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Diffraction grating

A diffraction grating is an optical component consisting of a large number of evenly spaced parallel slits or grooves etched onto a substrate, such as glass, plastic, or metal, which diffracts incoming light into multiple beams traveling in different directions, thereby separating the light into its spectral components through wave interference.^[1] This device produces a sharper and more detailed interference pattern compared to a simple double-slit setup, enabling precise wavelength dispersion.^[2] The grooves, typically numbering thousands per millimeter, act as secondary wave sources according to Huygens' principle, creating constructive interference at specific angles for each wavelength.^[3] The fundamental principle governing a diffraction grating's operation is the grating equation, d \sin \theta = m \lambda, where d is the distance between adjacent grooves (the grating constant), \theta is the angle of diffraction, m is the diffraction order (an integer), and \lambda is the wavelength of the light.^[4] For normal incidence, this equation predicts the positions of principal maxima, allowing the grating to resolve closely spaced wavelengths with higher resolution as the number of grooves increases. Diffraction gratings can be transmission-type, where light passes through the grating, or reflection-type, where light bounces off the grooved surface, with the latter often used in high-efficiency applications due to minimized light loss.^[3] Invented in its modern form by Joseph von Fraunhofer in 1821, the diffraction grating revolutionized spectroscopy by providing a more accurate alternative to prisms for wavelength measurement.^[5] Today, diffraction gratings are essential in numerous fields, including analytical chemistry for spectrometers that identify molecular compositions, astronomy for dispersing starlight to study elemental abundances, and laser systems for beam steering and pulse compression in high-intensity applications.^[6] Their ability to achieve high spectral resolution—often exceeding 10,000—makes them indispensable in precision optics and scientific instrumentation.^[1]

Basic Principles

Definition and Structure

A diffraction grating is an optical component featuring a periodic structure designed to diffract light into multiple beams traveling in different directions, thereby separating polychromatic light into its constituent wavelengths through the principle of interference.^[7] This separation occurs because the periodic elements of the grating act as multiple coherent sources of secondary wavelets, leading to constructive and destructive interference that produces distinct spectral orders.^[8] Diffraction gratings are essential in spectroscopy, telecommunications, and laser systems for their ability to achieve high spectral resolution.^[9] The basic structure of a diffraction grating consists of a flat substrate material onto which a series of closely spaced, parallel grooves or slits are formed, typically with spacings on the order of micrometers.^[10] Common substrates include optical glass such as soda-lime or fused silica for transmissive gratings, and metals like aluminum or gold for reflective ones, with polymers occasionally used for lightweight applications.^[11] Key parameters defining the grating's performance include the groove spacing d (the distance between adjacent grooves, often expressed as groove density in lines per millimeter, ranging from 30 to 5000 lines/mm), groove depth (which influences diffraction efficiency), and the profile shape of the grooves (such as rectangular or triangular).^[8] Additionally, the total grating area, typically several square centimeters, affects the overall light throughput and resolution.^[9] The historical origins of the diffraction grating trace back to 1821, when Joseph von Fraunhofer constructed the first practical device using a grid of fine wires stretched between screws, enabling precise measurement of light wavelengths and the observation of spectral lines.^[5] Earlier rudimentary attempts, such as David Rittenhouse's 1785 setup with hairs between threaded screws, demonstrated the concept but lacked precision.^[5] By the late 19th century, significant advancements came from Henry A. Rowland, who in 1882 invented a ruling engine to mechanically engrave high-quality grooves onto metal or glass surfaces, producing gratings with thousands of lines for superior resolution in astronomical spectroscopy.^[12] Up to the early 20th century, further refinements by researchers like Albert A. Michelson improved ruling engine accuracy, allowing gratings up to 10 inches in size and groove densities exceeding 10,000 lines per inch, which solidified their role in quantitative spectral analysis.^[12]^[13]

Diffraction Fundamentals

Diffraction is a fundamental wave phenomenon in which waves bend around obstacles or spread through apertures smaller than their wavelength, resulting in interference patterns that produce regions of constructive and destructive interference. This bending occurs because every point on a wavefront acts as a source of secondary spherical wavelets, which superimpose to form the new wavefront, as described by the Huygens-Fresnel principle.^[14]^[15] In the context of light waves, this principle explains how electromagnetic radiation deviates from straight-line propagation when encountering edges or openings, leading to observable patterns such as bright and dark fringes on a screen.^[16] In single-slit diffraction, light passing through a narrow aperture creates a central bright maximum flanked by alternating minima and secondary maxima, with the pattern's width determined by the slit size relative to the wavelength. The intensity decreases gradually away from the center due to the partial reinforcement of wavelets from different parts of the slit. In contrast, multi-slit diffraction, such as from multiple parallel apertures, amplifies the interference effects, producing sharper and more intense principal maxima separated by broader minima, as the wavelets from each slit constructively interfere at specific angles. This enhancement arises from the increased number of coherent sources, which narrows the peaks and improves resolution compared to the broader envelope of single-slit patterns.^[17]^[18] The extent of diffraction is highly dependent on wavelength, with longer wavelengths producing larger diffraction angles and more pronounced spreading, as the deviation angle scales inversely with the aperture size relative to wavelength. For visible light, which spans wavelengths from approximately 400 nm (violet) to 700 nm (red), this effect is particularly relevant in optical experiments, where shorter wavelengths like blue light exhibit less diffraction than longer red wavelengths.^[19]^[20] Optimal observation of diffraction patterns requires coherent light sources, where the phase relationship between waves remains constant over time and space, ensuring stable interference. Incoherent sources, like typical lamps, produce washed-out patterns due to random phase fluctuations, whereas lasers provide the necessary temporal and spatial coherence for clear, high-contrast fringes in diffraction setups.^[21]^[18] This coherence is essential for applications involving periodic structures that rely on precise wave superposition. Angular dispersion refers to the separation of different wavelengths into distinct directions based on their diffraction angles, allowing waves of varying frequencies to be spatially resolved. This concept underpins the ability of diffractive elements to disperse light, with the angular spread increasing for longer wavelengths, facilitating spectral analysis in the visible range.^[22]^[23]

Theoretical Foundations

Classical Diffraction Theory

Classical diffraction theory for gratings relies on the scalar approximation derived from Maxwell's equations, treating the electromagnetic field as a scalar quantity propagating according to the Helmholtz equation. This approach simplifies the analysis by assuming that the field components are nearly parallel and the wavelength is small compared to the grating dimensions, enabling the use of Kirchhoff's diffraction integral or the Rayleigh-Sommerfeld formulation to describe wave propagation near and far from the grating surface.^[24] In applying scalar theory to grating surfaces, the periodic structure is modeled as a series of secondary sources emitting spherical waves, with the far-field approximation (Fraunhofer regime) valid when the observation distance is much larger than the grating size squared over the wavelength, yielding diffraction patterns as the Fourier transform of the grating's transmission or reflection function. This framework captures the essential wave behavior without accounting for vectorial effects initially, providing a foundational understanding of how incident plane waves are scattered into discrete directions.^[25] The interference arising from the periodic array of grooves fundamentally governs the diffraction pattern, where path length differences between waves originating from adjacent grooves determine regions of constructive and destructive interference. For an incident wave at angle θ_i, the path difference is approximately d (sin θ_i ± sin θ_d), with d the groove spacing, leading to maxima when this difference is an integer multiple of the wavelength; for broadband light, this disperses the spectrum continuously across diffraction orders with high resolution, while for monochromatic light, it produces discrete sharp orders.^[26] Diffraction orders emerge from this interference: the zero-order (m=0) represents undiffracted light propagating straight through or reflecting specularly, while the first-order (m=±1) constitutes the primary diffracted beams used for dispersion, and higher orders (m>1) appear at larger angles with decreasing intensity. The blaze angle of the grooves modifies the order distribution by optimizing phase matching to concentrate energy into a specific order, enhancing efficiency without altering the order positions themselves.^[27] Polarization effects introduce vectorial corrections to the scalar model, particularly pronounced in reflection gratings where transverse electric (TE) modes (electric field parallel to the grooves) exhibit different boundary conditions than transverse magnetic (TM) modes (magnetic field parallel to the grooves), resulting in varying diffraction efficiencies; for instance, TE modes often couple more strongly to even orders in symmetric profiles. In transmission gratings, these differences are less severe but still influence order amplitudes due to the grating's refractive index contrast. The resolution limits of a grating are quantified by adapting the Rayleigh criterion, which sets the minimum resolvable wavelength separation Δλ such that the maximum of one spectral line coincides with the first minimum of the adjacent line in the diffraction envelope. This yields the resolving power R = λ / Δλ = m N, where m is the diffraction order and N the total number of illuminated grooves, establishing the grating's ability to distinguish closely spaced wavelengths proportional to its size and order.^[28]

Grating Equation and Efficiency

The grating equation governs the angles at which constructive interference occurs for light diffracted by a periodic structure with groove spacing d. Consider a plane wave of wavelength \lambda incident on the grating at angle \theta_i (measured from the normal). Light rays from adjacent grooves interfere constructively in the m-th diffraction order (where m is an integer) at angle \theta_m when the path length difference is an integer multiple of \lambda. For reflection gratings, this path difference arises from the extra distance traveled by the incident ray to the second groove, d \sin \theta_i, plus the difference in the diffracted paths, d \sin \theta_m, yielding the equation:

d (\sin \theta_i + \sin \theta_m) = m \lambda

For transmission gratings, the sign for the diffracted path is reversed, giving d (\sin \theta_i - \sin \theta_m) = m \lambda. This relation, derived by Joseph von Fraunhofer in the early 19th century through application of wave interference principles to ruled gratings, predicts the discrete directions of diffracted light for each order m.^[29]^[30] From the grating equation, the angular dispersion d\theta_m / d\lambda, which quantifies the angular separation of wavelengths, follows by differentiation with respect to \lambda at fixed \theta_i:

\frac{d\theta_m}{d\lambda} = \frac{m}{d \cos \theta_m}

Higher orders m or smaller groove spacings d increase dispersion, enabling finer spectral resolution. The free spectral range (FSR), defined as the wavelength interval between successive orders before spectral overlap occurs at a fixed \theta_m, is approximately FSR = \lambda / m for the m-th order.^[10]^[31] The resolving power R = \lambda / \Delta\lambda, where \Delta\lambda is the smallest resolvable wavelength difference, is given by R = m N with N the total number of illuminated grooves. This arises because phase coherence across the grating aperture limits the linewidth to roughly \lambda / N, scaled by the order m. For example, a grating with 1200 lines/mm over a 50 mm illuminated length has N = 60{,}000, yielding R = 60{,}000 in first order (m=1) at \lambda = 500 nm, sufficient to resolve lines separated by 0.008 nm.^[10]^[31] Diffraction efficiency \eta_m measures the fraction of incident power directed into the m-th order, critical for practical spectroscopic performance. In blazed gratings, efficiency peaks when the blaze angle \theta_b satisfies \theta_b \approx (\theta_i + \theta_m)/2, aligning the groove facet normal to bisect the incident and diffracted rays for specular-like reflection into the desired order; this can achieve \eta_1 > 80\% near the blaze wavelength.^[32]^[9] Simple scalar theories approximate efficiency via Fresnel reflection from idealized groove profiles, but they fail for fine gratings (d \approx \lambda) where polarization and multiple scattering matter. Rigorous coupled-wave analysis (RCWA), which expands fields in Fourier modes and solves coupled Maxwell equations layer-by-layer, provides accurate \eta_m computations, accounting for arbitrary profiles and materials; introduced by Moharam and Gaylord, it reveals efficiency variations up to 20% not captured by scalar models.^[31] Efficiency depends on groove shape—rectangular profiles exhibit sharp efficiency envelopes peaked at order boundaries, while sinusoidal profiles yield smoother, broader responses—and material properties, such as refractive index contrast in transmission gratings that modulates phase shifts, or dielectric/multilayer coatings in reflection gratings that boost peak \eta_m by enhancing reflectivity. Polarization further influences results, with TE modes often exceeding TM efficiencies by 10-15% in metallic gratings.^[10]^[31]

Types of Diffraction Gratings

Surface Relief Gratings

Surface relief gratings consist of periodic height variations etched or ruled directly onto the surface of a reflective or transmissive substrate, creating a physical structure that modulates the phase and amplitude of incident light through geometric relief. These gratings encompass ruled variants, mechanically scribed with diamond tools to form fine grooves, and etched variants, patterned via chemical or reactive ion processes for enhanced precision and uniformity. The relief depth typically ranges from tens to hundreds of nanometers, comparable to the wavelength of light in the UV-visible range, enabling efficient diffraction.^[33]^[34]^[35] Design features of surface relief gratings focus on groove profiles, such as rectangular, trapezoidal, or sinusoidal shapes, which determine the distribution of diffracted light and overall efficiency. Rectangular profiles offer straightforward fabrication but may produce symmetric diffraction patterns, while trapezoidal or sawtooth profiles approximate blazed structures to concentrate energy in a specific order, commonly used in reflection gratings for spectrometers. These profiles allow customization of groove spacing (typically 500–3600 grooves per millimeter) and depth to optimize performance across targeted wavelengths. Blazing of the groove facets can enhance efficiency in the desired diffraction order by aligning the reflection plane with the incident light.^[35]^[36] Surface relief gratings provide high diffraction efficiency in reflection mode, often exceeding 70% when coated with metals like aluminum or gold, making them suitable for compact optical systems. Their mechanical robustness and resistance to thermal damage enable use in high-power applications, such as laser pulse compression, without rapid degradation.^[37]^[38] However, these gratings are sensitive to the polarization state of incident light, with efficiency varying significantly between s- and p-polarizations due to the anisotropic groove structure, potentially reducing performance in unpolarized sources. Imperfections in groove uniformity, such as periodic errors from ruling or etching, can generate stray light in higher diffraction orders and unwanted ghosts, limiting resolution in precise spectroscopic measurements.^[39] The development of surface relief gratings dates to the early 19th century, with Joseph von Fraunhofer constructing the first ruled reflection gratings around 1821 using a hand-built ruling engine, which allowed the resolution of solar spectral lines and advanced astronomical spectroscopy. These early mechanical gratings, often with wire or ruled surfaces, became staples in UV-visible spectroscopy due to their reliability and ability to disperse light across broad spectral ranges.^[40]^[37]

Volume Phase Holographic Gratings

Volume phase holographic gratings (VPHGs), also known as volume Bragg gratings, consist of a periodic modulation of the refractive index embedded within the bulk of a transparent photosensitive material, distinguishing them from surface-based gratings by utilizing the entire thickness for diffraction. This volume structure enables Bragg diffraction, where incident light waves constructively interfere only at specific angles and wavelengths satisfying the Bragg condition, $2 n \Lambda \sin \theta_B = m \lambda, with n as the average refractive index, \Lambda the grating period, \theta_B the Bragg angle, m the diffraction order, and \lambda the wavelength. The result is highly selective wavelength dispersion with minimal losses, as the grating acts as a thick hologram recording the interference pattern of two coherent beams during fabrication.^[41]^[42]^[43] The diffraction behavior in VPHGs is rigorously described by Kogelnik's coupled wave theory, which models the coupling between the incident (reference) and diffracted waves propagating through the grating volume. For an unslanted transmission grating at the Bragg angle, the first-order diffraction efficiency \eta is expressed as

\eta = \sin^2 \left( \frac{\pi \Delta n \, d}{\lambda \cos \theta_0} \right),

where \Delta n is the refractive index modulation amplitude, d the grating thickness (typically several millimeters for high selectivity), \lambda the wavelength, and \theta_0 the internal Bragg angle. This theory predicts peak efficiencies exceeding 90% under ideal conditions, with off-Bragg sensitivity leading to sharp angular and spectral selectivity (e.g., bandwidths as narrow as 0.01 nm). Reflection-type VPHGs, conversely, exhibit similar efficiency formulas but with reversed wave propagation, enabling compact designs for broadband applications. Polarization effects are minimal in isotropic materials, though slight dependence arises from the recording geometry.^[43]^[42]^[44] Fabrication of VPHGs primarily employs holographic recording in photosensitive media like dichromated gelatin (DCG), a silver halide-free emulsion offering high resolution and low absorption after processing. The process begins with sensitizing a thin DCG layer (5–50 μm thick) on a glass or fused silica substrate, followed by exposure to the interference fringes from two collimated laser beams (e.g., at 488 nm or 633 nm) to imprint the volume index modulation. Post-exposure, the material undergoes chemical development—hardening, dehydration, and sealing between substrates—to stabilize the grating, achieving index modulations up to 0.05. Alternative materials include photopolymers or photorefractive crystals for replication, allowing large-area production (up to 500 mm × 500 mm) via step-and-repeat exposure or mosaic assembly, with groove densities from 500 to 3600 lines/mm. Common challenges include controlling shrinkage during processing, which can detune the Bragg angle, and ensuring uniformity over large formats.^[45]^[46]^[47] Compared to surface relief gratings, VPHGs provide superior performance in key metrics: diffraction efficiencies routinely reach 85–95% across visible to near-IR wavelengths, with stray light levels below 0.1% due to volume selectivity, and polarization sensitivity under 5% for unpolarized light. Their robustness stems from the encapsulated structure, resisting environmental factors like humidity, temperature variations (stable from -50°C to 100°C), and radiation doses up to 10^6 rad in space environments without significant degradation. These attributes enable compact, high-resolution spectrometers, as VPHGs can achieve resolving powers R = \lambda / \Delta \lambda > 10^5 in thinner formats than equivalent ruled gratings.^[48]^[49]^[50] In practice, VPHGs excel in astronomical spectroscopy, where they disperse light in instruments like the Subaru Telescope's FMOS, offering high throughput and low ghosting for faint object detection. They also facilitate spectral beam combining in high-power lasers, multiplexing multiple wavelengths into a single beam with >90% efficiency, and serve as notch filters rejecting narrow laser lines while transmitting broadband light. Emerging uses include integrated photonic devices and LIDAR systems, leveraging their design flexibility for custom blaze angles and periods.^[51]^[52]^[53]

Blazed and Echelle Gratings

Blazed gratings feature grooves with a sawtooth profile, designed to concentrate diffracted energy into a specific order by mimicking the reflection from a tilted mirror facet.^[10] This asymmetric profile redirects light more efficiently toward the desired diffraction angle compared to symmetric rectangular grooves.^[54] The blaze wavelength, \lambda_b, at which efficiency peaks in the Littrow configuration, is given by

\lambda_b = \frac{2d}{m} \sin \theta_b,

where d is the groove spacing, m is the diffraction order, and \theta_b is the blaze angle.^[32] Echelle gratings represent a specialized variant of blazed gratings, characterized by high blaze angles (typically greater than 45°) and coarse groove spacing (fewer than 100 grooves per millimeter), enabling operation in high diffraction orders (m > 10).^[55] This design trades low dispersion per order for high resolving power, making echelles particularly suited for high-resolution astronomical spectroscopy where broad wavelength coverage is needed across multiple overlapping orders.^[56] A cross-disperser is often required to separate these orders spatially.^[57] In design, both blazed and echelle gratings achieve maximum efficiency in the Littrow configuration, where the incident and diffracted beams coincide, aligning the groove facets optimally with the light path.^[10] For echelles, key trade-offs involve the free spectral range (FSR \approx \lambda / m), which decreases with higher orders, limiting the wavelength span per order but enhancing resolution (R = m N, where N is the number of grooves illuminated); coarser spacing widens the FSR to match detector sizes in compact spectrographs.^[58] Blazed gratings generally offer peak efficiencies exceeding 70% near \lambda_b, while echelles maintain 50-80% in their high-order use.^[54] These gratings excel in infrared applications, where blazed profiles can achieve efficiencies over 60% across near- to mid-IR bands due to reduced scattering losses on ruled surfaces.^[59] Echelle designs enable compact, high-resolution spectrographs for astronomical instruments, minimizing size while covering wide spectral ranges.^[56] However, their efficiency is narrowband, dropping significantly away from \lambda_b, and fabrication demands precise groove faceting (sub-micrometer accuracy) to avoid efficiency losses from profile irregularities.^[60]

