Optical glass

Abbe diagram. The notations are the names given by Schott to the different families of optical lenses.

The refractive index indicates the refractive power of a glass, i.e. its ability to deflect light rays to a greater or lesser extent. This deflection can be deduced from Descartes' law. The refractive index is a wavelength-dependent quantity, creating chromatic aberrations in a system by refracting rays more or less according to their wavelength: This is the phenomenon observed when light is decomposed by a prism. Several laws have approximated this relationship to wavelength, notably Cauchy's law and Sellmeier equation.

The refractive index of a glass is given for the yellow line known as the d line of helium (then noted n_d) or for the green e line of mercury (then noted n_e), depending on usage and the two main standards used.[9][10][11]

The dependence of refractive index on wavelength requires a measure of the glass's dispersion, i.e. the difference in deviation between two wavelengths. A highly dispersive glass will deflect short wavelengths to a great extent, but long wavelengths to a lesser extent. The measure of dispersion is the Abbe number, or constringence. The main dispersion is the difference nF-nC (helium lines) or nF'-nC' (cadmium lines), and constringencies for the same lines as the refractive index are deduced by ${\textstyle \nu _{d}={\frac {n_{d}-1}{n_{F}-n_{C}}}}$ and ${\textstyle \nu _{e}={\frac {n_{e}-1}{n_{F}'-n_{C}'}}}$. A high Abbe number means that the glass is not very dispersive, and vice versa.

Real and imaginary refractive indices for quartz or fused silica glass in the IR range.

Lenses are usually divided into two groups with the generic names of crown and flint, referring respectively to low-dispersion, low-index lenses and high-dispersion, high-index lenses. Typically, the distinction is made at around ν_d=50: lenses below this value are flints, the others are crowns.[9]

These two parameters alone are needed to differentiate between lenses: two lenses with equal n_d and ν_d are identical. Glasses are represented on the so-called Abbe diagram, a graph with abscissa nd and ordinate ν_d, where each glass is denoted by a point on the graph.

Oxide glasses fall into a range of n_d from 1.4 to 2.0 and ν_d from 20 to 90, with SiO₂ being the oxide glass with the highest contringency and lowest index. Fluoride glasses can go up to ν_d>100 and nd<1.4, BeF₂ being the fluoride glass at the highest constringency and lowest index. Chalcogenide glasses have indexes exceeding 2, a large proportion of which cannot be shown on an Abbe diagram due to their absorption in visible wavelengths preventing a relevant νd measurement. For optical materials that are opaque in the visible range, constringence is measured at longer wavelengths.[9]

This classification also has its limitations when it comes to active optical glasses (birefringence, acousto-optic effect, and non-linear effects), optical filters or graded-index lenses, so we restrict the term "classical optical glass" to the aforementioned glasses, i.e. those with limited index and dispersion, which can be described essentially by their dispersive behavior and refractive index.[13]

Another very important characteristic of optical glass is its absorption and transmission behaviour. The use to which the future lens will be put determines its behavior: filters that absorb in certain spectral bands, lenses that are highly transparent in the visible, ultraviolet or infrared, resistance to radiation.

As a general rule, the transmittance of the glass is given by the manufacturer, noted τ_i or T_i, a value that depends on the thickness of the material and whose measurement makes it possible to take into account the loss of transmission due to absorption and diffusion by internal defects in the glass. Since the transmittance term takes into account the refractive index via the Fresnel coefficient${\textstyle {\frac {2n}{n^{2}+1}}}$, it is also dependent on the wavelength and thickness of the sample via the formula ${\displaystyle \tau _{2}=\tau _{1}^{\frac {d_{1}}{d_{2}}}}$where ${\displaystyle \tau }$ is the transmittance and ${\displaystyle d}$ thickness.

Transmittance windows are of particular interest when it comes to choosing the right glass for applications such as far-infrared or far-ultraviolet. These windows are the result of the absorption of the materials making up the glass, which increases in the infrared and ultraviolet. Absorption in these two wavelength ranges is due to distinct phenomena, and can evolve differently depending on environmental conditions.

