Glasses especially suitable for local index modification by ultrashort pulse laser treatment and glass elements comprising the same

Abstract

The invention provides a glass or a glass substrate (1) with constituent phases which enable the inscription of waveguides (2) by ultra short pulsed-lasers. The glass therefore is especially suitable for the combination with semiconductor devices (50) or substrates, e.g. for the production of an electronic or optoelectronic devices (100).

Description

[0001] 19.01.2026

[0002] Glasses Especially Suitable for Local Index Modification by Ultrashort Pulse Laser Treatment and Glass Elements Comprising the same

[0003] The invention refers to glasses which combine suitability for local index modification by ultrashort pulse laser (usp-laser) treatment with good meltability and preferably also a low thermal expansion, advantageously matching especially to that of semiconductor materials such as silicon, i.e. a comparatively low thermal expansion coefficient (CTE), and devices incorporating those glasses, especially devices comprising the glass and a semiconductor element.

[0004] State of the Art

[0005] US 7262144 B2, published 28 August 2007, teaches glasses particularly suitable for photo structuring. Essentially, these are Lithium-Aluminium Silicate (LAS) glasses with minor contributions of other components.

[0006] The usp-laser treatment will lead, first, to a local melting of the glass in the focal area of the laser, and, second, to a high temperature gradient there, giving rise to a central hot zone (“central cylinder”) and a surrounding moderate temperature zone (“surrounding hollow cylinder”).

[0007] The latter will have an impact on Gibb's free energy G:

[0008] G = H -T-S, (1)

[0009] H is the enthalpy, T is the temperature, and S is the entropy.

[0010] As S is weighted with the temperature, S will play a more important part in the central cylinder than in the surrounding hollow cylinder. This means that if a glass is a mixture of at least two different components, one of them being a low entropy glass and one of them being a high entropy glass, demixing may occur because of the above temperature gradient which in return will give rise to an enrichment of the high entropy glass in the central cylinder and of the low entropy glass in the surrounding hollow cylinder. If the high entropy glass has a higher refractive index than the low entropy glass, the structure thus generated will be suitable to serve as waveguide.19.01.2026

[0011] Object

[0012] In the state of the art, there is a lack of glasses that combine suitability for local index modification by usp-laser treatment with an advantageous thermal expansion and a rational meltability. In addition, it should be advantageous to manufacture the glasses using modern flat glass production methods.

[0013] The goal of the present invention is therefore to provide glass substrates, which are suitable for the inscription of waveguides by local index modification. The inscription of the waveguides can especially be performed according to the following process: by moving the focus of an ultrashort pulse laser through the glass, permanent lines of modifications can be realized in within the glass substrate volume, without modifying the environment of the modification line, i.e. the volume outside both the above central cylinder and surrounding hollow cylinder. As will be later shown in Figs. 1a and 1b,, there usually is a demixing volume comprehending both the above central cylinder and the surrounding hollow cylinder. The demixing volume is embedded in a zone which is heat affected without being permanently changed in composition. The heat affected zone, in return, is surrounded by glass, which is not heat affected and, a forteriori, also not changed in composition.

[0014] Depending on the laser focus intensity and material thresholds as well as application time, the material modification of the line can consist of micro voids, optical damages, birefringent nanovoids, density or compositional changes that will result in locally different refractive indices, with the higher index preferably being in the central cylinder. The latter modification, the central rise of the refractive index, is favorable in the context of this invention, because the modification lines can then serve as waveguide cores. The flexibility of “writing” the modification lines freely within the glass substrate volume enables complex 3-dimensional waveguide circuits. Evanescent coupling between waveguides can be achieved by placing waveguide cores in close vicinity (so that the evanescent parts of the waveguide modes overlap). Based on this principle coupling from one to N waveguides, waveguide splitters can thus be achieved. They may optionally be combined by optical elements which may also be generated by an usp-laser, e.g., diffractive optical structures which serve as filters or in-line reflectors (Bragg-Gratings). Also, the modification lines itself can have a sub-structure, e.g. a periodic or non-periodic modulation along the line or a modification profile across the transversal cross-section.19.01.2026

[0015] The object is solved by the subject-matter of the independent claims. Preferred embodiments can be derived from the dependent claims.

[0016] Description of the invention

[0017] The object is solved by a specific combination of stoichiometric glasses, i.e. glasses which exist in the same stoichiometry also as crystals and whose properties can be assumed to be very similar for both glass and crystal because of the identical topology of the assemblies. This theorem can be verified in the literature in many examples by NMR measurements or the like. For this purpose, such stoichiometric glasses are selected whose mixture provide a behavior in the sense of a solution of the object according to the invention attainable. In the present invention, these stoichiometric glasses are also referred to as "constituent phases".

[0018] The concept to describe glasses based on the constituent phases to be assigned to them has been applied before. By specifying the constituent phases, conclusions can be drawn about the chemical structure of a glass.

[0019] The composition is chosen with regard to the phases constituting the glass within the limits described herein. The phases constituting the glass are, of course, not present as such in the glass product in crystalline, but amorphous form. This does not mean, however, that the constituent phases have completely different building units in the amorphous state than in the crystalline state. As stated above, the topology of the building units is comparable, e.g., the coordination of the cations involved with surrounding oxygen atoms or the interatomic distance resulting from the coordination and the strength of the bond between these cations and surrounding oxygen atoms. Therefore, many properties of the glass of the invention can be well described on the basis of the constituent phases, in particular to illustrate the inventive achievement and the problems overcome by the invention. Of course, the glass can be produced not only by using the corresponding crystals, but also by using the usual glass raw materials, as long as only the stoichiometric ratios allow the formation of the corresponding building blocks of the constituent phases.19.01.2026

[0020] Systems suitable for local index modification by usp-laser

[0021] With respect to the above, the invention relates to a glass composed of pairs of high en-tropy / high refractive index constituent phases and low entropy / low refractive index constituent phases or combinations of such pairs. As both glassy SiO2 and glassy B2O3have low entropies due to their limited number of components and as both glassy SiC>2 and B2O3have low refractive indices, with both the entropies and the refractive indices being compared to typical values of multi-component glasses, these two materials are chosen for the low entropy / low refractive index constituent phase in all cases.

[0022] In the following tables, numerous possible multi-component glasses suitable as high en-tropy / high index counterpart of either glassy SiC>2 or glassy B2O3are listed. In all cases, normalized formulas are given. If the corresponding stoichiometric crystal bears a particular name, this name is given also. If known, the densities of these glasses as well as the refractive indices at 589.3 nm which may be calculated from those densities are listed. In addition, the working points of these glasses are listed, if known. Generally, when referring to the refractive index, the refractive index at the wavelength of 589.3 nm is meant, unless indicated otherwise.

[0023] Table 1: constituent phases to be combined with glassy SiO2 (density 2.203g / cm3, refractive index 1.45769, working point 2357°C)

[0024] Constituent Phase Normalized Formula Density / Refractive Working (g / cm3) Index Point / °C Eucryptite (Li2O·Al2O3·2SiO2) / 4 2.363 1.51692

[0025] Nepheline (Na2O·Al2O3·2SiO2) / 4 2.5526 1.50704 1323

[0026] (K2O·Al2O3·2SiO2) / 4 2.551 1.50894

[0027] Cordierite (2MgO-2Al2O3-5SiO2) / 9 2.6281 1.54672 1208 Anorthite (CaO·Al2O3·2SiO2) / 4 2.6836 1.56536 1210

[0028] (SrO·Al2O3·2SiO2) / 4 3.021 1.55585

[0029] Celsian (BaO·Al2O3·2SiO2) / 4 3.39 1.57505

[0030]

[0031] 19.01.2026

[0032] Constituent Phase Normalized Formula Density / Refractive Working (g / cm3) Index Point / °C (Li2O·B2O3·4SiO2) / 6

[0033] Malinkoite (Na2O·B2O3·2SiO2) / 4 2.5447 1.51497

[0034] (La2O3·B2O3·2SiO2) / 4 3.9 1.66996 (Na2O·TiO2·4SiO2) / 6 2.638 1.61814

[0035] (K2O·TiO2·3SiO2) / 5 2.633375 1.62041

[0036] (BaO·TiO2·3SiO2) / 5 3.53 1.74172 (Na2O·ZrO2·4SiO2) / 6 2.8899 1.59249

[0037] (K2O·ZrO2·3SiO2) / 5

[0038] (2CaO·ZrO2·4SiO2) / 7 3.0906 1.65098 1194°C (BaO·ZrO2·3SiO2) / 5

[0039] (K2O Nb2O5-4SiO2) / 6 3.050 1.69433

[0040] (Na2O·ZnO·2SiO2) / 4 3.05 1.55872

[0041] (Na2O·ZnO·3SiO2) / 5 2.85 1.523446

[0042] (K2O·ZnO·2SiO2) / 4 2.95 1.53940

[0043] (Li2O·2SiO2) / 3 2.351 1.53497

[0044] (Na2O-2SiO2) / 3 2.491 1.49152

[0045] (K2O-2SiO2) / 3 2.477 1.48798 (MgO·SiO2) / 2 2.7575 1.55817 (CaO·SiO2) / 2 2.901 1.62505

[0046]

[0047] 19.01.2026

[0048] Constituent Phase Normalized Formula Density / Refractive Working (g / cm3) Index Point / °C

[0049] Sanbornite (BaO-2SiO2) / 3 3.7081 1.58936

[0050] (3BaO·3B2O3·2SiO2) / 8 3.872 1.635

[0051]

[0052] The density values have either been measured at the accredited laboratories of Schott AG, Mainz, Germany, or taken from the literature.

[0053] Table 2: constituent phases to be combined with glassy B2O3(density 1.82g / cm3, refractive index 1.47891, working point 554°C)

[0054] Constituent Phase Normalized Formula Density / Refractive Working (g / cm3) Index Point / °C

[0055] (4ZnO·3B2O3) / 7 3.57 1.65570 710°C (ZrO2·B2O3) / 2

[0056] (La2O3·Nb2O5·2B2O3) / 4 4.6818

[0057] (La2O3Ta2O5'2B2O3) / 4

[0058] (3BaO·3B2O3·2SiO2) / 8 3.872 1.635

[0059]

[0060] The density values have either been measured at the accredited laboratories of Schott AG, Mainz, Germany, or taken from the literature.

[0061] With respect to the three-dimensional structure of the glass, there are also embodiments where all binary alkaline and alkaline earth silicates, i.e. (Li2O·2SiO2) / 3 and (Na2O 2SiO2) / 3 and (K2O·2SiO2) / 3 and (MgO·SiO2) / 2 and (CaO·SiO2) / 2 and (BaO 2SiO2) / 3, are left out.

[0062] With respect to the refractive index, there are embodiments where the overall molar contribution of the alkaline earth aluminosilicates, i.e. the sum of the molar concentrations of (2MgO-2Al2O3-5SiO2) / 9 and (CaO Al2O3-2SiO2) / 4 and (SrO Al2O3-2SiO2) / 4 and19.01.2026

[0063] (BaO Al2O3'2SiO2) / 4 is bigger than the overall molar contribution of the alkaline aluminosilicates, i.e. the sum of the molar concentrations of (Li2O Al2O3'2SiO2) / 4 and

[0064] (Na2O AI2O3-2SiO2) / 4 and (K2O Al2O3-2SiO2) / 4.

[0065] Note that to calculate the refractive index, it is necessary to know the coordination numbers of the cations involved. With respect to the equivalence of topologies referred to above, the coordination numbers of the stoichiometrically corresponding crystals are used for the glassy constituent phases.

[0066] As all the above constituent phases are either ternary or binary compounds, their entropy is higher than the ones of the unary glasses made from SiC>2 or B2O3. Therefore, the suitability of these constituent phases for the purpose of this invention is obvious. To underline this statement, Gibbs' free energy G has been calculated for mixtures of one of the ternary or binary constituent phases of table 1 with SiO2, which have been exposed to a temperature profile with 3000K in the central cylinder and 2000K in the surrounding hollow cylinder. The mixture of the homogeneous glass is 50% ternary or binary phase: 50% SiO2 which means that 0.5 moles of the ternary or binary phase and 0.5 moles of SiO2, in total one mole of input material, are mixed. This one mole is the reference for all calculations. All percentage values refer to molar percents throughout this patent application. If there is a thermodynamic driving force for a demixing due to the above temperature profile, then a calculation of G for the case that both the central cylinder and the surrounding hollow cylinder are occupied by a 50%: 50% mixture of the ternary or binary phase and SiO2 should return a higher level of G than in the case that the central cylinder is occupied by a 60%: 40% mixture of the ternary or binary phase and SiO2 whereas the surrounding hollow cylinder is occupied by a 40%: 60% mixture of the ternary or binary phase and SiO2.

[0067] Note that the densities of the 60%: 40% mixture and the 40%: 60% mixture may be different. The temperature profile shall be such that the radius of the central cylinder has exactly the value that the integration of the composition over the cross section reproduces the original 50%: 50% mixture.

[0068] It is assumed that the dependence of the density on the composition is linear so that the size of the cross-section is not affected by the demixing.19.01.2026

[0069] Table 3: compositions consisting of 50% ternary or binary phase and 50% glassy SiO2

[0070] Constituent Phase (G(60%:40% @ 3000K, Refractive Refractive Refractive 40%: 60% @ 2000 K) Index Index Index - G(50%:50% both @ (60%:40%) (40%: 60%) (50%: 50%) 3000K &

[0071] 2000K)) / (kJ / mol)

[0072] (Li2O Al2O3-2SiO2) / 4 -2.75665 1.49287 1.48102 1.48693 (Na2O Al2O3-2SiO2) / 4 -3.04435 1.48751 1.47764 1.48258 (K2O Al2O3-2SiO2) / 4 -2.85535 1.48996 1.47975 1.48492 (2MgO-2Al2O3-5SiO2) / 9 -2.05925 1.50890 1.49114 1.49993 (CaO Al2O3-2SiO2) / 4 -1.63495 1.52071 1.49920 1.50989 (SrO·Al2O3·2SiO2) / 4 -2.1781 1.51618 1.49656 1.50635 (BaO Al2O3-2SiO2) / 4 -2.2764 1.52834 1.50487 1.51662 (Li2O·B2O3·4SiO2) / 6 -1.79765

[0073] (Na2O·B2O3·2SiO2) / 4 -2.93835 1.49066 1.47924 1.48489 (La2O3·B2O3·2SiO2) / 4 1.59385 1.55176 1.57317 (Na2O·TiO2·4SiO2) / 6 -1.45780 1.54880 1.51687 1.53263 (K2O·TiO2·3SiO2) / 5 -1.87650 1.55437 1.52185 1.53807 (BaO·TiO2·3SiO2) / 5 -0.58315 1.61592 1.55964 1.58729 (Na2O·ZrO2·4SiO2) / 6 1.53485 1.50798 1.52126 (K2O·ZrO2·3SiO2) / 5

[0074] (2CaO·ZrO2·4SiO2) / 7 -0.43040 1.56284 1.52470 1.54333

[0075]

[0076] 19.01.2026

[0077] Constituent Phase (G(60%:40% @ 3000K, Refractive Refractive Refractive 40%: 60% @ 2000 K) Index Index Index - G(50%:50% both @ (60%:40%) (40%: 60%) (50%: 50%) 3000K &

[0078] 2000K)) / (kJ / mol)

[0079] (BaO·ZrO2·3SiO2) / 5 -0.66835

[0080] (K2O·Nb2O5·4SiO2) / 6 1.60892 1.56197 1.58583 (Na2O·ZnO·2SiO2) / 4 -0.59515 1.51240 1.49248 1.50220 (Na2O·ZnO·3SiO2) / 5 1.49456828 1.48138099 1.48785209 (K2O·ZnO·2SiO2) / 4 -0.94535 1.50496 1.48865 1.49673 (Li2O·2SiO2) / 3 -1.02180 1.49929 1.48407 1.49148 (Na2O·2SiO2) / 3 -1.71080 1.47706 1.47031 1.47365 (K2O·2SiO2) / 3 -1.86615 1.47626 1.47021 1.47325 (MgO·SiO2) / 2 1.36115 1.50782 1.48852 1.49778 (CaO·SiO2) / 2 1.07300 1.54494 1.51230 1.52810 (BaO-2SiO2) / 3 0.032 1.53312 1.50688 1.51985 (3BaO·3B2O3·2SiO2) / 8 -2.998 1.56090 1.52542 1.54302

[0081]

[0082] The following table is an analogue to Table 3, with the difference that the average glass composition is 60% ternary or binary phase and 40% glassy SiO2. Again, it is argued that if there is a driving force leading to demixing, the combination of 70% ternary or binary phase and 30% glassy SiO2 in the central cylinder at 3000K, and 50% ternary or binary phase and 50% glassy SiO2 in the surrounding hollow cylinder at 2000K should be more favorable in terms of Gibbs' free energy than a homogeneous composition of 60% ternary or binary phase and 40% glassy SiC>2.19.01.2026

[0083] This case is considered also because with respect to other properties like thermal expansion or meltability, it may be advantageous to choose other pairs of ternary or binary constituent phases and glassy SiO2 than the 50%:50% mixture or combinations of those pairs.

[0084] Table 4: compositions consisting of 60% ternary or binary phase and 40% glassy SiO2

[0085] Constituent Phase (G(70%:30% @ 3000K, Refractive Refractive Refractive 50%: 50% @ 2000 K) Index Index Index - G(60%:40% both @ (70%: 30%) (50%: 50%) (60%:40%) 3000K & 2000K)) / (kJ / mol)

[0086] (Li2O·Al2O3·2SiO2) / 4 -2.67405 1.49883 1.48693 1.49287 (Na2O·Al2O3·2SiO2) / 4 -2.87135 1.49242 1.48258 1.48751 (K2O·Al2O3·2SiO2) / 4 -2.89925 1.49488 1.48492 1.48996 (2MgO·2Al2O3·5SiO2) / 9 -1.95065 1.51805 1.49993 1.50890 (CaO Al2O3-2SiO2) / 4 -1.5757 1.53166 1.50989 1.52071 (SrO·Al2O3·2SiO2) / 4 -2.08915 1.52605 1.50635 1.51618 (BaO Al2O3-2SiO2) / 4 -2.1598 1.54004 1.51662 1.52834 (Li2O·B2O3·4SiO2) / 6 -1.72890

[0087] (Na2O·B2O3·2SiO2) / 4 -2.8996 1.49655 1.48489 1.49066 (La2O3·B2O3·2SiO2) / 4 1.61383 1.57317 1.59385 (Na2O·TiO2·4SiO2) / 6 -1.41720 1.56542 1.53263 1.54880 (K2O·TiO2·3SiO2) / 5 -1.83210 1.57075 1.53807 1.55437 (BaO·TiO2·3SiO2) / 5 -0.51640 1.64560 1.58729 1.61592 (Na2O·ZrO2·4SiO2) / 6 1.54875 1.52126 1.53485 (K2O·ZrO2·3SiO2) / 5

[0088]

[0089] 19.01.2026

[0090] Constituent Phase (G(70%:30% @ 3000K, Refractive Refractive Refractive 50%: 50% @ 2000 K) Index Index Index - G(60%:40% both @ (70%: 30%) (50%: 50%) (60%:40%) 3000K & 2000K)) / (kJ / mol)

[0091] (2CaO·ZrO2·4SiO2) / 7 -0.26550 1.58328 1.54333 1.56284 (BaO·ZrO2·3SiO2) / 5 -0.61640

[0092] (K2O·Nb2O5·4SiO2) / 6 1.63128 1.58583 1.60892 (Na2O·ZnO·2SiO2) / 4 -0.41310 1.52311 1.50220 1.51240 (Na2O·ZnO·3SiO2) / 5 1.50154398 1.48785209 1.49456828 (K2O·ZnO·2SiO2) / 4 -0.80330 1.51333 1.49673 1.50496 (Li2O·2SiO2) / 3 -0.94100 1.50750 1.49148 1.49929 (Na2O·2SiO2) / 3 -1.51950 1.48055 1.47365 1.47706 (K2O·2SiO2) / 3 -1.75915 1.47924 1.47325 1.47626 (MgO·SiO2) / 2 1.58105 1.51874 1.49778 1.50782 (CaO·SiO2) / 2 1.36905 1.56292 1.52810 1.54494 (BaO-2SiO2) / 3 0.04365 1.54669 1.51985 1.53312 (3BaO·3B2O3·2SiO2) / 8 -2.88620 1.57906786 1.54301701 1.56089503

[0093]

[0094] The following table is again an analogue to Table 3, with the difference that the average glass composition is 40% ternary or binary phase and 60% glassy SiO2. Again, it is argued that if there is a driving force leading to demixing, the combination of 50% ternary or binary phase and 50% glassy SiO2 in the central cylinder at 3000K, and 30% ternary or binary phase and 70% glassy SiO2 in the surrounding hollow cylinder at 2000K should be more favorable in terms of Gibbs' free energy than a homogeneous composition of 40% ternary or binary phase and 60% glassy SiO2.19.01.2026

[0095] This case is considered also because with respect to other properties like thermal expansion or meltability, it may be advantageous to choose other pairs of ternary or binary constituent phases and glassy SiO2 than the 50%: 50% mixture or combinations of those pairs.