Specialized Modern Gratings

Liquid crystal gratings represent a class of electrically tunable diffractive elements that leverage the reorientation of liquid crystal molecules via patterned electrodes or photoalignment techniques to achieve dynamic control over diffraction patterns. These devices enable switchable beam steering and polarization manipulation, offering significant advantages in compactness and low power consumption compared to traditional static gratings. Recent advances, such as the integration of double-layer structures in vertical-field in-plane switching configurations, have improved phase modulation depth and response times, achieving diffraction efficiencies exceeding 80% under applied voltages as low as 5 V.^[61] Further innovations in 2024 include diffractive liquid crystal devices incorporating polymer walls formed through phase separation processes, which enhance mechanical stability and reduce scattering losses in tunable gratings. These polymer-wall configurations allow for precise control of liquid crystal domains, enabling applications in adaptive optics with sub-millisecond switching speeds. Building on volume phase holographic principles, such structures maintain high transparency while providing electrical tunability for real-time wavefront correction. By 2025, switchable chiral nematic liquid crystal diffraction gratings have been developed, operable at room temperature with low voltages below 3 V, demonstrating rotatable diffraction orders for versatile optical routing.^[62]^[63] Plasmonic gratings utilize metal nanostructures, such as gold or silver periodic arrays, to couple incident light with surface plasmons, thereby enhancing diffraction efficiency in the infrared and terahertz spectral ranges. This plasmonic enhancement confines electromagnetic fields to subwavelength scales, boosting sensitivity for grating-coupled surface plasmon resonance sensors that detect refractive index changes as small as 10^{-6} RIU. A 2024 design featuring asymmetric bow-tie grating metasurfaces achieves extraordinary terahertz transmission with field enhancements up to 100-fold, attributed to strong plasmon hybridization at the grating interfaces. These gratings excel in integrated THz optoelectronics due to their ability to support highly confined modes with propagation losses below 0.1 dB/mm.^[64]^[65] Metamaterial gratings consist of subwavelength periodic structures engineered to exhibit anomalous diffraction behaviors, including negative refraction where light bends opposite to conventional Snell's law. These designs suppress undesired diffraction orders through tailored unit cell geometries, directing energy into specific anomalous channels with efficiencies over 90%. In 2025, electromagnetic metagratings incorporating dielectric resonators enable large-angle negative refraction at microwave frequencies, with tilt adjustments optimizing beam deflection angles up to 60 degrees. Such capabilities arise from the effective negative permittivity and permeability provided by the subwavelength elements, facilitating compact beam manipulation without bulky prisms.^[66] Recent developments in 2025 have addressed challenges in low-index-contrast gratings by introducing profile optimization techniques that elevate first-order diffraction efficiency from below 20% to over 70% without modifying the grating period or material. This enhancement relies on asymmetric phase profiles that redistribute energy from zero-order leakage, particularly beneficial for polymer-based or waveguide-integrated devices where index differences are limited to Δn < 0.1. Overall, these specialized modern gratings provide inherent tunability and miniaturization, enabling integration into portable spectrometers and lidar systems for real-time spectral analysis and ranging with footprints under 1 cm².^[67]

Fabrication Techniques

Mechanical Ruling and Ruling Engines

Mechanical ruling is a traditional fabrication technique for producing surface relief diffraction gratings, where a diamond-tipped tool is precisely moved across a substrate coated with a soft metal layer, such as gold or aluminum, to scribe periodic grooves. The ruling engine, a sophisticated mechanical apparatus, controls the tool's motion to ensure groove spacing and depth are maintained with sub-micron accuracy, typically achieving positioning precision better than 0.1 μm. This process creates the periodic structure necessary for diffraction, with the substrate often being optical glass or a metal blank prepared to minimize surface irregularities before coating.^[68]^[69]^[70] The historical foundation of mechanical ruling was laid in the 1880s by Henry A. Rowland, who developed the first effective ruling engine at Johns Hopkins University to address the limitations of earlier imprecise gratings made by hand or rudimentary methods. Rowland's engine employed a precision lead screw to advance the diamond tool in incremental steps, enabling the production of concave gratings up to 12 cm in diameter with groove densities around 15,000 lines per inch, revolutionizing spectral analysis by providing higher resolution than contemporary alternatives. Subsequent advancements, such as those by George Harrison at MIT in the mid-20th century, introduced interferometric feedback control to the ruling mechanism, allowing for real-time correction of errors and the ruling of larger plane gratings up to 25 cm wide.^[5]^[71] Key parameters in mechanical ruling include groove density, which ranges from 300 to 2,000 grooves per mm depending on the application, and ruling speed, which is deliberately slow—often less than 1 mm per minute—to preserve accuracy and minimize tool wear. The engine's lead screw and carriage systems are lapped to extreme tolerances, with periodic error control being critical to avoid deviations that could degrade performance. After ruling, the grating surface is typically cleaned and may undergo thermal treatment to stabilize the structure, though the process demands a vibration-isolated environment to prevent disruptions during the extended ruling times, which can span weeks for high-density gratings.^[68]^[72]^[73] One primary advantage of mechanical ruling is its ability to produce highly uniform groove densities across large areas and to form blazed profiles by precisely controlling the diamond tool's angle, which directs more light into a desired diffraction order for enhanced efficiency in spectroscopic applications. Modern interferometrically controlled engines further improve this by achieving groove placement errors below 1 nm, enabling master gratings suitable for replication with minimal wavefront aberrations. However, the technique is inherently time-intensive due to its sequential groove formation, limiting throughput, and susceptible to periodic errors from mechanical imperfections in the screw or bearings, which can produce unwanted "ghost" lines in the diffracted spectrum; these errors are often mitigated in echelle gratings through coarser groove spacings that reduce the impact of systematic deviations.^[68]^[73]^[74]

Holographic and Lithographic Methods

Holographic methods for fabricating diffraction gratings involve recording interference patterns in photosensitive materials to create periodic refractive index modulations or surface relief structures. In the case of volume phase holographic (VPH) gratings, two coherent laser beams are interfered within a thin layer of material such as dichromated gelatin (DCG), forming a stationary fringe pattern that induces a volume refractive index variation upon development.^[75] These lasers typically operate at wavelengths ranging from ultraviolet (e.g., 351 nm from argon-ion lasers) to near-infrared (e.g., 1064 nm from Nd:YAG lasers), selected based on the material's sensitivity and the desired grating period.^[76] The process begins with preparing the DCG layer by coating a glass substrate with a solution of gelatin and ammonium dichromate, followed by drying in a controlled environment to form a uniform film.^[77] During exposure, the interference of the two beams creates a sinusoidal intensity pattern, which cross-links the gelatin molecules in exposed regions, establishing the grating structure. Post-exposure steps include washing the plate in running water to remove unreacted dichromate, followed by a series of alcohol dehydration baths (typically isopropyl alcohol in increasing concentrations from 50% to 100%) to harden the gelatin and prevent shrinkage. The grating is then fixed by drying in a desiccator and sealing with an index-matching cement to stabilize the structure and protect against environmental degradation.^[78] Multiple exposures can be used to achieve complex profiles, such as slanted fringes for optimized efficiency in specific diffraction orders.^[79] Alternative photosensitive materials, like photopolymers, simplify the process by eliminating chemical development, relying instead on polymerization during exposure for direct formation of the index modulation.^[79] Lithographic techniques enable the creation of high-precision gratings with sub-micron features, particularly suited for surface relief types. Electron-beam lithography (EBL) uses a focused electron beam to scan and expose a pattern directly onto a photoresist-coated substrate, allowing for arbitrary groove shapes and periods down to 100 nm resolution.^[80] The process involves spin-coating the substrate with a positive photoresist like PMMA, exposing the resist with the e-beam according to the grating design, and developing in a solvent to remove exposed areas, revealing the pattern. This is followed by etching—often reactive ion etching (RIE)—to transfer the pattern into the substrate material, such as fused silica or silicon, before stripping the remaining resist.^[81] Nanoimprint lithography (NIL), in contrast, employs a pre-patterned mold (master) pressed into a resist layer under heat or UV curing, displacing material to form the grating relief in a single step for large areas up to several square centimeters.^[82] Development and etching steps mirror those in EBL, but NIL's mechanical replication reduces exposure time, enabling higher throughput for periodic structures.^[83] These methods offer key advantages, including the ability to produce aberration-free gratings over large apertures by using curved wavefronts in holography or precise beam control in lithography, resulting in lower stray light and higher diffraction efficiencies up to 90% in optimized VPH designs.^[84] Holographic masters are particularly mass-producible for subsequent replication, while lithographic approaches excel in customizing profiles for specialized applications without mechanical wear.^[80] Recent advances include single-exposure holographic techniques that optimize grating efficiency in multiple orders simultaneously, as demonstrated in 2023 designs for broadband spectrographs, reducing fabrication complexity.^[85] Additionally, integration with micro-electro-mechanical systems (MEMS) has enabled tunable gratings, where lithographically patterned structures on deformable substrates allow dynamic adjustment of groove spacing via electrostatic actuation, achieving wavelength tunability over 20 nm in compact devices.^[86]

