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Optical cavity

An optical cavity, also known as an optical resonator, is an arrangement of mirrors or other reflective optical elements that confines electromagnetic waves in the optical domain, allowing light to circulate in a closed path and undergo repeated reflections to achieve resonance at specific frequencies through constructive interference.^[1] This resonance builds up the light intensity within the cavity, creating standing waves or circulating modes that are fundamental to enhancing light-matter interactions. The basic principles of optical cavities rely on the wave nature of light, where the cavity length and mirror curvatures determine the resonant frequencies via the condition that the round-trip phase shift is an integer multiple of $2\pi.^[1] Key concepts include resonator modes, which are self-consistent transverse and longitudinal field distributions that satisfy Maxwell's equations within the cavity boundaries, and the quality factor (Q), defined as Q = \omega_0 / \Delta \omega, where \omega_0 is the resonant angular frequency and \Delta \omega is the full width at half maximum of the resonance, quantifying energy storage efficiency.^[1] Stability of the cavity, governed by the ABCD ray matrix formalism, ensures that light rays remain confined rather than escaping, with stable configurations typically featuring concave mirrors separated by distances less than the radius of curvature sum.^[1] The free spectral range (FSR), given by \Delta \nu = c / (2L) for a linear cavity of length L, separates adjacent longitudinal modes and is crucial for mode selection.^[1] Optical cavities come in various types tailored to specific needs, including linear resonators like the Fabry-Pérot cavity, formed by two parallel or slightly curved mirrors for high-finesse applications, and ring resonators, which support traveling waves without standing wave nodes, often used in fiber optics or integrated photonics.^[1] Other variants include planar microcavities for distributed feedback and whispering-gallery-mode resonators exploiting total internal reflection in microspheres or disks for ultra-high Q factors exceeding $10^{10}.^[2] Bulk-optical cavities dominate in free-space lasers, while waveguide-based designs enable compact integration on chips.^[1] In applications, optical cavities are indispensable in lasers, providing optical feedback to amplify stimulated emission and sustain coherent output, as in solid-state and gas lasers where the cavity defines the lasing mode.^[3] They enable cavity quantum electrodynamics (QED), where strong coupling between cavity photons and atomic dipoles leads to phenomena like vacuum Rabi splitting, advancing quantum information processing.^[4] In precision sensing, high-Q cavities enhance absorption spectroscopy for trace gas detection, achieving sensitivities down to parts per trillion via cavity ring-down techniques.^[5] Emerging fields like cavity optomechanics couple optical modes to mechanical vibrations for quantum ground-state cooling and force sensing at the attonewton level.^[6] Additionally, they support nonlinear optics, such as frequency doubling in enhancement cavities, and metrology standards like absolute pressure measurement through refractive index determination.^[7]

Fundamentals

Definition and principles

An optical cavity, also known as an optical resonator, consists of a pair of facing mirrors or equivalent structures that define a confined region where electromagnetic waves, specifically light, can undergo repeated reflections to achieve resonance through constructive interference at particular wavelengths.^[8] This setup traps light within the cavity volume, enhancing interactions between the electromagnetic field and matter.^[9] The fundamental principles of operation rely on confining light via high-reflectivity dielectric mirrors, which leverage multiple thin layers of alternating refractive index materials to achieve reflectivities approaching 100%, or through total internal reflection at dielectric interfaces in certain configurations.^[1] The simplest model is the Fabry–Pérot cavity, formed by two parallel mirrors separated by distance L.^[8] Key parameters include the cavity length L, mirror reflectivity R, and the finesse F \approx \pi \sqrt{R} / (1 - R) for high-R mirrors, which quantifies the sharpness of the resonance peaks relative to the free spectral range.^[8] Due to the wave nature of light, resonance occurs when standing waves form inside the cavity, satisfying the condition for constructive interference after a round trip: the round-trip phase shift $2kL = 2\pi m, where k = 2\pi \nu / c is the wave number, m is a positive integer, \nu is the frequency, and c is the speed of light in the medium.^[8] This yields the resonance frequencies \nu_m = m c / (2L).^[8] The spacing between adjacent modes, known as the free spectral range, is \Delta \nu = c / (2L).^[8] The cavity enables significant energy storage through the build-up of electromagnetic field intensity over multiple passes, as light circulates without substantial loss until it decays.^[9] This is characterized by the quality factor Q = \omega \tau, where \omega = 2\pi \nu is the angular resonance frequency and \tau is the photon lifetime, representing the average time a photon remains confined before escaping.^[10] High Q values indicate low damping and prolonged storage, crucial for applications requiring intense fields.^[11]