[0096] Table 5: compositions consisting of 40% ternary or binary phase and 60% glassy SiO2

[0097] Constituent Phase (G(50%:50% @ 3000K, Refractive Refractive Refractive 30%: 70% @ 2000 K) Index Index Index - G(40%:60% both @ (50%: 50%) (30%: 70%) (40%: 60%) 3000K &

[0098] 2000K)) / (kJ / mol)

[0099] (Li2O·Al2O3·2SiO2) / 4 -2.866 1.48693 1.47515 1.48102 (Na2O·Al2O3·2SiO2) / 4 -3.22705 1.48258 1.47268 1.47764 (K2O·Al2O3·2SiO2) / 4 -2.884 1.48492 1.47445 1.47975 (2MgO·2Al2O3·5SiO2) / 9 -2.20025 1.49993 1.48253 1.49114 (CaO Al2O3-2SiO2) / 4 -1.7384 1.50989 1.48864 1.49920 (SrO Al2O3-2SiO2) / 4 -2.2851 1.50635 1.48679 1.49656 (BaO Al2O3-2SiO2) / 4 -2.41105 1.51662 1.49311 1.50487 (Li2O·B2O3·4SiO2) / 6 -1.88620

[0100] (Na2O·B2O3·2SiO2) / 4 -2.98475 1.48489 1.47369 1.47924 (La2O3·B2O3·2SiO2) / 4 1.57317 1.52955 1.55176 (Na2O·TiO2·4SiO2) / 6 -1.49740 1.53263 1.50151 1.51687 (K2O·TiO2·3SiO2) / 5 -1.92300 1.53807 1.50571 1.52185 (BaO·TiO2·3SiO2) / 5 -0.66970 1.58729 1.53291 1.55964 (Na2O·ZrO2·4SiO2) / 6 1.52126 1.49500 1.50798

[0101]

[0102] 19.01.2026

[0103] Constituent Phase (G(50%:50% @ 3000K, Refractive Refractive Refractive 30%: 70% @ 2000 K) Index Index Index - G(40%:60% both @ (50%: 50%) (30%: 70%) (40%: 60%) 3000K &

[0104] 2000K)) / (kJ / mol)

[0105] (K2O·ZrO2·3SiO2) / 5

[0106] (2CaO·ZrO2·4SiO2) / 7 -0.60615 1.54333 1.50687 1.52470 (BaO·ZrO2·3SiO2) / 5 -0.73550

[0107] (K2O Nb2O5-4SiO2) / 6 1.58583 1.53728 1.56197 (Na2O·ZnO·2SiO2) / 4 -0.87635 1.50220 1.48319 1.49248 (Na2O·ZnO·3SiO2) / 5 1.48785209 1.47514165 1.481381

[0108] (K2O·ZnO·2SiO2) / 4 -1.15450 1.49673 1.48071 1.48865 (Li2O·2SiO2) / 3 -1.08025 1.49148 1.47700 1.48407 (Na2O-2SiO2) / 3 -1.90980 1.47365 1.46705 1.47031 (K2O-2SiO2) / 3 -1.97715 1.47325 1.46713 1.47021 (MgO·SiO2) / 2 1.05315 1.49778 1.47995 1.48852 (CaO·SiO2) / 2 0.67880 1.52810 1.49743 1.51230 (BaO-2SiO2) / 3 -0.02360 1.51985 1.49419 1.50688 (3BaO·3B2O3·2SiO2) / 8 -3.13510 1.54302 1.50810 1.52542

[0109]

[0110] Although a similar effect is expected for the mixtures of binary or ternary borate glasses with pure borate glass, no corresponding calculations have been carried out for the borate systems, i.e. Lanthanum Niobium Borate and Lanthanum Tantalum Borate.19.01.2026

[0111] Table 6: compositions consisting of 50% ternary or binary phase and 50% glassy B2O3

[0112] Constituent Phase (G(60%:40% @ Refractive Refractive Refractive 3000K, 40%:60% @ Index Index Index 2000K) (60%:40%) (40%:60%) (50%:50%) - G(50%:50% both

[0113] @ 3000K &

[0114] 2000K)) / (kJ / mol)

[0115] (4ZnO·3B2O3) / 7 1,55897778 1,52648078 1,54179250

[0116] (ZrO2·B2O3) / 2

[0117] (La2O3·Nb2O5·2B2O3) / 4

[0118] (La2O3·Ta2O5·2B2O3) / 4

[0119] (3BaO·3B2O3·2SiO2) / 8 1.55671314 1.52669413 1.54108673

[0120]

[0121] Table 7: compositions consisting of 60% ternary or binary phase and 40% glassy B2O3

[0122] Constituent Phase (G(60%:40% @ 3000K, Refractive Refractive Refractive 40%: 60% @ 2000 K) Index Index Index -G(50%:50% both @ (70%: 30%) (50%: 50%) (60%:40%) 3000K & 2000K)) / (kJ / mol)

[0123] (4ZnO·3B2O3) / 7 1,57840675 1,5417925 1,55897778 (ZrO2·B2O3) / 2

[0124] (La2O3·Nb2O5·2B2O3) / 4

[0125] (La2O3·Ta2O5·2B2O3) / 4

[0126] (3BaO·3B2O3·2SiO2) / 8 1.57374184 1.54108673 1.55671314

[0127]

[0128] 19.01.2026

[0129] Table 8: compositions consisting of 40% ternary or binary phase and 60% glassy B2O3

[0130] Constituent Phase (G(60%:40% @ 3000K, Refractive Refractive Refractive 40%: 60% @ 2000 K) Index Index Index -G(50%:50% both @ (50%: 50%) (30%: 70%) (40%: 60%) 3000K & 2000K)) / (kJ / mol)

[0131] (4ZnO·3B2O3) / 7 1,5417925 1,51275012 1,52648078

[0132] (ZrO2·B2O3) / 2

[0133] (La2O3·Nb2O5·2B2O3) / 4

[0134] (La2O3 Ta2O5‘2B2O3) / 4

[0135] (3BaO·3B2O3·2SiO2) / 8 1.54108673 1.51339306 1.52669413

[0136]

[0137] Note again that a negative value in the second column of the above Tables indicates that demixing with an enrichment of the binary or ternary phase in the centre is favorable which results in a central peak of the refractive index. A negative value in the second column of the above tables 3 - 5 indicates the opposite.

[0138] General composition of the glasses

[0139] As has been said above, the invention relates to a glass composed of pairs of high en-tropy / high refractive index constituent phases and low entropy / low refractive index constituent. Therefore, the basic building unit of an inventive glass is a mixture of one of the above binary or ternary constituent phases with either glassy SiO2or glassy B2O3, respectively. This mixtures contain at least 20% of either glassy SiO2or glassy B2O3, preferably at least 30% of either glassy SiO2or glassy B2O3, more preferably at least 40% of either glassy SiO2or glassy B2O3, most preferably at least 50% of either glassy SiO2or glassy B2O3, and at maximum 80% of either glassy SiO2or glassy B2O3, preferably 70% or less of either glassy SiO2or glassy B2O3, more preferably 60% or less of either glassy SiO2or glassy B2O3, most preferably 50% or less of either glassy SiO2or glassy B2O3.

[0140] Those mixtures and the inventive ratios of mixing are listed below:19.01.2026

[0141] Table 9: Mixtures and ratios of mixing (molar mixtures) involving SiO2

[0142] Mixture consisting of binary or terMinimum ratio of binary Maximum ratio of binary nary constituent phase and SiO2 or ternary constituent or ternary constituent phase to SiO2 phase to SiO2

[0143] (Li2O Al2O3'2SiO2) / 4-mixture 20%: 80% 80%:20% (Na2O Al2O3'2SiO2) / 4-mixture 20%: 80% 80%:20% (K2O Al2O3'2SiO2) / 4-mixture 20%: 80% 80%:20% (2MgO'2Al2O3'5SiO2) / 9-mixture 20%: 80% 80%:20% (CaO Al2O3'2SiO2) / 4-mixture 20%: 80% 80%:20% (SrO Al2O3'2SiO2) / 4-mixture 20%: 80% 80%:20% (BaO Al2O3'2SiO2) / 4-mixture 20%: 80% 80%:20% (Li2O B2O3'4SiO2) / 6-mixture 20%: 80% 80%:20% (Na2O B2O3'2SiO2) / 4-mixture 20%: 80% 80%:20% (La2O3'B2O3'2SiO2) / 4-mixture 20%: 80% 80%:20% (Na2O TiO2'4SiO2) / 6-mixture 20%: 80% 80%:20% (K2O TiO2'3SiO2) / 5-mixture 20%: 80% 80%:20% (BaO TiO2'3SiO2) / 5-mixture 20%: 80% 80%:20% (Na2O ZrO2'4SiO2) / 6-mixture 20%: 80% 80%:20% (K2O ZrO2'3SiO2) / 5-mixture 20%: 80% 80%:20% (2CaO ZrO2'4SiO2) / 7-mixture 20%: 80% 80%:20% (BaO ZrO2'3SiO2) / 5-mixture 20%: 80% 80%:20% (K2O Nb2O5'4SiO2) / 6-mixture 20%: 80% 80%:20%

[0144]

[0145] 19.01.2026

[0146] Mixture consisting of binary or terMinimum ratio of binary Maximum ratio of binary nary constituent phase and SiO2 or ternary constituent or ternary constituent phase to SiO2 phase to SiO2

[0147] (Na2O ZnO'2SiO2) / 4-mixture 20%: 80% 80%:20% (Na2O ZnO'3SiO2) / 5-mixture 20%: 80% 80%:20% (K2O ZnO'2SiO2) / 4-mixture 20%: 80% 80%:20% (Li2O 2SiO2) / 3-mixture 20%: 80% 80%:20% (Na2O 2SiO2) / 3-mixture 20%: 80% 80%:20%

[0148] (K2O 2SiO2) -mixture 20%: 80% 80%:20% (MgO SiO2) / 2-mixture 20%: 80% 80%:20% (CaO SiO2) / 2-mixture 20%: 80% 80%:20% (BaO 2SiO2) / 3-mixture 20%: 80% 80%:20% (3BaO'3B2O3'2SiO2) / 8-SiO2-mixture 20%: 80% 80%:20%

[0149]

[0150] Table 10: Mixtures and ratios of mixing (molar mixtures) involving B2O3

[0151] Mixture consisting of binary or terMinimum ratio of binary Maximum ratio of binary nary constituent phase and B2O3or ternary constituent or ternary constituent phase to B2O3phase to B2O3

[0152] (4ZnO'3B2O3) / 7 20%:80% 80%:20% (ZrO2·B2O3) / 2 20%:80% 80%:20% (La2O3'Nb2O5'2B2O3) / 4-mixture 20%: 80% 80%:20% (La2O3'Ta2O5'2B2O3) / 4-mixture 20%: 80% 80%:20% (3BaO'3B2O3'2SiO2) / 8-B2O3-mixture 20%: 80% 80%:20%

[0153]

[0154] 19.01.2026

[0155] The inventive glasses are combinations of the above mixtures. Note that these combinations may consist of mixtures with different mixing ratio, for example a 50%: 50% combination of a first mixture which in return consists of 60% of ternary No.1 plus 40% SiO2 and a second mixture which in return consists of 70% of ternary No. 2 plus 30% SiO2.

[0156] The most advantageous combinations are listed below:

[0157] Table 11: Combinations of the above mixtures (molar combinations)

[0158] Mixture consisting of binary or ternary conMinimum Maximum stituent phase

[0159] (Li2O Al2O3'2SiO2) / 4-mixture 0% 100% (Na2O Al2O3'2SiO2) / 4-mixture 0% 100% (K2O Al2O3'2SiO2) / 4-mixture 0% 100% (2MgO'2Al2O3'5SiO2) / 9-mixture 0% 100% (CaO Al2O3'2SiO2) / 4-mixture 0% 100% (SrO Al2O3'2SiO2) / 4-mixture 0% 100% (BaO Al2O3'2SiO2) / 4-mixture 0% 100% (Li2O B2O3'4SiO2) / 6-mixture 0% 100% (Na2O B2O3'2SiO2) / 4-mixture 0% 100% (La2O3'B2O3'2SiO2) / 4-mixture 0% 100% (Na2O TiO2'4SiO2) / 6-mixture 0% 100% (K2O TiO2'3SiO2) / 5-mixture 0% 100% (BaO TiO2'3SiO2) / 5-mixture 0% 100% (Na2O ZrO2'4SiO2) / 6-mixture 0% 100% (K2O ZrO2'3SiO2) / 5-mixture 0% 100%

[0160]

[0161] 19.01.2026

[0162] Mixture consisting of binary or ternary conMinimum Maximum stituent phase

[0163] (2CaO ZrO2'4SiO2) / 7-mixture 0% 100% (BaO ZrO2'3SiO2) / 5-mixture 0% 100% (K2O Nb2O5'4SiO2) / 6-mixture 0% 100% (Na2O ZnO'2SiO2) / 4-mixture 0% 100% (Na2O ZnO'3SiO2) / 5-mixture 0% 100% (K2O ZnO'2SiO2) / 4-mixture 0% 100% (Li2O 2SiO2) / 3-mixture 0% 100% (Na2O 2SiO2) / 3-mixture 0% 100% (K2O 2SiO2) / 3-mixture 0% 100% (MgO SiO2) / 2-mixture 0% 100% (CaO SiO2) / 2-mixture 0% 100% (BaO 2SiO2) / 3-mixture 0% 100% (4ZnO 3B2O3) / 7-mixture 0% 100%

[0164] (ZrO2·B2O3) / 2-mixture 0% 100% (La2O3'Nb2O5'2B2O3) / 4-mixture 0% 100% (La2O3'Ta2O5'2B2O3) / 4-mixture 0% 100% (3BaO'3B2O3'2SiO2) / 8-SiO2-mixture 0% 100% (3BaO'3B2O3'2SiO2) / 8-B2O3-mixture 0% 100%

[0165] B2O30% 10%

[0166]

[0167] 19.01.2026

[0168] Mixture consisting of binary or ternary conMinimum Maximum stituent phase

[0169] SiO20% 10%

[0170]

[0171] Note that some minor additional contributions of SiO2 and / or B2O3are also part of the preferred combinations. They come on top of the SiO2 and / or B2O3content which is already part of the mixtures.

[0172] The calculation to obtain the composition in constituent phases instead of the above mixtures (plus the minor additional contributions fromSiCh and B2O3) is straight forward and does not have to be explained here. Essentially, the composition in constituent phases will look like this:

[0173] Table 12: Inventive composition in constituent phases (molar)

[0174] Constituent phase Minimum Maximum

[0175] (Li2O·Al2O3·2SiO2) / 4 0% 80% (Na2O·Al2O3·2SiO2) / 4 0% 80%

[0176] (K2O·Al2O3·2SiO2) / 4 0% 80%

[0177] (2MgO·2Al2O3·5SiO2) / 9 0% 80%

[0178] (CaO·Al2O3·2SiO2) / 4 0% 80%

[0179] (SrO·Al2O3·2SiO2) / 4 0% 80%

[0180] (BaO·Al2O3·2SiO2) / 4 0% 80%

[0181] (Li2O·B2O3·4SiO2) / 6 0% 80% (Na2O·B2O3·2SiO2) / 4 0% 80% (La2O3·B2O3·2SiO2) / 4 0% 80%

[0182] (Na2O·TiO2·4SiO2) / 6 0% 80%

[0183]

[0184] 19.01.2026

[0185] Constituent phase Minimum Maximum (K2O·TiO2·3SiO2) / 5 0% 80% (BaO·TiO2·3SiO2) / 5 0% 80% (Na2O·ZrO2·4SiO2) / 6 0% 80% (K2O·ZrO2·3SiO2) / 5 0% 80% (2CaO·ZrO2·4SiO2) / 7 0% 80% (BaO·ZrO2·3SiO2) / 5 0% 80% (K2O Nb2O5-4SiO2) / 6 0% 80% (Na2O·ZnO·2SiO2) / 4 0% 80% (Na2O·ZnO·3SiO2) / 5 0% 80% (K2O·ZnO·2SiO2) / 4 0% 80%

[0186] (Li2O·2SiO2) / 3 0% 80%

[0187] (Na2O-2SiO2) / 3 0% 80%

[0188] (K2O-2SiO2) / 3 0% 80% (MgO·SiO2) / 2 0% 80% (CaO·SiO2) / 2 0% 80%

[0189] (BaO-2SiO2) / 3 0% 80%

[0190] (4ZnO·3B2O3) / 7 0% 80% (ZrO2·B2O3) / 2 0% 80% (La2O3·Nb2O5·2B2O3) / 4 0% 80% (La2O3·Ta2O5·2B2O3) / 4 0% 80%

[0191]

[0192] 19.01.2026

[0193] Constituent phase Minimum Maximum

[0194] (3BaO-3B2O3-2SiO2) / 8 0% 80%

[0195] B2O30% 80%

[0196] SiO20% 80%

[0197] B2O3+SiO220% 80%

[0198]

[0199] With respect to the further combination of such glasses with semiconductor materials these glasses will preferably be furnished with a corresponding coefficient of thermal expansion (CTE). In particular, when referring to the CTE, herein the linear coefficient of thermal expansion in the range from 20°C to 300°C is addressed.

[0200] To allow, for instance, a combination of the glasses with silicon, it is preferred to furnish the glasses with a CTE of 3.3 ppm / K, with a tolerance of the CTE value of 2ppm / K, more preferably of 1.9 ppm / K, more preferably of 1.9 ppm / K, even more preferably of 1.8 ppm / K, even more preferably of 1.7 ppm / K, even more preferably of 1.6 ppm / K, even more preferably of 1.5 ppm / K, even more preferably of 1.4 ppm / K, even more preferably of 1.3 ppm / K, even more preferably of 1.2 ppm / K, even more preferably of 1.1 ppm / K, even more preferably of 1.0 ppm / K, even more preferably of 0.9 ppm / K, even more preferably of 0.8 ppm / K, even more preferably of 0.7 ppm / K, even more preferably of 0.6 ppm / K, even more preferably of 0.5 ppm / K, even more preferably of 0.4 ppm / K, even more preferably of 0.3 ppm / K, even more preferably of 0.2 ppm / K, most preferably of 0.1 ppm / K.

[0201] To allow, for instance, a combination of the glasses with Indiumphosphide, it is preferred to furnish the glasses with a CTE of 4.7 ppm / K, with the above scale of tolerances.

[0202] To allow, for instance, a combination of the glasses with Germanium, it is preferred to furnish the glasses with a CTE of 6.3 ppm / K, with the above scale of tolerances.

[0203] The adjustment of the glass properties to the desired thermal expansion is done by screening the inventory glasses with respect to the CTE value as calculated with the below formula (3).19.01.2026

[0204] To ensure easy melting, the working point (fixpoint of the viscosity vs. temperature curve at which the viscosity is equal to 104dP·s) should preferably not exceed 1400°C.

[0205] The adjustment of the glass properties to the desired working point is done by screening the inventory glasses with respect to the CTE value as calculated with the below formula (11).

[0206] Coefficient of thermal expansion

[0207] Remarkably, the position of the thermal expansion coefficient in the target range can be represented with the aid of a calculation rule taking into account the average bond strength.

[0208] It is known in the art that the coefficient of thermal expansion for metals, for example, is inversely proportional to the binding energy (or to the "depth of the interatomic potential wells").

[0209] In an abstract picture of oxidic glasses, the cations are placed in a potential well formed by the surrounding oxygen atoms and the depth of the potential well is assumed to be the sum of the bond strengths of the various single bonds to the surrounding oxygen atoms, i.e. the entire interaction energy is concentrated in potential wells with the cations in the center and the oxygen atoms in the periphery. Thus, the reverse case needs no longer be considered; it would also be more difficult to analyze, since an oxygen atom can be located between several different types of cations, which conversely cannot occur in purely oxide glasses. These values are tabulated as follows:

[0210] Table 6

[0211] Cation Potential well depth / (kJ / mol)

[0212] Si 1864

[0213] Ti 1913

[0214] Zr 2203

[0215] B 1572.5

[0216] Al 1537

[0217]

[0218] 19.01.2026

[0219] Cation Potential well depth / (kJ / mol)

[0220] La 1701.1

[0221] Nb 2298.5

[0222] Ta 2427.5

[0223] Zn 728

[0224] Mg 999

[0225] Ca 1063

[0226] Sr 1005

[0227] Ba 976

[0228] Li 585

[0229] Na 440.5

[0230] K 395

[0231] P 1691.5

[0232]

[0233] From the composition of a glass comprising or consisting of the constituent phases given above, the numbers of different cations contained in the respective phases, and the potential well depths per cation tabulated above, a mean potential well depth Epotcan be calculated:

[0234] -p - - 2d=ici'T.j=izi J'Epot J Zpot ~ ynr?m 7.. (2)

[0235]

[0236] Z.i=lci Z.y=i^i,j

[0237] Where m is the number of cation types occurring in each constituent phase (the numerical value of m depends on the constituent phase), Epot,j is the potential well depth tabulated above for the j-th cation type, and Zj is the number of cations of the j-th type in the i-th constituent phase. The sums over j are tabulated below:19.01.2026

[0238] Table 14

[0239] Constituent Phase m m

[0240] Yzi’i

[0241] j=l 7 = 1

[0242] Eucryptite (Li2O Al2O3-2SiO2) / 4 1.5 1993

[0243] Nepheline (Na2O Al2O3-2SiO2) / 4 1.5 1920.75

[0244] (K2O Al2O3-2SiO2) / 4 1.5 1898

[0245] Cordierite (2MgO·2Al2O3·5SiO2) / 9 1.22 1940.67

[0246] Anorthite (CaO Al2O3-2SiO2) / 4 1.25 1966.25

[0247] (SrO·Al2O3·2SiO2) / 4 1.25 1951.75

[0248] Celsian (BaO Al2O3-2SiO2) / 4 1.25 1944.5

[0249] (Li2O·B2O3·4SiO2) / 6 1.33 1961.833 Malinkoite (Na2O·B2O3·2SiO2) / 4 1.5 1938.5

[0250] (La2O3·B2O3·2SiO2) / 4 1.5 2568.9

[0251] (Na2O·TiO2·4SiO2) / 6 1.166 1708.33

[0252] (K2O·TiO2·3SiO2) / 5 1.2 1659

[0253] (BaO·TiO2·3SiO2) / 5 1 1696.2

[0254] (Na2O·ZrO2·4SiO2) / 6 1.166 1756.66

[0255] (K2O·ZrO2·3SiO2) / 5 1.2 1717

[0256] (2CaO·ZrO2·4SiO2) / 7 1 1683.57

[0257] (BaO·ZrO2·3SiO2) / 5 1 1754.2

[0258] (K2O Nb2O5-4SiO2) / 6 1.33 2140.5

[0259] (Na2O·ZnO·2SiO2) / 4 1.25 1334.25

[0260]

[0261] 19.01.2026

[0262] Constituent Phase m m

[0263] Yzi’i

[0264] j=l 7=1

[0265] (Na2O·ZnO·3SiO2) / 5 1.2 1440.2

[0266] (K2O·ZnO·2SiO2) / 4 1.25 1311.5

[0267] Lithium-Disilicate (Li2O'2SiO2) / 3 1.33 1632.67

[0268] (Na2O·2SiO2) / 3 1.33 1536.33

[0269] (K2O·2SiO2) / 3 1.33 1506

[0270] (MgO·SiO2) / 2 1 1431.5

[0271] (CaO·SiO2) / 2 1 1463.5

[0272] Sanbornite (BaO-2SiO2) / 3 1 1420

[0273] (4ZnO·3B2O3) / 7 1.42 1763.85

[0274] (ZrO2B2O3) / 2 1.5 2674

[0275] (La2O3 Nb2O5-2B2O3) / 4 1.5 2786.5 (La2O3·Ta2O5·2B2O3) / 4 1.5 2850.75

[0276] (3BaO-3B2O3-2SiO2) / 8 1.375 2011.375 Diborontrioxide B2O32 3145

[0277] Quartz Glass SiO21 1864

[0278]

[0279] This average bond strength is inversely proportional to the coefficient of thermal expansion, as is the case for metals. Evaluation of a number of different glasses, including commercial glasses such as Borofloat33, Borofloat40, AF45, AF32 leads to the following semi-empirical formula:

[0280] - VMoi7_27 205\ppm

[0281] Epot j

[0282] CTE =

[0283]

[0284] 19.01.2026

[0285] By checking the CTE value thus obtained for any inventory glass, it be made assessed if this value matches the desired one.