In the ultraviolet, or UV, the drop in transmission is due to the electronic transitions of the elements making up the glass: valence electrons absorb wavelengths whose energy corresponds to their band gap. According to solid-state band theory, electrons can only take on certain specific energy values in particular energy levels, but with sufficient energy, an electron can move from one of these levels to another. Light waves are charged with an energy hν, inversely proportional to wavelength (ν=c/λ), which can enable an electron to pass from one level to another if this energy is sufficient and therefore if the wavelength is short enough. A silica glass absorbs wavelengths below 160 nm, a glass based on boron trioxide (B₂O₃) absorbs below 172 nm, a phosphorus pentoxide glass (P₂O₅) absorbs below 145 nm.

Given the chemical structure of glassy silica, the proportion of non-bridging oxygen will determine its ultraviolet transmission.

There are two types of oxygen in oxide glasses: bridging and non-bridging (possessing an excess electron charge), detectable by photoelectron spectroscopy. Non-bridging oxygen possesses electrons whose kinetic energy after release by monochromatic X-rays is higher than that of bridging oxygen. Bonds between non-bridging oxygens and cations are generally ionic. These characteristics give the glass its energetic band properties, making it more or less effective at transmitting radiation.[14] Depending on the intensity of the bonds with the cations in the glass, the transmission window varies: in the presence of alkali metals, electrons can move from one band to the other more easily, as they are less bound to the non-bridging oxygens. On the other hand, the introduction of aluminium (Al₂O₃) to replace silica will increase the glass's transmission window, as the tetrahedral configuration of alumina reduces the proportion of non-contacting oxygens and therefore of electrons able to move from the valence band to the conduction band.[15]

As a result, glasses containing heavy metals (such as Ti⁺ or Pb²⁺) tend to transmit less well than others, since the oxygen will tend to share its electrons with the cation and thus reduce the band gap. The disadvantage is that the addition of these metals results in higher refractive indices.[15] Depending on the heavy metal used, the drop in UV transmission will be more or less rapid, so lead lenses transmit better than niobium or titanium lenses. Attention to crucible and furnace materials is therefore very important, as these can also influence the UV transmission window. Platinum, for example, is widely used in glass melting, but inclusions of platinum particles in the glass paste can cause undesirable transmission losses due to impurities.[16]

Another source of variation in UV transmission loss is ambient temperature: the higher the temperature of the glass, the more the UV drop will shift towards longer wavelengths, due to the material's reduced band gap.[16]

Solarization, which is the exposure of glass (or paint, for that matter) to electromagnetic radiation, can "yellow" glass[nb 2] depending on the wavelength and intensity of the radiation. Lenses with the best UV transmission are the most affected by solarization, which modifies their transmission window. Lenses can be doped with cerium dioxide (C_eO₂), which shifts the transmission drop to longer wavelengths and stabilizes it. This doping is one of the processes used to create anti-radiation glasses, since a glass doped in this way has the particular ability to protect against the most energetic types of radiation, such as X-rays and gamma rays.[16]

In infrared, or IR, the physical phenomena leading to a drop in transmission are different. When a molecule receives a given amount of energy, it begins to vibrate in different modes: fundamental, first harmonic, second harmonic, etc., corresponding to periodic movements of the atoms in the molecule; each frequency associated with the energy of the molecule's vibration mode is absorbed.

In silica glass, the Si-O bond has two main modes of vibration, rotation and elongation. Since the frequency of elongation is 0.34 × 10¹⁴ Hz, absorption will take place at 8.8 µm (fundamental), 4.4 µm (harmonic 1), 2.9 µm (harmonic 2), etc. As the absorption due to this vibration is very strong, silica becomes opaque from the first harmonic onwards. Most quartz glasses even show a marked drop in transmission at harmonic 2.[15]

Chalcogenide glasses are used to reduce the frequency of molecular vibrations: as sulfur or selenium are heavier, their vibration modes are weaker, and their transmission is, therefore, better in the infrared. However, this comes at the price of visible transmission, since chalcogenide glasses are opaque in the visible. Another solution is to produce halide glasses, in particular fluoride glasses. As fluorine is highly electronegative, the bonds between anions and cations are weakened, and vibrations are therefore weaker.[15]

Glass humidity, i.e. the presence of water in the material, has a strong influence on the transmission curve of glasses in the 2.9 µm to 4.2 µm region. Water takes the form of OH^- groups, whose O-H bond vibrates at a frequency of around 90 THz, equivalent to an absorption of wavelengths from 2.9 µm to 3.6 µm. The higher the humidity of the sample, the greater the local drop in transmission, with very high humidity even causing absorption at the harmonics of the O-H bond vibration, at around 200 nm.[15]