Historical development

The development of optical cavities originated in the late 19th century amid advances in interferometry. In the 1880s, Albert A. Michelson invented the Michelson interferometer, a device that split and recombined light beams to measure interference fringes, establishing key principles of light wave manipulation that influenced subsequent resonant structures.^[12] Building directly on such interferometric techniques, Charles Fabry and Alfred Pérot introduced the Fabry–Pérot etalon in 1899, consisting of two parallel, partially reflecting plates forming a simple optical resonator to produce sharp interference patterns for high-resolution spectroscopy of spectral lines.^[13] This etalon represented the first practical optical cavity, enabling precise wavelength selection and foreshadowing applications in precision measurement.^[14] The mid-20th century saw optical cavities evolve from passive interferometers to active amplifiers through the advent of stimulated emission devices. In the early 1950s, Charles Townes and colleagues at Columbia University developed the maser, utilizing resonant microwave cavities to amplify signals via population inversion in ammonia gas, marking the initial use of cavities for coherent wave generation.^[15] Extending this to optical wavelengths, Townes and Arthur Schawlow proposed the "optical maser" in 1958, theorizing a Fabry–Pérot-style resonator with mirrors to confine and amplify light in a gain medium, which laid the theoretical groundwork for lasers.^[16] This concept was realized in 1960 when Theodore Maiman at Hughes Research Laboratories demonstrated the first working laser using a ruby crystal as the gain medium within a linear optical cavity formed by reflective ends, achieving pulsed stimulated emission at 694 nm and inaugurating the era of laser technology.^[17] Advancements in the 1960s and 1970s focused on enhancing cavity stability and integrating feedback mechanisms for practical laser systems. In 1964, Donald Herriott, Hermann Kogelnik, and Rudolph Kompfner analyzed off-axis beam paths in spherical-mirror resonators, introducing configurations that ensured stable Gaussian mode propagation over multiple reflections, crucial for reliable laser operation.^[18] By 1971, Kogelnik and Christopher Shank pioneered distributed feedback (DFB) cavities in dye-doped gelatin films, where periodic refractive index gratings provided wavelength-selective feedback without end mirrors, enabling single-mode lasing in compact semiconductor structures. In the 1980s and 1990s, optical cavities became central to quantum optics through cavity quantum electrodynamics (QED), exploring strong light-matter interactions. Serge Haroche's group at École Normale Supérieure achieved the strong-coupling regime in 1987 by trapping Rydberg atoms in superconducting microwave cavities, observing reversible Rabi oscillations between atomic and photonic states, which demonstrated quantum coherence in a controlled environment. Complementing this, David Wineland's team at NIST advanced trapped-ion quantum systems in the 1990s, using radiofrequency Paul traps to confine ions and laser fields to couple and manipulate their quantum states, enabling precise quantum state control and entanglement.^[19] Their pioneering methods for measuring and controlling individual quantum systems earned the 2012 Nobel Prize in Physics. Post-2000 developments have emphasized miniaturization, with photonic crystal microcavities emerging as high-quality-factor (Q > 10^6) structures in silicon and III-V semiconductors, facilitating on-chip integration for quantum information processing and nonlinear optics.^[20]