[0286] Viscosity curve, especially working point (WP)

[0287] Remarkably, a mixing rule can also be given for viscosity of glass, with which the viscosity is calculated from the viscosities of the constituent phases.

[0288] The starting point is the Adam-Gibbs relationship in its formulation for viscosity:

[0289] Q

[0290] rj = r]0- 10TScm (4)

[0291] r|0is a prefactor. Q is a constant. SC(T) is the configurational entropy, which according to Hodge is calculated from the configurational fraction ACP(T) of the specific heat (“excess specific heat”) under the assumption ACP(T) = D / T by (see C. A. Angell, loc. cit., and the literature cited there):

[0292] SC(T» = fr ^rdT' = --- (5)

[0293]

[0294] 7 JTK T' TKTV’ TK is the Kauzmann temperature, which is identified with the Vogel-Fulcher-Tammann temperature To. Thus, the Adam-Gibbs relation can be transformed into the Vogel-Fulcher-Tamman equation (VFT equation):

[0295] <2 QTQ *Tn(l DA+B'

[0296]

[0297] ■ 10 r) =.10T-TO =:io T-T0(6)

[0298] A, B, To are the parameters of the VFT equation, which are determined by fit to a measurement curve.

[0299] With the assumptions of Angell and Hodge, Adam-Gibbs and VFT correspond to each other. Thus, the parameters r|0and D / Q, which are in the Adam-Gibbs relationship, can be calculated from the VFT parameters A, B, To.

[0300] η0= 10AdPa · s (7a)

[0301]

[0302] 19.01.2026

[0303] From the relationships between Adam-Gibbs and VFT, a mixing rule can be derived that can be used to calculate the VFT parameters of a glass from the VFT parameters of the constituent phases known from measurements.

[0304] The first approach is:

[0305] *7 = TJo ■ 10TSc(T)mit SC(T) = const.- P- - 1) = ■ const, f (8)

[0306]

[0307] It is used here that the entropy is an additive quantity and is summed over all constituent phases. The mixture entropy is neglected.

[0308] V; is the fraction of the i-th constituent phase in atom% rather than in mol%; the fact that atom%s have to be used here follows from the derivation of the Adam-Gibbs equation.

[0309] If in addition, one assumes that Q has one and the same value for all constituent phases as well as the glass formed by mixing them, one can calculate:

[0310] -Q= ^'iD<9a)

[0311] = (9b)

[0312]

[0313] B = (9c)

[0314] The values for Dj or Dj / Q refer to the individual constituent phases and are obtained from their VFT parameters Aj, Bi, To,i according to (7). The sum over “i” is from 1 to n, as above.

[0315] With B and To, two of the three VFT parameters of the glass formed by mixing the constituent phases are known.

[0316] For the determination of A, it is made use of that the VFT equation approaches an Arrhenius relationship q = 10A+B / Tat high temperatures, and there are several literature references to an approximately linear relationship between A and B for an Arrhenius-conforming viscosity. This leads to the formula:

[0317] (10)

[0318]

[0319] 19.01.2026

[0320] " Vj" again refers to atomic percentages. The sum over “i” is from 1 to n, as above.

[0321] For the calculation of the VFT parameters of a glass expressed as a mixture of the constituent phases forming the basic system of the invention, the VFT parameters of these phases are required. For a part of the above listed constituent phases, they are listed below.

[0322] Table 15

[0323] Constituent Phase A B / K T0 / °C Eucryptite (Li2O Al2O3-2SiO2) / 4

[0324] Nepheline (Na2O Al2O3-2SiO2) / 4 -4.382 9132.1 233.9

[0325] (K2O Al2O3-2SiO2) / 4

[0326] Cordierite (2MgO·2Al2O3·5SiO2) / 9 -4.50166 6790.97 418.162 Anorthite (CaO Al2O3-2SiO2) / 4 -3.66253 5318. 530.043

[0327] (SrO Al2O3-2SiO2) / 4

[0328] Celsian (BaO Al2O3-2SiO2) / 4

[0329] (Li2O·B2O3·4SiO2) / 6

[0330] Malinkoite (Na2O·B2O3·2SiO2) / 4

[0331] (La2O3·B2O3·2SiO2) / 4

[0332] (Na2O·TiO2·4SiO2) / 6

[0333] (K2O·TiO2·3SiO2) / 5

[0334] (BaO·TiO2·3SiO2) / 5

[0335] (Na2O·ZrO2·4SiO2) / 6 -3.29 5450.9 521.1 (K2O·ZrO2·3SiO2) / 5

[0336] (2CaO·ZrO2·4SiO2) / 7 -4.2404 5246.35 542.72

[0337]

[0338] 19.01.2026

[0339] Constituent Phase A B / K To / °C (BaO·ZrO2·3SiO2) / 5

[0340] (K2O Nb2O5-4SiO2) / 6 -2.602 3824 459.9 (Na2O·ZnO·2SiO2) / 4

[0341] (Na2O·ZnO·3SiO2) / 5 -1.7495 3368.04 300.06 (K2O·ZnO·2SiO2) / 4

[0342] Lithium-Disilicate (Li2O'2SiO2) / 3 0.29 2379.5 267.1 (Na2O·2SiO2) / 3 -4 5538 119.8 (K2O·2SiO2) / 3 -4 7461 59.8 (MgO·SiO2) / 2

[0343] (CaO·SiO2) / 2

[0344] Sanbornite (BaO'2SiO2) / 3 -2.341 4098.2 419.8 (3BaO·3B2O3·2SiO2) / 8

[0345] (4ZnO'3B2O3) / 7 -2.23077 1581.66 456.154 (ZrO2·B2O3) / 2

[0346] (La2O3·Nb2O5·2B2O3) / 4

[0347] (La2O3Ta2O5·2B2O3) / 4

[0348] Diborontrioxide B2O3-0.087154 1650.04 149.859 Quartz glass SiO2-6.01651 26018.9 -240.131

[0349]

[0350] The VFT parameters of (Na2O Al2O3-2SiO2) / 4, (2MgO·2Al2O3·5SiO2) / 9,

[0351] (CaO Al2O3-2SiO2) / 4, (Na2O·ZrO2·4SiO2) / 6, (2CaO·ZrO2·4SiO2) / 7, (K2O Nb2O5-4SiO2) / 6,19.01.2026

[0352] (Na2O·ZnO·3SiO2) / 5, (BaO·2SiO2) / 3, B2O3have been measured at Schott. The other VFT parameters were obtained by a fit to measurement data from the known literature or referred to from the known literature..

[0353] If A, B, To are known from the formulas (9) - (10), the working point WP is calculated by transforming (6) according to:

[0354] WP = B / (4-A) + T0(11)

[0355] and the annealing point AP according to:

[0356] AP = B / (13-A) + T0(12)

[0357]

[0358] For example, mixing the constituent phases SiO2and B2O3in a molar ratio of 9: 1 or 0.9: 0.1 which is equivalent to an atomic ratio of 9*3 / (9*3+1*5): 1*5 / (9*3+1*5) (note that SiO2has 3 atoms whereas B2O3has 5 atoms), we first obtain according to equation (7b) DSiO2 / Q = (273.2-240.131) / 26018.9 = 0.00127 and DBO / Q = (273.2+149.859) / 1650.5 = 0.25632. From this, the mixture is calculated according to equation (9a) D / Q = (9*3*DSiO2 / Q +1*5*DBO / Q) / (9*3+1*5) = 0.04112. From this, the T0value of the mixture is calculated according to equation (9b) T0= 0.04112 / ((9*3 / 26018.9+1*5 / 1650.5) / (9*3+1*5)) = 323.533 K, i.e. 50.333°C. According to equation (9c), the B value of the mixture is calculated as 323.533K / 0.04112 = 7868.03K. According to equation (10),

[0359] A = (9*3*(-6.01651) / 26018.9+1*5*(-0.0871546) / 1650.04) / ((9*3+1*5) / 7868.03) = -1.6.

[0360] This gives the working point WP as (7868. 03 / 5.6+323.533) K = 1728.54 K, i.e. 1455.34 °C, and the annealing point AP to (7868.03 / 5.6+323.533) K = 862.439 K, i.e. 589.239 °C.

[0361] With respect to flat glass production, e.g., by drawing, the working point is advantageously at most 1400°C, more advantageously at most 1390°C, more advantageously at most 1380°C, more advantageously at most 1370°C, more advantageously at most 1360°C, more advantageously at most 1350°C, more advantageously at most 1340°C, more advantageously at most 1330°C, more advantageously at most 1320°C, more advantageously at most 1310°C, more advantageously at most 1300°C, more advantageously at most 1290°C, more advantageously at most 1280°C, more advantageously at most 1270°C, more advantageously at most 1260°C, more advantageously at most 1250°C.19.01.2026

[0362] As a low value of the working point indicates a small bonding forces between the atoms which in return may give rise to a low chemical resistivity, the working point is preferably above 1000°C, more preferably above 1050°C, and most preferably above 1100°C.

[0363] Refractive Index

[0364] The bigger the fraction of high polarization components is, the higher the refractive index difference between the central cylinder and the surrounding hollow cylinder will be after demixing when the central cylinder will contain significantly more high polarization components than the surrounding hollow cylinder where the fraction of the low polarization components SiO2and / or B2O3has been increased.

[0365] Therefore, one advantageous embodiment of the invention is a combination of mixtures with high refractive index. The inventive glass has a refractive index higher than 1.5, more preferred higher than 1.51, even more preferred higher than 1.52, even more preferred higher than 1.53, even more preferred higher than 1.54, even more preferred higher than 1.55, even more preferred higher than 1.56, even more preferred higher than 1.57, even more preferred higher than 1.58, even more preferred higher than 1.59, even more preferred higher than 1.6, even more preferred higher than 1.6, even more preferred higher than 1.61, even more preferred higher than 1.62, even more preferred higher than 1.63, even more preferred higher than 1.64, even more preferred higher than 1.65, even more preferred higher than 1.66, even more preferred higher than 1.67, even more preferred higher than 1.68, even more preferred higher than 1.69, most preferred higher than 1.70.

[0366] By refractive index, the following calculated value is addressed. First, the polarizability of the molecular units is calculated for each constituent phase in the crystalline state according to Shannon and Fischer, loc. cit. This calculation requires the coefficients published by Shannon and Fischer in said publication, the molecular mass, the density in the crystalline state and the coordination of each cation in this crystalline state. The latter data are taken from the mineralogical literature. From this polarizability value and, again, the molecular mass and the density in the crystalline state, the refractive index in the crystalline state can be calculated.

[0367] Note that one must distinguish between the molar and the molecular mass as well as between the molar volume and the molecular volume. The factor in between is Avogadro's constant.19.01.2026

[0368] To derive the refractive index in the glassy state, it is assumed that the polarizability does not differ from the one in the crystalline state, and that it is only the different density which causes a different refractive index. Thus, the above values for the refractive indices of the constituent phases have been calculated.

[0369] To derive the refractive index n of a combination of constituent phases, first, the weighted sum pwof the polarizabilities p; of the constituent phases as listed in the below table is calculated. Second, the weighted sum vwof the molecular volumes vias listed in the below table is calculated. The weights are the molar fractions in all cases. From the weighted sum of the polarizabilities and the molecular volumes thus obtained, the refractive index is calculated with the Lorentz- Lorenz equation

[0370] pw= Σni=1ci· pi(13)

[0371] vw= Σni=1ci· vi(14)

[0372] in-Pw (15) “

[0373]

[0374] The required mineralogical data and for the densities in the crystalline state have been taken from the literature.

[0375] As it has been said above, the polarizabilities of the constituent phases can be calculated from the above mineralogical data and the densities in the crystalline state together with the coefficients. From these polarizabilities and the molar volumes in the glassy state the refractive indices are calculated. The molar volumes in the glassy state are calculated from the molar masses and the densities in the glassy state. With the exception of the densities in the glassy state which are listed above, all quantities are listed in the following table.

[0376] Table 16

[0377] Constituent Density in PolariMolar Glassy Phase crystalline zabimass / g molar state / (g / cm3) lity / volume / A3cm3

[0378] Eucryptite (Li2O Al2O3-2SiO2) / 4 2.663 3.8203 63.0025 26.6621

[0379]

[0380] 19.01.2026

[0381] Constituent Density in PolariMolar Glassy Phase crystalline zabimass / g molar state / (g / cm3) lity / volume /

[0382] A3cm3Nepheline (Na2O Al2O3-2SiO2) / 4 2.642 3.9103 71.0270 27.8254

[0383] (K2O·Al2O3·2SiO2) / 4 2.594 4.3728 79.0810 31.0000 Cordierite (2MgO·2Al2O3·5SiO2) / 9 2.639 3.7484 64.9944 24.7306 Anorthite (CaO Al2O3-2SiO2) / 4 2.744 4.0470 69.5515 25.8210

[0384] (SrO·Al2O3·2SiO2) / 4 3.098 4.1541 81.4370 26.9570 Celsian (BaO Al2O3-2SiO2) / 4 3.39 4.4139 93.8638 27.6884

[0385] (Li2O·B2O3·4SiO2) / 6

[0386] Malinkoite (Na2O·B2O3·2SiO2) / 4 2.927 3.5306 62.9415 24.7343

[0387] (La2O3·B2O3·2SiO2) / 4 4.7 6.1286 128.899 33.0510 (Na2O·TiO2·4SiO2) / 6 2.775 4.1357 63.6967 24.1458 (K2O·TiO2·3SiO2) / 5 2.984 4.6258 70.8624 26.9093 (BaO·TiO2·3SiO2) / 5 3.73 4.7966 82.6886 23.4245 (Na2O·ZrO2·4SiO2) / 6 2.97 4.0304 70.9228 24.5416 (K2O·ZrO2·3SiO2) / 5

[0388] (2CaO·ZrO2·4SiO2) / 7 3.11 3.9637 67.9589 21.9889 (BaO·ZrO2·3SiO2) / 5

[0389] (K2O Nb2O5-4SiO2) / 6 3.2 6.2996 100.0566 32.8054 (Na2O·ZnO·2SiO2) / 4 3.09 3.3458 65.8815 21.6005

[0390]

[0391] 19.01.2026

[0392] Constituent Density in PolariMolar Glassy Phase crystalline zabimass / g molar state / (g / cm3) lity / volume /

[0393] A3cm3(Na2O·ZnO·3SiO2) / 5 2.95 3.2998 64.722 22.70947 (K2O·ZnO·2SiO2) / 4 3.12 3.7478 73.9355 25.0629 Lithium- Disili(Li2O'2SiO2) / 3 2.449 3.1552 50.0163 21.2745 cate

[0394] (Na2O·2SiO2) / 3 2.51 3.3198 60.7157 24.3740 (K2O·2SiO2) / 3 2.61 3.9004 71.4543 28.8471 (MgO·SiO2) / 2 3.21 2.8167 50.1940 18.2027 (CaO·SiO2) / 2 2.912 3.4671 58.0805 20.0209 Sanbornite (BaO-2SiO2) / 3 3.77 4.0163 91.1657 24.5855

[0395] (4ZnO·3B2O3) / 7 4.2397 3.8820 76.339 21.38295 (ZrO2·B2O3) / 2

[0396] (La2O3 Nb2O5-2B2O3) / 4

[0397] (La2O3·Ta2O5·2B2O3) / 4

[0398] (3BaO-3B2O3-2SiO2) / 8 4.17 4.4838 98.6253 25.473 DiborontriB2O31.82 5.0752 69.6190 38.2522 oxide

[0399] Quartz SiO22.65 3.4566 60.0840 27.2737

[0400]

[0401] 19.01.2026

[0402] Further components

[0403] In addition to the components already mentioned, the glass may contain further constituents, referred to herein as "balance". The proportion of balance in the glass according to the invention is preferably at most 5 mol-%, so as not to disturb the glass properties set by careful selection of suitable base glasses. In particularly advantageous embodiments, the proportion of balance in the glass is at most 3 mol%, more advantageously at most 2 mol% or at most 1 mol% or at most 0.5 mol%. The balance contains in particular oxides which are not contained in the base glasses mentioned herein. Thus, the balance in particular does not contain SiO2, B2O3, Al2O3, TiO2, ZrO2, Nb2O5, Ta2O5, ZnO, MgO, CaO, SrO, BaO, Li2O, Na2O or K2O.

[0404] When this description states that the glasses are free of a component or constituent phase or do not contain a certain component or constituent phase, it is meant that this component or constituent phase may be present at most as an impurity in the glasses. This means that it is not added in substantial amounts. According to the invention, non-substantial amounts are amounts of less than 500 ppm (molar), preferably less than 300 ppm (molar), particularly preferably less than 100 ppm (molar), even more preferably less than 50 ppm (molar), and most preferably less than 10 ppm (molar). Preferably, the glasses of the present invention are free of lead, arsenic, antimony, and / or cadmium.

[0405] Other Glass Properties

[0406] The glass according to this invention will preferably be provided as sheet or endless sheet, with a medium thickness of 30pm to 3mm.

[0407] Production

[0408] Also, according to the invention is a method for producing a glass of the present invention, comprising the steps of:

[0409] - Melting the glass raw materials,

[0410] - optionally forming a glass article, in particular a glass sheet, from the molten glass

[0411] - Cooling of the glass.19.01.2026

[0412] Forming the glass may comprise a drawing process or a floating process. Cooling may involve active cooling using a coolant, such as a cooling fluid, or passive cooling.

[0413] Uses and glass articles

[0414] According to the invention, the glass may be used as substrate glass in an electronic and / or optoelectronic device. It is especially suitable to inscribe optical waveguides by ultra short pulse (usp) laser inscription into the glass substrate and / or to mount semiconductor elements on it, including the coupling to semiconductor devices and / or substrates.

[0415] The invention also covers a substrate comprising the glass described above, wherein the glass contains an inscribed waveguide and / or wherein the substrate is mounted to a semiconductor device, or the semiconductor device is mounted to an area of the substrate comprising the aforesaid glass.

[0416] The invention relates to an electronic or optoelectronic device as well which comprises the glass or the substrate described above.

[0417] The method of inscribing a waveguide into a substrate, comprising the steps of providing a usp-laser source and directing a focused laser beam from said usp-laser source onto the substrate, whereas the substrate is selected from a glass described above, is also subject to the invention.

[0418] Suitable lasers for waveguide inscription are ultra short pulse lasers, thus lasers that emit their power as pulse trains, where the temporal distance between the pulses is 1 / R, with R being the repetition rate of the laser. The repetition rate can be in the range from 1 Hz to 100 GHz, but preferred, 1 kHz, 10 kHz, 50 kHz, 100 kHz, 500 kHz, 1 MHz, 50 MHz. The pulse duration (FWHM, full width, half max) of these lasers is typically between 30 fs up to 20 ps. For waveguide inscription the preferred duration is 80 fs to 300 fs, most preferred 100 fs or 250 fs. They emit their laser light at center wavelength of 800 nm in case of Titanium-Sapphire lasers or at 1030 nm or 1064 nm for Nd: YAG lasers. However, for some wave guide inscription processes, converting the laser wavelength into the VIS or UV range can be favorable, e.g. with second harmonic generation (SHG) or third harmonic generation (THG) by means of non-linear crystals. Thus, the center wavelengths can also be 200 nm, 355 nm, 400 nm, 515 nm, 532 nm. The spectral bandwidth can be 1 nm and up to 100 nm. The output beam parameter of the collimated laser beam is usually 3 to 5 mm (1 / e2), but19.01.2026

[0419] can also be increased with telescope setup to 10 mm or 20 mm. Some of these lasers can not only emit their energy single pulses, but also divide the energy in sub-pulse trains, so-called “burst”, where the inter-subpulse distance Atpis much smaller than 1 / R, typically in the range of 1-200 ns, most preferred to be 20 ns - 30 ns. These bursts consist of 2 to 50 sub pulses. Preferred are bursts of 2 to 4 or 3 to 7 sub pulses. The output power P of the lasers is typically between 1 W and 500 W. The pulse energy or burst energy is P / R. For the waveguide process pulse energies or burst energies of 0.1 to 8 J, preferred 0.5 to 2 pj. For this regime it might be necessary to attenuate the output power of the laser system.

[0420] For the waveguide inscription microscope objectives or especially laser inscription objectives are used. Those represent an example of generally suitable optical systems. Whilst the microscope objectives are usually optimized for imaging in the VIS range, laser inscription objectives are designed to focus a collimated, quasi-monochromatic laser beam to a diffraction limited spot. In both cases, the objective can be characterized by its numerical aperture (NA), the ration of the half opening aperture to the nominal focal length. For waveguide inscription, NA of 0.05 to 0.9 are suitable, the preferred range of NA is 0.1, 0.2 or 0.4. For the waveguide inscription, the laser beam is incident on the input aperture of the optical system and the glass substrate is placed, so that the focal point of the optical system is located within the glass substrate. Mostly applied are optical systems with a high NA of 0.8, where the input diameter is matched to the input aperture of the optical system. In advanced setups, the optical system allows to compensate for optical aberration, namely spherical aberrations. Typically for placing the focus in a certain depth in the volume of the glass, the correction of the wavefront should be better than 0.3 wavelengths; where the wavelength is the one of the inscribing ultrashort pulse laser.

[0421] The translation velocity is the velocity at which the focus of the optical system is moved relative to the glass substrate. This can be achieved by translating the sample via a motion controlled stage or by moving the laser focus, e.g. with a mirror ensemble that ensures that the laser beam is still incident on the input aperture of the optical system, when the optical system is moved with a mechanical axis. Another implementation is the integration of deformable mirror or a spatial light modulator (SLM) before the optical system; thus translating the spot by imprinting a defocus and / or a tilt on the wavefront of the incident beam. Also, a combination of both of the translation mechanisms can be favorable, e.g. for achieving precision for longer modification lines. The translation velocities are in the range of 119.01.2026

[0422] mm / min to 10 m / min, preferably 10 mm / min to 1 m / min, more preferred 20 mm / min to 200 mm / min, most preferred 50 mm / min to 100 mm / min. It can also be favorable to set the translation velocity v in relation to the repetition rate of the laser R in order to achieve a periodicity of A=v / R. For waveguides with a double function as Bragg- Reflectors A is in the range of 100 nm to 10 pm, more preferred 200 nm to 2 pm, most preferred 500 nm to 1.5 pm. For steering the inherent waveguide properties, much smaller periodicities A of 0.1 to 10 nm are favourable, most preferred 0.2 to 5 nm. A combination of two modification can be achieved with pulse bursts: the longer periodicity is steered with the repetition rate R to be Λlarge=v / R, while the smaller periodicity is steered with inter-subpulse distance Δtpto be Λsmall= v* Δtp.