Injecting an optical supercontinuum into an optical fiber

Lasers are often used at very high illuminance levels. It has been found that in this high illumination range, the refractive index follows a law that deviates from the linear domain and becomes proportional to the intensity of the luminous flux: ${\textstyle n(\lambda ,I)=n_{0}(\lambda )+\gamma I}$ where ${\textstyle n}$ is the refractive index of the material, ${\textstyle \lambda }$ the wavelength, ${\textstyle I}$ the intensity of the light beam, ${\textstyle n}$ the refractive index for low powers. For silica, for example, ${\displaystyle \gamma }$ is 3.2 × 10–20 m² W⁻¹ for ${\textstyle \lambda }$=1,060 nm. The most dispersive glasses tend to have the highest non-linear refractive indices, probably due to the metal ions present in the glass.

Above TW mm⁻², the fluence (or flux) is sufficient to create higher-order non-linear optical phenomena such as multiphonon absorption and avalanche photo-ionization. The first phenomenon makes the material absorbent through the addition of two photons, which release an electron. The second phenomenon is the acceleration of an electron released by the electromagnetic field, the electron's kinetic energy being transmitted to other neighboring electrons. These two combined effects can cause damage to glass by destroying the vitreous lattice (freed electrons give energy to other electrons which are more easily freed, and the lattice bonds are weakened by electron depletion). The material may be vaporized at sufficient speed that the phonons cannot transmit the energy in the form of heat to the rest of the glass.[17]

In 1988, an experiment showed that silica, whose lattice is isotropic, is capable of emitting green radiation when crossed by powerful infrared radiation. The generation of a second harmonic in this setting is atypical, but could be explained by the presence of F-center.[17]

Fluorescence can appear in optical glasses. Fluorescence is the re-emission of higher-wavelength radiation from an illuminated material. The energy of the incident light excites the material's electrons, which then de-excite and return to their ground state, emitting a photon with a longer wavelength than the original one. This phenomenon is particularly troublesome in applications where the presence of stray light or light of a different wavelength from the reference wavelength poses a problem. In lasers, for example, it's important to agree on a single, precise spectral line. Causes of fluorescence include rare-earth ions, impurities and color centers.[18]

Flints and crowns are glasses composed of oxides, often SiO₂ or TiO₂ titanates. Their index ranges from 1.4 to 2.4. This large group can be identified by its characteristic transmission profile ranging from 200 nm to 2.5 µm, due to the high gap energies and photon absorption peaks of hydroxyl groups in the infrared.

A variety of oxides are used, the most common being silica-based glasses, but other molecules can also be used to form glassy systems, such as :[24][25]

• germanium dioxide (GeO₂) ;
• diboron trioxide (B₂O₃);
• phosphorus pentoxide (P₂O₅);
• aluminosilicates and borosilicates;
• phosphates.

Phosphate glasses have lower melting temperatures and are more viscous than borosilicate glasses, but they are less resistant to chemical attack and less durable.[25] Glasses based on a phosphate, borate or borophosphate vitreous system are good candidates for athermalization, since their ${\textstyle {\frac {dn}{dT}}}$, i.e. the variation in refractive index with temperature, is generally negative. Athermalization consists in compensating for thermal expansion of the material by changing its index. The family of phosphate glasses is particularly well-suited to these possibilities.[26]

Borosilicate crowns are the most widely produced glass family, and the ones with the best control over final homogeneity. This family includes BK₇, the glass widely used in optics. Alkali oxides and boron trioxide B₂O₃ make it easier to melt silicon dioxide SiO₂, which requires very high temperatures to liquefy.

Barium crowns and dense crowns were developed for barium's ability to significantly increase the refractive index without significantly reducing the glass's constringency or ultraviolet transmission, which lead oxide tends to do. Some lenses use a mixture of zinc oxide ZnO and barium oxide BaO.

Crowns, zinc crowns and crown flints are small families of glasses containing a wide variety of oxides (CaO or BaO, ZnO and PbO respectively) to increase hardness or durability.