Theoretical foundations

Resonator modes

In optical cavities, the supported light modes are solutions to the time-independent Maxwell's equations that satisfy the boundary conditions at the cavity reflectors. These modes characterize the spatial and frequency distribution of the electromagnetic field within the cavity and determine its resonant frequencies and field patterns. The modes are typically classified into longitudinal and transverse categories, with the former varying along the optical axis and the latter in the perpendicular plane. Longitudinal modes arise from the standing-wave condition along the cavity axis, resulting in discrete frequencies spaced by the free spectral range \Delta \nu = \frac{c}{2L}, where c is the speed of light in the medium and L is the effective cavity length. This spacing corresponds to the frequency difference between consecutive axial resonances, enabling the cavity to select specific wavelengths from a broadband source. Transverse modes, denoted as TEM_{mn} where m and n are integers labeling the nodal lines in the transverse plane, describe the orthogonal patterns perpendicular to the propagation direction; in stable cavities, the fundamental TEM_{00} mode exhibits a Gaussian intensity profile, while higher-order modes include additional intensity nulls. These transverse structures were first systematically analyzed using iterative diffraction methods for spherical mirror resonators.^[21]^[22] Mathematically, the cavity modes satisfy the scalar Helmholtz equation \nabla^2 E + k^2 E = 0, where E is the electric field amplitude and k = 2\pi / \lambda is the wavenumber, derived from the wave equation under monochromatic assumptions. For paraxial propagation in stable cavities, the Gaussian modes are approximated using the paraxial wave equation, leading to the beam radius evolution w(z) = w_0 \sqrt{1 + \left( \frac{z}{z_R} \right)^2}, where w_0 is the beam waist radius at z=0 and z_R = \frac{\pi w_0^2}{\lambda} is the Rayleigh range defining the distance over which the beam remains approximately collimated. This description captures the diffraction-limited spreading of the mode beyond the waist.^[23]^[24] The effective mode volume V_\mathrm{eff} quantifies the spatial confinement of the field, typically defined as V_\mathrm{eff} = \frac{\int |E|^2 \, dV}{\max |E|^2}, which normalizes the total energy to the peak intensity and is crucial for assessing enhancement factors in cavity quantum electrodynamics. In multimode cavities, coupling between modes can occur due to misalignments or perturbations, leading to mode overlap that mixes longitudinal and transverse components and broadens the effective linewidth. Polarization effects further diversify the modes, with linear or circular polarizations possible in isotropic cavities, while birefringence in anisotropic media introduces vector modes or splits degenerate resonances, altering the field ellipticity and enabling polarization-dependent resonances.^[25]^[26]

Stability analysis

The stability of an optical cavity is determined using geometric ray optics, where paraxial rays are traced through the resonator to assess whether they remain confined after multiple round trips. This analysis employs the ABCD matrix formalism, a 2×2 ray transfer matrix that relates the position r and angle r' of a ray before and after propagation through optical elements, given by

\begin{pmatrix} r_2 \\ r'_2 \end{pmatrix} = \begin{pmatrix} A & B \\ C & D \end{pmatrix} \begin{pmatrix} r_1 \\ r'_1 \end{pmatrix}.

Common elements include free-space propagation over distance L with matrix \begin{pmatrix} 1 & L \\ 0 & 1 \end{pmatrix} and a spherical mirror of radius R with matrix \begin{pmatrix} 1 & 0 \\ -2/R & 1 \end{pmatrix}. For cavity stability, the round-trip matrix (product of matrices for one full cycle) must ensure rays do not diverge; the condition is \left| \frac{A + D}{2} \right| \leq 1, where A and D are the trace elements of the round-trip matrix, preventing exponential growth in ray displacement.^[27] For a simple two-mirror linear resonator with mirror curvatures R_1 and R_2 separated by length L, the stability is characterized by the parameters g_1 = 1 - L/R_1 and g_2 = 1 - L/R_2. These g-parameters allow construction of a stability diagram by plotting g_1 versus g_2, where stable regions satisfy $0 < g_1 g_2 < 1, with marginal stability on the boundaries g_1 g_2 = 0 and g_1 g_2 = 1; outside these regions, rays escape, leading to an unstable cavity. The diagram reveals hyperbolic boundaries delineating stability zones, with the primary stable area between the axes g_1 g_2 = 0 (in the first and third quadrants) and the hyperbola g_1 g_2 = 1. In unstable cavities, confinement fails due to mechanisms like diffraction losses, where rays leak out despite partial focusing.^[28] Specific configurations illustrate these criteria: a confocal cavity, with R_1 = R_2 = L (so g_1 = g_2 = 0), lies on the stability boundary and supports well-confined modes with minimal diffraction loss. A hemispherical cavity, featuring one flat mirror (R_1 = \infty, g_1 = 1) and one curved mirror with R_2 = L (g_2 = 0), is also marginally stable but offers a compact design for applications requiring a waist at the flat mirror. Unstable cavities, such as those with g_1 g_2 < 0, exhibit high diffraction losses as rays amplify transversely over round trips.^[29] Perturbations like mirror tilt or misalignment significantly impact stability, as even small angular deviations (e.g., 1 mrad) can cause beam pointing errors and power loss, with sensitivity increasing near stability boundaries. For instance, near-concentric or confocal designs show high sensitivity to tilt, where a small rotation displaces the optical axis, reducing mode overlap and introducing losses; perturbation theory quantifies this via first-order changes in the ABCD matrix elements. Hemispherical cavities are relatively robust to longitudinal misalignment but sensitive to transverse shifts.^[30]