[0423] With these laser parameters a local raise of the refractive index of Δnmaxof up to 0.001 or more can be achieved with in the modification line. The preferred An is in the range of 0.0001 to 0.002, most preferred 0.0005 to 0.005 (or even more). By adjusting certain laser parameters, e.g. the pulse energy, the An can be continuously altered. This can be done during inscription, so that An varies along the modification line of length L along the z-axis. The variation of can be linear or non-linear function of the modification line coordinate I, 0<l< L. It can also be periodic or an-periodic.

[0424] For the waveguiding properties, the transversal refractive index profile of the modification line is relevant. For the following, we introduce the local coordinate vectors x and y, which are both perpendicular to the modification line vector z and centered at the modification line. For most laser parameters, the refractive index profile An(x,y) is approximately rectangular: e.g. it can be described with An (x,y) = A nmax for |x| < wx / 2 and |y|< wy / 2 and An = 0 elsewhere. Here wxand wyare the transversal widths of the waveguides, which are typically 0.2 pm to 100 pm, more preferred 0.5 to 20 pm, even more preferred 1-15 pm, most preferred 2- 12 pm.

[0425] However, due to the Soret effect, for the glass substrates in this invention, the refractive crossection of the waveguide can be steered with the aforementioned laser parameters, so that the profile is more gradient like, e.g. Δn (x,y) = Δnmax- ( a

[0426]

[0427] a1|x| + a2x2+ a3|x|3+ a4x4+... + b1|y| + b2y2+ b3|y|3+ b4y4+.... This profile can also be altered along the modification line. In this case we relate to the FWHM definition of the waveguide width along the local x and y axis.19.01.2026

[0428] The waveguides lines of this invention have low losses for light at the wavelength of 1550 nm, namely below 1 dB / cm, preferably 0.3 dB / cm, most preferred smaller than 0.1 dB / cm, mostly preferred below 0.05 dB / cm.

[0429] Also provided herein is a method of manufacturing an electronic or optoelectronic device, comprising the steps of mounting a semiconductor element to an element comprising the glass according to this description.

[0430] Advantageously, the invention is represented in a method of manufacturing an electronic or optoelectronic device comprising a semiconductor element and a glass substrate, comprising the steps of determining the CTE of the semiconductor element, then selecting the CTE of glass of the glass substrate by selecting a composition range of the glass according to this description.

[0431] Examples

[0432] For comparison with the prior art, we first provide a conversion matrix for the mutual conversion of both compositional data.

[0433] As above, the composition in constituent phases is given in the following normalized form for the purpose of conversion:

[0434] Table 17

[0435] Constituent Phase

[0436] Eucryptite (Li2O·Al2O3·2SiO2) / 4

[0437] Nepheline (Na2O·Al2O3·2SiO2) / 4

[0438] (K2O·Al2O3·2SiO2) / 4

[0439] Cordierite (2MgO·2Al2O3·5SiO2) / 9

[0440] Anorthite (CaO·Al2O3·2SiO2) / 4

[0441] (SrO·Al2O3·2SiO2) / 4

[0442] Celsian (BaO·Al2O3·2SiO2) / 4

[0443]

[0444] 19.01.2026

[0445] Constituent Phase

[0446] (Li2O·B2O3·4SiO2) / 6

[0447] Malinkoite (Na2O·B2O3·2SiO2) / 4

[0448] (La2O3·B2O3·2SiO2) / 4

[0449] (Na2O·TiO2·4SiO2) / 6

[0450] (K2O·TiO2·3SiO2) / 5

[0451] (BaO·TiO2·3SiO2) / 5

[0452] (Na2O·ZrO2·4SiO2) / 6

[0453] (K2O·ZrO2·3SiO2) / 5

[0454] (2CaO·ZrO2·4SiO2) / 7

[0455] (BaO·ZrO2·3SiO2) / 5

[0456] (K2O Nb2O5-4SiO2) / 6

[0457] (Na2O·ZnO·2SiO2) / 4

[0458] (Na2O ZnO S3iO2) / 5

[0459] (K2O·ZnO·2SiO2) / 4

[0460] Lithium-Disilicate (Li2O·2SiO2) / 3

[0461] (Na2O-2SiO2) / 3

[0462] (K2O-2SiO2) / 3

[0463] (MgO·SiO2) / 2

[0464] (CaO·SiO2) / 2

[0465] Sanbornite (BaO-2SiO2) / 3

[0466]

[0467] 19.01.2026

[0468] Constituent Phase

[0469] (4ZnO·3B2O3) / 7

[0470] (ZrO2·B2O3) / 2

[0471] (La2O3·Nb2O5·2B2O3) / 4

[0472] (La2O3Ta2O5·2B2O3) / 4

[0473] (3BaO·3B2O3·2SiO2) / 8

[0474] Diborontrioxide B2O3

[0475] Quartz glass SiO2

[0476]

[0477] The conversion of these compositions into a composition statement in mol% with respect to the following simple oxides contained in Table 18 is carried out with the aid of elementary linear algebra. The composition in mol% with respect to the constituent phases is multiplied as a column vector from the right to the appropriate matrix.

[0478] Table 18

[0479] Oxide

[0480] SiO2

[0481] TiO2

[0482] ZrO2

[0483] B2O3

[0484] Al2O3

[0485] La2O3

[0486] Nb2O5

[0487] Ta2O5

[0488]

[0489] 19.01.2026

[0490] Oxide

[0491] ZnO

[0492] MgO

[0493] CaO

[0494] SrO

[0495] BaO

[0496] Li2O

[0497] Na2O

[0498] K2O

[0499]

[0500] As a result of the multiplication of the column vector to the matrix, the composition of the glass in mole percent with respect to simple oxides is obtained.

[0501] In case the number of constituent phases involved equals the number of simple oxides involved, the matrix will be quadratic and invertible. As a result of the multiplication of the column vector with the simple oxides to the inverse matrix, the composition of the glass in mole percent with respect to constituent phases will be obtained in this case.

[0502] As reference, we consider a composition as listed in Table 19.

[0503] Table 19

[0504] Constituent Phase Fraction / mol% Eucryptite (Li2O Al2O3-2SiO2) / 4 0

[0505] Nepheline (Na2O Al2O3-2SiO2) / 4 0

[0506] (K2O Al2O3-2SiO2) / 4 10

[0507] Cordierite (2MgO-2Al2O3-5SiO2) / 9 0

[0508]

[0509] 19.01.2026

[0510] Constituent Phase Fraction / mol% Anorthite (CaO Al2O3-2SiO2) / 4 0

[0511] (SrO Al2O3-2SiO2) / 4 0

[0512] Celsian (BaO Al2O3-2SiO2) / 4 0

[0513] (Li2O·B2O3·4SiO2) / 6 0

[0514] Malinkoite (Na2O·B2O3·2SiO2) / 4 0

[0515] (La2O3·B2O3·2SiO2) / 4 0

[0516] (Na2O·TiO2·4SiO2) / 6 0

[0517] (K2O·TiO2·3SiO2) / 5 0

[0518] (BaO·TiO2·3SiO2) / 5 0

[0519] (Na2O·ZrO2·4SiO2) / 6 0

[0520] (K2O·ZrO2·3SiO2) / 5 0

[0521] (2CaO·ZrO2·4SiO2) / 7 0

[0522] (BaO·ZrO2·3SiO2) / 5 0

[0523] (K2O Nb2O5-4SiO2) / 6 0

[0524] (Na2O·ZnO·2SiO2) / 4 0

[0525] (Na2O·ZnO·3SiO2) / 5 0

[0526] (K2O·ZnO·2SiO2) / 4 0

[0527] Lithium-Disilicate (Li2O·2SiO2) / 3 54

[0528] (Na2O-2SiO2) / 3 0

[0529] (K2O-2SiO2) / 3 0

[0530]

[0531] 19.01.2026

[0532] Constituent Phase Fraction / mol% (MgO·SiO2) / 2 0

[0533] (CaO·SiO2) / 2 0

[0534] Sanbornite (BaO-2SiO2) / 3 0

[0535] (4ZnO·3B2O3) / 7 0

[0536] (ZrO2·B2O3) / 2 0

[0537] (La2O3·Nb2O5·2B2O3) / 4 0 (La2O3·Ta2O5·2B2O3) / 4 0

[0538] (3BaO·3B2O3·2SiO2) / 8 0

[0539] Diborontrioxide B2O30

[0540] Quartz glass SiO236

[0541]

[0542] Table 20: Reference in simple oxides

[0543] Oxide Fraction / mol%

[0544] SiO277

[0545] TiO20

[0546] ZrO20

[0547] B2O30

[0548] Al2O32.5

[0549] La2O30

[0550]

[0551] 19.01.2026

[0552] Oxide Fraction / mol%

[0553] Ta2O5 0

[0554] ZnO 0

[0555] MgO 0

[0556] CaO 0

[0557] SrO 0

[0558] BaO 0

[0559] Li2O 18

[0560] Na2O 0

[0561] K2O 2.5

[0562]

[0563] The calculated properties are:

[0564] 1. The thermal expansion coefficient calculated according to (3) amounts to 9.31 ppm / K.

[0565] 2. The refractive index calculated according to (15) amounts to 1.50.

[0566] In order to adjust the CTE calculated according to (3) close to the above mentioned value of 3.3 ± 0.3 ppm / K, which is favourable with respect to a combination with silicon, in order to fix the working point WP calculated according to (11) in the range from 1100°C to 1400°C, and in order to ensure the refractive index calculated according to (15) amounting to 1.5 or more, the following compositional range has been found to be favourable:

[0567] Table 7: Composition in constituent phases (molar) particularly favourable for combinations with silicon

[0568] Constituent phase Minimum Maximum (Li2O Al2O3-2SiO2) / 4 0% 0%

[0569]

[0570] 19.01.2026

[0571] Constituent phase Minimum Maximum (Na2O Al2O3-2SiO2) / 4 0% 10% (K2O Al2O3-2SiO2) / 4 0% 0% (2MgO·2Al2O3·5SiO2) / 9 0% 50% (CaO Al2O3-2SiO2) / 4 0% 50% (SrO·Al2O3·2SiO2) / 4 0% 0% (BaO Al2O3-2SiO2) / 4 0% 0% (Li2O·B2O3·4SiO2) / 6 0% 0% (Na2O·B2O3·2SiO2) / 4 0% 0% (La2O3·B2O3·2SiO2) / 4 0% 0% (Na2O·TiO2·4SiO2) / 6 0% 0% (K2O·TiO2·3SiO2) / 5 0% 0% (BaO·TiO2·3SiO2) / 5 0% 0% (Na2O·ZrO2·4SiO2) / 6 0% 40% (K2O·ZrO2·3SiO2) / 5 0% 0% (2CaO·ZrO2·4SiO2) / 7 0% 80% (BaO·ZrO2·3SiO2) / 5 0% 0% (K2O Nb2O5-4SiO2) / 6 0% 60% (Na2O·ZnO·2SiO2) / 4 0% 0% (Na2O·ZnO·3SiO2) / 5 0% 0%

[0572] (K2O·ZnO·2SiO2) / 4 0% 0%

[0573]

[0574] 19.01.2026

[0575] Constituent phase Minimum Maximum (Li2O·2SiO2) / 3 0% 10%

[0576] (Na2O-2SiO2) / 3 0% 10%

[0577] (K2O-2SiO2) / 3 0% 10% (MgO·SiO2) / 2 0% 0% (CaO·SiO2) / 2 0% 0%

[0578] (BaO-2SiO2) / 3 0% 0%

[0579] (4ZnO·3B2O3) / 7 0% 0% (ZrO2·B2O3) / 2 0% 0% (La2O3·Nb2O5·2B2O3) / 4 0% 0% (La2O3Ta2O5‘2B2O3) / 4 0% 0%

[0580] (3BaO·3B2O3·2SiO2) / 8 0% 0%

[0581] B2O30% 10%

[0582] SiO20% 65% B2O3+SiO230% 70%

[0583]

[0584] The above compositional ranges comprehend, in particular, the following embodiments:

[0585] Table 22: Examples of compositions in constituent phases (molar) particularly favourable for combinations with silicon19.01.2026

[0586] Example 1 Example 2 Example 3 Example 4 Example 5 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0 (Na2O Al2O3-2SiO2) / 4 0 0 0 0 20 (K2O Al2O3-2SiO2) / 4 0 0 0 0 0 (2MgO-2Al2O3-5SiO2) / 9 50 30 40 40 20 (CaO Al2O3-2SiO2) / 4 0 20 0 0 0 (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 0 0 0 0 0 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (La2O3·B2O3·2SiO2) / 4 0 0 0 0 0 (Na2O·TiO2·4SiO2) / 6 0 0 0 0 0 (K2O·TiO2·3SiO2) / 5 0 0 0 0 0 (BaO·TiO2·3SiO2) / 5 0 0 0 0 0 (Na2O·ZrO2·4SiO2) / 6 0 0 0 0 0 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 0 10 0 10 (BaO·ZrO2·3SiO2) / 5 0 0 0 0 0 (K2O Nb2O5-4SiO2) / 6 0 0 0 10 0

[0587]

[0588] 19.01.2026

[0589] Example 1 Example 2 Example 3 Example 4 Example 5 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Na2O·ZnO·3SiO2) / 5 0 0 0 0 0 (K2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Li2O·2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0 (K2O-2SiO2) / 3 0 0 0 0 0 (MgO·SiO2) / 2 0 0 0 0 0 (CaO·SiO2) / 2 0 0 0 0 0 (BaO-2SiO2) / 3 0 0 0 0 0 (4ZnO·3B2O3) / 7 0 0 0 0 0 (ZrO2·B2O3) / 2 0 0 0 0 0 (La2O3·Nb2O5·2B2O3) / 4 0 0 0 0 0 (La2O3Ta2O5·2B2O3) / 4 0 0 0 0 0 (3BaO·3B2O3·2SiO2) / 8 0 0 0 0 0 B2O35 5 5 5 5 SiO245 45 45 45 55 CTE / (ppm / K) 3.36145 3.43982 3.179 3.34088 3.57144 Refractive index 1.50058 1.50453 1.50871 1.51935 1.50029

[0590]

[0591] 19.01.2026

[0592] Example 1 Example 2 Example 3 Example 4 Example 5 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% WP / °C 1265.89 1266.52 1258.69 1235. 1335.09

[0593]

[0594] If one allows the CTE calculated according to (3) to lie in the broader range 3.3 ± 0.5 ppm / K, the following embodiment may be considered also:

[0595] Table 23: Examples composition in constituent phases (molar) particularly favourable for combinations with silicon

[0596] Example 1

[0597] Constituent Phase Fraction /

[0598] mol%

[0599] (Li2O Al2O3-2SiO2) / 4 0

[0600] (Na2O Al2O3-2SiO2) / 4 0

[0601] (K2O Al2O3-2SiO2) / 4 0

[0602] (2MgO'2Al2O3'5SiO2) / 9 19.8

[0603] (CaO Al2O3-2SiO2) / 4 17.6

[0604] (SrO Al2O3-2SiO2) / 4 0

[0605] (BaO Al2O3-2SiO2) / 4 4.8

[0606] (Li2O·B2O3·4SiO2) / 6 0

[0607] (Na2O·B2O3·2SiO2) / 4 0

[0608] (La2O3·B2O3·2SiO2) / 4 0

[0609] (Na2O·TiO2·4SiO2) / 6 0

[0610]

[0611] 19.01.2026

[0612] Example 1

[0613] Constituent Phase Fraction /

[0614] mol%

[0615] (K2O·TiO2·3SiO2) / 5 0

[0616] (BaO·TiO2·3SiO2) / 5 0

[0617] (Na2O·ZrO2·4SiO2) / 6 0

[0618] (K2O·ZrO2·3SiO2) / 5 0

[0619] (2CaO·ZrO2·4SiO2) / 7 0

[0620] (BaO·ZrO2·3SiO2) / 5 0

[0621] (K2O Nb2O5-4SiO2) / 6 0

[0622] (Na2O·ZnO·2SiO2) / 4 0

[0623] (Na2O·ZnO·3SiO2) / 5 0

[0624] (K2O·ZnO·2SiO2) / 4 0

[0625] (Li2O·2SiO2) / 3 0

[0626] (Na2O-2SiO2) / 3 0

[0627] (K2O-2SiO2) / 3 0

[0628] (MgO·SiO2) / 2 0

[0629] (CaO·SiO2) / 2 0

[0630] (BaO-2SiO2) / 3 0

[0631] (4ZnO·3B2O3) / 7 3.85

[0632] (ZrO2·B2O3) / 2 4

[0633]

[0634] 19.01.2026

[0635] Example 1

[0636] Constituent Phase Fraction /

[0637] mol%

[0638] (La2O3 Nb2O5-2B2O3) / 4 0

[0639] (La2O3·Ta2O5·2B2O3) / 4 0

[0640] (3BaO-3B2O3-2SiO2) / 8 0

[0641] B2O35.15

[0642] SiO240.9

[0643] Rest 0.1

[0644] CTE / (ppm / K) calculated 3.7689

[0645] CTE / (ppm / K) measured 3.24

[0646] WP / °C measured

[0647]

[0648] In order to adjust the CTE calculated according to (3) close to the above mentioned value of 4.7 ± 0.3 ppm / K, which is favourable with respect to a combination with Indiumphosphide, and in order to fix the working point WP calculated according to (11) in the range from 1100°C to 1400°C, and in order to ensure the refractive index calculated according to (15) amounting to 1.5 or more, the following compositional range has found to be favourable:

[0649] Table 24: Composition in constituent phases (molar) particularly favourable for combinations with Indiumphosphide

[0650] Constituent phase Minimum Maximum (Li2O Al2O3-2SiO2) / 4 0% 0%

[0651]

[0652] 19.01.2026

[0653] Constituent phase Minimum Maximum (Na2O Al2O3-2SiO2) / 4 0% 20% (K2O Al2O3-2SiO2) / 4 0% 0% (2MgO·2Al2O3·5SiO2) / 9 0% 80% (CaO Al2O3-2SiO2) / 4 0% 80% (SrO·Al2O3·2SiO2) / 4 0% 0% (BaO Al2O3-2SiO2) / 4 0% 0% (Li2O·B2O3·4SiO2) / 6 0% 0% (Na2O·B2O3·2SiO2) / 4 0% 0% (La2O3·B2O3·2SiO2) / 4 0% 0% (Na2O·TiO2·4SiO2) / 6 0% 0% (K2O·TiO2·3SiO2) / 5 0% 0% (BaO·TiO2·3SiO2) / 5 0% 0% (Na2O·ZrO2·4SiO2) / 6 0% 60% (K2O·ZrO2·3SiO2) / 5 0% 0% (2CaO·ZrO2·4SiO2) / 7 0% 60% (BaO·ZrO2·3SiO2) / 5 0% 0% (K2O Nb2O5-4SiO2) / 6 0% 60% (Na2O·ZnO·2SiO2) / 4 0% 0% (Na2O·ZnO·3SiO2) / 5 0% 0% (K2O·ZnO·2SiO2) / 4 0% 0%

[0654]

[0655] 19.01.2026

[0656] Constituent phase Minimum Maximum (Li2O'2SiO2) / 3 0% 30%

[0657] (Na2O-2SiO2) / 3 0% 20%

[0658] (K2O-2SiO2) / 3 0% 20% (MgO·SiO2) / 2 0% 0% (CaO·SiO2) / 2 0% 0%

[0659] (BaO-2SiO2) / 3 0% 0%

[0660] (4ZnO·3B2O3) / 7 0% 0% (ZrO2·B2O3) / 2 0% 0% (La2O3·Nb2O5·2B2O3) / 4 0% 0% (La2O3Ta2O5‘2B2O3) / 4 0% 0%

[0661] (3BaO·3B2O3·2SiO2) / 8 0% 20%

[0662] B2O30% 10%

[0663] SiO20% 65% B2O3+SiO220% 75%

[0664]

[0665] Table 25: Example compositions in constituent phases (molar) particularly favourable for combinations with Indiumphosphide

[0666] Example 1 Example 2 Example 3 Example 4 Example 5 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0

[0667]

[0668] 19.01.2026

[0669] Example 1 Example 2 Example 3 Example 4 Example 5 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Na2O Al2O3-2SiO2) / 4 0 0 0 10 10 (K2O Al2O3-2SiO2) / 4 0 0 0 0 0 (2MgO·2Al2O3·5SiO2) / 9 0 0 80 10 20 (CaO Al2O3-2SiO2) / 4 70 60 0 40 20 (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 0 0 0 0 0 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (La2O3·B2O3·2SiO2) / 4 0 0 0 0 0 (Na2O·TiO2·4SiO2) / 6 0 0 0 0 0 (K2O·TiO2·3SiO2) / 5 0 0 0 0 0 (BaO·TiO2·3SiO2) / 5 0 0 0 0 0 (Na2O·ZrO2·4SiO2) / 6 0 0 0 0 0 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 0 0 0 0 (BaO·ZrO2·3SiO2) / 5 0 0 0 0 0 (K2O Nb2O5-4SiO2) / 6 0 10 0 0 10 (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0

[0670]

[0671] 19.01.2026

[0672] Example 1 Example 2 Example 3 Example 4 Example 5 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Na2O·ZnO·3SiO2) / 5 0 0 0 0 0 (K2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Li2O·2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0 (K2O-2SiO2) / 3 0 0 0 0 0 (MgO·SiO2) / 2 0 0 0 0 0 (CaO·SiO2) / 2 0 0 0 0 0 (BaO-2SiO2) / 3 0 0 0 0 0 (4ZnO·3B2O3) / 7 0 0 0 0 0 (ZrO2·B2O3) / 2 0 0 0 0 0 (La2O3·Nb2O5·2B2O3) / 4 0 0 0 0 0 (La2O3Ta2O5·2B2O3) / 4 0 0 0 0 0 (3BaO·3B2O3·2SiO2) / 8 0 0 0 0 0 B2O35 5 5 5 5 SiO225 25 15 35 35 CTE / (ppm / K) 4.53764 4.46893 4.72706 4.73678 4.62872 Refractive index 1.53166 1.54768 1.5275 1.5134 1.5279 WP / °C 1181.2 1157.78 1138.71 1231.9 1203.79