Replication and Large-Scale Production

Replication of diffraction gratings typically involves embossing techniques derived from ruled or holographic masters to produce multiple copies efficiently. In this process, a master grating is used to imprint the groove pattern onto a substrate coated with a photosensitive resin or polymer, such as epoxy or UV-curable materials, through pressure and heat application.^[87]^[88] For metallic replicas, electroforming with nickel is employed to create durable shims from the master, which can then be used for repeated embossing cycles.^[89] Ion-beam etching provides an alternative for high-durability copies, particularly in multilayer dielectric gratings, where reactive ion beams transfer the pattern into the substrate material like fused silica, ensuring groove depths and profiles suitable for high-power applications.^[90]^[6] The replication workflow begins with master preparation, where the original ruled or holographic grating serves as the template, often protected by a release layer to prevent adhesion issues. Substrates, typically glass or plastic, are coated with a thin layer of resin via spin-coating or vapor deposition, followed by precise alignment and embossing under controlled pressure (e.g., 10-100 MPa) and temperature (up to 150°C for hot embossing). Curing is achieved through UV exposure or thermal annealing to solidify the pattern, after which the replica is separated and inspected. Quality control emphasizes groove fidelity, using atomic force microscopy (AFM) or interferometry to verify parameters like groove depth (typically 100-500 nm), period uniformity (<0.1% variation), and blaze angle accuracy, ensuring diffraction efficiency remains above 70% of the master.^[87]^[88] Large-scale production addresses the limitations of single-master fabrication by employing grating tiling, or mosaicking, where multiple smaller replicas (e.g., 300 mm × 300 mm segments) are assembled into arrays exceeding 1 m in size for astronomical spectrographs. This technique involves precise alignment of segments using mechanical frames or optical interferometry to minimize seam discontinuities, enabling meter-class gratings for telescopes like the Extremely Large Telescope.^[80]^[91] In the 2020s, advances in ruling technology, including next-generation mechanical ruling engines with enhanced precision, have supported larger masters up to 400 mm × 500 mm, while scanner-based systems in holographic lithography allow continuous exposure over extended areas via translating optics.^[92]^[80] These methods offer significant advantages, including cost reduction by factors of 10-100 compared to original fabrication for commercial spectrometers and optical devices, as embossing enables thousands of copies from a single master. For astronomy, tiled replicas facilitate high-resolution instruments with ruling densities up to 1200 grooves/mm over large apertures, improving light collection efficiency. However, challenges persist, such as alignment errors in tiling that can introduce wavefront aberrations up to λ/10, leading to reduced resolving power. Recent solutions, including adaptive mosaicking devices with sub-micron adjustment capabilities developed in 2025, mitigate these by real-time error correction during assembly.^[80]^[93]^[94]

Applications

Dispersion in Spectroscopy

Diffraction gratings function as dispersive elements in spectroscopy by angularly separating wavelengths of incident light, allowing for the isolation and analysis of spectral components across a broad range. This dispersion arises from the constructive interference of light diffracted by the grating's periodic grooves, as described by the grating equation m\lambda = d (\sin i + \sin \theta), where m is the diffraction order, \lambda the wavelength, d the groove spacing, i the incidence angle, and \theta the diffraction angle.^[10]^[95] In common configurations like the Littrow mount, the grating is oriented such that the incident and diffracted beams overlap, with a single mirror collimating the light from the entrance slit and refocusing the dispersed spectrum back toward the detector near the slit, enabling compact designs with high optical efficiency at the blaze wavelength.^[96] The Czerny-Turner configuration, in contrast, uses two separate concave mirrors—one to collimate the input beam onto a plane grating and another to focus the diffracted light onto the exit slit or detector—offering improved aberration correction, such as reduced astigmatism for anastigmatic imaging, and lower stray light levels compared to Littrow setups.^[96]^[97] Advanced spectrograph designs incorporate gratings for enhanced performance, particularly in echelle systems where a coarse, high-blaze-angle echelle grating operates in high orders (typically m > 30) to achieve compact, high-dispersion layouts suitable for broadband spectroscopy. A cross-disperser, often a secondary low-dispersion grating or prism oriented perpendicular to the echelle, then separates the overlapping high-order spectra into a two-dimensional array on a detector, facilitating simultaneous coverage of large wavelength ranges without order overlap in the primary dispersion direction.^[98]^[99] The resolving power R = \lambda / \Delta\lambda, which measures the ability to distinguish closely spaced lines, is fundamentally limited by R \approx mN (with N as the number of illuminated grooves), enabling values exceeding $10^5 in astronomical echelle spectrographs for resolving Doppler shifts in exoplanet atmospheres or stellar radial velocities.^[100]^[99] Throughput, or the fraction of incident light reaching the detector, trades off with resolution via entrance slit width: narrower slits (e.g., <10 μm) yield higher R by minimizing the projected slit image's spectral broadening but reduce photon collection, critical for faint sources in astronomical observations.^[101]^[102] The shift from prism to grating spectrometers gained momentum after 1900, driven by improved ruling engines that produced high-quality, uniform gratings, overcoming prisms' nonlinear dispersion and limited transparency in UV and IR regions.^[103]^[104] Early gratings, pioneered by Fraunhofer in the 1820s, were rudimentary, but Rowland's screw-based ruling engine in the 1880s and subsequent refinements enabled precise groove spacing down to 1/10000 mm, making gratings the preferred dispersive element for quantitative spectroscopy by the early 20th century due to their linear wavelength-to-angle mapping and extended spectral coverage from ultraviolet to near-infrared.^[103]^[105] Efficiency in these systems requires blazed gratings to direct most energy into the desired order, typically achieving 70-90% at the blaze wavelength, while order-sorting filters or prisms block unwanted higher orders to prevent spectral contamination and ensure accurate throughput across the observed band.^[38]^[106]

Optical Systems and Devices

Diffraction gratings play a crucial role in laser cavities, particularly in configurations that enable precise wavelength selection and tuning. In the Littrow configuration, the grating is oriented such that the first-order diffracted beam retraces the path of the incident beam back into the laser gain medium, allowing the cavity to resonate at a specific wavelength determined by the grating's angle. This setup is widely used for wavelength tuning in dye lasers and titanium-sapphire (Ti:sapphire) lasers, where rotating the grating adjusts the lasing wavelength across broad spectral ranges, often exceeding 100 nm in Ti:sapphire systems operating near 800 nm. Additionally, Littrow gratings serve as output couplers, with the zeroth-order reflection providing the laser output while the first-order diffraction feedback ensures narrow-linewidth operation, achieving linewidths below 1 GHz in pulsed Ti:sapphire lasers.^[107]^[108]^[109]^[110]^[111] Beyond tuning, diffraction gratings are integral to beam shaping in ultrafast optical systems. In chirped pulse amplification (CPA) setups, gratings facilitate pulse compression by compensating for temporal dispersion introduced during amplification; pairs of parallel gratings, often with groove densities around 1200-1700 lines/mm, recompress femtosecond pulses to durations under 100 fs while managing peak powers in the terawatt range. For array generation, multilevel phase gratings diffracted a collimated laser beam into uniform spot arrays, such as 7x7 patterns with efficiencies up to 74% and uniformity exceeding 95%, enabling applications in parallel optical processing and laser beam delivery. These gratings exploit Fraunhofer diffraction to split a single input beam into multiple equal-intensity outputs, with binary designs optimizing for specific array geometries in compact setups.^[112]^[113]^[114]^[115]^[116] In telecommunications, arrayed waveguide gratings (AWGs) function as key multiplexers and demultiplexers for wavelength division multiplexing (WDM) systems. These integrated devices consist of an array of waveguide paths with incrementally varying lengths, inducing phase shifts that produce wavelength-dependent focusing via diffraction at slab waveguide interfaces, enabling channel spacings as fine as 25 GHz for dense WDM (DWDM) with up to 64 channels. AWGs operate across the C-band (1530-1565 nm), achieving insertion losses below 5 dB and crosstalk under -30 dB, supporting data rates exceeding 100 Gbps per channel in fiber optic networks deployed since the 1990s.^[117]^[118]^[119] Diffractive optics incorporating gratings enhance imaging systems by addressing chromatic aberrations inherent in refractive lenses. The negative dispersion of diffraction gratings—where longer wavelengths diffract at larger angles compared to shorter ones—counters the positive dispersion of glass lenses, allowing hybrid diffractive-refractive designs to achieve achromatic performance over visible and near-infrared spectra. In camera objectives, thin diffractive elements, such as Fresnel zone plates or blazed gratings with subwavelength features, reduce axial chromatic shift by over 90% while maintaining f-numbers around f/2, enabling compact, lightweight lenses for consumer and scientific imaging without sacrificing resolution.^[120]^[121]^[122] Device integration of diffraction gratings with other optical components has advanced since the mid-20th century, particularly in fiber optics. Hybrid assemblies combine gratings with mirrors and lenses to form compact modules, such as grating-Fresnel lens pairs that couple light into single-mode fibers with efficiencies above 50%, used in early wavelength-selective switches developed in the 1980s. Micromachined integrated optics further embed gratings alongside reflective mirrors and refractive microlenses on silicon substrates, enabling self-aligned free-space interconnects for parallel data transmission at rates up to 10 Gbps in the 1990s fiber optic era. These integrations leveraged periodic nanostructures for multifunctional performance, paving the way for scalable photonic circuits.^[123]^[124]^[125]