Design and types

Basic resonator configurations

Optical cavities, also known as optical resonators, are fundamental structures that confine light through repeated reflections, enabling the buildup of intense electromagnetic fields. Among the basic configurations, the plane-parallel resonator, commonly referred to as the Fabry–Pérot cavity, employs two flat mirrors positioned parallel to each other, separated by a distance that determines the resonant wavelengths. This design supports standing waves formed by counterpropagating beams interfering between the mirrors, making it the simplest linear resonator geometry. However, its reliance on precise parallelism renders it highly sensitive to misalignment, where even small angular deviations can drastically reduce the cavity's finesse and output intensity.^[1]^[31] Variants of the Fabry–Pérot include etalons, which maintain the plane-parallel structure but incorporate solid spacers to fix the mirror separation rigidly, often using materials like fused silica for thermal stability. Solid etalons feature parallel reflecting surfaces directly on a single transparent plate, leveraging refractive index discontinuities or coatings for reflection, whereas air-spaced etalons use discrete mirrors with spacers such as Zerodur to minimize expansion effects. These configurations enhance mechanical robustness while preserving the high spectral resolution inherent to the plane-parallel design.^[32]^[33] Curved-mirror resonators introduce focusing elements to improve beam confinement and stability over linear paths. In the confocal configuration, both mirrors have equal radii of curvature R_1 = R_2 = L, where L is the mirror separation, causing their foci to coincide at the cavity center for symmetric mode propagation. Symmetric curved resonators feature identical curvatures with R_1 = R_2 > L, promoting balanced arm lengths and effective beam waist control, while asymmetric variants with R_1 \neq R_2 allow tailored focusing for applications requiring divergent beam properties. These geometries enable self-focusing of the intracavity beam, distinguishing them from plane-parallel designs by reducing diffraction losses.^[1] (Siegman, 1986) Ring cavities represent a nonlinear alternative, where light circulates unidirectionally in a closed loop formed by multiple mirrors, typically three or four in bow-tie or triangular arrangements, or via optical fibers for compact setups. This circulating path eliminates standing waves and end-mirror reflections, inherently reducing backscattering from mirror imperfections compared to linear resonators. Fiber-based ring cavities further minimize losses through evanescent coupling, supporting continuous propagation without discrete bounces. Specialized Sagnac configurations within ring cavities, involving counterpropagating beams in a looped interferometer, exploit phase differences for high-precision rotation sensing and interferometric applications.^[1]^[34]^[35] Material selections critically influence resonator performance, particularly for mirror reflectivity. Dielectric coatings, consisting of multilayer thin films of materials like silica and titania, routinely achieve reflectivities exceeding 99.9% at specific wavelengths, enabling low-loss confinement essential for high-finesse operation. In integrated optics, evanescent wave mirrors utilize total internal reflection at waveguide boundaries, such as in monolithic ring resonators, obviating the need for deposited coatings and facilitating compact, on-chip designs with whispering-gallery modes.^[1] (Siegman, 1986)^[32]