[0673]

[0674] 19.01.2026

[0675] Example Example Example Example Example 1 b 2b 3b 4b 5b Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0 (Na2O Al2O3-2SiO2) / 4 4 8 0 0 0 (K2O Al2O3-2SiO2) / 4 0 0 0 0 0 (2MgO-2Al2O3-5SiO2) / 9 9 9 0 0 0 (CaO Al2O3-2SiO2) / 4 8 8 8 8 8 (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 8 8 16 24 24 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (La2O3·B2O3·2SiO2) / 4 0 0 0 0 0 (Na2O·TiO2·4SiO2) / 6 0 0 0 0 0 (K2O·TiO2·3SiO2) / 5 0 0 0 0 0 (BaO·TiO2·3SiO2) / 5 0 0 0 0 0 (Na2O·ZrO2·4SiO2) / 6 12 6 6 12 12 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 0 0 0 0 (BaO·ZrO2·3SiO2) / 5 0 0 0 0 0 (K2O Nb2O5-4SiO2) / 6 6 6 12 0 0

[0676]

[0677] 19.01.2026

[0678] Example Example Example Example Example 1b 2b 3b 4b 5b Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Na2O·ZnO·3SiO2) / 5 0 0 10 5 0 (K2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Li2O·2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0 (K2O-2SiO2) / 3 0 0 0 0 0 (MgO·SiO2) / 2 0 0 0 0 0 (CaO·SiO2) / 2 0 0 0 0 0 (BaO-2SiO2) / 3 0 0 0 0 0 (4ZnO·3B2O3) / 7 7 7 7 7 14 (ZrO2·B2O3) / 2 0 0 0 0 0 (La2O3·Nb2O5·2B2O3) / 4 0 0 0 0 0 (La2O3Ta2O5·2B2O3) / 4 0 0 0 0 0 (3BaO·3B2O3·2SiO2) / 8 0 0 0 0 0 B2O36 8 2 4 0 SiO240 40 39 40 42 CTE / (ppm / K) 4.74709 4.97738 5.16569 4.9435 5.02558 Refractive index 1.52878 1.52314 1.54356 1.52504 1.53394

[0679]

[0680] 19.01.2026

[0681] Example Example Example Example Example 1 b 2b 3b 4b 5b Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% WP / °C 1113.29 1075.37 1149.47 1165.88 1184.84

[0682]

[0683] Example

[0684] 6b

[0685] Constituent Phase Fraction /

[0686] mol%

[0687] (Li2O Al2O3-2SiO2) / 4 0

[0688] (Na2O Al2O3-2SiO2) / 4 0

[0689] (K2O Al2O3-2SiO2) / 4 0

[0690] (2MgO'2Al2O3'5SiO2) / 9 9

[0691] (CaO Al2O3-2SiO2) / 4 12

[0692] (SrO Al2O3-2SiO2) / 4 0

[0693] (BaO Al2O3-2SiO2) / 4 20

[0694] (Li2O·B2O3·4SiO2) / 6 0

[0695] (Na2O·B2O3·2SiO2) / 4 0

[0696] (La2O3·B2O3·2SiO2) / 4 0

[0697] (Na2O·TiO2·4SiO2) / 6 0

[0698] (K2O·TiO2·3SiO2) / 5 0

[0699] (BaO·TiO2·3SiO2) / 5 0

[0700]

[0701] 19.01.2026

[0702] Example

[0703] 6b

[0704] Constituent Phase Fraction /

[0705] mol%

[0706] (Na2O·ZrO2·4SiO2) / 6 0

[0707] (K2O·ZrO2·3SiO2) / 5 0

[0708] (2CaO·ZrO2·4SiO2) / 7 0

[0709] (BaO·ZrO2·3SiO2) / 5 0

[0710] (K2O Nb2O5-4SiO2) / 6 0

[0711] (Na2O·ZnO·2SiO2) / 4 0

[0712] (Na2O·ZnO·3SiO2) / 5 0

[0713] (K2O·ZnO·2SiO2) / 4 0

[0714] (Li2O·2SiO2) / 3 0

[0715] (Na2O-2SiO2) / 3 0

[0716] (K2O-2SiO2) / 3 0

[0717] (MgO·SiO2) / 2 0

[0718] (CaO·SiO2) / 2 0

[0719] (BaO-2SiO2) / 3 0

[0720] (4ZnO·3B2O3) / 7

[0721] (ZrO2·B2O3) / 2 2

[0722] (La2O3·Nb2O5·2B2O3) / 4 0

[0723] (La2O3·Ta2O5·2B2O3) / 4 0

[0724]

[0725] 19.01.2026

[0726] Example

[0727] 6b

[0728] Constituent Phase Fraction /

[0729] mol%

[0730] (3BaO-3B2O3-2SiO2) / 8 4

[0731] B2O36.25

[0732] SiO238

[0733] CTE / (ppm / K) calculated 4.64

[0734] CTE / (ppm / K) measured 3.81

[0735] WP / °C measured 1188

[0736]

[0737] If one allows the CTE calculated according to (3) to lie in the broader range 4.7 ± 0.5 ppm / K, the following embodiment may be considered also:

[0738] Table 26: Example compositions in constituent phases (molar) particularly favourable for combinations with indiumphosphide

[0739] Example Example

[0740] 1b 2b

[0741] Constituent Phase Fraction / Fraction /

[0742] mol% mol%

[0743] (Li2O·Al2O3·2SiO2) / 4 0 0

[0744] (Na2O·Al2O3·2SiO2) / 4 0 0

[0745] (K2O·Al2O3·2SiO2) / 4 0 0

[0746] (2MgO·2Al2O3·5SiO2) / 9 18 9

[0747]

[0748] 19.01.2026

[0749] Example Example

[0750] 1 b 2b

[0751] Constituent Phase Fraction / Fraction /

[0752] mol% mol%

[0753] (CaO Al2O3-2SiO2) / 4 8 12

[0754] (SrO Al2O3-2SiO2) / 4 0 0

[0755] (BaO Al2O3-2SiO2) / 4 16 20

[0756] (Li2O·B2O3·4SiO2) / 6 0 0

[0757] (Na2O·B2O3·2SiO2) / 4 0 0

[0758] (La2O3·B2O3·2SiO2) / 4 0 0

[0759] (Na2O·TiO2·4SiO2) / 6 0 0

[0760] (K2O·TiO2·3SiO2) / 5 0 0

[0761] (BaO·TiO2·3SiO2) / 5 0 0

[0762] (Na2O·ZrO2·4SiO2) / 6 0 6

[0763] (K2O·ZrO2·3SiO2) / 5 0 0

[0764] (2CaO·ZrO2·4SiO2) / 7 0 0

[0765] (BaO·ZrO2·3SiO2) / 5 0 0

[0766] (K2O Nb2O5-4SiO2) / 6 0 0

[0767] (Na2O·ZnO·2SiO2) / 4 0 0

[0768] (Na2O·ZnO·3SiO2) / 5 0 0

[0769] (K2O·ZnO·2SiO2) / 4 0 0

[0770] (Li2O·2SiO2) / 3 0 0

[0771]

[0772] 19.01.2026

[0773] Example Example

[0774] 1b 2b

[0775] Constituent Phase Fraction / Fraction /

[0776] mol% mol%

[0777] (Na2O·2SiO2) / 3 0 0

[0778] (K2O-2SiO2) / 3 0 0

[0779] (MgO·SiO2) / 2 0 0

[0780] (CaO·SiO2) / 2 0 0

[0781] (BaO-2SiO2) / 3 0 0

[0782] (4ZnO·3B2O3) / 7 8.75 7

[0783] (ZrO2·B2O3) / 2 3.2 0

[0784] (La2O3·Nb2O5·2B2O3) / 4 0 0

[0785] (La2O3Ta2O5‘2B2O3) / 4 0 0

[0786] (3BaO·3B2O3·2SiO2) / 8 0 8

[0787] B2O35.15 6

[0788] SiO240.8 32

[0789] Rest 0.1 0

[0790] CTE / (ppm / K) calculated 4.28546 5.07

[0791] CTE / (ppm / K) measured 3.59 4.45

[0792] WP / °C measured

[0793]

[0794] 19.01.2026

[0795] In order to adjust the CTE calculated according to (3) close to the above mentioned value of 6.3 ± 0.3 ppm / K, which is favorable with respect to a combination with germanium, and in order to fix the working point WP calculated according to (11) in the range from 1100°C to 1400°C, and in order to ensure the refractive index calculated according to (15) amounting to 1.5 or more, the following compositional range has found to be favorable:

[0796] Table 27: Composition in constituent phases (molar) particularly favourable for combinations with Germanium

[0797] Constituent phase Minimum Maximum (Li2O Al2O3-2SiO2) / 4 0% 0%

[0798] (Na2O Al2O3-2SiO2) / 4 0% 40%

[0799] (K2O Al2O3-2SiO2) / 4 0% 0%

[0800] (2MgO-2Al2O3-5SiO2) / 9 0% 60%

[0801] (CaO Al2O3-2SiO2) / 4 0% 60%

[0802] (SrO·Al2O3·2SiO2) / 4 0% 0%

[0803] (BaO Al2O3-2SiO2) / 4 0% 0%

[0804] (Li2O·B2O3·4SiO2) / 6 0% 0%

[0805] (Na2O·B2O3·2SiO2) / 4 0% 0%

[0806] (La2O3·B2O3·2SiO2) / 4 0% 0%

[0807] (Na2O·TiO2·4SiO2) / 6 0% 0%

[0808] (K2O·TiO2·3SiO2) / 5 0% 0%

[0809] (BaO·TiO2·3SiO2) / 5 0% 0%

[0810] (Na2O·ZrO2·4SiO2) / 6 0% 80%

[0811] (K2O·ZrO2·3SiO2) / 5 0% 0%

[0812]

[0813] 19.01.2026

[0814] Constituent phase Minimum Maximum (2CaO·ZrO2·4SiO2) / 7 0% 50% (BaO·ZrO2·3SiO2) / 5 0% 0% (K2O Nb2O5-4SiO2) / 6 0% 60% (Na2O·ZnO·2SiO2) / 4 0% 0% (Na2O·ZnO·3SiO2) / 5 0% 0% (K2O·ZnO·2SiO2) / 4 0% 0%

[0815] (Li2O·2SiO2) / 3 0% 40%

[0816] (Na2O-2SiO2) / 3 0% 30%

[0817] (K2O-2SiO2) / 3 0% 30% (MgO·SiO2) / 2 0% 0% (CaO·SiO2) / 2 0% 0%

[0818] (BaO-2SiO2) / 3 0% 0%

[0819] (4ZnO·3B2O3) / 7 0% 0% (ZrO2·B2O3) / 2 0% 0% (La2O3·Nb2O5·2B2O3) / 4 0% 0% (La2O3Ta2O5·2B2O3) / 4 0% 0%

[0820] (3BaO·3B2O3·2SiO2) / 8 0% 40%

[0821] B2O30% 10%

[0822] SiO20% 45% B2O3+SiO220% 55%

[0823]

[0824] 19.01.2026

[0825] Table 28: Example compositions in constituent phases (molar) particularly favourable for combinations with Germanium

[0826] Example 1 Example 2 Example 3 Example 4 Example 5 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0 (Na2O Al2O3-2SiO2) / 4 30 30 30 30 2 (K2O Al2O3-2SiO2) / 4 0 0 0 0 0 (2MgO-2Al2O3-5SiO2) / 9 40 30 30 20 40 (CaO Al2O3-2SiO2) / 4 0 0 0 20 20 (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 0 0 0 0 0 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (La2O3·B2O3·2SiO2) / 4 0 0 0 0 0 (Na2O·TiO2·4SiO2) / 6 0 0 0 0 0 (K2O·TiO2·3SiO2) / 5 0 0 0 0 0 (BaO·TiO2·3SiO2) / 5 0 0 0 0 0 (Na2O·ZrO2·4SiO2) / 6 0 0 0 0 0 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 10 0 0 0

[0827]

[0828] 19.01.2026

[0829] Example 1 Example 2 Example 3 Example 4 Example 5 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (BaO·ZrO2·3SiO2) / 5 0 0 0 0 0 (K2O Nb2O5-4SiO2) / 6 0 0 10 0 0 (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Na2O·ZnO·3SiO2) / 5 0 0 0 0 0 (K2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Li2O·2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0 (K2O-2SiO2) / 3 0 0 0 0 0 (MgO·SiO2) / 2 0 0 0 0 0 (CaO·SiO2) / 2 0 0 0 0 0 (BaO-2SiO2) / 3 0 0 0 0 0 (4ZnO·3B2O3) / 7 0 0 0 0 0 (ZrO2·B2O3) / 2 0 0 0 0 0 (La2O3·Nb2O5·2B2O3) / 4 0 0 0 0 0 (La2O3Ta2O5·2B2O3) / 4 0 0 0 0 0 (3BaO·3B2O3·2SiO2) / 8 0 0 0 0 0 B2O35 5 5 0 5 SiO225 25 25 30 15

[0830]

[0831] 19.01.2026

[0832] Example 1 Example 2 Example 3 Example 4 Example 5

[0833] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol%

[0834] CTE / (ppm / K) 6.57354 6.43432 6.52091 6.42269 6.32282

[0835] Refractive index 1.50705 1.51513 1.52536 1.51046 1.52341

[0836] WP / °C 1209.57 1203.45 1184.94 1398.09 1161.85

[0837]

[0838] A most advantageous selection of constituent phases can be performed as follows:

[0839] Starting again at the list of constituent phases to be combined with either SiO2or B2O3, we first eliminate all constituent phases which contain ions that cannot be expected to move at a sufficient speed when the temperature gradient is imposed by the usp-laser. These are especially Ti and Nb which are supposed to hardly exist as free ions without any oxygen attached to them. Ta-containing phases are also advantageously eliminated.

[0840] Si and B are not taken into account in the above consideration. These two ions are part of the matrix in which the other ions move.

[0841] Second, all constituent phases are eliminated for which there is presumably no driving force for demixing. By this, we mean those phases for which the change of free enthalpy resulting from a demixing in a temperature gradient with 3000K in the centre and 2000K in the cladding, with a 50%:50% mixture of the constituent phase with SiC>2 or B2O3at the beginning changing to a 60%:40% mixture at 3000K and a 40% : 60% mixture at 2000K, i.e., where (G(60%:40% @ 3000K, 40%:60% @ 2000K)- G(50%:50% both @ 3000K & 2000K)) I (kJ / mol) > 0 holds. The only exception is (BaO 2 SiO2) / 3 where said G-difference is almost zero.

[0842] Note that for 50%:50% mixture of (4 ZnO · 3 B2O3) / 7 and B2O3we recognize there is no driving force for the desired demixing with an enrichment of Zn in the core whereas for an analogous mixture of (4 ZnO · 3 B2O3) / 7 and SiO2it is assumed that there is one. The19.01.2026

[0843] same holds for a 50% : 50% mixture of (3 BaO · 3B2O3· 2SiO2) / 8 and B2O3or SiO2, respectively. Consequently, the matrix should overwhelmingly consist of SiO2rather than B2O3. Therefore, the content of B2O3is limited to ≤ 10%, advantageously ≤ 7.5%, and the ratio of SiO2 / B2O3is 3 at minimum, advantageously bigger than 4, further advantageously bigger than 5.

[0844] Third, all constituent phases are advantageously eliminated for which the calculated refractive index is smaller than 1.51, because any enrichment of such phases in the core will not lead to a high index difference between core and cladding. The exception is the newly introduced (3Al2O3·2SiO2) / 5 which is needed for a fine adjustment of the coefficient of thermal expansion and the viscosity.

[0845] In the following Tables 29 and 30, the remaining most advantageous constituent phases are listed, together with a measure for the driving force of the demixing of a 50%: 50% mixture with SiO2or B2O3and the refractive index of the pure constituent phase.

[0846] The most advantageous glasses are combinations of the constituent phases of Tables 23 and 24 with SiO2and B2O3wherein the molar percentage of SiO2and B2O3together is 20% at minimum and which fulfill certain requirements, i.e., a certain refractive index (which one, depends on the required guidance of the later usp-laser-written waveguides) in combination with one of the smallest coefficients of thermal expansion (CTE) which are compatible with the chosen value for the refractive index (in order to ensure compatibility with the semiconductor materials which usually have small coefficients of thermal expansion) and a small working point (WP; to ensure easy melting).

[0847] Note that refractive index, CTE and WP are related. Increasing values for the refractive index are correlated with decreasing values of the WP and increasing values of the CTE. This is because of the increasing fraction of network modifiers like Barium which lead to an increase of the refractive index, but also a decrease of the WP and an increase of the CTE.

[0848] To increase the refractive index, it is also envisaged to prefer high polarizability network modifiers like Barium to low polarizability network modifiers like Magnesium.

[0849] The minimum molar percentage of SiO2and B2O3together is set, first, because of the fact that the driving force of demixing must decrease eventually with the SiO2plus B2O3content together approaching zero. Note that by SiO2and B2O3, the constituent phases are meant,19.01.2026

[0850] not the SiO2or B2O3content of complex constituent phases. With respect to the above calculations for demixing starting at different compositions and other glass properties like chemical resistivity for which a high molar percentage of SiO2and B2O3are favourable, an advantageous molar percentage of SiO2and B2O3together of at least 25%, more advantageously of at least 30%, and most advantageously of at least 35% is targeted at.

[0851] Rules to calculate the coefficient of thermal expansion, the Vogel-Fulcher-Tamann (VFT) parameters of the viscosity, and the refractive index have been given above. In the above mentioned Tables, the necessary parameters are listed. Most of them have been given above already.

[0852] Also with respect to a later lamination with semiconductor materials, an advantageous embodiment of the invention does not include alkaline-containing constituent phases.

[0853] Table 8: Selection of advantagous constituent phases in combination with glassy SiO2 (density 2.203g / cm3, refractive index 1.45769, working point 2357°C)

[0854] Constituent Normalized Formula DG = (G(60%:40% @ 3000 K, Refractive InPhase 40%:60% @ 2000K) dex

[0855] - G(50%:50% both @ 3000K & 2000K)) / (kJ / mol)

[0856] Eucryptite (Li2O·Al2O3·2SiO2) / 4 -2.75665 1.51692 Cordierite (2MgO-2Al2O3-5SiO2) / 9 -2.05925 1.54672 Anorthite (CaO·Al2O3·2SiO2) / 4 -1.63495 1.56536

[0857] (SrO·Al2O3·2SiO2) / 4 -2.1781 1.55585 Celsian (BaO·Al2O3·2SiO2) / 4 -2.2764 1.57505

[0858] (Li2O·B2O3·4SiO2) / 6 -1.79765

[0859] Malinkoite (Na2O·B2O3·2SiO2) / 4 -2.93835 1.51497 Lisitsynite (K2O·B2O3·4SiO2) / 6 1.51244

[0860] (La2O3·B2O3·2SiO2) / 4 1.66996

[0861]

[0862] 19.01.2026

[0863] Constituent Normalized Formula DG = (G(60%:40% @ 3000 K, Refractive InPhase 40%:60% @ 2000K) dex

[0864] - G(50%:50% both @ 3000K & 2000K)) / (kJ / mol)

[0865] (Na2O·ZrO2·4SiO2) / 6 -1.44120 1.59249 (K2O·ZrO2·3SiO2) / 5 -1.85525

[0866] (2CaO·ZrO2·4SiO2) / 7 -0.43040 1.65098 (BaO·ZrO2·3SiO2) / 5 -0.66835 1.697834 (Na2O·ZnO·2SiO2) / 4 -0.59515 1.55872 (Na2O·ZnO·3SiO2) / 5 -0.79145 1.523446 (K2O·ZnO·2SiO2) / 4 -0.94535 1.53940 (Li2O·2SiO2) / 3 -1.02180 1.53497 Sanbornite (BaO-2SiO2) / 3 0.032 1.58936 (3BaO·3B2O3·2SiO2) / 8 -2.998 1.635 Mullite (3Al2O3'2SiO2) / 5 -5.08585 1.48843

[0867]

[0868] Table 30: Selection of advantagous constituent phases incombination with glassy B2O3(density 1.82g / cm3, refractive index 1.47891, working point 554°C)

[0869] Constituent Normalized Formula DG = (G(60%:40% @ 3000K, Refractive InPhase 40%:60% @ 2000K) dex

[0870] - G(50%:50% both @ 3000K & 2000K)) / (kJ / mol)

[0871] (4ZnO 3B2O3) / 7 3.98675 1.65570 (ZrO2·B2O3) / 2

[0872]

[0873] 19.01.2026

[0874] Constituent Normalized Formula DG = (G(60%:40% @ 3000K, Refractive InPhase 40%:60% @ 2000K) dex

[0875] - G(50%:50% both @ 3000K & 2000K)) / (kJ / mol)

[0876] (3BaO-3B2O3-2SiO2) / 8 3.64685 1.635

[0877]

[0878] Table 31: Selection of advantagous constituent phases: data required to calculate the coefficient of thermal expansion

[0879] Constituent Phase m m

[0880] Yzi’i

[0881] j=l 7 = 1

[0882] Eucryptite (Li2O·Al2O3·2SiO2) / 4 1.5 1993

[0883] Cordierite (2MgO·2Al2O3·5SiO2) / 9 1.22 1940.67

[0884] Anorthite (CaO Al2O3-2SiO2) / 4 1.25 1966.25

[0885] (SrO·Al2O3·2SiO2) / 4 1.25 1951.75

[0886] Celsian (BaO Al2O3-2SiO2) / 4 1.25 1944.5

[0887] (Li2O·B2O3·4SiO2) / 6 1.33 1961.833

[0888] Malinkoite (Na2O·B2O3·2SiO2) / 4 1.5 1938.5

[0889] Lisitsynite (K2O·B2O3·4SiO2) / 6 1.33 1898.5

[0890] (La2O3·B2O3·2SiO2) / 4 1.5 2568.9

[0891] (Na2O·ZrO2·4SiO2) / 6 1.166 1756.66

[0892] (K2O·ZrO2·3SiO2) / 5 1.2 1717 (2CaO ZrO2'4SiO2) / 7 1 1683.57

[0893] (BaO·ZrO2·3SiO2) / 5 1 1754.2

[0894]

