Special glass for silver-sodium ion exchanged waveguides

2.1 Glass's composition and characteristics

The glass used in this study contains ${\mathit{SiO}}_2$ as network former oxide with quantity in weight (%) of 61–64%. This amount gives the glass strength and high transparency in the visible and near infrared ranges. The alumina ( ${\mathit{Al}}_2{O}_3$ ) is introduced as network intermediate oxide with 11–13%. The intermediate oxide, contribute to the glass strength, causes an elevation of refractive index. The existence of this quantity in the glass permits to increase the electrical conductivity, the chemical durability of glass and the diffusion efficiency in the material. As network modifier oxides, Na₂O, Li₂O, MgO and CaO are introduced with 12–14, 0.5–1, 3–4 and 3–5% respectively. The addition of alkaline oxides (Na₂O and Li₂O) permits to reduce the elaboration temperature, the viscosity and the chemical durability of glass. Moreover, the presence of alkaline oxides increases the dilatation coefficient, the electrical conductivity and the refractive index. The MgO and CaO improve also the chemical resistance of glass and reduce the electrical conductivity. The introduction of B₂O₃, in this case (4–6%), increases the chemical resistance and decreases the dilatation coefficient. It should be noted, that the composition do not contains FeO, As₂O₃ or Sb₂O₃ since these elements cause the reduction of silver ions leading to excessive losses in the substrate. The glass samples, with size of 6 cm, were prepared starting from high purity powders according the weight (%) composition mentioned above by melt-quenching method. This method includes a series of classical steps: mixing of starting materials, melting, fining, casting and annealing (Murugasen et al., 2015). The refractive index of this glass is nearly of 1.51 (λ = 0.8 μm) and the temperature of fusion (Tg) is in order of 560 °C.

2.2 Ion-exchanged waveguide's parameters

In order to design optical waveguides made by ion-exchange in this glass, it is important to characterize the diffusion properties of cations in the substrate. The kinetic of diffusion is obtained by analysis of the refractive index profile of planar waveguides calculated by the inverse WKB method from the effective index of multimode structures (Hocker and Burns, 1975; Kaul and Thyagarajan, 1984; Ding et al., 2004).

The diffusion coefficient and ionic mobility are deduced from this experiment by fitting numerically the index profiles by finite difference program. Such program simulates the differential equation (Fick’s law) which governs the diffusion kinetic of the two cations. The diffusion coefficient D ( $\mathrm{\mu }{\text{m}}^2/\text{min}$ ) is determined experimentally for two different concentrations (2% and 10% Molar fraction) of silver in a molten bath of Sodium Nitrate (NaNO₃). The measurements of D were performed for different temperatures varying from 250 to 350 °C (Table 1). The time of diffusion is a few seconds for each operation.

The refractive index variation (Δn) after the thermal exchange depends also on the silver concentration in the molten bath. The experimental results are given in the table 2.

We assume that D (T) has temperature dependence given by the following law:

The Fig. 1 illustrates the variation of D as a function of temperature (°C).

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Fig. 1

The variation of D as function of silver concentration and temperature.

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A glass waveguide elaborated with a silver concentration of 10% has a diffusion coefficient which is equal to 0.00002 µm²/min at 80 °C, which is not negligible. That is to say that it takes about 9 days for Ag⁺ ion move over a distance of 1 µm ( $x=2\sqrt{\mathit{Dt}}$ ) into the glass. This aspect is confirmed by heating the fabricated planner waveguides in a furnace, at low temperature (100 °C), for several days (until 750 h). It observed that the variation of refractive index of the fundamental mode, decrease from 0.055 to 0.047.

The diffusion of K⁺ is also tested, by immersing the glass substrate in a molten bath of KNO₃. The temperature of the exchange is more than 400 °C, for a time of diffusion more than four hours. From the obtained planner waveguides, the diffusion coefficient D and Δn are determined experimentally. D depends on the temperature of diffusion. For T varies from 390 to 460 °C, D changes from 0.012 to 0.065 µm²/min. The refractive index variation depends only on the kind of the dopant. In this case, it is about 0.0125. This glass is not well-suited for K⁺ exchange due to the qualities of the obtained buried waveguides (Tervonen et al., 2011).

A channel-waveguides are made by two-step exchange process (Rehouma et al., 1995). During the first step, a surface channel-waveguide is fabricated by purely thermal exchange between the Ag⁺ cations of the bath and the Na⁺ cations present in the glass, through a mask previously deposited on the glass surface. This mask is then removed; the waveguide is buried below the surface by application of an external electric field across the substrate, during the second step. The obtained waveguides, 3 cm of length, are well compatible with optical fiber. The insertion losses (input, output coupling and propagation losses) of such waveguides are less than 0.8 dB. These losses were divided as follow: 0.4 dB in input and output coupling losses (Rehouma et al., 2007), less than 0.39 dB (0.13 dB/cm) in propagation losses (at λ= 0.785 μm) (Rehouma and Aiadi, 2008). The propagation losses are measured by the Cut back method (Cai et al., 2013; Kaminow and Stulz, 1978).