Practical cavity implementations

Practical optical cavities are constructed using fabrication techniques that ensure high reflectivity and precise geometry. Multilayer dielectric mirrors, essential for confining light, are typically produced through physical vapor deposition (PVD) processes, such as electron-beam evaporation or ion-assisted deposition, where alternating layers of materials like silica (SiO₂) and tantala (Ta₂O₅) or hafnia (HfO₂) are applied in vacuum to achieve reflectivities exceeding 99.99%.^[36] In micro-optics, integration leverages microelectromechanical systems (MEMS) or silicon photonics platforms, where cavities are etched using photolithography and reactive ion etching on silicon substrates, enabling compact Fabry-Pérot resonators with tunable elements via electrostatic actuation.^[37]^[38] Losses in practical cavities arise from several sources, including material absorption in mirror coatings, surface scattering due to roughness, and diffraction at finite apertures, which degrade the quality factor (Q) and limit photon lifetime.^[39] To mitigate these, supermirrors with optimized multilayer stacks, often incorporating low-loss crystalline materials like AlGaAs, reduce absorption and scattering to levels below 10 ppm, while cryogenic cooling to temperatures around 17 K suppresses thermoelastic and thermo-refractive noise, enabling finesse values up to 470,000 and corresponding Q factors on the order of 10^{11}.^[36]^[40] Active elements are incorporated to enhance functionality, such as gain media for amplification or nonlinear materials for frequency conversion. Dye-based gain media, like rhodamine derivatives, or semiconductor quantum wells are embedded within the cavity to provide optical gain, compensating for intrinsic losses and enabling lasing operation.^[41]^[42] Nonlinear crystals, such as periodically poled lithium niobate (PPLN), are placed inside the resonator for processes like second-harmonic generation, where phase-matching conditions are satisfied to efficiently convert wavelengths.^[43] Tunability is achieved using piezoelectric actuators, which adjust mirror spacing or crystal orientation with sub-nanometer precision, allowing continuous wavelength shifts over tens of gigahertz.^[44] Miniaturization extends cavity performance to chip-scale devices, with whispering gallery mode (WGM) resonators in microspheres—fabricated from fused silica or polymers via melting and shaping—supporting ultra-high Q factors through total internal reflection, confining light in volumes below 10 μm³.^[45] Photonic crystal cavities, patterned in semiconductor membranes using electron-beam lithography and selective etching, achieve sub-wavelength mode volumes (on the order of (λ/n)^3) while maintaining strong light-matter interactions, ideal for integrated quantum optics.^[46]

Alignment methods

Passive alignment techniques provide an initial setup for optical cavities by establishing a reference optical axis without continuous feedback. Kinematic mounts enable precise adjustments of mirrors and lenses through constrained degrees of freedom, typically allowing translations and rotations in three dimensions to position components accurately.^[47] Fiducials, such as apertures or mechanical stops, define the cavity's optical axis by creating a reference path, often separated by distances of 0.5 m or more to ensure alignment stability during assembly.^[47] Autocollimation alignment using retroreflectors, or self-aligning via retroreflected beams, uses retroreflectors to send light back along its incident path, verifying overlap and centering without external sensors; this method is particularly effective for initial beam path confirmation in linear cavities.^[48]^[47] Active alignment refines the cavity by incorporating real-time feedback to optimize beam coupling to the fundamental mode. Photodetectors monitor transmitted or reflected power, enabling mode matching by adjusting mirror positions to maximize coupling efficiency, often achieving over 99% overlap in precision setups.^[49] Dithering methods introduce small, periodic oscillations—such as angular vibrations or radio-frequency modulations—to the input beam or mirrors, detecting misalignment through signal variations on quadrant photodetectors and iteratively correcting for tilt or offset.^[50] These techniques ensure the incoming beam remains collinear with the cavity eigenmode, enhancing stability in dynamic environments.^[49] Diagnostic tools are essential for verifying alignment quality. Beam profilers capture transverse intensity profiles to confirm Gaussian mode shapes, identifying deviations like waist mismatch or astigmatism that reduce coupling.^[48] Interferometric alignment employs low-power He–Ne lasers in setups like Michelson interferometers to observe fringe patterns from beam overlap, allowing sub-microradian adjustments of mirror tilts.^[47] Alignment faces challenges from environmental and operational factors. Thermal lensing, induced by absorbed power distorting refractive indices in intracavity elements, alters focal lengths and requires adaptive optics—such as deformable mirrors—to dynamically compensate aberrations and maintain mode stability.^[48]^[51] In high-power systems, excessive intensity risks mirror damage during alignment, necessitating low-power auxiliary beams (under 1 mW) for initial tuning and protective measures like attenuators to prevent coating ablation.^[47]^[52]