Emerging and Advanced Uses

Recent advancements in diffraction grating technology have enabled the development of miniaturized spectrometers suitable for portable devices, integrating on-chip gratings with CMOS sensors to achieve compact, high-resolution spectral analysis. For instance, diffractive speckle spectrometers fabricated on silicon chips have demonstrated channel densities up to 10021 channels per square millimeter, facilitating applications in environmental monitoring and medical diagnostics during the 2020s.^[126] These on-chip designs leverage computational reconstruction algorithms to enhance resolution, allowing for smartphone-compatible spectroscopy with resolutions exceeding 5 nm in the visible range.^[127] In lidar and sensing technologies, diffraction gratings support non-mechanical beam steering, particularly through liquid crystal (LC) configurations that enable dynamic control without moving parts. LC diffraction gratings have been shown to achieve steering angles of up to 30 degrees with response times under 1 ms, improving efficiency in automotive lidar systems for autonomous vehicles.^[128] Additionally, grating-coupled surface plasmon resonance (SPR) biosensors have advanced biomarker detection, with 2024 developments demonstrating sensitivities of 459 nm/RIU for real-time analysis of stress-related proteins like cortisol in portable formats.^[129] These gratings couple incident light to plasmons on metallic nanostructures, enabling label-free detection limits down to 1 pM for biomolecules.^[130] Quantum optics applications have incorporated diffraction gratings for precise control in entangled photon sources and wavepacket manipulation. Focusing grating couplers integrated into photonic chips have facilitated efficient generation of entangled photon pairs with fidelities above 90%, supporting quantum key distribution and sensing protocols.^[131] In nanoparticle studies from 2025, gratings have enabled controlled expansion of quantum wavepackets in levitated particles, achieving superposition states with displacements up to 100 nm while maintaining coherence times of several milliseconds.^[132] This approach uses optical potentials modulated by grating diffraction to probe gravitational effects on massive quantum systems. Metasurface-based flat gratings have revolutionized augmented reality (AR) and virtual reality (VR) holography by providing compact, high-efficiency beam shaping. Inverse-designed metasurface gratings have enabled full-color 3D holographic displays with field-of-view angles exceeding 50 degrees and efficiencies over 80% across RGB wavelengths.^[133] These structures also allow control of anomalous dispersion, where metasurface gratings manipulate group velocity dispersion to achieve broadband achromatic performance, reducing chromatic aberrations in AR waveguides by factors of 10 compared to traditional optics.^[134] The global diffraction grating market is projected to grow from $246 million in 2024 to $356 million by 2031, at a CAGR of 5.5%, driven by demand in photonics for telecommunications and automotive lidar applications.^[135] This expansion reflects increasing adoption in high-volume sectors, where gratings enable wavelength-division multiplexing in 5G/6G networks and precise ranging in solid-state lidar sensors.^[128]

Examples and Phenomena

Man-Made Examples

Compact discs (CDs), digital versatile discs (DVDs), and Blu-ray discs incorporate microscopic pits etched into their polycarbonate substrates, serving as reflection gratings with track spacings of approximately 1.6 μm for CDs, 0.74 μm for DVDs, and 0.32 μm for Blu-ray discs.^[136]^[137] These structures diffract incident white light into its spectral components, producing the characteristic iridescent rainbow patterns visible on the disc surfaces when tilted or illuminated.^[138] The nanoscale periodicity mimics a traditional ruled grating, enabling casual observation of diffraction phenomena in everyday consumer media.^[139] In electronic components, security holograms embedded in credit cards, passports, and anti-counterfeiting labels utilize holographic diffraction gratings to generate angle-dependent color shifts and three-dimensional images that resist replication.^[140] These gratings, often produced via interference lithography, exploit volume phase effects to create optically variable devices (OVDs) with high diffraction efficiency.^[141] Similarly, advanced diffractive barcodes employ nanostructured gratings to encode multidimensional data through unique diffraction patterns, enabling high-capacity tagging for authentication and tracking applications.^[142] Historically, Joseph von Fraunhofer pioneered man-made gratings in 1821 by constructing the first diffraction grating from 260 parallel wires stretched across a frame, which allowed precise measurement of solar spectral lines and laid the foundation for modern spectroscopy.^[143]^[144] Modern replicas of such wire gratings, along with mechanically ruled gratings produced on ruling engines, are used in laboratory demonstrations to illustrate groove precision and diffraction orders.^[145]^[146] Commercial products like handheld spectrometers frequently incorporate replicated volume phase holographic (VPH) gratings, which offer compact size, high efficiency up to 98% in the first diffraction order, and broad wavelength coverage for portable spectral analysis in field environments.^[147]^[148] Laser line generators also rely on diffraction gratings to fan out a laser beam into a straight, uniform line with controlled divergence, essential for alignment, profiling, and machine vision tasks.^[149] For educational and demonstration purposes, rainbow glasses equipped with fine holographic diffraction gratings (typically 1000 lines/mm) disperse white light from stage lights or fireworks into visible spectra, creating rainbow effects; these inexpensive tools are popular at concerts and public events to engage audiences with optical principles.^[150]^[151] Such replicated gratings, derived from holographic mastering, highlight the scalability of production techniques for accessible optics education.^[140]

Natural Diffraction Gratings

Natural diffraction gratings occur in various biological and inorganic structures, where periodic arrangements of materials at the nanoscale produce iridescent colors through light diffraction and interference, analogous to artificial gratings but arising without human design. These structures exploit the wave nature of light to selectively reflect specific wavelengths, creating vivid structural coloration that enhances camouflage, mating displays, or optical signaling in organisms.^[152] In biological systems, iridescent feathers of birds like the peacock (Pavo cristatus) serve as prominent examples, with their blue neck and breast feathers deriving color from intricate photonic crystal structures in the barbules composed of keratin nanostructures. These periodic arrangements of melanin rods and keratin layers act as diffraction elements, scattering light to produce angle-dependent hues without relying on pigments. Similarly, the wing scales of Morpho butterflies feature ridge-like gratings with spacings around 500 nm, equivalent to a groove density of approximately 2000 lines per millimeter, which diffract blue light efficiently to generate their characteristic metallic sheen through multilayer interference and diffraction.^[153]^[154]^[155]^[156] Inorganic natural gratings include opal gemstones, formed by closely packed silica spheres typically 150–400 nm in diameter, which create a three-dimensional photonic lattice responsible for their play-of-color. This lattice functions as a Bragg diffraction grating, selectively reflecting wavelengths based on the sphere spacing and viewing angle, resulting in iridescent flashes of red, blue, and green. Ice crystals in the atmosphere also exhibit diffraction effects; hexagonal plate crystals can produce circular diffraction patterns around light sources like the sun when rays strike at normal incidence, mimicking a simple grating through their ordered molecular structure.^[157]^[158]^[159] The study of these natural gratings has illuminated their role in evolutionary optics, where such structures have persisted for over 500 million years, evolving to optimize light manipulation for survival advantages like visual signaling. In Morpho butterflies, for instance, the precise nanoscale periodicity enhances color purity and directionality, demonstrating biological adaptation that rivals the efficiency of engineered blazed gratings in concentrating light into specific orders, though achieved through self-assembly rather than mechanical ruling. These phenomena underscore how nature harnesses diffraction principles to produce adaptive, non-pigment-based coloration across diverse taxa and materials.^[160]^[161]

