Specific Features in the Design of Gradient-Index Elements from Glasses by Ion Exchange

Theoretical Aspects of the Ion Exchange in the Fabrication of Focusing Gradient-Index Lenses

“…GRADIENT-INDEX ELEMENTS In [1], we proposed a model for the formation of a gradient-index element of the radial type through the ion-exchange synthesis according to the reaction + + due to incomplete conformal substitution of ions. 1 The gradient-index element was represented as a combination of cylindrical glass layers of different compositions.…”

“…1 The gradient-index element was represented as a combination of cylindrical glass layers of different compositions. In the case where it is necessary to obtain a parabolic spatial distribution of the refractive index, the concentrations of exchanging components, as was shown in [2], should vary according to the hyperbolic law.…”

“…In our recent work [1], we proposed a new method providing the proper choice of the optimum composition of the initial glasses used in the fabrication of focusing gradient-index elements with a parabolic spatial distribution of the refractive index and obtained the appropriate relationships describing the dependences of the molar concentrations of exchanging components on the reduced radius of the cylindrical gradient-index element. Taking into account this dependence, it is possible to obtain an optimum, approximately parabolic spatial distribution of the refractive index during synthesis of gradient-index elements through ion exchange between the softened glass and the melt of the salt mixture.…”

“…This quantity is defined as the product of the refractive index of the material multiplied by its molar volume. Historical evidence regarding the origin of the notion of the moleadditive modification of the refractive index and the use of this quantity both in the physicochemical analysis (the concept of the metric of an equilibrium chemical diagram) and as a characteristic of vitreous systems have already been reported elsewhere [1][2][3][4][5][6]. In the present paper, we will dwell briefly on the advantages of the application of this concept in practice.…”

“…Earlier [1], we offered only a qualitative description of the spatial distribution of the refractive index obtained as a result of the redistribution of the concentrations attained upon ion exchange between the softened glass and the melts of salt mixtures. The distribution of the refractive index gradient of a focusing cylindrical gradient-index element approaches a parabolic distribution in the central near-axial region extended, in the best cases, to 70% of the diameter and has a local minimum at the axis, two inflection points, and side maxima in the surface region.…”