Applications and extensions

Role in lasers

The optical cavity serves as the essential feedback mechanism in lasers, confining photons within the resonator to enable multiple passes through the gain medium and amplify stimulated emission until lasing occurs. By reflecting light back into the active medium, the cavity sustains coherent oscillation, distinguishing lasers from incoherent light sources like LEDs. The lasing threshold is achieved when the round-trip gain balances the round-trip losses, expressed as g L = -\ln(R_1 R_2), where g is the gain coefficient, L is the gain medium length, and R_1, R_2 are the mirror reflectivities.^[53] Mode selection within the optical cavity ensures operation on specific resonator modes, suppressing unwanted wavelengths to achieve single-mode or narrow-linewidth output. Intracavity etalons, consisting of parallel partially reflecting plates, filter longitudinal modes by transmitting only those wavelengths satisfying the etalon's resonance condition, typically reducing the mode spacing to enable single-longitudinal-mode lasing in broadband gain media like dye or solid-state lasers. Similarly, diffraction gratings inserted at an angle in the cavity provide wavelength-selective feedback via the Littrow or Littman-Metcalf configurations, allowing tunable single-mode operation by rotating the grating to alter the diffraction angle and select the desired wavelength. For pulsed lasers, Q-switching involves rapidly varying the cavity Q-factor using electro-optic or acousto-optic modulators to store energy in the gain medium before releasing a high-peak-power pulse, while mode-locking synchronizes multiple longitudinal modes through amplitude or phase modulation, producing ultrashort pulses with durations on the order of the cavity round-trip time. Common cavity designs leverage the optical resonator's geometry to optimize performance for specific laser types. Linear cavities, formed by two parallel or curved mirrors enclosing the gain medium, are prevalent in solid-state lasers such as Nd:YAG systems, where the standing-wave pattern enhances gain interaction but requires careful alignment to avoid spatial hole burning. In contrast, ring cavities, arranged in a closed loop with multiple mirrors or fiber components, are favored in fiber lasers for their unidirectional operation, which eliminates bidirectional interference and standing waves through an integrated optical isolator or nonreciprocal elements like Faraday rotators, enabling higher efficiency and stable single-direction propagation.^[54] Output coupling from the optical cavity is achieved via partial mirror reflectivity, where one mirror (typically R_2 < 1) transmits a fraction of the intracavity power as the laser beam while reflecting the rest for sustained oscillation. This design balances high internal intensity for efficient gain saturation with sufficient extraction for practical output powers, often yielding efficiencies up to 50% in optimized systems. Intracavity elements such as polarizers or Brewster windows further refine beam quality by selecting polarization states, minimizing losses and enabling high-brightness emission in applications like precision spectroscopy.^[53]

Optical delay lines

Optical cavities serve as passive devices for generating controlled time delays in light propagation by confining photons to undergo multiple round trips, thereby extending the effective optical path length without amplification.^[55] This recirculating process leverages the cavity's resonance to store light temporarily, with the fundamental round-trip delay given by \tau = \frac{2 L n}{c}, where L is the cavity length, n is the refractive index of the medium, and c is the speed of light in vacuum.^[56] In high-finesse cavities, where finesse exceeds 10^5, photon lifetimes can extend to milliseconds, enabling storage times up to 2.5 ms through enhanced light-matter interactions and low-loss designs.^[57] Recirculating delay lines typically employ partial mirrors in a linear Fabry-Pérot configuration, where input light partially transmits into the cavity and exits after several round trips controlled by mirror reflectivity.^[55] Fiber-based ring resonators, optimized for telecom wavelengths near 1550 nm, consist of a looped optical fiber evanescently coupled to a straight bus waveguide, allowing tunable delays via coupling coefficient adjustments and supporting compact integration on photonic chips.^[56] These delay lines find applications in buffering optical packets in communication networks to resolve contention and synchronize data streams, achieving delays matching bit periods in high-speed systems.^[58] In ultrafast optics, they enable pulse shaping by imparting frequency-dependent phase shifts, preserving waveform integrity for applications like coherent control.^[56] They also provide precision timing in interferometric setups, such as optical coherence tomography, where sub-picosecond delays align signals for enhanced resolution.^[55] Key limitations include dispersion, which broadens pulses over multiple round trips due to varying group velocities across the spectrum, and round-trip losses from absorption or scattering that cap the achievable finesse and delay duration.^[56] Additionally, preserving pulse integrity demands that the total delay remain below the source's coherence length, as longer storage leads to temporal smearing in partially coherent light.^[55]