References

[1]
Diffraction Gratings – University Physics Volume 3 - UCF Pressbooks
A diffraction grating consists of a large number of evenly spaced parallel slits that produce an interference pattern similar to but sharper than that of a ...Missing: definition | Show results with:definition
[2]
27.4 Multiple Slit Diffraction – College Physics
A diffraction grating is a large number of evenly spaced parallel slits. (a) Light passing through is diffracted in a pattern similar to a double slit, with ...
[3]
Diffraction Grating - SMU Physics
A diffraction grating is made by making many parallel scratches on the surface of a flat piece of transparent material.
[4]
[PDF] A Brief Introduction to Diffraction Gratings
The m-th order principle maxima (bright fringes) from each wavelength appear at angles d sin θm,i = mλi. With the small-angle approximation, θm,i ≈ mλi/d and ...
[5]
[PDF] A Brief History of Gratings and the Making of the MIT Nanoruler Carl ...
Mar 11, 2004 · It was not until 1813 that the German physicist Joseph von Fraunhofer (1787-1826) reinvented the diffraction grating. A master instrument maker, ...
[6]
[PDF] Diffraction Gratings for High-Intensity Laser Applications - OSTI
Feb 7, 2008 · Since the advent of coherent light sources (lasers) in the 1960's, applications of diffraction gratings in spectroscopy have further exploded.
[7]
What Is Diffraction Gratings & Diffraction Uses- Oxford Instruments
A diffraction grating is an optical element, which separates (disperses) polychromatic light into its constituent wavelengths (colors).
[8]
Diffraction Grating Physics - Newport
This is more commonly reported as the groove density (G), which is the reciprocal of dG, e.g., typical gratings have G values between 30 and 5000 grooves per mm ...
[9]
https://www.edmundoptics.com/knowledge-center/application-notes/optics/all-about-diffraction-gratings/
[10]
Diffraction Gratings Tutorial - Thorlabs
Sep 1, 2022 · Diffraction gratings, either transmissive or reflective, can separate different wavelengths of light using a repetitive structure embedded within the grating.
[11]
Diffraction Gratings - Omega Optical
Typical holographic diffraction gratings are produced on soda lime and fused silica glass substrates from high quality holographic master gratings and are ...
[12]
This Month in Physics History | American Physical Society
In 1821, a German physicist named Joseph von Fraunhofer built a very similar device. However, these early attempts at building diffraction gratings were rough, ...
[13]
The Production of Diffraction Gratings I. Development of the Ruling Art
Father of the modern diffraction grating was H. A. Rowland,[5] who within two years of accepting the challenge of grating ruling had produced gratings of 6-in. ...
[14]
Huygens–Fresnel Principle
We can determine the diffraction pattern that appears on the projection screen by using a more accurate version of Huygen's principle known as the Hugyens– ...
[15]
[PDF] Fresnel Diffraction - Waves & Oscillations
Huygens-Fresnel Principle The secondary spherical waves are preferentially emitted in the forward direction. Fresnel presented a very different way of thinking ...
[16]
[PDF] Huygens principle; young interferometer; Fresnel diffraction
The intensity of plane and spherical waves, observed on a screen, is very similar so they cannot be reliably discriminated.
[17]
Multiple Slit Diffraction - HyperPhysics
The multiple slit interference typically involves smaller spatial dimensions, and therefore produces light and dark bands superimposed upon the single slit ...
[18]
[PDF] Diffraction and Interference
OBJECTIVES: 1) Observe Fraunhofer diffraction and interference from a single slit, double-slit and multiple-slit (a diffraction grating).
[19]
[PDF] Chapter 5: Diffraction
The grating equation: The previous discussion showed that an incoming plane perpendicular to the grating results in one plane wave angled up at an angle ...
[20]
Lecture 27 - UW-Stevens Point
Red light has a longer wavelength than blue, and the separation between adjacent maxima in the diffraction pattern is linearly dependent upon the wavelength.
[21]
[PDF] Physics 1CL · WAVE OPTICS: INTERFERENCE AND DIFFRACTION
In this experiment, light from a laser source is incident on a double slit so that each slit behaves as a coherent source resulting in an interference pattern ...
[22]
Lecture 29
The angular separation between wavelengths is proportional to the wavelength divided by the separation d between adjacent lines. Therefore the smaller d ...
[23]
Dispersion, Diffraction and Diffraction Gratings - Physics
Aug 1, 2000 · Light of different colors (ie, wavelengths) travels at different speeds in a particular material, so they will be refracted through slightly different angles ...Missing: separation | Show results with:separation
[24]
Diffraction -- from Eric Weisstein's World of Physics - ScienceWorld
Born, M. and Wolf, E. "Elements of the Theory of Diffraction" and "Rigorous Diffraction Theory." Chs. 8 and 11 in Principles of Optics: Electromagnetic ...<|separator|>
[25]
https://www.spiedigitallibrary.org/ebook/Download?urlid=10.1117%2F3.527861.ch2&isFullBook=False
[26]
[PDF] E. Popov: Introduction to Diffraction Gratings - Institut Fresnel
Classical diffraction theories show that the spectral resolution is proportional to the number of grooves illuminated by the incident beam, and inversely ...
[27]
Diffraction Orders - Newport
Diffraction orders are values of integers (m) that satisfy the grating equation, where path differences are multiples of the wavelength. Only orders where |mλ/ ...
[28]
[PDF] Diffraction Grating Handbook
The theoretical resolving power of a planar diffraction grating is given in elementary optics textbooks as. R = mN,. (2-18) where m is the diffraction order ...
[29]
https://www.newport.com/n/the-grating-equation
[30]
Diffraction Gratings - RP Photonics
They are typically made with a relatively low groove density, used with a high angle of incidence, and high diffraction orders are utilized to obtain increased ...Missing: key | Show results with:key
[31]
Diffraction Grating Efficiency - Newport
... grating efficiency (for reflection gratings) is the blaze condition. mλ= 2dsinθB (2-30). where θB (often called the blaze angle of the grating) is the angle ...
[32]
Surface Relief Grating on Chitosan-N,N-dimethyl-4-(2-pyridylazo ...
Feb 18, 2022 · A surface relief grating (SRG) is defined as a two-dimensional and periodic structure on the material surface that has dimensions of the ...
[33]
Introduction to Diffraction Gratings: Summary of Applications
According to the well-known grating equations, 46 the angles between the zero order and higher order diffraction beams decrease with increasing frequency.Missing: definition | Show results with:definition
[34]
Diffraction analysis of dielectric surface-relief gratings
Diffraction by a dielectric surface-relief grating is analyzed using rigorous coupled-wave theory. The analysis applies to arbitrary grating profiles, groove ...
[35]
Surface Relief Gratings (RIBE) - scia Systems
One type is the so called Surface Relief Grating (SRG). Within this group the gratings are divided into blazed gratings, slanted gratings, binary gratings and ...
[36]
Diffraction gratings: from principles to applications in high-intensity ...
Diffraction gratings were discovered during the 18th century, and they are now widely used in spectrometry analysis, with outstanding achievements spanning ...
[37]
Diffraction Gratings: Selection Guidelines | Optics - Photonics Spectra
The usual material is copper due to its high thermal conductivity. Transmission grating substrates must be matched to the spectral range of the application so ...
[38]
Diffraction on a surface-relief grating: mechanisms and interpretation
This contribution concentrates on theoretical studies of diffraction processes in surface-relief gratings. The characterization of diffraction processes and ...
[39]
Understanding diffraction grating behavior: including conical ...
Aug 28, 2019 · Joseph von Fraunhofer began his detailed study of diffraction gratings about 1821. He built the first ruling engine for fabricating ...Missing: history | Show results with:history
[40]
Volume Bragg Gratings - RP Photonics
Volume Bragg gratings (also called volume holographic gratings) are Bragg gratings which are written inside some transparent material, eg in the form of a cube ...
[41]
Study on the Design Method of High-Resolution Volume-Phase ...
Oct 9, 2024 · In contrast, volume-phase holographic gratings (VPHGs) can improve the performance of spectrometers while significantly reducing the size and ...
[42]
Understanding Diffraction in Volume Gratings and Holograms
Kogelnik's Coupled wave theory [1], published in 1969, has provided an extremely successful approach to understanding diffraction in sinusoidal volume gratings.
[43]
Volume Phase Holographic Gratings: Polarization Properties and ...
An in- strument that exploits the advantages of VPH gratings can, in principle, greatly reduce systematic error in the detected signal. VPH gratings are ...Missing: fabrication | Show results with:fabrication
[44]
[PDF] Volume-phase holographic gratings and their potential for ...
Volume-phase gratings use Bragg diffraction in a thin layer with modulated refractive index, offering high efficiency, large sizes, and high dispersion.
[45]
Dichromated gelatin for the fabrication of holographic optical elements
Hardened dichromated gelatin is the best material available today for the fabrication of holographic optical elements (HOEs) because of its low scattering, ...
[46]
[PDF] Fabrication and testing of large area VPH gratings
Large area volume phase holographic (VPH) gratings have been made for use in spectrographs attached to large telescopes and for scanning LIDAR systems. Examples ...
[47]
Advantages of VPH Gratings - Wasatch Photonics
Click here to learn the top 10 advantages of VPH Gratings, from superior efficiency to Low Polarization Sensitivity, durability, flexibility, ...Missing: principles | Show results with:principles
[48]
Advantages of volume phase holographic gratings
Mar 25, 2021 · With benefits ranging from superior optical performance and design flexibility to robustness and consistency, VPH gratings are ideal for ...Missing: principles | Show results with:principles
[49]
(PDF) Performances of volume phase holographic grating for space ...
The special properties of volume phase holographic gratings make them promising candidates for spectrometry applications where high spectral resolution, ...
[50]
Spectral multiplexing using stacked volume-phase holographic ...
... holographic films, used to fabricate common volume-phase holographic gratings (VPHGs). Thanks to the various advantages made available by these materials in ...
[51]
Development of a large mosaic volume phase holographic (VPH ...
A step-and-repeat exposure method was chosen to fabricate a three-segment mosaic on a 305 mm × 508 mm monolithic fused-silica substrate. Specification ...
[52]
Advantages of VPH Transmission Gratings
Oct 20, 2020 · VPH gratings' advantages range from design flexibility and superior optical performance to consistency and robustness.Missing: fabrication | Show results with:fabrication
[53]
Blazed Gratings | Ossila
Blazed diffraction gratings will maximize the grating efficiency in one desired diffraction order at a specific wavelength, while other orders are minimized.
[54]
Build to Order Echelle Diffraction Gratings - Newport
An echelle is coarse with fewer grooves per millimeter and is used at high angles in high diffraction orders.
[55]
Astronomical near-infrared echelle gratings - SPIE Digital Library
High-resolution near-infrared echelle spectrographs require coarse rulings in order to match the free spectral range to the detector size.
[56]
Echelle Grating Spectroscopic Technology for High-Resolution and ...
Oct 31, 2022 · The echelle is a kind of grating whose property is between the echelette and the echelon. It is coarsely ruled with large blaze angles and low ...Missing: coarse | Show results with:coarse