Phosphate crowns are characterized by their relatively low dispersion and medium index, with generally higher dispersion in the blue, making them useful for correcting chromatism in optical combinations.

Fluorine crowns use fluorine's properties to reduce the dispersion and index of the glass: fluorine's high electronegativity and the smaller radius of fluorine ions are responsible for this. As with phosphate crowns, these lenses are particularly suitable for correcting chromatic aberration, thanks to their partial dispersion in the blue.[27]

Dense or light flints are long-established families, such as borosilicate crowns, and are used as optical glass as well as crystal for everyday glassmaking. Their main properties derive from the proportion of PbO introduced. PbO increases refractive index while decreasing Abbe number, and also affects partial dispersion. Lead oxide will also increase the density of the glass and reduce its resistance to chemical attack. The ability of the PbO-SiO₂ couple to vitrify enables PbO proportions of over 70 mol per 100 to be achieved, which would not be possible if PbO were merely a chemical mesh modifier. Indeed, a high PbO concentration produces tetrahedral PbO₄, which can form a glass-like mesh.

The inclusion of PbO has several drawbacks. Firstly, the glasses are slightly yellow due to the high concentration of lead oxide. Secondly, inclusions and impurities such as iron(III) oxide Fe₂O₃ or chromium(III) oxide Cr₂O₃ degrade glass transmission to a far greater extent than in soda, potash or lime glasses. Thirdly, a chemical equilibrium between Pb²⁺ and Pb⁴⁺ is established and, in the presence of oxygen-saturated glass, leads to the creation of lead dioxide PbO₂, a brown compound that darkens glass. However, this latter coloration can be reversed by a redox transformation of the glass paste, since it does not originate from impurities.

Structure of La₂O₃, used in lanthanum glasses, flints and crowns.

To overcome these problems, titanium dioxide TiO₂ and zirconium dioxide ZrO₂ can be added, increasing the glass's chemical stability and preserving its ultraviolet transmission.

Barium flints crystallize less easily than other glass families due to the presence of lead(II) oxide (PbO) in the mixture. The higher the proportion of PbO, the higher the refractive index and the lower the melting temperature, so these are glasses which, although very useful for their high indexes, present complications during melting. The BaO in these glasses is sometimes replaced by ZnO.

Lanthanum flints and lanthanum crowns are extended families achieving high refractive indices with medium dispersion. The use of SiO₂ in the paste creates crystallization instabilities, a pitfall avoided by replacing silica with boron trioxide B₂O₃ and divalent oxides. To further increase their refractive index, the use of multiple oxides has become widespread, including gadolinium, yttrium, titanium, niobium, tantalum, tungsten and zirconium oxides (Gd₂O₃, Y₂O₃, TiO₂, Nb₂O₅, Ta₂O₅, WO₃ and ZrO₂).

Short flints are a family distinguished not by their index or constringency, but by their partial dispersion. Named for their narrow blue spectrum, short flints are also an asset in optical system design for their low blue impact. They are obtained by replacing the lead oxide in flint glasses with Sb₂O₃ antimony oxide.[27]

Structure of BeF₂ berryllium fluoride glass. Its amorphous structure is very similar to that of silica. Fluoroberyllate glasses have an index of around 1.4, a constringency of 80 and transmit up to 150 nm.

The first fluoride glasses appeared around 1970 to meet a growing need for mid-infrared transmitting glasses.[25] These glasses are composed by replacing the oxygen in oxide glasses with a halogen, fluorine or chlorine, and more rarely with heavy halogens. Their transmission covers the visible and mid-infrared range, from 200 nm to 7 µm, due to the rather high band gap (on average, a fluoride glass has its transmission dip at around 250 nm, due to its band gap of around 5 eV)[25] and the low-frequency vibrations of the heavy-metal fluoride bonds; silica absorption results from vibrations of Si-O bonds at 1.1 × 10³ cm⁻¹, whereas fluorozirconate absorption will result from vibrations of Zr-F bonds at a frequency of 0.58 × 103 cm⁻¹, which is why oxide and halide glasses behave so differently in the infrared.