[0895] 19.01.2026

[0896] Constituent Phase m m

[0897] Yzi’i

[0898] j=l 7=1

[0899] (Na2O·ZnO·2SiO2) / 4 1.25 1334.25

[0900] (Na2O·ZnO·3SiO2) / 5 1.2 1440.2

[0901] (K2O·ZnO·2SiO2) / 4 1.25 1311.5

[0902] Lithium-Disilicate (Li2O'2SiO2) / 3 1.33 1632.67

[0903] Sanbornite (BaO-2SiO2) / 3 1 1420

[0904] (4ZnO·3B2O3) / 7 1.42 1763.85

[0905] (ZrO2B2O3) / 2 1.5 2674

[0906] (3BaO·3B2O3·2SiO2) / 8 1.375 2011.375

[0907] Mullite (3Al2O3·2SiO2) / 5 1.6 2590

[0908] Diborontrioxide B2O32 3145

[0909] Quartz Glass SiO21 1864

[0910]

[0911] Table 32: Selection of advantageous constituent phases: densities in the glassy and the crystalline state

[0912] Constituent Phase Density in glassy Density in crystalstate / (g / cm3) line state / (g / cm3) Eucryptite (Li2O AI2O3-2SiO2) / 4 2.363 2.663 Cordierite (2MgO·2Al2O3·5SiO2) / 9 2.6281 2.639 Anorthite (CaO·Al2O3·2SiO2) / 4 2.6836 2.744

[0913] (SrO·Al2O3·2SiO2) / 4 3.021 3.098

[0914]

[0915] 19.01.2026

[0916] Constituent Phase Density in glassy Density in crystalstate / (g / cm3) line state / (g / cm3) Celsian (BaO Al2O3-2SiO2) / 4 3.39 3.39

[0917] (Li2O·B2O3·4SiO2) / 6

[0918] Malinkoite (Na2O·B2O3·2SiO2) / 4 2.5447 2.927 Lisitsynit (K2O·B2O3·4SiO2) / 6 2.4849 2.68

[0919] (La2O3·B2O3·2SiO2) / 4 3.9 4.7 (Na2O·ZrO2·4SiO2) / 6 2.8899 2.97 (K2O·ZrO2·3SiO2) / 5

[0920] (2CaO·ZrO2·4SiO2) / 7 3.0906 3.11 (BaO·ZrO2·3SiO2) / 5 3.7805 3.85 (Na2O·ZnO·2SiO2) / 4 3.05 3.09 (Na2O·ZnO·3SiO2) / 5 2.85 2.95 (K2O·ZnO·2SiO2) / 4 2.95 3.12

[0921] Lithium- Disilicate (Li2O·2SiO2) / 3 2.351 2.449

[0922] (Na2O-2SiO2) / 3 2.491 2.51

[0923] (K2O-2SiO2) / 3 2.477 2.61 Sanbornite (BaO-2SiO2) / 3 3.7081 3.77

[0924] (4ZnO·3B2O3) / 7 3.57 4.2397 (ZrO2·B2O3) / 2

[0925] (3BaO·3B2O3·2SiO2) / 8 3.872 4.17

[0926]

[0927] 19.01.2026

[0928] Constituent Phase Density in glassy Density in crystalstate / (g / cm3) line state / (g / cm3) Mullite (3Al2O3·2SiO2) / 5 2.41 3.17 Diborontrioxide B2O31.82 1.82

[0929] Quartz SiO22.203 2.65

[0930]

[0931] Table 33: Selection of advantageous constituent phases: further data required to calculate the refractive index

[0932] Constituent Phase PolarizabiMolar Glassy molar lity / A3mass / g volume / cm3Eucryptite (Li2O·Al2O3·2SiO2) / 4 3.8203 63.0025 26.6621 Cordierite (2MgO-2 Al2O3-5SiO2) / 9 3.7484 64.9944 24.7306 Anorthite (CaO- Al2O3-2SiO2) / 4 4.0470 69.5515 25.8210

[0933] (SrO- Al2O3-2SiO2) / 4 4.1541 81.4370 26.9570 Celsian (BaO- Al2O3-2SiO2) / 4 4.4139 93.8638 27.6884

[0934] (Li2O- Al2O3-4SiO2) / 6

[0935] Malinkoite (Na2O·B2O3·2SiO2) / 4 3.5306 62.9415 24.7343 Lisitsynit (K2O- B2O3-4SiO2) / 6 3.850197 65.53975 27.11546

[0936] (La2O3- B2O3-2SiO2) / 4 6.1286 128.899 33.0510 (Na2O·ZrO2·4SiO2) / 6 4.0304 70.9228 24.5416 (K2O·ZrO2·3SiO2) / 5

[0937] (2CaO- ZrO2'4SiO2) / 7 3.9637 67.9589 21.9889

[0938]

[0939] 19.01.2026

[0940] Constituent Phase PolarizabiMolar Glassy molar lity / A3mass / g volume / cm3(BaO- ZrO2'3SiO2) / 5 4.66349 91.36 24.166 (Na2O·ZnO·2SiO2) / 4 3.3458 65.8815 21.6005 (Na2O·ZnO·3SiO2) / 5 3.2998 64.722 22.70947 (K2O·ZnO·2SiO2) / 4 3.7478 73.9355 25.0629 Lithium- Dis(Li2O·2SiO2) / 3 3.1552 50.0163 21.2745 ilicate

[0941] (Na2O·2SiO2) / 3 3.3198 60.7157 24.3740 (K2O·2SiO2) / 3 3.9004 71.4543 28.8471 Sanbornite (BaO·2SiO2) / 3 4.0163 91.1657 24.5855

[0942] (4ZnO·3B2O3) / 7 3.8820 76.339 21.38295 (ZrO2·B2O3) / 2

[0943] (3BaO-3B2O3-2SiO2) / 8 4.4838 98.6253 25.473 Mullite (3Al2O3-2SiO2) / 5 4.7851 85.2102 35.356929 Diborontrioxide B2O35.0752 69.6190 38.2522 Quartz SiO2 3.4566 60.0840 27.2737

[0944]

[0945] Table 34: Selection of advantagous onstituent phases: VFT parameters

[0946] Constituent Phase A B / K To / °C Eucryptite (Li2O Al2O3-2SiO2) / 4

[0947] Cordierite (2MgO-2Al2O3-5SiO2) / 9 -4.50166 6790.97 418.162

[0948]

[0949] 19.01.2026

[0950] Constituent Phase A B / K To / °C Anorthite (CaO Al2O3-2SiO2) / 4 -3.66253 5318. 530.043

[0951] (SrO Al2O3-2SiO2) / 4

[0952] Celsian (BaO Al2O3-2SiO2) / 4 -3.70208 6596.47 485.298

[0953] (Li2O·B2O3·4SiO2) / 6 -1.437 3250.6 262.8 Malinkoite (Na2O·B2O3·2SiO2) / 4

[0954] Lisitsynit (K2O·B2O3·4SiO2) / 6 -2.16 3492.9 381.3 (La2O3·B2O3·2SiO2) / 4 -0.489408 2055.7247 533.72452 (Na2O·ZrO2·4SiO2) / 6 -3.29 5450.9 521.1 (K2O·ZrO2·3SiO2) / 5

[0955] (2CaO·ZrO2·4SiO2) / 7 -4.2404 5246.35 542.72 (BaO·ZrO2·3SiO2) / 5 -2.835156 4615.3861 654.9064 (Na2O·ZnO·2SiO2) / 4

[0956] (Na2O·ZnO·3SiO2) / 5 -1.7495 3368.04 300.06 (K2O·ZnO·2SiO2) / 4

[0957] Lithium-Disilicate (Li2O·2SiO2) / 3 0.29 2379.5 267.1 (Na2O-2SiO2) / 3 -4 5538 119.8 (K2O-2SiO2) / 3 -4 7461 59.8 Sanbornite (BaO-2SiO2) / 3 -2.341 4098.2 419.8 (3BaO·3B2O3·2SiO2) / 8 -3.46 2524.1 460 (4ZnO·3B2O3) / 7 -2.23077 1581.66 456.154

[0958]

[0959] 19.01.2026

[0960] Constituent Phase A B / K To / °C (ZrO2·B2O3) / 2

[0961] Mullite (3Al2O3·2SiO2) / 5 -2.89663 5033.37 312.323 Diborontrioxide B2O3-0.087154 1650.04 149.859 Quartz glass SiO2-6.01651 26018.9 -240.131

[0962]

[0963] The sources of the VFT parameters which are given here but have not listed above in the referring table above are the following. The VFT-parameters of (BaO Al2O3'2SiO2) / 4 are derived from a fit to a viscosity curve which consists of high temperature data the literature and the position of the dilatometric softening point, i.e., the temperature at which the viscosity equals 1011.2dPa·s. The VFT-parameters of (3Al2O3'2SiO2) / 5 are derived from a fit to a viscosity curve which consists of interpolated high temperature data and the temperature at which the viscosity equals 1014.6dPa·s). The VFT-parameters of (Li2O B2O3'4SiO2) / 6 are derived from a fit to a viscosity curve which consists of high temperature data measured by rotational viscosimetry at Schott AG and the onset temperature of the calorimetric glass transition in a 10K / min dynamic scanning calorimeter which is taken as approximative value for the annealing point, i.e., the temperature at which the viscosity equals 1013dPa·s. The VFT-parameters of (BaO·ZrO2·3SiO2) / 5 are derived from a fit to a viscosity curve measured at Schott AG. The VFT-parameters of (La2O3·B2O3·2SiO2) / 4 are derived from the literature. The VFT-parameters of (K2O·B2O3·4SiO2) / 6 are derived from a fit to a viscosity curve measured at Schott AG. The VFT-parameters of (3BaO·3B2O3·2SiO2) / 8 are derived from a fit to a viscosity curve measured at Schott AG.

[0964] In the following, a detailed description of most advantageous inventive glasses will be given. The starting point is the desired refractive index. As stated above, the desired values of the refractive index depend on the desired value of the refractive index difference between core and cladding, or demixing zone and bulk glass material. The higher the latter, the stronger the guidance of the waveguide and, consequently, the smaller the sensitivity to waveguide curvatures. So, the desired refractive index will depend on the application. For all desired minimum indices, the inventory glasses are combinations of a preferably small19.01.2026

[0965] upper limit of the coefficient of thermal expansion (CTE) and the corresponding corresponding viscosity (usually, the upper limit of the working point (WP), i.e., the temperature at which the viscosity amounts to 104dPa·s, is taken as representative value).

[0966] With this, those combinations of the above selection of constituent phases, advantageously such without any alkaline content, are most advantageous which fulfill the following requirements concerning the relation of the listed properties.

[0967] Table 35: Criteria for advantageous glasses

[0968] Refractive InCTE / WP / °C Fraction of phases with x = SiO2+ B2O3SiO2 / dex (ppm / K) DG < -2.0 B2O3>1.542 <4.35 <1180 >40% 45%>x>40% >4 >1.544 <4.45 <1130 >40% 45%>x>40% >4 >1.55 <4.55 <1080 >45% 40%>x>35% >5 >1.56 <4.55 <1025 >45% 40%>x>35% >6 >1.56 <4.7 <1015 >45% 40%>x>35% >6 >1.56 <4.8 <995 >50% 40%>x>35% >6 >1.56 <5.0 <985 >50% 40%>x>35% >6 >1.57 <4.9 <990 >50% 35%>x>30% >5 >1.57 <5.2 <960 >50% 35%>x>30% >5 >1.57 <5.35 <940 >50% 35%>x>30% >5 >1.58 <5.25 <960 >50% 30%>x>25% >4 >1.58 <5.5 <935 >50% 30%>x>25% >4 >1.58 <5.65 <925 >50% 30%>x>25% >4 >1.58 <5.7 <910 >50% 30%>x>25% >4

[0969]

[0970] 19.01.2026

[0971] >1.58 <5.75 <900 >50% 30%>x>25% >4 >1.59 <5.55 <900 >55% 30%>x>50% >4 >1.59 <5.75 <890 >55% 30%>x>50% >4

[0972] >1.59 <7 <800 >80% 25%>x>20% >3 >1.6 <6.25 <840 >65% 25%>x>20% >3 >1.6 <6.55 <830 >65% 25%>x>20% >3 >1.6 <6.7 <820 >65% 25%>x>20% >3 >1.6 <6.85 <815 >70% 25%>x>20% >3 >1.526 <4.3 <1080 >30% 45%>x>40% >5 >1.526 <4.15 <1155 >25% 50%>x>45% >8 >1.526 <3.8 <1210 >50% 40%>x>35% >7 >1.526 <3.7 <1220 >50% 35%>x>30% >7 >1.526 <3.5 <1285 >50% 45%>x>40% >7

[0973]

[0974] In the following tables, examples for advantageous glasses according to the criteria of the above mentioned tables are listed and comparative examples are provided.19.01.2026

[0975] Table 36: Examples of advantageous composition in constituent phases (molar)

[0976] Example 1 Example 2 Example 3 ComparaComparative tive Example 4 Example 5 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0 (2MgO·2Al2O3·5SiO2) / 9 0 0 0 0 0 (CaO Al2O3-2SiO2) / 4 0 0 0 0 0 (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 42 37 37 37 32 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (K2O·B2O3·4SiO2) / 6 0 0 0 0 0 (La2O3·B2O3·2SiO2) / 4 6 6 6 6 6 (Na2O·ZrO2·4SiO2) / 6 0 0 0 0 0 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 0 0 0 0 (BaO·ZrO2·3SiO2) / 5 5 5 5 6.5 6.5 (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Na2O·ZnO·3SiO2) / 5 0 0 0 0 0 (K2O·ZnO·2SiO2) / 4 0 0 0 0 0

[0977]

[0978] 19.01.2026

[0979] Example 1 Example 2 Example 3 ComparaComparative tive Example 4 Example 5 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O'2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0 (K2O-2SiO2) / 3 0 0 0 0 0 (BaO-2SiO2) / 3 3 3 0 0 0 (4ZnO·3B2O3) / 7 3.5 3.5 0 3.5 3.5 (ZrO2·B2O3) / 2 0 0 0 0 0 (3Al2O3-2SiO2) / 5 0 0 0 0 0 (3BaO-3B2O3-2SiO2) / 8 0 5 15 10 15 B2O37.5 7.5 6 6 6 SiO233 33 31 31 31 B2O3+SiO240.5 40.5 37 37 37 SiO2 / B2O34.4 4.4 5.1 5.1 5.1 Properties

[0980] Fraction of phases with DG 0.42 0.42 0.52 0.47 0.47 from table 23 < -2.0

[0981] Fraction of phases with DG 0 0.05 0.15 0.1 0.15 from table 23 < -2.5

[0982] CTE / (ppm / K) 4.31269 4.42099 4.42056 4.52 4.62782

[0983]

[0984] 19.01.2026

[0985] Example 1 Example 2 Example 3 ComparaComparative tive Example 4 Example 5 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% Refractive index 1.54213 1.54472 1.5518 1.55277 1.55544 WP / °C 1175.76 1124.85 1077.9 1076.59 1038.69

[0986]

[0987] Table 37: Examples advantageous composition in constituent phases (molar), continued

[0988] Example 6 Example 7 Example 8 Example 9 Comparative Example 10 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0 (2MgO·2Al2O3·5SiO2) / 9 0 0 0 0 0 (CaO Al2O3-2SiO2) / 4 0 0 0 0 0 (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 24 24 24 24 29 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (K2O·B2O3·4SiO2) / 6 0 0 0 0 0

[0989]

[0990] 19.01.2026

[0991] Example 6 Example 7 Example 8 Example 9 Comparative Example 10 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (La2O3·B2O3·2SiO2) / 4 6 6 6 6 6 (Na2O·ZrO2·4SiO2) / 6 0 0 0 0 0 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 0 0 0 0 (BaO·ZrO2·3SiO2) / 5 10 10 5 5 5 (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Na2O·ZnO·3SiO2) / 5 0 0 0 0 0 (K2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Li2O·2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0 (K2O-2SiO2) / 3 0 0 0 0 0 (BaO-2SiO2) / 3 0 0 0 0 0 (4ZnO·3B2O3) / 7 0 3.5 0 3.5 3.5 (ZrO2·B2O3) / 2 0 0 0 0 0 (3Al2O3'2SiO2) / 5 0 0 0 0 0 (3BaO·3B2O3·2SiO2) / 8 25 21.5 30 26.5 22.5

[0992]

[0993] 19.01.2026

[0994] Example 6 Example 7 Example 8 Example 9 Comparative

[0995] Example 10

[0996] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol%

[0997] B2O35 5 5 5 5

[0998] SiO230 30 30 30 29

[0999] B2O3+SiO235 35 35 35 35

[1000] SiO2 / B2O36 6 6 6 5.8

[1001] Fraction of phases with DG 0.49 0.455 0.54 0.505 0.515 from table 23 < -2.0

[1002] Fraction of phases with DG 0.25 0.215

[1003] from table 23 < -2.5

[1004] CTE / (ppm / K) 4.51213 4.69694 4.79003 4.97485 4.94048

[1005] Refractive index 1.56498 1.56523 1.56225 1.56248 1.56147

[1006] WP / °C 1021.86 1010.84 990.282 980.471 1002.96

[1007]

[1008] 19.01.2026

[1009] Table 37: Examples advantageous composition in constituent phases (molar), continued

[1010] Example 11 Example 12 ComparaComparaExample 15 tive tive

[1011] Example 13 Example 14 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0 (2MgO·2Al2O3·5SiO2) / 9 0 0 0 0 0 (CaO Al2O3-2SiO2) / 4 0 0 0 0 0 (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 24 24 24 24 20 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (K2O·B2O3·4SiO2) / 6 0 0 0 0 0 (La2O3·B2O3·2SiO2) / 4 6 6 6 6 6 (Na2O·ZrO2·4SiO2) / 6 0 0 0 0 0 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 0 0 0 0 (BaO·ZrO2·3SiO2) / 5 10 5 5 6.5 6.5 (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Na2O·ZnO·3SiO2) / 5 0 0 0 0 0 (K2O·ZnO·2SiO2) / 4 0 0 0 0 0

[1012]

[1013] 19.01.2026

[1014] Example 11 Example 12 ComparaComparaExample 15 tive tive

[1015] Example 13 Example 14 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O'2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0

[1016] (K2O-2SiO2) / 3 0 0 0 0 0 (BaO-2SiO2) / 3 0 0 0 0 0 (4ZnO·3B2O3) / 7 0 0 3.5 3.5 3.5 (ZrO2·B2O3) / 2 0 0 0 0 0 (3Al2O3-2SiO2) / 5 0 0 0 0 0 (3BaO-3B2O3-2SiO2) / 8 30 35 31.5 30 34 B2O35 5 5 5 5 SiO225 25 25 25 25 B2O3+SiO230 30 30 30 30 SiO2 / B2O35 5 5 5 5

[1017] Fraction of phases with 0.54 0.59 0.555 0.54 0.54 DG from table 23 < -2.0

[1018] Fraction of phases with 0.3 0.35 0.315 0.3 0.34 DG from table 23 < -2.5

[1019] CTE / (ppm / K) 4.87686 5.15145 5.33715 5.25514 5.34016

[1020]

[1021] 19.01.2026

[1022] Example 11 Example 12 ComparaComparaExample 15 tive tive

[1023] Example 13 Example 14 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% Refractive index 1.57362 1.57086 1.57113 1.57197 1.57421 WP / °C 986.215 958.708 950.053 957.751 938.297

[1024]

[1025] Table 37: Examples advantageous composition in constituent phases (molar), continued

[1026] Example Example Example Example Example 16 17 18 19 20 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0 (2MgO·2Al2O3·5SiO2) / 9 0 0 0 0 0 (CaO Al2O3-2SiO2) / 4 0 0 0 0 0 (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 24 22.5 22.5 17.5 15 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (K2O·B2O3·4SiO2) / 6 0 0 0 0 0 (La2O3·B2O3·2SiO2) / 4 6 6 6 6 6

[1027]

[1028] 19.01.2026

[1029] Example Example Example Example Example 16 17 18 19 20 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Na2O·ZrO2·4SiO2) / 6 0 0 0 0 0 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 0 0 0 0 (BaO·ZrO2·3SiO2) / 5 10 6.5 6.5 8 8 (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Na2O·ZnO·3SiO2) / 5 0 0 0 0 0 (K2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Li2O·2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0 (K2O-2SiO2) / 3 0 0 0 0 0 (BaO-2SiO2) / 3 0 0 0 0 0 (4ZnO·3B2O3) / 7 0 0 3.5 3.5 3.5 (ZrO2·B2O3) / 2 0 0 0 0 0 (3Al2O3-2SiO2) / 5 0 0 0 0 0 (3BaO-3B2O3-2SiO2) / 8 35 40 36.5 40 42.5 B2O35 5 5 5 5 SiO220 20 20 20 20 B2O3+SiO225 25 25 25 25

[1030]

[1031] 19.01.2026

[1032] Example Example Example Example Example 16 17 18 19 20

[1033] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol%

[1034] SiO2 / B2O34 4 4 4 4

[1035] Fraction of phases with DG 0.59 0.625 0.59 0.575 0.575 from table 23 < -2.0

[1036] Fraction of phases with DG

[1037] from table 23 < -2.5

[1038] CTE / (ppm / K) 5.23895 5.4608 5.64741 5.67166 5.72428

[1039] Refractive index 1.58233 1.58122 1.58155 1.58526 1.5867

[1040] WP / °C 955.757 931.768 924.036 909.607 899.7

[1041]

[1042] Table 37: Examples advantageous composition in constituent phases (molar), continued

[1043] Example Example ComparaComparaExample 21 22 tive Exative 25

[1044] mple 23

[1045] Example

[1046] 24

[1047] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol%

[1048] (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0

[1049] (2MgO·2Al2O3·5SiO2) / 9 0 0 0 0 0

[1050]

[1051] 19.01.2026

[1052] Example Example ComparaComparaExample 21 22 tive Exative 25

[1053] mple 23

[1054] Example

[1055] 24

[1056] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (CaO Al2O3-2SiO2) / 4 0 0 0 0 0 (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 10 10 10 0 0 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (K2O·B2O3·4SiO2) / 6 0 0 0 0 0 (La2O3·B2O3·2SiO2) / 4 6 6 6 0 0 (Na2O·ZrO2·4SiO2) / 6 0 0 0 0 0 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 0 0 0 0 (BaO·ZrO2·3SiO2) / 5 10 10 5 5 0 (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Na2O·ZnO·3SiO2) / 5 0 0 0 0 0 (K2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Li2O·2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0

[1057]