[57]
Diffraction Grating Selection Guide - Newport
The situation can be improved somewhat by using toroidal grating substrates; however, their use is restricted because of high costs. Though most ruled gratings ...
[58]
Near-IR Ruled Reflective Diffraction Gratings - Thorlabs
Near-IR Ruled Reflective Diffraction Gratings · Gratings with 750 nm to 1600 nm Blaze Wavelengths · High Grating Efficiency of 60 to 80% at the Blaze Wavelength.
[59]
3. Grating Grooves : SHIMADZU CORPORATION
Blaze Wavelength. Gratings with grooves that have a sawtooth profile (blazed gratings) exhibit a high diffraction efficiency for certain orders and wavelengths.Missing: formula | Show results with:formula
[60]
Electrically Tunable Liquid Crystal Phase Grating with Double ...
Aug 10, 2023 · A tunable liquid crystal (LC) phase grating based on vertical-field in-plane electrical switching (VIS) is proposed.
[61]
Advances in diffractive liquid crystal grating devices using patterned ...
Diffractive LC grating devices can be produced through methods such as photo alignment, using polymer walls, or employing patterned electrodes.
[62]
https://www.tandfonline.com/doi/full/10.1080/15980316.2024.2343294
[63]
Extraordinary terahertz transmission and field enhancement via ...
Nov 5, 2024 · In this paper, we propose a composite aperture THz metasurface to enhance the hybrid coupling of a surface plasmon. By introducing bow-tie ...
[64]
Plasmonics for microwave photonics in the THz range - Frontiers
Apr 12, 2023 · This paper overviews recent achievements on plasmonic-based modulators displaying characteristics of speed, efficiency and linearity<|separator|>
[65]
Electromagnetic metagratings for diffraction fields manipulation
Sep 22, 2025 · Adjusting the tilt allows for effective suppression of the −1 and 0 diffraction orders, leading to efficient large-angle anomalous refraction, ...
[66]
https://pubs.aip.org/aip/jap/article/138/12/120701/3364203/Electromagnetic-metagratings-for-diffraction
[67]
Ruled Diffraction Gratings - Newport
The first diffraction gratings made for commercial use were mechanically ruled, manufactured by burnishing grooves individually with a diamond tool.
[68]
[PDF] Introduction to Diffraction Grating - Thorlabs
A ruled grating is produced by physically forming grooves on a reflective surface by using a diamond tool mounted on a ruling engine. The distance between ...
[69]
Buyer's Guide to Diffraction Grating - Optometrics
Under this condition (in 1st order), the grating equation reduces to λ = 2d(sin i). This is the equation used to calculate the 1st order blaze angle for a ...
[70]
Interferometrically Controlled Ruling of Ten-Inch Diffraction Gratings*
More then one-hundred test plane gratings have now been ruled on the large M.I.T. engine with interferometric control, as part of a program begun in 1948.Missing: modern | Show results with:modern<|control11|><|separator|>
[71]
[PDF] 22-009- 167 techniques for ruling improved large diffraction gratings
Development of the B engine (1961 - 1970) resulted in the ruling of echelles of unparalleled size and quality. These were successfully ruled with spacings of 3 ...<|control11|><|separator|>
[72]
Design and construction of a large grating ruling engine
The periodic error in the groove spacing of a master grating is required to be less than 1 nm and many applications require the grating to be fabricated over an ...
[73]
Volume Phase Holographic (VPH) Gratings in Astronomy
VPH gratings are used in astronomy due to high diffraction efficiencies, caused by a near-sinusoidal refractive index variation, and are used in transmission.<|control11|><|separator|>
[74]
Simplified dichromated gelatin hologram recording process
In this paper we describe a simplified method for making highly efficient DCG HOEs. Beginning with a silver halide film plate, the complete process including ...
[75]
Dichromated Gelatin in Optics - PMC - PubMed Central
Apr 17, 2025 · Characterization of two ultraviolet–blue volume-phase holographic gratings based on dichromated gelatin and photopolymer recording materials.
[76]
(PDF) Fabrication reflection holographic grating - ResearchGate
Mar 23, 2019 · In this work we fabrication a reflection holographic grating by using dichromated gelatin, To perform that we have to use the Nd-yaG laser ...
[77]
Photopolymer materials for volume phase holographic optical ...
Sep 25, 2017 · Volume Phase Holographic Gratings (VPHGs) cover a relevant position as dispersing elements in spectrographic instrumentations with low and ...Missing: VPH | Show results with:VPH
[78]
Technologies for Fabricating Large-Size Diffraction Gratings - PMC
This paper reviews the fabrication technologies for large diffraction gratings, including grating tiling technology, grating ruling technology, single-exposure ...Missing: historical | Show results with:historical
[79]
Technologies for Fabricating Large Aperture Diffraction Gratings
Dec 25, 2024 · The principle of electron beam lithography (EBL) is to use an extremely small-aperture electron beam to draw a grating pattern on the ...
[80]
(PDF) Fabrication of sawtooth diffraction gratings using nanoimprint ...
Aug 6, 2025 · We report a process which integrates interference lithography, nanoimprint lithography, and anisotropic etching to fabricate replicated ...
[81]
Large-area patterning using interference and nanoimprint lithography
Jul 19, 2016 · We are working on interference lithography (IL) and nanoimprint lithography (NIL) as a means to an industrially feasible technology for pattern replication.
[82]
Holographic Diffraction Gratings - Newport
Holographic gratings are made by recording a stationary interference fringe field using photoresist, which is then developed to create a surface relief pattern.Missing: DCG VPH
[83]
Volume 12188 - SPIE Digital Library
... single exposure, by projecting two diffraction orders on the detector. The VPHG is optimized in both first and second orders and a combination of two prisms ...
[84]
MEMS Tunable Diffraction Grating for Spaceborne Imaging ... - MDPI
We have designed, modeled, fabricated and tested a silicon based pitch tunable diffraction grating (PTG) with relatively large resolving power.
[85]
The Diffraction Grating Replication Process - Newport
The process involves using a casting method, submaster selection, transfer coating, resin cementing, and separation to replicate the grating.
[86]
Research on manufacturing technology of nanoimprinted grating
Dec 12, 2024 · This article reviews the recent advancements in nanoimprinting for grating preparation both domestically and internationally.
[87]
Development of diffraction binary grating using hot embossing ...
Aug 7, 2025 · As a test we have developed of checker-board diffraction grating using the hot embossing process. The nickel (Ni) shim fabricated using low-cost ...
[88]
[PDF] Reactive Ion Beam Etching of Large Diffraction Gratings
AbStrACt. Large area Multilayer Dielectric (MLD) diffraction gratings are essential components for temporal pulse compression in high energy laser systems.Missing: replication embossing
[89]
History and construction of large mosaic diffraction gratings - ADS
Today's large aperture telescopes have created a demand for diffraction gratings that are larger than the capabilities of the largest ruling engines.
[90]
Ruled Diffraction Gratings - OPCO Laboratory
Ruled diffraction gratings separate light into different wavelengths using evenly spaced parallel slits, creating a clear separation between wavelengths.
[91]
Zoned blaze broadband gratings mosaicked using a device made ...
Feb 25, 2025 · A highly stable mosaicking-error-adjustment device made of special materials is designed, and a grating is fabricated.
[92]
Modelling of Tiled Grating Arrangement Efficiency - MDPI
The simulation results presented in this study provide a foundation for defining practical alignment strategies and tolerances in the assembly of tiled grating ...
[93]
1. Introduction to Diffraction Gratings - Shimadzu
A diffraction grating is an optical element that divides(disperses) light composed of lots of different wavelengths(e.g., white light) into light components by ...Missing: sorting spectroscopy throughput
[94]
Spectrometer Configurations: Littrow, Czerny-Turner and More | Ossila
In Czerny-Turner configurations, the mirrors do not have to be the same size or placed the same distance from the slits or the diffraction grating.
[95]
Advanced Spectrometer Optics and Design - Avantier Inc.
The Czerny-Turner design, featuring toroidal mirrors and diffraction gratings, enables asymmetrical optimization for reduced aberrations. Performance specs such ...<|separator|>
[96]
Overview of Echelle Spectograph Flexible Spectroscopy Tool
Echelle Systems: Application Given their ability to capture large bandpass spectral coverage of ~750 nm and simultaneously provide high resolution of 0.04 nm ( ...<|control11|><|separator|>
[97]
Cross-Dispersed Echelle Spectrograph - McDonald Observatory
Two-pixel resolving powers in its two modes of operation are 60,000 (TS23) and up to 240,000 (TS21). Two echelle gratings offer minimum inter-order separations ...
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spectrographs - dispersion and spectral resolution - vik dhillon
The diffraction-limited spectral resolution (or simply limiting resolution) of a spectrograph is then given by, R = Nn, where N is the total number of lines ...
[99]
Understanding slit width, grating, and optical principles in ...
Jun 19, 2025 · A wider slit increases light throughput, making your measurements brighter, but it can blur the details and reduce spectral resolution. Studies ...Missing: sorting | Show results with:sorting
[100]
How To Optimize Spectrometer Light Throughput
Diffraction grating efficiency peaks at a single wavelength (the blaze ... For line emission spectra: Light throughput increases linearly with slit width.Missing: sorting spectroscopy
[101]
A Timeline of Atomic Spectroscopy
Oct 1, 2006 · This timeline provides a short history of the experimental and theoretical development of atomic spectroscopy for elemental spectrochemical analysis.
[102]
The Era of Classical Spectroscopy - MIT
With a prism, the angle at which a spectral line is dispersed depends on the type of glass used. This makes it difficult to compare different spectral ...
[103]
The Johns Hopkins University and Diffraction Gratings
“This combined prism-grating spectrometer was first assembled for the use of Sleator and Imes, Sleator for water vapor, Imes for the halogen acid gases. Their ...
[104]
Optimum order sorting filters for spectrometers - Delta Optical Thin Film
Learn why a Continuously Variable Order Sorting Filter is the ideal solution for blocking all higher orders in your wideband spectrometer.Missing: efficiency throughput
[105]
Continuously tunable pulsed Ti:Sa laser self-seeded by an extended ...
By coupling the grating cavity oscillation into the power oscillator, a power-enhanced narrow-linewidth laser oscillation is achieved. Compared to the classic ...
[106]
Low-threshold, single-frequency, coupled cavity Ti:sapphire laser
Coarse wavelength tuning was achieved by rotation of the grating, and the fourth diffraction order escaping the cavity was designated as the laser output.
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[PDF] Titanium-Doped Sapphire Laser
Output power could be maximized by first tuning the etalon for maximum output and then tuning the main laser cavity. ... Littrow-mounted grating as the tuning ...
[108]
Single-mode tunable Ti:sapphire laser over a wide frequency range
The continuous, single-mode tuning is achieved by a pseudoexternal cavity consisting of highly reflective mirrors and a diffraction grating. The advantages ...<|control11|><|separator|>
[109]
[PDF] metrologia - National Institute of Standards and Technology
The first-order diffraction off this grating contains roughly 95 % of the power and is coupled back into the laser, while the zeroth-order reflection is used ...
[110]
Pulse compression and beam focusing with segmented diffraction ...