By using rare earths instead of heavy metals, we obtain a rare-earth fluoride glass that transmits even further into the infrared. Another way of transmitting further into the infrared is to make chloride glass instead of fluoride glass, but this reduces the stability of the glass.[24] A type of glass recently developed at the University of Rennes uses a tellurium halide. As the energy gap in the visible is greater, the drop in transmission in the visible advances to 700 nm-1.5 µm, while its transmission improves in the far infrared. As the refractive index of such a glass is very high, it behaves like a chalcogenide glass, with a strong reflection that reduces its transmission.[24]

Fluoride lenses are also useful for their near-UV transmission. Near-UV transmitting glasses are few in number, but include lithium fluoride, calcium fluoride and magnesium fluoride glasses.[28]

Chalcogenide glasses have been specifically developed since the 1980s[25] to improve the infrared transmission of optical glasses. Oxygen is replaced by another chalcogen (sulfur, selenium, tellurium), and silicon is replaced by heavier metals such as germanium, arsenic, antimony and others. Their index is greater than 2, and they appear black due to their weak gap and multiple absorption bands in the visible range. The transmission of these glasses ranges from 1 µm to 12 µm, but is lower than that of oxide or halide glasses due to their very high refractive index, which results in a high reflection coefficient.[24]

This group can be divided into two families: glasses that can be doped with rare-earth ions or not. The former are mainly composed of germanium and gallium sulfides and selenides, while the latter, although not doped, offer the best transmission performance in the far infrared.[25]

Quartz glass is distinguished from other optical glass by the source of the material used in its manufacture. Many manufacturers produce quartz glass, but the differences lie mainly in the nature of the impurities and the water content. These differences give each quartz glass its own special characteristics, such as transmission and resistance to chemical attack.[29]

Quartz glass is made from a single material: silica. Its main properties are low expansion (α≈0.5 × 10⁻⁶ K⁻¹),[30] high thermal stability (up to 1,000 K)[30] and transmission in the ultraviolet and infrared, which can be adapted as required.

Filters are glasses designed to transmit only certain parts of the spectrum of incident light. A filter can be colorless, a simple optical glass whose transmission drop serves to cut off wavelengths beyond a certain value, or colored in various ways, by the introduction of heavy metal or rare-earth ions, by molecular coloration or even by a colloidal suspension. Filter glasses show noticeable photoluminescence.[31]

Optical filters in colored glass take the form of a blade with a parallel face and a thickness that depends on the transmission qualities required; like electronic filters, they are referred to as high-pass, low-pass, band-pass or notch filters.

Several types of glass are used for lasers, including Li₂O-CaO-SiO₂ glasses for their resistance to thermal shock, and potassium-barium-phosphate glasses, whose effective cross-section is large enough for stimulated emission. The addition of sodium, lithium or aluminum oxides drastically reduces distortion. These glasses are athermalized. In addition to these two types of glass, lithium-aluminum phosphates can be used. These are treated by ion exchange and are particularly resistant, making them ideal for applications where the average laser power is very high (e.g. femtosecond pulsed lasers), or fluorophosphates, which have a slightly non-linear index.[32]

These Nd³⁺-doped glasses are used as active laser medium.

Gradient-index lenses exploit the special properties of light propagation in a variable-index medium. In 1854, James Clerk Maxwell invented the "Fisheye lens" in response to a problem from the Irish Academy asking for the refractive index of an image-perfect material. This theoretical lens, spherical in shape, has an index of the form ${\displaystyle n(r)={\frac {2}{1+(r/R)^{2}}}}$ where ${\textstyle n}$ is the refractive index of the glass at a point on the spherical lens and ${\textstyle R}$ the radius of this lens; it enables any point on its surface to be imaged perfectly at another point diametrically opposite. A generalization of this spherical lens was proposed in 1966 by Rudolf Karl Lüneburg (de), using a different index profile. In 1905, Robert Williams Wood developed a lens consisting of a blade with a parallel face whose index varies parabolically, with the extremum of the index lying on the axis of revolution of the component. The Wood lens can be used to focus or diverge rays, just like a conventional lens.[33][34]

Since around 1970, glass manufacturing technology has made it possible to develop, qualify and machine graded-index glasses. Two main uses for graded-index glasses are in telecommunications, with optical fibers, and in imaging, with lenses machined from graded-index material. Gradients can also be divided into three types of profile: spherical gradients, cylindrical gradients and axial gradients.[35]