[1058] 19.01.2026

[1059] Example Example ComparaComparaExample 21 22 tive Exative 25

[1060] mple 23

[1061] Example

[1062] 24

[1063] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (K2O·2SiO2) / 3 0 0 0 0 0 (BaO-2SiO2) / 3 0 0 0 0 0 (4ZnO·3B2O3) / 7 0 3.5 3.5 0 0 (ZrO2·B2O3) / 2 0 0 0 0 0 (3Al2O3-2SiO2) / 5 0 0 0 0 0 (3BaO-3B2O3-2SiO2) / 8 49 45.5 50.5 75 80 B2O35 5 5 5 5 SiO220 20 20 15 15 B2O3+SiO225 25 25 20 20 SiO2 / B2O34 4 4 3 3

[1064] Fraction of phases with DG 0.59 0.555 0.555 0.75 0.8 from table 23 < -2.0

[1065] Fraction of phases with DG 0.75 0.8 from table 23 < -2.5

[1066] CTE / (ppm / K) 5.53459 5.72157 5.98976 6.723 6.98462 Refractive index 1.59037 1.59075 1.58788 1.59913 1.59617

[1067]

[1068] 19.01.2026

[1069] Example Example ComparaComparaExample 21 22 tive Exative 25

[1070] mple 23

[1071] Example

[1072] 24

[1073] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% WP / °C 895.342 888.702 870.261 813.259 799.863

[1074]

[1075] Table 37: Examples advantageous composition in constituent phases (molar), continued

[1076] Example ComparaExample Example Example 26 tive 28 29 30

[1077] Example

[1078] 27

[1079] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0 (2MgO·2Al2O3·5SiO2) / 9 0 0 0 0 0 (CaO Al2O3-2SiO2) / 4 0 0 0 0 0 (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 0 0 0 0 0 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (K2O·B2O3·4SiO2) / 6 0 0 0 0 0

[1080]

[1081] 19.01.2026

[1082] Example ComparaExample Example Example 26 tive 28 29 30

[1083] Example

[1084] 27

[1085] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (La2O3·B2O3·2SiO2) / 4 4 4 4 4 4 (Na2O·ZrO2·4SiO2) / 6 0 0 0 0 0 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 0 0 0 0 (BaO·ZrO2·3SiO2) / 5 10 5 5 2.5 7.5 (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Na2O·ZnO·3SiO2) / 5 0 0 0 0 0 (K2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Li2O·2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0 (K2O-2SiO2) / 3 0 0 0 0 0 (BaO-2SiO2) / 3 0 0 0 0 0 (4ZnO·3B2O3) / 7 0 0 3.5 3.5 3.5 (ZrO2·B2O3) / 2 0 0 0 0 0 (3Al2O3'2SiO2) / 5 0 0 0 0 0 (3BaO·3B2O3·2SiO2) / 8 66 71 67.5 70 65

[1086]

[1087] 19.01.2026

[1088] Example ComparaExample Example Example 26 tive 28 29 30

[1089] Example

[1090] 27

[1091] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% B2O35 5 5 5 5 SiO215 15 15 15 15 B2O3+SiO220 20 20 20 20 SiO2 / B2O33 3 3 3 3

[1092] Fraction of phases with DG 0.66 0.71 0.675 0.70 0.65 from table 23 < -2.0

[1093] Fraction of phases with DG 0.66 0.71 0.675 0.70 0.65 from table 23 < -2.5

[1094] CTE / (ppm / K) 6.21735 6.48093 6.67047 6.80098 6.53913 Refractive index 1.60422 1.60126 1.60171 1.60024 1.6032 WP / °C 838.789 824.119 819.428 812.632 826.45

[1095]

[1096] 19.01.2026

[1097] Table 9 Examples advantageous composition in constituent phases (molar), continued

[1098] Example ComparaExample ComparaCompara31 tive 33 tive Exative mple 34

[1099] Example Example 32 35 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0 (2MgO·2Al2O3·5SiO2) / 9 18 8 4.5 0 0 (CaO Al2O3-2SiO2) / 4 8 8 8 8 8 (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 9.6 17 22.5 31 33.5 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (K2O·B2O3·4SiO2) / 6 0 0 0 0 0 (La2O3·B2O3·2SiO2) / 4 0 0 0 0 0 (Na2O·ZrO2·4SiO2) / 6 0 0 0 0 0 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 0 0 0 0 (BaO·ZrO2·3SiO2) / 5 8 8 8 8 8 (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Na2O·ZnO·3SiO2) / 5 0 0 0 0 0

[1100]

[1101] 19.01.2026

[1102] Example ComparaExample ComparaCompara31 tive 33 tive Exative mple 34

[1103] Example Example 32 35 Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (K2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Li2O·2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0 (K2O-2SiO2) / 3 0 0 0 0 0 (BaO-2SiO2) / 3 0 0 0 0 0 (4ZnO·3B2O3) / 7 8.75 7 7 3.5 3.5 (ZrO2·B2O3) / 2 0 0 0 0 0 (3Al2O3-2SiO2) / 5 2.6666 5 5 2.5 0 (3BaO-3B2O3-2SiO2) / 8 0 0 0 0 0 B2O36.75 7 5 5 5 SiO238.2334 40 40 42 42 B2O3+SiO244.9834 47 45 47 47 SiO2 / B2O35.7 5.7 8 8.4 8.4

[1104] Fraction of phases with DG 0.276 0.25 0.27 0.31 0.335 from table 23 < -2.0

[1105]

[1106] 19.01.2026

[1107] Example ComparaExample ComparaCompara31 tive 33 tive Exative mple 34

[1108] Example Example 32 35

[1109] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol%

[1110] Fraction of phases with DG

[1111] from table 23 < -2.5

[1112] CTE / (ppm / K) 4.28545 4.11058 4.12315 3.81162 3.83579

[1113] Refractive index 1.52645 1.52394 1.52732 1.52695 1.52941

[1114] WP / °C 1079.11 1105.05 1153.31 1234.72 1244.82

[1115]

[1116] Table 37: Examples advantageous composition in constituent phases (molar), continued

[1117] Example ComparaComparaExample Example 36 tive tive 39 40

[1118] Example Example

[1119] 37 38

[1120] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol%

[1121] (Li2O Al2O3-2SiO2) / 4 0 0 0 0 0

[1122] (2MgO·2Al2O3·5SiO2) / 9 0 0 0 0 0

[1123] (CaO Al2O3-2SiO2) / 4 0 0 0 0 0

[1124]

[1125] 19.01.2026

[1126] Example ComparaComparaExample Example 36 tive tive 39 40

[1127] Example Example

[1128] 37 38

[1129] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (SrO Al2O3-2SiO2) / 4 0 0 0 0 0 (BaO Al2O3-2SiO2) / 4 32.5 40 40 38 34.5 (Li2O·B2O3·4SiO2) / 6 0 0 0 0 0 (Na2O·B2O3·2SiO2) / 4 0 0 0 0 0 (K2O·B2O3·4SiO2) / 6 0 0 0 0 0 (La2O3·B2O3·2SiO2) / 4 0 0 0 0 0 (Na2O·ZrO2·4SiO2) / 6 0 0 0 0 0 (K2O·ZrO2·3SiO2) / 5 0 0 0 0 0 (2CaO·ZrO2·4SiO2) / 7 0 0 0 0 0 (BaO·ZrO2·3SiO2) / 5 10 8 8 10 10 (Na2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Na2O·ZnO·3SiO2) / 5 0 0 0 0 0 (K2O·ZnO·2SiO2) / 4 0 0 0 0 0 (Li2O·2SiO2) / 3 0 0 0 0 0 (Na2O-2SiO2) / 3 0 0 0 0 0 (K2O-2SiO2) / 3 0 0 0 0 0

[1130]

[1131] 19.01.2026

[1132] Example ComparaComparaExample Example 36 tive tive 39 40

[1133] Example Example

[1134] 37 38

[1135] Constituent Phase Fraction / Fraction / Fraction / Fraction / Fraction / mol% mol% mol% mol% mol% (BaO-2SiO2) / 3 0 0 0 0 0 (4ZnO 3B2O3) / 7 3.5 0 0 0 3.5 (ZrO2·B2O3) / 2 0 0 0 0 0 (3Al2O3-2SiO2) / 5 0 0 0 0 0 (3BaO-3B2O3-2SiO2) / 8 2 0 2 2 2 B2O36 8 6 6 6 SiO246 44 44 44 44 B2O3+SiO252 52 50 50 50 SiO2 / B2O37.6 5.5 7.3 7.3 7.3

[1136] Fraction of phases with DG 0.345 0.4 0.42 0.4 0.365 from table 23 < -2.0

[1137] Fraction of phases with DG 0.02 0 0.02 0.02 0.02 from table 23 < -2.5

[1138] CTE / (ppm / K) 3.63066 3.52108 3.54596 3.47362 3.73767 Refractive index 1.52764 1.52281 1.52607 1.52813 1.52999 WP / °C 1214.43 1250.1 1279.65 1279.72 1207.98

[1139]

[1140] 19.01.2026

[1141] Note that there may be equivalent partitions of a glass composition in different sets of constituent phases (constraint: they all have to be glassforming systems). Within the error bars resulting from the models and model parameters involved, they will lead to equivalent results concerning the glass property calculation. It is therefore recommendable to choose a partition which consists of constituent phases which are all well characterized. With respect to this, another partition has been chosen for example 31 in table 37 than for the almost identical example 1.

[1142] As said above, the refractive index is advantageously higher than 1.5. Upper limits of 2.0 can be achieved. An example range for the refractive index can especially be from 1.5 to 1.8.

[1143] An even higher refractive index, e.g., > 1.61, in combination with a CTE < 7.21ppm / K and a working point < 810°C, may be achieved with glasses that lie outside the above constraints for the inventory glasses, e,g,, a glass consisting of 83.5% (3BaO*3B2O3*2SiO2) / 8, 3.5% (La2O3*B2O3*2SiO2) / 4, 3.8% B2O3, and 9.2% SiO2 (refractive index 1.61118, CTE 7.2109ppm / K, working point 802.628°C).

[1144] A particularly advantageous embodiment is represented by a glass comprising the following constituent phases (in mol%):

[1145] Constituent phase Minimum Maximum (Li2O Al2O3-2SiO2) / 4 0% 85% (2MgO·2Al2O3·5SiO2) / 9 0% 85% (CaO Al2O3-2SiO2) / 4 0% 85%

[1146] (SrO Al2O3-2SiO2) / 4 0% 85%

[1147] (BaO Al2O3-2SiO2) / 4 0% 85%

[1148] (Li2O·B2O3·4SiO2) / 6 0% 85%

[1149]

[1150] 19.01.2026

[1151] Constituent phase Minimum Maximum (Na2O·B2O3·2SiO2) / 4 0% 85% (K2O·B2O3·4SiO2) / 6 0% 85% (La2O3·B2O3·2SiO2) / 4 0% 85% (Na2O·ZrO2·4SiO2) / 6 0% 85% (K2O·ZrO2·3SiO2) / 5 0% 85% (2CaO·ZrO2·4SiO2) / 7 0% 85% (BaO·ZrO2·3SiO2) / 5 0% 85% (Na2O·ZnO·2SiO2) / 4 0% 85% (Na2O·ZnO·3SiO2) / 5 0% 85% (K2O·ZnO·2SiO2) / 4 0% 85%

[1152] (Li2O·2SiO2) / 3 0% 85%

[1153] (Na2O-2SiO2) / 3 0% 85%

[1154] (K2O-2SiO2) / 3 0% 85%

[1155] (BaO-2SiO2) / 3 0% 10%

[1156] (4ZnO·3B2O3) / 7 0% 10% (ZrO2·B2O3) / 2 0% 10%

[1157] (3Al2O3-2SiO2) / 5 0% 85%

[1158] (3BaO-3B2O3-2SiO2) / 8 0% 85%

[1159] B2O30% 10%

[1160] SiO20% 60%

[1161]

[1162] 19.01.2026

[1163] Constituent phase Minimum Maximum

[1164] B2O3+SiO220% 60%

[1165]

[1166] Most advantageously, the aforesaid glasses have a thermal expansion coefficient CTE, a working point WP, a refractive index ng in the ranges as defined in any of the line numbers of following table

[1167] Line number Refractive Index CTE / (ppm / K) WP / °C

[1168] 1 >1.542 <4.35 <1180

[1169] 2 >1.544 <4.45 <1130

[1170] 3 >1.55 <4.55 <1080

[1171] 4 >1.56 <4.55 <1025

[1172] 5 >1.56 <4.7 <1015

[1173] 6 >1.56 <4.8 <995

[1174] 7 >1.56 <5.0 <985

[1175] 8 >1.57 <4.9 <990

[1176] 9 >1.57 <5.2 <960

[1177] 10 >1.57 <5.35 <940

[1178] 11 >1.58 <5.25 <960

[1179] 12 >1.58 <5.5 <935

[1180] 13 >1.58 <5.65 <925

[1181] 14 >1.58 <5.7 <910

[1182] 15 >1.58 <5.75 <900

[1183] 17 >1.59 <5.55 <895

[1184]

[1185] 19.01.2026

[1186] 18 >1.59 <5.75 <890

[1187] 19 >1.59 <5.85 <870

[1188] 20 >1.59 <7 <795

[1189] 21 >1.6 <6.25 <840

[1190] 22 >1.6 <6.55 <825

[1191] 23 >1.6 <6.7 <820

[1192] 24 >1.6 <6.85 <810

[1193] 25 >1.526 <4.3 <1080

[1194] 26 >1.526 <4.15 <1155

[1195] 27 >1.526 <3.8 <1210

[1196] 28 >1.526 <3.7 <1220

[1197] 29 >1.526 <3.5 <1290

[1198]

[1199] The invention further relates to a glass element with an embedded waveguide, whereas the glass of the glass element has a composition as described above. The waveguide is embedded within the glass element, which means within the bulk glass and can be inscribed therein by the usp-laser process as described above as well. The waveguide is especially a permanent structure which is especially represented by the demixing volume.

[1200] In an advantageous embodiment of an aforesaid glass element, the waveguide comprises a demixing volume of the glass element. As described above, the initial glass composition is altered by the interaction with the usp-laser irradiation to form the demixing volume in the area if the interaction of the laser irradiation and the glass material.

[1201] Most advantageously, the glass element comprises a waveguide, whereas the waveguide comprises a demixing volume of the glass element which contains at least an area with a19.01.2026

[1202] refractive index ndem which is higher than the refractive index ng of the glass element and / or an inner demixing volume with a refractive index nid and an outer demixing volume with an refractive index nod, whereas nid is higher than nod and advantageously higher than ng. Or with other words, the relations ndem > ng and / or nid > nod and / or

[1203] ng < nid > nod are present. Thereby, a confinement of the transported electromagnetic wave within the waveguide and / or the demixing volume and / or inner demixing volume is provided.

[1204] Another advantageous embodiment is a glass element, whereas the refractive index ndem of demixing volume is greater than the refractive index ng of the glass of the glass element by 0.0001 to 0.02, advantageously by 0.0005 to 0.01, and / or nid is greater than nod by 0.0001 to 0.02, advantageously by 0.0005 to 0.01. With other words, the equations ndem -ng is in the range of 0.0001 to 0.02 or more advantageously in the range 0.0005 to 0.01. Or nid - nod ist in the range 0.0001 to 0.02, advantageously by 0.0005 to 0.01. As said before, the relations ndem > ng and / or nid > nod hold true.

[1205] When referring to the refractive index ng, ndem, nid, nod, the refractive index at the wavelength 589.3 nm is meant. It is assumed that the refractive index change An is approximately independent from the wavelength so that the An from 589.3 nm also applies to a propagation wavelength of, e.g., 1310 nm or 1550 nm.

[1206] In a further advantageous glass element the CTE of the demixing volume and / or the inner demixing volume is differing from the CTE of the glass (1) by at maximum 0.2 ppm / K, advantageously by at maximum 0.1 ppm / K.

[1207] Most advantageously, the waveguide can have a height h and a width w, whereas the ration w / h is greater than 0.5, advantageously greater than 0.8, most advantageously at least 0,9. It is obvious that the maximum value of this ratio is 1, namely when h and w are identical.

[1208] Another most advantageous embodiment is represented by a glass element with a waveguide, whereas the waveguide has a height h and a width w, with

[1209] dmax= max(w, h) < 0.76 λ / NA19.01.2026

[1210] NA is the numerical aperture of the waveguide and A is the wavelength of the electromagnetical wave being transported in the waveguide in the operating status. Usually A is in the range from 1300 nm to 1600 nm, most commonly 1310 nm or 1550 nm. max(w,h) stand for the maximum value of either w or h. In most cases, h > w.

[1211] The numerical NA aperture can be calculated as commonly known from the refractive indices as

[1212] NA = √(n + Δn)² − n²

[1213] The following table lists examples of waveguides inscribed into a glass substrate with he glass composition as described herein.

[1214] Here n is the refractive index of the glass material and An the difference to the refractive index of the demixing volume ndem or inner demixing volume nid, as the case might be.

[1215] The inventors found out that by the aforesaid formula 0.76 · λ / NA the dimensions for the waveguide can be provided which enable the waveguide to transport a single mode electromagnetic wave. Such is especially suitable for data transmission by optical signals through the waveguide.

[1216] Table 38: Waveguide examples

[1217] Ex 1 Ex 2 Ex 3 Ex4 Ex 5 Ex 6 Ex 7 Ex 8 Ex 9 Ex 10 Ex 11 Ex 12 λ [nm] 1310 1310 1310 1310 1310 1310 1550 1550 1550 1550 1550 1550 Δn 0.0025 0.0025 0.005 0.005 0.01 0.01 0.0025 0.0025 0.001 0.005 0.01 0.01 ng 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.5 1.5 NA 0.087 0.087 0.123 0.123 0.173 0.173 0.087 0.087 0.123 0.123 0.173 0.173 dmax [μm] 11.5 11.5 8.1 8.1 5.7 5.7 13.6 13.6 9.6 9.6 6.8 6.8 w [μm] 5 8 5 7 5 5 9 10 7 7 6 6.6 h [μm] 11 13 8 12 5 7 13 15 16 16 6.4 6.9 single mode y n y n y n y n y n y n

[1218]

[1219] The Table 38, shown above, summarizes properties of exemplary glass elements Ex 1 to Ex 12 with inscribed waveguides. The wavelength of the transported electromagnetic wave within the waveguide, with other words within the demixing volume and / or the inner demixing volume as special case, is represented by λ. The criteria for the maximal dimension for19.01.2026

[1220] single mode waveguide dmax computed based on the wavelength and the NA of the waveguide (thus the refractive index difference obtained by laser inscription). Width w and height h are listed. If those are smaller than dmax, single mode propagation can be achieved.

[1221] Whether or not a single mode transmission is enabled is indicated by y for yes or n for no. The examples showing a single mode transmission all satisfy the above mentioned equation max(w,h) < 0.76 · λ / NA.

[1222] The described glass element is especially suitable for electronic and / or optoelectronic applications. Especially, the glass element can be combined with a semiconductor element. In a most advantageous embodiment, at least one semiconductor element is mounted on a surface of the glass element.

[1223] Furthermore it is foreseen that the glass element comprises at least one through-glass-via (TGV), which is advantageously metallized. Furthermore or alternatively, metallizations on a surface of the glass element can be present. The metallizations can especially represent electric conductors connecting semiconductor elements with other semiconductor elements or other items. The TGV can especially be used to access surfaces of the glass element and / or semiconductor elements mounted thereto.

[1224] The invention further comprises the use of a glass or a glass element described herein for the manufacturing of electronic and / or optoelectronic devices, especially for the combination with semiconductor devices, advantageously for mounting semiconductor elements onto the glass element (1), most preferably in combination with metallizations on the surface of the glass element or througholes (TGVs) within the glass element.

[1225] The Figures shall further support the understanding of principles of the invention. The Figures represent schematics with a schematical scale. The dimensions of real items might differ from the dimensions and / or aspect ratios shown herein. Reference numbers described referring to one Figure and contained in other Figures have the same meaning. Where applicable, the figures as well represent examples of devices manufactured according to the description provided herein.19.01.2026

[1226] Fig. 1a shows the cross section of a waveguide obtained by inscription with lower repetition rate.

[1227] Fig, 1b shows the cross section of a waveguide inscribed in the heat accumulation regime.

[1228] Fig. 3a shows the embodiment of a waveguide with a single demixing volume in a cross-sectional view

[1229] Fig. 3b shows the waveguide according to Fig. 3a in a longitudinal cross-sectional view,

[1230] Fig. 4a shows the embodiment of a waveguide with inner and an outer demixing volume in a cross-sectional view.

[1231] Fig. 4b shows the waveguide according to Fig. 4a in a longitudinal cross-sectiona view.

[1232] Fig. 5a shows a waveguide according to Fig. 3a.

[1233] Fig. 5b represents the refractive index profile of a waveguide according to Fig. 5a.

[1234] Fig. 6a shows a waveguide according to Fig. 4a.

[1235] Fig. 6b represents the refractive index profile of a waveguide according to Fig. 6a.

[1236] Fig. 7 is a schematics of a glass element with an ebedded waveguide and an attached semiconductor

[1237] Fig. 8 represents a schematics of an optoelectronic glass board

[1238] Fig. 9a shows a typical transversal geometry of a waveguide

[1239] Fig. 9b shows an image of the light intensities transmitted in the waveguide

[1240] Fig. 9b shows an image of another scheme of light transmitted in the waveguide19.01.2026

[1241] Here a heat accumulation regime and / or a microscope with lower NA < 0.0 is applied. A heat affected volume 30 is formed above the absorption volume 40 as transient effect of the fast sequence of ultrashort laser pulses. Within the heat affected volume 30, the demixing volume 20 showing the desired refractive index change to embody the waveguide is formed within the heat affected volume, here having an outer boundary facing the absorption volume 40. According to the inventions both principles can be applied, whereas the heat accumulation regime is advantageous because of the minimized processing times. However, both principles lead to a permanent refractive index modification within the glass substrate 1 and can provide waveguides therein.

[1242] A principle of a setup for inscribing such waveguides applying the heat accumulation regime is shown in Fig. 2.

[1243] The beam of an usp-laser 200 is focused by an optical system 210 into the volume of a glass substrate 1. At the position of the focus within the glass substrate, indicated by the focal point distance fpd, the absorption volume 40 is created, resulting in a heat affected volume 30 being formed above the absorption volume 40 and the demixing volume 20 within the heat affected volume as described above. In order to create an elongated waveguide with an longitudinal axis along the x plane, the glass substrate 1 is moved relative to the optical system 210 or the usp-laser 200 in the transport direction tr.

[1244] The Rayleigh zone 2zr corresponds to the depth of field of the microscope objective and denotes the longitudial section of a Gaussian beam, where the Intensity along the beam propagation axis is in between its maxium intensity I0 and 1 10.