Pulse compression and beam focusing with segmented diffraction gratings in a high-power chirped-pulse amplification glass laser system.
[111]
[PDF] Fabrication and Applications of Large Aperture Diffractive Optics
Feb 19, 2002 · Laboratory [2] used 94-cm diameter diffraction gratings for pulse compression. These were submicron-pitch, holographically ruled plane gratings.
[112]
Array generation with multilevel phase gratings
Our method for array generation is based on Fraunhofer diffraction. An optical setup as is shown in Fig. 1 is used. A collimated laser beam strikes the grating ...
[113]
Design and optimization of a high-efficiency array generator in the ...
The goal is to calculate a binary subwavelength grating able to split, with a good diffraction efficiency, one incident beam into N = 7 coplanar beams of equal ...
[114]
Highly efficient multicolor multifocus microscopy by optimal design of ...
Jul 13, 2017 · We report the design and fabrication of a binary array generator of 3 × 3 equal-intensity diffraction orders with 74% efficiency, 95% uniformity and dual color ...
[115]
An arrayed waveguide grating (AWG) for DWDM/CWDM application ...
Arrayed waveguide grating (AWG) multiplexer is a key element for wavelength division multiplexing (WDM) systems in optical telecommunication. This paper ...
[116]
Low-loss Si 3 N 4 arrayed-waveguide grating (de)multiplexer using ...
A 16-channel 200GHz arrayed-waveguide grating (AWG) (de)-multiplexer ... (WDM) has been used widely in many applications, including optical communications.Missing: telecommunications | Show results with:telecommunications
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[PDF] design and simulation of novel arrayed waveguide grating
Arrayed waveguide grating (AWG) is playing an increasingly important role in dense wavelength division multiplexing (DWDM) system. The regular AWG device ...
[118]
Controlling the sign of chromatic dispersion in diffractive optics with ...
Diffraction gratings disperse light in a rainbow of colors with the opposite order than refractive prisms, a phenomenon known as negative dispersion.
[119]
Controlling the sign of chromatic dispersion in diffractive optics with ...
Diffraction gratings disperse light in a rainbow of colors with the opposite order than refractive prisms, a phenomenon known as negative dispersion.
[120]
Computational imaging using lightweight diffractive-refractive optics
In this article, we jointly design lightweight diffractive-refractive optics and post-processing algorithms to enable imaging under white light illumination.
[121]
Demonstration of a PDMS based hybrid grating and Fresnel lens (G ...
Fiber optics ... Here we explore planar diffractive optical elements that integrate the functions of lenses (or concave mirrors) and diffraction gratings.
[122]
[PDF] Micromachined integrated optics for free-space interconnections
mirrors and diffraction gratings, beam splitters, lens mount. Self-aligned hybrid integration of active optical devices with MOB is also realized using ...
[123]
[PDF] Integrated Optics Components and Devices Using Periodic Structures
Abstract-The selected research activities on integrated optics com- ponents and devices using periodic structures are reviewed, with em-.
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Scalable on-chip diffractive speckle spectrometer with high spectral ...
Mar 20, 2025 · The on-chip diffractive spectrometer has a benchmark channel density of up to 10021 ch/mm 2 , which compares favorably against other state-of-art waveguide ...
[125]
Ultra-simplified diffraction-based computational spectrometer - Nature
Jan 5, 2024 · We propose an ultra-simplified computational spectrometer that employs a one-to-broadband diffraction decomposition strategy facilitated by a numerical ...Results · Schematic Of... · Experimental Validation<|control11|><|separator|>
[126]
Advancements in Diffraction Grating Aim to Change the Rules
Trends toward smaller spectrometers and nonmechanical lidar are calling for new dispersive elements with denser lines and designs. By Hank HoganMissing: 2024-2025 | Show results with:2024-2025
[127]
High-performance portable grating-based surface plasmon ...
May 1, 2024 · A miniaturized grating-coupled biosensor with a sensitivity of 459 nm/RIU was used to analyze thrombin [23]. Guner et al. demonstrated a ...Fig. 1. · Fig. 2. · Fig. 4. · Fig. 5.
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Recent Advances in Grating Coupled Surface Plasmon Resonance ...
Sep 14, 2024 · This work evaluates the technical aspects influencing the performance of GC-SPR and reviews recent progress in the fabrication of such platforms ...
[129]
Focusing grating coupler for the generation of quantum sensors
Jul 2, 2025 · This periodic modulation of the refractive index creates a diffraction grating that enables phase-matching between the optical mode propagating ...
[130]
Physicists demonstrate controlled expansion of quantum ... - Phys.org
Sep 9, 2025 · The primary objective of the team's recent study was to try to increase a nanoparticle's quantum wavepacket of motion. If they could ...
[131]
Full-colour 3D holographic augmented-reality displays with ... - Nature
May 8, 2024 · Here we introduce a holographic AR system that overcomes these challenges using a unique combination of inverse-designed full-colour metasurface gratings.
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An achromatic metasurface waveguide for augmented reality displays
Feb 25, 2025 · This unique achromatic metasurface waveguide technology is expected to advance the development of visually compelling experience in compact AR display systems.
[133]
Global Diffraction Gratings Market Research Report 2025
Diffraction Gratings Market was US$ 246 million in year and is expected to reach US$ 356 million by 2031, at a CAGR of 5.5% during the years 2025 - 2031.
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[PDF] Physical Optics
A diffraction grating can separate white light into individual wavelengths. This is why diffraction gratings, CDs, DVDs, and Blu-‐ray discs all appear to ...
[135]
Lesson 5: Spectra - Clackamas Community College
... diffraction grating ... rainbow effect of the surface. Today the most common examples of this effect are music CD's, video DVD's, and computer CD-ROM disks.Missing: Blu- | Show results with:Blu-
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Principles of Interference | Nikon's MicroscopyU
The very close spacing of these tracks mimics the ultra-fine lines present on a diffraction grating to produce a spectacular rainbow-like effect of color when ...Missing: DVD Blu-
[137]
[PDF] Seeing Color with CD's - LIGO Caltech
In fact, they are so close together that they act as a diffraction grating for light. The reflections will interfere with each other constructively and ...Missing: DVD Blu- ray
[138]
Karl Fey's Holography Page - Stony Brook University
Holographic diffraction gratings are cheaper and easier to produce than other kinds. Security Holograms are difficult to duplicate. Some credit cards have ...
[139]
Computer-generated holograms and diffraction gratings in optical ...
CGHs are able to form 2D and 3D images. Optically, variable devices (OVDs) composed of diffractive gratings are often used in security applications. There are ...
[140]
High capacity tagging using nanostructured diffraction barcodes
Feb 20, 2006 · We describe a new non-contact high capacity optical tagging technique based on the use of nanostructured barcodes.
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Joseph von Fraunhofer (1787–1826) | High Altitude Observatory
Well versed in the mathematical wave theory of light, Fraunhofer used his diffraction grating to actually measure the wavelength of specific colors and dark ...
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Science, Optics and You - Timeline - Joseph von Fraunhofer
Nov 13, 2015 · Von Fraunhofer is also renowned for building the first diffraction grating, made up of 260 close parallel wires, in 1821. The rudimentary ...
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[PDF] N94-1 , 332
Joseph von Fraunhofer independently invented the diffraction grating in 1821 and used it to look at the sun's spectrum. He derived and verified the grating.
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[PDF] DIFFRACTION GRATING HANDBOOK - Joseph A DiVerdi
All light that reaches the detector of a grating-based instrument from anywhere other than the grating, by any means other than diffraction as governed by ...
[145]
[PDF] IMPROVING EFFICIENCY OF DIFFRACTION GRATINGS FOR HIGH ...
May 21, 2024 · The diffraction efficiency of the pulse compression gratings (PCGs) has a huge impact on your laser performances in terms of efficiency and beam ...Missing: index 2024-2025
[146]
A Comprehensive Framework for the Development of a Compact ...
Jun 10, 2025 · Additionally, compared to traditional diffraction gratings, VPH grisms deliver higher diffraction efficiency across a broad wavelength range ...
[147]
https://science.osti.gov/-/media/sbir/pdf/Application_Resources/2024/CPE---ARDAP-Diffraction-Gratings-for-HEP-Public-May-2024.pdf
[148]
Maryland Day 2025 | The Institute for Research in Electronics and ...
Apr 26, 2025 · Diffraction "grating" rainbow discs Looking out the window normally. The same scene using diffraction "grating" rainbow glasses or disc.
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[PDF] Diffraction grating experiments - Purdue Physics
The diffraction glasses are holographic diffraction gratings. Diffraction gratings are made of many fine transparent vertical stripes (1,000 lines/mm), or ...
[150]
Structural colors in nature: the role of regularity and irregularity in the ...
In this Review, we first explain the fundamental optical properties underlying the structural colors, and then survey these mysteries of nature.
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Reflections on iridescent neck and breast feathers of the peacock ...
Dec 14, 2018 · The blue neck and breast feathers of the peacock are structurally coloured due to an intricate photonic crystal structure in the barbules.
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Wrinkle nanostructures generate a novel form of blue structural color ...
Jan 20, 2023 · Currently known structural colors in feathers are caused by light scattering from periodic or amorphous arrangements of keratin, melanin, and ...
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Theoretical and experimental analysis of the structural pattern ...
Morpho butterflies' iridescence comes from alternating lamellae layers, a "Christmas tree" shape, and offsets between ridges in their wing scales.
[154]
Unique wing scale photonics of male Rajah Brooke's birdwing ...
Aug 12, 2016 · The diffraction pattern's first order for 500 nm light was ~45 ... Quantified interference and diffraction in single Morpho butterfly scales.<|separator|>
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Light diffraction from opal-based photonic crystals with growth ...
May 23, 2006 · We report on a comprehensive experimental and theoretical study of light diffraction from synthetic opals. A general theory of coherent ...
[156]
The 'fire' of opals - Europhysics News
tals, Bragg diffraction of visible light by opals is governed by the spacing between the layers of the silica spheres which corresponds to their sizes. To ...<|separator|>
[157]
Note on Reflection and Diffraction from Ice Crystals in the Sky
If the sun rays fall on the crystals at normal incidence, one would obtain a circular diffraction pattern.
[158]
Physics, Development, and Evolution of Structural Coloration
The structural colors of organisms are produced by the physical interactions of light with nanometer scale biological structures.
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[PDF] 515 million years of structural colour - Lifescaped
The array of structural colours found in animals today results from millions of years of evolution. Structures that produce metallic colours have also been ...