There are several techniques for producing graded-index glass: neutron bombardment, ion filling or glass layer superposition. Depending on the technique used, the gradient will be stronger or weaker, and its profile more or less controlled. Injection or ionic filling methods can produce gradients of 10 to 50 mm, with an index amplitude of 0.04. Neutron bombardment and chemical vapor deposition methods produce shallow gradients (approx. 100 µm) of low amplitude. For larger gradients, there is partial lens polymerization of a monomer reacting to UV exposure (gradients of around one hundred millimeters for an index amplitude of 0, 01), or superimposing and then partially melting layers of borosilicate or flint glass (lanthanum-containing glasses are not suitable for this technique due to their recrystallization problems and thermal instability). A final technique consists of melting and then rotating the paste so that a material gradient, and therefore an index gradient, is established in the glass.[36]

Certain extreme environments are not conducive to the use of conventional lenses; when the system is exposed to far-field UV radiation (X, gamma, etc.) or particle fluxes such as alpha or beta, a drop in lens transmission is observed, due to discoloration of the material. Generally speaking, electromagnetic radiation causes a drop in blue transmission, a phenomenon known as solarization. As this is detrimental to system performance, it was necessary to develop new types of radiation-resistant lenses.[37]

Radiation has a variety of effects: ionization, electron or hole capture, fission of Si-O bonds, etc. These effects can easily be amplified by the presence of impurities that change the valence of molecules or concentrate radiation, causing local degradation of the glass.

In order to reduce the drop in glass transmission and performance, they are doped with CeO₂, which slightly shifts the glass's transmission drop, but makes it virtually impossible to feel the effects of radiation on the glass's optical performance.[37]

In addition to the lenses already mentioned, all of which are specific in their design or use, there are also special glass-like materials.

These include athermalized lenses, which are produced in such a way that the optical path through the lens is independent of temperature. Note that the difference in optical path as a function of temperature is ${\textstyle \Delta L=s(\alpha (n-1)+dn/dt)\Delta T=sGT}$ determined by ${\displaystyle s}$ the thickness of the glass, ${\textstyle \alpha }$ the coefficient of thermal expansion, ${\textstyle n}$ the index, ${\textstyle T}$ the temperature and ${\textstyle G}$ the thermo-optical coefficient. Athermalized glasses can be found in the fluorinated crowns, phosphate crowns, dense crowns, barium and titanium flints and other families.[38]

Glass-ceramics or ceramic glasses are glasses in which the crystal-forming process has been stimulated over a long, complex heating period. The addition of crystals to initiate crystallization results in a glass with a crystallized proportion ranging from 50 to 90%. Depending on the crystals incorporated and the proportion of glass in the ceramic glass, the properties will differ. Generally speaking, ceramic glass is highly resistant to thermal shock and has near-zero thermal expansion (Schott AG's Zerodur, for example, was used specifically for the Very Large Telescope for these thermal properties).[39]

• David Whitehouse, "World's oldest telescope?" archive, on BBC News, BBC Online Network, September 1, 1999 (accessed on March 22nd, 2012)