[1245] For example by application of the apparatus described in connection with Fig. 2, a demixing volume 20 within a glass substrate according to Figs. 3a and 3b can be achieved. The demixing volume 20 is permanently present within the glass substrate 1 and shows a local refractive index modification, wherein the refractive index of the demixing volume 20 differs from the refractive index of the glass matrix of the glass substrate 1.

[1246] Of course, the same or similar waveguide can be manufactured applying low repetition rates and high NA microscope objectives and therefore not applying the heat accumulation19.01.2026

[1247] regime. The glasses according to the invention allow for all usp-laser based processes to be applied.

[1248] Fig. 3a shows the cross-sectional view through a glass element 1 with a demixing volume 20 embedded therein. The demixing volume is an area where the glass is permanently modified by demixing as described above. The demixing volume 20 can represent a waveguide. The demixing volume 20 in this example is completely surrounded by the glass of the glass element 1. However, it is of course possible that at least a part of the demixing volume 20 is facing the sidewall of a glass element, so that it is a part of the outer wall of the glass element as well.

[1249] The diameter shape of the demixing volume can in most cases be round or oval. Other shapes are of course possible as well, especially depending in the laser focus, the applied modification regime and the number of passes of the laser focus during the inscription process.

[1250] Fig. 3b shows the cross-sectional view of the glass element 1 with the embedded demixing volume 20 in a view perpendicular to the view shown in Fig. 3a. The demixing volume 20 forms a path within the glass. In the example shown here, the path is a straight line. Of course, bends, crossing paths, branches and every other geometry is possible and enabled by the laser inscription process as described above.

[1251] In analogy to Fig. 3a, Fig. 4a shows a cross-sectional view of a glass element 1 in which an inner demixing volume 21 and an outer demixing volume 22 are embedded. The outer demixing volume 22 is surrounding the inner demixing volume 21. Both, inner demixing volume 21 and outer demixing volume 22, represent permanent modifications of the glass composition as well and can represent a waveguide. The diameter of the demixing volumes 21, 22 can especially be round or oval as described in connection with Fig. 3a.

[1252] Fig. 4b represents a cross-sections view of the glass element 1 of Fig. 4a perpendicular to the view shown in Fig 4a. Again, the inner demixing volume 21 and the surrounding outer demixing volume 22 build a path which represents a waveguide. Bend, crossing, branches etc. are of course possible in this structure as well.19.01.2026

[1253] Fig. 5a shows the same item as Fig, 3a in the same view. The waveguide is represented by the demixing volume 20. The waveguide has the height h and the width w. h and w are attributed to the boundary surface where a refractive index has been raised compared to the surrounding glass material 1, as described herein desirably by the interaction with the usp-laser. It is expressly noted that the raised refractive index can also occur at an area within the demixing volume 20 itself.

[1254] Mostly all of the demixing volume 20 shows a significant modification of the refractive index. Fig. 5b demonstrates the refractive index profile of an item according to Fig. 5a. The refractive index ndem of the demixing volume 20 is significantly larger than the refractive index ng of the surrounding glass material. Therefore, an electromagnetic wave, here, especially light, can be guided within the demixing volume 20 due to the reflection on the boundary surface of the area of the high refractive index towards the lower refractive index, hence leading to the forming of a waveguide.

[1255] The same principle applies for waveguides with an inner and an outer demixing volume. Fig. 6a shows the same item in the same view as Fig. 4a. The refractive index change from a higher refractive index to a lower refractive index which provides total reflection for guided electromagnetic waves is achieved at the boundary surface between inner demixing volume 21 and outer demixing volume 22. Again, mostly the waveguide 2 is represented by the inner demixing volume 21. A height h and width w can again be attributed to the location of the refractive index-change, which can also lie within the inner demixing volume 21.

[1256] Fig. 6b represents the refractive index profile of an item according to Fig. 6a. The refractive index nid of the inner demixing volume 21 is higher than the refractive index nod of the outer demixing volume 21. Therefore, light can be guided within the area of nid, here within the inner demixing volume 21, which herein represents a lightguide. The refractive index ng of the surrounding glass material 1 can be lower or even be higher than nid, the relevant aspect ist that nid is higher than nod.

[1257] This configuration might also provide the advantage that light coupled into the surrounding glass material 1 can less likely couple into the waveguide 2 being surrounded by the outer19.01.2026

[1258] demixing volume 22 when nod is lower than ng, because then total reflection at the boundary surface between the areas of the higher nd and the lower nod will occur. This can attribute to maintain a high signal quality when data is transmitted within the waveguide 2,

[1259] For both, the embodiments with a single demixing volume 20 according to Figs, 5a and 5b and / or the embodiments containing an inner demixing volume 21 and an outer demixing volume 22 according to Figs, 6a and 6b, the slope of the refractive index profile is extremely steep according to the figures, However, in reality a certain slope can also be advantageous in order to provide a low dampening within the waveguide.

[1260] Another aspect for the quality of a waveguide is the relation between the width w and the height h of the waveguide. Advantageously, w / h is greater than 0.5, more advantageously greater than 0.8, most advantageously at least 0.9, an ideally equal 1.

[1261] The glass material described herein allow for a waveguide to be permanently inscribed which provie w / h ratios in the above mentioned range, especially by application of the heat-accumulation regime as described above.

[1262] The glass material and / or the glass element 1 as described herein can advantageously used as basis for an optoelectronic device, where at least one waveguide is embedded in the glass material and the glass material itself is a substrate for mounting semiconductor devices. For example, the semiconductor device can be an optoelectronic chip, which can receive and / or transmit light into the waveguide.

[1263] Fig. 7 represents a schematics of a glass element 100 with a glass substrate 1 containting the glass material described herein in a cross-sectional view. The glass element 100 can in the case especially represent an optoelectronic device and / or a section thereof. Within the glass substrate 1, there is an embedded waveguide 2 as described above. A semiconductor device 50 is mounted onto the surface of the glass element 1. The mounting structures and / or metallisations used therefore are not shown in the figure. The semiconductor device 50 in this example is an optoelectronic device as mentioned above.19.01.2026

[1264] According to the figure, the waveguide 2 is embedded and the light guided therein must be redirected towards the semiconductor device 50. Therefore, a redirection device 70 is present within the glass substrate 1. This can be a mirror, a prisma and the like, e.g. an air filled volume that forms a planar surface to the intersecting waveguide. A 3-D rerouting of the waveguide 2 is of course possible as well, resulting in a continuous waveguide crossing planes of substrate 1.

[1265] Optionally, the glass substrate 1 can contain through-glass-vias (TGVs) 75, which are advantageously filled with metal as electric conductor and or have metallized sidewalls. The glass materials described herein also provide the capability to being metallized, which means metal layer can be permanently attached to the glasses with good mechanical stability. TGVs can be produced by known usp-laser based processes as well.

[1266] Fig. 8 is a top-view of an item at least similar to the item shown in Fig, 7. Fig. 8 represents at least a section of an optoelectronic device 100 comprising a glass substrate 1 comprising or consisting of the glass materials described herein with embedded waveguides 2. The waveguide 2 can be branched as shown here in order to be routed to a plurality of semiconductor devices 50. Semiconductor devices 50 can be connected with metallized structures 76 on the surface of the glass element 1 or with through-glass-vias 75. A connection between semiconductor elements 50 via waveguides 2 is possible as well. The glass element 1 can for example be present in the form of a glass wafer. Hence, the glass materials described herein provide a toolbox for manufacturing optoelectronic devices which can combine optical data transmission via waveguides and electronics.

[1267] Especially, the glass material as described herein is capable of efficient enscription of waveguides 2 with usp-laser techniques, has a thermal expansion which allows the combination with semiconductor elements 40, has a rational meltability, can advantageously be laser structured in order to obtain TGVs and can most advantageously be metallized in order obtain electrically conductive paths 76 on the surface of the glass substrate 1 and / or electrically conductive TGVs 75.

[1268] Fig. 9a shows a scheme of a typical transversal geometry of a waveguide 2 in a glass substrate 1, based on refractive index measurement. Its form is irregular pear shaped, its width19.01.2026

[1269] w is 7 microns, while the height is 16 pm. It corresponds to example 9 and 10 in table Ta-belle 32.

[1270] Fig. 9b shows the image of light intensities at the end of a waveguide of Fig. 9a, where light of the propagation wavelength 1550 nm has been coupled in at the start of it. The laser parameters have been chosen, so that the max. refractive index change does not exceed 0.001. This corresponds to the parameters of example 9 in table Table 38. The result is large mode field with a diameter lager than 10 pm. In particular, this image or Fig. respectively correspond to a single mode transmission of light in the waveguide.

[1271] Fig. 9c shows the light intensities at the end of a waveguide of Fig. 9a, where light of the propagation wavelength 1550 nm has been coupled in at the start of it. The laser parameters have been chosen, so that the max. possible refractive index change of the glass can be obtained, in this case of Dn = 0.005. This corresponds to the parameters of example 9 in table xxx. However, the wave guide is not single mode, but support a further mode that exends along the y-axis. The result is a more confined intensity distribution, that is superposi-ton of the fundamental mode and the next higher order mode. Their respective ampltidute depend on the in-coupling conditions, namely the relative position of in-coupling spot and waveguide (2) cross-section. The centre of gravity of the intensity distribution has shifted toward a lower y-position.19.01.2026

[1272] Reference numbers

[1273] 1 glass

[1274] 2 waveguide

[1275] 20 demixing volume

[1276] 21 inner demixing volume

[1277] 22 outer demixing volume

[1278] 30 heat affected volume

[1279] 40 absorption volume

[1280] 50 semiconductor element

[1281] 70 redirection element

[1282] 75 TGV

[1283] 76 metallized path

[1284] 100 glass product

[1285] 200 laser

[1286] 210 optical system

[1287] 2zr Raleigh zone

[1288] ndem refractive index demixing volume

[1289] ng refractive index glass element

[1290] nid refractive index inner demixing volume

[1291] nod refractive index outer demixing volume

[1292] fpd focal point distance

[1293] tr transport direction

[1294] h height

[1295] w with

Claims

19. 01.2026Patent Claims1. Glass comprising the following constituent phases (in mol%):Constituent phase Minimum Maximum(Li2O Al2O3-2SiO2) / 4 0% 0%(Na2O Al2O3-2SiO2) / 4 0% 10%(K2O Al2O32SiO2) / 4 0% 0%(2MgO-2Al2O3'5SiO2) / 9 0% 50%(CaO Al2O3-2SiO2) / 4 0% 50%(SrO Al2O3-2SiO2) / 4 0% 0%(BaO Al2O3-2SiO2) / 4 0% 0%(Li2O·B2O3·4SiO2) / 6 0% 0%(Na2O·B2O3·2SiO2) / 4 0% 0%(La2O3- B2O32SiO2) / 4 0% 0%(Na2O·TiO2·4SiO2) / 6 0% 0%(K2O TiO2'3SiO2) / 5 0% 0%(BaO·TiO2·3SiO2) / 5 0% 0%(Na2O·ZrO2·4SiO2) / 6 0% 40%(K2O ZrO2'3SiO2) / 5 0% 0%(2CaO·ZrO2·4SiO2) / 7 0% 80%(BaO·ZrO2·3SiO2) / 5 0% 0%19.01.2026Constituent phase Minimum Maximum(K2O Nb2O5-4SiO2) / 6 0% 60%(Na2O·ZnO·2SiO2) / 4 0% 0%(Na2O·ZnO·3SiO2) / 5 0% 0%(K2O·ZnO·2SiO2) / 4 0% 0%(Li2O·2SiO2) / 3 0% 10%(Na2O-2SiO2) / 3 0% 10%(K2O·2SiO2) / 3 0% 10%(MgO·SiO2) / 2 0% 0%(CaO·SiO2) / 2 0% 0%(BaO-2SiO2) / 3 0% 0%(4ZnO·3B2O3) / 7 0% 0%(ZrO2·B2O3) / 2 0% 0%(La2O3·Nb2O5·2B2O3) / 4 0% 0%( La2O3■ T a2Os ■ 2 B2O3) / 4 0% 0%(3BaO·3B2O3·2SiO2) / 8 0% 20%B2O30% 10%SiO20% 65%B2O3+SiO230% 70%19.01.2026with a thermal expansion coefficient calculated according to (3) in the range 3.3 ± 0.3 ppm / K and a working point calculated according to (11) between 1100°C and 1400°C and a refractive index calculated according to (15) of 1.5 or higher, especially from 1.5 to 2.0 or from 1.5 to 1.8.

2. Glass comprising the following constituent phases (in mol%):Constituent phase Minimum Maximum(Li2O Al2O3-2SiO2) / 4 0% 0%(Na2O Al2O3-2SiO2) / 4 0% 20%(K2O Al2O32SiO2) / 4 0% 0%(2MgO-2Al2O3'5SiO2) / 9 0% 80%(CaO Al2O3-2SiO2) / 4 0% 80%(SrO Al2O3-2SiO2) / 4 0% 0%(BaO Al2O3-2SiO2) / 4 0% 0%(Li2O·B2O3·4SiO2) / 6 0% 0%(Na2O·B2O3·2SiO2) / 4 0% 0%(l_a2O3' B2O32SiO2) / 4 0% 0%(Na2O·TiO2·4SiO2) / 6 0% 0%(K2O TiO2'3SiO2) / 5 0% 0%(BaO·TiO2·3SiO2) / 5 0% 0%(Na2O·ZrO2·4SiO2) / 6 0% 60%19.01.2026Constituent phase Minimum Maximum(K2O·ZrO2·3SiO2) / 5 0% 0%(2CaO·ZrO2·4SiO2) / 7 0% 60%(BaO·ZrO2·3SiO2) / 5 0% 0%(K2O·Nb2O5·4SiO2) / 6 0% 60%(Na2O·ZnO·2SiO2) / 4 0% 0%(Na2O·ZnO·3SiO2) / 5 0% 0%(K2O·ZnO·2SiO2) / 4 0% 0%(Li2O·2SiO2) / 3 0% 30%(Na2O-2SiO2) / 3 0% 20%(K2O·2SiO2) / 3 0% 20%(MgO·SiO2) / 2 0% 0%(CaO·SiO2) / 2 0% 0%(BaO-2SiO2) / 3 0% 0%(4ZnO·3B2O3) / 7 0% 0%(ZrO2·B2O3) / 2 0% 0%(La2O3·Nb2O5·2B2O3) / 4 0% 0%( La2O3■ T a2Os ■ 2 B2O3) / 4 0% 0%(3BaO·3B2O3·2SiO2) / 8 0% 30%B2O30% 10%19.01.2026Constituent phase Minimum MaximumSiO20% 65%B2O3+SiO220% 75%with athermal expansion coefficient calculated according to (3) in the range 4.7 ± 0.3 ppm / K and a working point calculated according to (11) between 1100°C and 1400°C and a refractive index calculated according to (15) of 1.5 or bigger.

3. Glass comprising the following constituent phases (in mol%):Constituent phase Minimum Maximum(Li2O Al2O3-2SiO2) / 4 0% 0%(Na2O Al2O3-2SiO2) / 4 0% 40%(K2O Al2O3-2SiO2) / 4 0% 0%(2MgO-2Al2O3'5SiO2) / 9 0% 60%(CaO Al2O3-2SiO2) / 4 0% 60%(SrO Al2O3-2SiO2) / 4 0% 0%(BaO Al2O3-2SiO2) / 4 0% 0%(Li2O·B2O3·4SiO2) / 6 0% 0%(Na2O·B2O3·2SiO2) / 4 0% 0%(La2O3·B2O3·2SiO2) / 4 0% 0%(Na2O·TiO2·4SiO2) / 6 0% 0%19.01.2026Constituent phase Minimum Maximum(K2O·TiO2·3SiO2) / 5 0% 0%(BaO·TiO2·3SiO2) / 5 0% 0%(Na2O·ZrO2·4SiO2) / 6 0% 80%(K2O·ZrO2·3SiO2) / 5 0% 0%(2CaO·ZrO2·4SiO2) / 7 0% 50%(BaO·ZrO2·3SiO2) / 5 0% 0%(K2O·Nb2O5·4SiO2) / 6 0% 60%(Na2O·ZnO·2SiO2) / 4 0% 0%(Na2O·ZnO·3SiO2) / 5 0% 0%(K2O·ZnO·2SiO2) / 4 0% 0%(Li2O·2SiO2) / 3 0% 40%(Na2O-2SiO2) / 3 0% 30%(K2O·2SiO2) / 3 0% 30%(MgO·SiO2) / 2 0% 0%(CaO·SiO2) / 2 0% 0%(BaO-2SiO2) / 3 0% 0%(4ZnO·3B2O3) / 7 0% 0%(ZrO2·B2O3) / 2 0% 0%(La2O3·Nb2O5·2B2O3) / 4 0% 0%19.01.2026Constituent phase Minimum Maximum(La2O3·Ta2O5·2B2O3) / 4 0% 0%(3BaO·3B2O3·2SiO2) / 8 0% 40%B2O30% 10%SiO20% 45%B2O3+SiO2 20% 55%with a thermal expansion coefficient calculated according to description which is in the range 6.3 ± 0.3 ppm / K and a the working point calculated according to the description between 1100°C and 1400°C and that the refractive index calculated according to the description being 1.5 or higher.

4. Glass comprising the following constituent phases (in mol%):Constituent phase Minimum Maximum(Li2O Al2O3-2SiO2) / 4 0% 85%(2MgO·2Al2O3·5SiO2) / 9 0% 85%(CaO Al2O3-2SiO2) / 4 0% 85%(SrO Al2O3-2SiO2) / 4 0% 85%(BaO Al2O3-2SiO2) / 4 0% 85%(Li2O·B2O3·4SiO2) / 6 0% 85%(Na2O·B2O3·2SiO2) / 4 0% 85%19.01.2026Constituent phase Minimum Maximum(K2O·B2O3·4SiO2) / 6 0% 85%(La2O3·B2O3·2SiO2) / 4 0% 85%(Na2O·ZrO2·4SiO2) / 6 0% 85%(K2O·ZrO2·3SiO2) / 5 0% 85%(2CaO·ZrO2·4SiO2) / 7 0% 85%(BaO·ZrO2·3SiO2) / 5 0% 85%(Na2O·ZnO·2SiO2) / 4 0% 85%(Na2O·ZnO·3SiO2) / 5 0% 85%(K2O·ZnO·2SiO2) / 4 0% 85%(Li2O·2SiO2) / 3 0% 85%(Na2O-2SiO2) / 3 0% 85%(K2O·2SiO2) / 3 0% 85%(BaO-2SiO2) / 3 0% 10%(4ZnO·3B2O3) / 7 0% 10%(ZrO2·B2O3) / 2 0% 10%(3Al2O3-2SiO2) / 5 0% 85%(3BaO-3B2O3-2SiO2) / 8 0% 85%B2O30% 10%19.01.2026Constituent phase Minimum MaximumSiO20% 60%B2O3+SiO220% 60%preferably with a thermal expansion coefficient CTE, a working point WP, a refractive index ng in the ranges as defined in any of the line numbers of following tableLine number Refractive Index CTE / (ppm / K) WP / °C1 >1.542 <4.35 <11802 >1.544 <4.45 <11303 >1.55 <4.55 <10804 >1.56 <4.55 <10255 >1.56 <4.7 <10156 >1.56 <4.8 <9957 >1.56 <5.0 <9858 >1.57 <4.9 <9909 >1.57 <5.2 <96010 >1.57 <5.35 <94011 >1.58 <5.25 <96012 >1.58 <5.5 <93513 >1.58 <5.65 <92519.01.202614 >1.58 <5.7 <91015 >1.58 <5.75 <90017 >1.59 <5.55 <90018 >1.59 <5.75 <89020 >1.59 <7 <80021 >1.6 <6.25 <84022 >1.6 <6.55 <83023 >1.6 <6.7 <82024 >1.6 <6.85 <81525 >1.526 <4.3 <108026 >1.526 <4.15 <115527 >1.526 <3.8 <121028 >1.526 <3.7 <122029 >1.526 <3.5 <12855. Glass element (1, 100) with an embedded waveguide (2), whereas the glass of the glass element (1, 100) has a composition according to at least one of the preceding claims, whereas the waveguide (2) comprises a demixing volume (20) of the glass element (1).19.01.20266. Glass element (1, 100) according to claim 5, whereas the waveguide (2) comprises a demixing volume (20) of the glass element (1) which contains at least an area with a refractive index ndem which is higher than the refractive index ng of the glass element (1) and / or an inner demixing volume (21) with an refractive index nid and an outer demixing volume (21) with an refractive index nod, whereas nid is higher than nod and advantageously higher than ng. The refractive indices are measured at a wavelength 589.3 nm.

7. Glass element (1, 100) according at least one of the claims 5 to 6, whereas the refractive index ndem of demixing volume (20) is greater than the refractive index ng of the glass of the glass element (1 ) by 0.0001 to 0.02, preferably by 0.0005 to 0.01 and / or nid is greater than ng by 0.0001 to 0.02, preferably by 0.0005 to 0.01.

8. Glass element (1, 100) according to at least one of the claims 5 to 7, whereas the CTE of the demixing volume (20) and / or the inner demixing volume (21 ) is differing from the CTE of the glass (1) by at maximum 0.2 ppm / K, preferably by at maximum 0.1 ppm / K.

9. Glass element (1, 100) according to at least one of the claims 5 to 8, whereas the waveguide (2) has a height (h) and a width (w), whereas the ratio w / h is greater than 0.5, preferably greater than 0.8, most preferably at least 0.9.

10. Glass element (1, 100) according to at least one of the claims 5 to 9, whereas the waveguide (2) has a height (h) and a width (w), with19.01.2026max(w, h) < 0.76 λ / NA,with NA being the numerical aperture of the waveguide (2) and λ being the wavelength of the electromagnetical wave being transported in the waveguide in the operating status; preferably λ is in the range from 1300 nm to 1600 nm, more preferably λ is 1310 nm or 1550 nm.

11. Glass element (1, 100) according to at least one of claims 5 to 10, whereas at least one semiconductor element (50) is mounted on a surface of the glass element (1, 100).

12. Glass element (1, 100) according to least one of claims 5 to 11, whereas the glass element comprises at least one through-glass-via (75), which is preferably metallized, and / or metallizations (76) on a surface of the glass element.

13. Use of a glass (1 ) or a glass element (100) according to at least one of the preceding claims for the manufacturing of electronic and / or optoelectronic devices, preferably for mounting semiconductor elements (50) onto the glass element (1), most preferably in combination with metallizations (76) on the surface of the glass element (1 ) or througholes (75) within the glass element (1 ).

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