Advanced and specialized uses

In cavity quantum electrodynamics (cQED), optical cavities enable the strong coupling regime, where the interaction between a single atom or photon and the cavity mode dominates over dissipation, leading to coherent quantum dynamics on timescales faster than decoherence. This regime is characterized by the coupling strength g exceeding the atomic decay rate \gamma and cavity loss rate \kappa, allowing for the observation of vacuum Rabi oscillations even in the absence of initial photons. The foundational theoretical framework is provided by the Jaynes-Cummings model, which describes a two-level atom interacting with a single quantized cavity mode, predicting dressed states that split the energy levels and manifest as oscillatory energy exchange between the atom and field. Seminal experimental demonstrations of strong coupling were achieved in the late 1980s using Rydberg atoms in microwave cavities, confirming the predicted AC Stark shifts and Rabi splittings. In nonlinear optics, optical cavities enhance processes such as frequency doubling and parametric oscillation by confining intense fields within nonlinear media, increasing interaction lengths and efficiencies. Intracavity frequency doubling, or second-harmonic generation, occurs when a nonlinear crystal like potassium titanyl phosphate is placed inside the cavity, converting fundamental laser light to its second harmonic with conversion efficiencies exceeding 50% in optimized setups. Optical parametric oscillation in doubly resonant cavities, where pump, signal, and idler waves all resonate, enables tunable output across wide spectral ranges, with thresholds reduced to milliwatts due to high finesse. Kerr nonlinearity in cavities, arising from the intensity-dependent refractive index n = n_0 + n_2 I, supports the formation of dissipative Kerr solitons—stable, localized pulses balanced by dispersion, nonlinearity, and drive—enabling broadband frequency comb generation for applications in precision timing. These solitons were first observed in silica microresonators driven by continuous-wave lasers, achieving pulse durations below 100 fs. Optical cavities play a pivotal role in advanced sensing and metrology, leveraging their high sensitivity to refractive index changes for trace detection and fundamental measurements. Cavity-enhanced absorption spectroscopy confines light paths to effective lengths of kilometers within compact volumes, achieving detection sensitivities down to parts per trillion by volume for gases like NO₂ through enhanced interaction with absorbing species. In gravitational wave detection, kilometer-scale Fabry-Pérot cavities in detectors like LIGO form the arms of Michelson interferometers, recycling light to amplify phase shifts induced by displacements as small as $10^{-19} m/√Hz (corresponding to strains of approximately $2.5 \times 10^{-23} /\sqrt{\mathrm{Hz}}), enabling the first direct observation of gravitational waves from binary black mergers. These cavities, with arm finesse of approximately 450, store over 100 kW of circulating power to reach quantum-limited sensitivity.^[59]^[60] In integrated and nanophotonics, optical cavities push confinement beyond the diffraction limit, enabling compact devices with enhanced light-matter interactions. Plasmonic cavities, formed by metal nanostructures like nanoparticle dimers or bowtie antennas, achieve sub-diffraction mode volumes on the order of ( \lambda / 50 )^3 through surface plasmon polaritons, concentrating fields by factors up to $10^4 for applications in single-molecule sensing and nano-lasing. Optomechanical cavities couple optical modes to mechanical vibrations via radiation pressure, with the interaction Hamiltonian H_\mathrm{int} = - \hbar g_0 a^\dagger a (b + b^\dagger) describing frequency shifts proportional to phonon number, enabling ground-state cooling of mechanical resonators to below 1 phonon and quantum state transfer between light and motion. These systems, often realized in photonic crystal membranes or suspended waveguides, have demonstrated coupling rates g_0 / 2\pi up to 1 GHz, facilitating hybrid quantum networks.^[61]

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The software RP Resonator can be used to calculate stability zones of laser resonators, and to find optimized resonator designs e.g. concerning the location of ...
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The change from a type II to a type I resonator can make the alignment much easier and allow more output power to be obtained with better stability, even if the ...
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Etalons – Fabry--Pérot interferometer - RP Photonics
An etalon acts as an optical resonator (cavity), where the transmissivity varies approximately periodically with the optical frequency.<|control11|><|separator|>
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Stable and rugged etalon for the Dynamics Explorer Fabry-Perot ...
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[PDF] Highly stable piezoelectrically tunable optical cavities
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Ring Lasers - RP Photonics
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[PDF] Optical Transmission Characteristics of Fiber Ring Resonators
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