light propagating through atmosphere or vacuum rather than guided through a waveguide. Encompasses optical wireless links, deep-space communications, lidar, and many laboratory measurement systems.
Frequency comb: An optical spectrum consisting of equally-spaced narrow lines. Provides a calibrated frequency ruler linking optical to microwave frequencies, the enabling technology of optical clocks and broadband precision spectroscopy.
Fresnel equations: Expressions for the reflection and transmission of light at an interface between two media. Derived from Maxwell's equations with boundary conditions.
Gaussian beam: A laser beam with transverse intensity profile described by a Gaussian function. The fundamental solution to the paraxial wave equation in free space; the typical mode emerging from a single-mode laser or fiber.
Group index (n_g): The ratio of the speed of light in vacuum to the group velocity of a guided mode. Governs pulse propagation, resonator free spectral range, and dispersion.
Group velocity: The propagation velocity of an optical pulse envelope through a dispersive medium. Generally differs from the phase velocity (the propagation velocity of a single-frequency wave's phase fronts).
Group velocity dispersion (GVD): The wavelength dependence of group velocity that causes optical pulses to broaden in time as they propagate through a dispersive medium. The fundamental mechanism underlying chromatic dispersion in fibers.
Heterojunction: An interface between two semiconductor materials with different bandgaps. The structural basis of modern diode lasers, LEDs, and high-speed transistors.
III-V semiconductors: Compound semiconductors pairing group-III and group-V elements: GaAs, InP, GaN, and their alloys. Direct band gaps make them the gain, emission, and high-speed detection materials of photonics.
Jones vectors: A 2×1 complex column vector representation of the polarization state of fully-polarized light. Compact mathematical framework for analyzing polarization optics in the coherent regime.
Kerr effect: An intensity-dependent change in refractive index in an optical medium. The third-order nonlinear optical effect underlying self-phase modulation, four-wave mixing, and ultrafast optical switching.
Longitudinal mode spacing: The frequency separation between adjacent longitudinal modes of an optical cavity, equal to the free spectral range $c/(2 n_g L)$. Sets the discrete frequency comb on which laser oscillation can occur.
Longitudinal modes: The discrete set of optical frequencies that satisfy the round-trip phase condition in a Fabry-Perot resonator. The fundamental mode structure of any laser cavity along the propagation direction.
Mach–Zehnder interferometer (MZI): A two-arm interferometer that splits light, applies a phase difference between the arms, and recombines them. The most common interferometric building block in integrated photonics.
Non-radiative recombination: Recombination processes that release energy as heat or phonons rather than photons. The principal loss mechanisms competing with radiative emission in semiconductors: Shockley-Read-Hall, Auger, and surface recombination.
Numerical aperture (NA): The sine of the maximum acceptance half-angle for light entering an optical fiber, lens, or waveguide. Quantifies light-gathering or focusing capability.
Optical cavity: A bounded optical region with reflective surfaces that supports specific resonant frequencies. The structural framework that converts an amplifying gain medium into a laser oscillator.
Optical density (OD): The logarithmic measure of optical attenuation of a sample or filter. $\text{OD} = -\log_{10}(T)$ where $T$ is the transmittance. Standard specification for absorbing materials and neutral-density filters.
Optical soliton: A pulse that propagates without changing shape because nonlinear self-phase modulation exactly balances chromatic dispersion. The natural pulse shape for ultra-long-haul transmission and microresonator frequency combs.
Phase matching: The condition that the wave vectors of interacting fields in a nonlinear optical process sum to zero, allowing efficient energy transfer. The central design requirement for second-harmonic generation, parametric oscillators, and frequency conversion.
Photon energy: The energy carried by a single photon, set by its frequency or wavelength. The fundamental quantum unit of optical energy and the basis for all energy-wavelength conversions.
Photon lifetime (τ_p): The mean residence time of a photon in an optical cavity before being lost to absorption, scattering, or output coupling. Sets resonator response time, linewidth, and modulation bandwidth.
Photonic crystal: A structure whose refractive index repeats with a period comparable to the wavelength, opening photonic band gaps where light cannot propagate. The route to wavelength-scale cavities with extreme Q-to-volume ratios.
Pockels effect (linear electro-optic effect): The change in refractive index linearly proportional to an applied electric field, occurring only in crystals without inversion symmetry. The basis for the fastest commercial optical modulators.
Point spread function (PSF): The image of a single point source formed by an optical system, fully characterizing the system's response to any input. Convolving a true scene with the PSF produces the imaged scene.
Polarization states: The orientation and rotation behavior of the electric-field vector of a light wave. Linear, circular, elliptical, and unpolarized states form the standard classification with specific applications across optics and telecom.