• ^(fr) Charles Chevalier, Des microscopes et de leur usage : Manuel complet du micrographe, Paris, Proux et Cie, 1839, 284 p. (read online archive)
• ^(fr) Pierre de Félice, Histoire de l'optique, Paris, Éditions L'Harmattan, coll. "Acteurs de la Science", 2009, 128 p. (ISBN 978-2-296-08572-5, read online archive)
• ^(fr) James L. Barton and Claude Guillemet, Le verre, science et technologie, Les Ulis, EDP Sciences, 2005, 440 p. (ISBN 2-86883-789-1, read online archive)
• ^(fr) Jean-Marie F. Haussonne, Claude Carry, Paul Bowen et James L. Barton, Céramiques et verres : Principes et techniques d'élaboration, vol. 16, Lausanne, PPUR, coll. "raité de Matériaux", 2005, 1st ed., 830 p. (ISBN 2-88074-605-1, read online archive, read online archive)
• Marvin J. Weber et al. (pref. Marvin J. Weber), Handbook of Optical Materials, Boca Raton, CRC Press, September 24, 2002, 1st ed., 536 p. (ISBN 978-0-8493-3512-9, read online archive), part 2.
• Matthias Brinckmann et al., Springer Handbook of Lasers and Optics, New York, Springer, 2007, 1332 p. (ISBN 978-0-387-95579-7, 0-387-95579-8 and 0-387-30420-7, LCCN 2007920818, read online archive), part 5.
• Hans Bach and Norbert Neuroth, The properties of optical glass, Berlin, Springer, 1998, 2nd ed., 419 p. (ISBN 3-540-58357-2, read online archive)
• Norme MIL-G-174 version B, Département de la Défense des États-Unis, December 5, 1986, 2nd ed., 16 p. (read online archive)
• Heinz G. Pfaender, Schott guide to glass, Londres, Chapman & Hall, 1996, 2nd ed., 207 p. (ISBN 0-412-71960-6, read online archive)
• ^(fr) Jean-Paul Marioge, Surfaces optiques : Méthodes de fabrication et de contrôle, recherches, Les Ulis, EDP Sciences, 2000, 310 p. (ISBN 2-86883-486-8)
• Joseph Habib Simmons and Kelly S. Potter, Optical materials, San Diego/San Francisco/New York etc., Elsevier, November 2, 1999, 1st ed., 391 p. (ISBN 978-0-12-644140-6, LCCN 99-65137, read online archive)
• Rudolf Kingslake and R. Barry Jonhson, Lens design fundamentals, SPIE, February 16, 2010, 2nd ed., 576 p. (ISBN 978-0-8194-7939-6 and 978-0-12-374301-5, read online archive)
• ^(fr) Christian Janot (dir.) and Bernhard Ilschner (dir.), Matériaux émergents, vol. 19, Lausanne, PPUR, coll. "Traité des matériaux", 2001, 432 p. (ISBN 2-88074-455-5, read online archive)

• ^(fr) James L. Barton, "L'évolution de la composition des verres industriels : perspective historique", Revue VERRE, Institut du verre, vol. 7, no 2, May 2001 (read online archive)
• Jay Kumler, "Changing glass catalogs", SPIE's oemagazine, June 31, 2004, p. 30 (DOI 10.1117/2.5200406.0009, read online archive)
• H. Rosu et M. Reyes, "Electromagnetic modes of Maxwell Fisheye lens", Nuovo Cimento (it), vol. 19, no 5, May 1994, p. 5 (DOI 10.1007/BF02463739)
• Duncan T. Moore, "Gradient-index optics: a review", Applied Optics (en), vol. 19, no 7, April 1980, p. 4
• Paul K. Manhart et Richard Bankenbecler, "Fundamentals of macro axial gradient index optical design and engineering" Optical Engineering, SPIE, vol. 36, no 6, June 1997, p. 1607-1621 (ISSN 0091-3286, DOI 10.1117/1.601179, abstract archive, read online archive)
• Eric Tong Yih Lee et Elizabeth M. Taylor, "Study of the optical and thermal properties of phosphate glasses", in Trends in Optical Materials Research, Owen G. Gardens, 2007 (ISBN 1-60021-290-5, read online archive), p. 137-183.

• Official records: LCCN GND Japan Israel Czech Republic
• "How the generic optical glass code works" archive, on Newport Glass, 2003 (accessed March 12, 2012)
• "Cross reference list between similar glasses" archive [PDF], on Ohara corp, 2012 (accessed March 12, 2012)
• "Optical glass" archive [PDF], on Hoya, 2012 (consulted on March 12, 2012)
• "Sumita Optical Glass" archive [PDF], on Sumita, 2012 (accessed March 12, 2012)
• "Potapenko special glass" archive, on opticalglass.com.ua, 2012 (accessed March 12, 2012)
• Transmittance of optical glass, Schott AG, coll. "Technical information" (no. 35), October 2005, 12 p. (read online archive)
• Fluorescence of optical glass, Schott AG, coll. "Technical information" (no. 36), August 2010 (read online archive)
• Stress in optical glass, Schott AG, coll. "Technical information" (no. 27), July 2004 (read online archive)
• "Norme ISO 10110" archive, International Organization for Standardization.
• "Info Vitrail" archive, on infovitrail.com, SARL ARBO-COM (accessed July 1, 2012) Site featuring a fairly comprehensive glossary of technical glassmaking terms.
• "Verre online" archive, on verreonline.fr, Institut du verre (consulted July 1, 2012)