Population inversion: A non-equilibrium condition in which more atoms (or carriers) occupy an upper energy level than a lower one. A necessary condition for net stimulated emission and laser oscillation.
Propagation constant (β): The spatial rate of phase advance of a guided mode along its propagation direction. The fundamental wave parameter from which effective index, group index, and dispersion are all derived.
Quality factor (Q): A dimensionless figure of merit describing how lightly damped an optical resonator is. Defined as 2π times the ratio of stored energy to energy dissipated per oscillation cycle, equivalently as resonance frequency divided by linewidth.
Quasi-Fermi level: Separate effective Fermi levels for electrons ($E_{Fn}$) and holes ($E_{Fp}$) under non-equilibrium conditions. Their splitting characterizes the degree of injection and is the formal threshold for optical gain via the Bernard-Duraffourg condition.
Radiative recombination: The process by which an electron-hole pair recombines, emitting a photon. The fundamental light-generation mechanism in LEDs, semiconductor lasers, and solar cells (operating in reverse).
Raman scattering: Inelastic scattering of light by optical phonons or molecular vibrations, producing frequency-shifted output. Used for spectroscopy, Raman amplification, and distributed sensing.
Rayleigh range (z_R): The propagation distance from the waist of a Gaussian beam over which the beam radius increases by a factor of √2. Sets the depth of focus for any optical system.
Rayleigh scattering: Elastic scattering of light by particles much smaller than the wavelength. Produces the fundamental attenuation floor of optical fibers and the dominant backscatter in OTDR measurement.
Refractive index (n): The ratio of the speed of light in vacuum to its phase velocity in a medium. The single most fundamental parameter in optics, governing refraction, reflection, dispersion, and waveguiding.
Ring resonator: A closed-loop waveguide evanescently coupled to one or two bus waveguides, resonant at wavelengths where the round-trip optical path equals an integer number of wavelengths. The workhorse filter, modulator, and sensor element of integrated photonics.
Self-phase modulation (SPM): An intensity-dependent phase shift acquired by an optical wave propagating in a Kerr nonlinear medium. The dominant intra-channel nonlinear effect in optical fiber communication.
Shot noise: The fundamental noise floor of photodetection caused by the discrete nature of photons (or electrons). The Poisson-statistics fluctuation that sets the ultimate sensitivity limit of any optical measurement.
Snell's law: The relationship between angles of incidence and refraction at the boundary between two media, $n_1 \sin\theta_1 = n_2 \sin\theta_2$. The foundational equation of geometric optics.
Spontaneous emission: Radiative decay of an excited state without external stimulus, emitting a photon of random phase and direction. The light of LEDs, the seed of laser noise, and the process stimulated emission competes against.
Stimulated emission: The process by which an incident photon induces a population-inverted atom or molecule to emit a coherent photon identical in frequency, phase, and polarization. The mechanism of all laser amplification.
Stokes parameters: A four-parameter set $(S_0, S_1, S_2, S_3)$ that fully characterizes the polarization state of light, including partially polarized states. The standard polarization representation in measurement, remote sensing, and statistical optics.
TE and TM polarization: Transverse electric (TE) and transverse magnetic (TM) are the two principal polarization states of a guided mode in a waveguide. Many photonic devices respond very differently to the two.
TEM00 mode: The fundamental transverse mode of a laser cavity, with a Gaussian intensity profile and the lowest divergence achievable for a given beam waist. The desired output mode for nearly all laser applications.
Total internal reflection (TIR): The complete reflection of light at the interface between a higher-index medium and a lower-index medium when the angle of incidence exceeds the critical angle. The physical mechanism that confines light in optical fibers and waveguides.
Transverse modes: The spatial intensity patterns supported by an optical cavity or waveguide perpendicular to the propagation direction. The mode label specifies the field structure across the beam cross-section.
Two-photon absorption (TPA): A nonlinear absorption process in which two photons are simultaneously absorbed to excite an electron across a bandgap larger than either photon's individual energy. Limits high-power operation of silicon photonic devices at telecom wavelengths.
V number: Dimensionless parameter determining the number of guided modes in a step-index optical fiber. Single-mode operation requires V < 2.405.
Walk-off: The lateral separation of interacting optical beams within a birefringent crystal due to different Poynting-vector directions of the ordinary and extraordinary waves. Limits the useful interaction length in nonlinear frequency conversion.
Waveplate (retarder): A birefringent optical element that introduces a specific phase delay between two orthogonal polarization components, transforming polarization states. Half-wave plates rotate linear polarization; quarter-wave plates convert between linear and circular.

Materials

Fused silicaSiO₂

The quiet foundation of all of photonics: the fiber that spans oceans at 0.2 dB/km, the cladding on every integrated platform, and the substrate under most free-space optics.