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We report on a simple and versatile method of fabricating polymer microlenses that can be easily integrated with optical devices. UV-curable epoxy resin is dropped onto optical devices by an ink-jet apparatus. When the droplets touch the surface, they form into partial spheres due to their surface tension. UV light irradiation for less than five minutes can easily turn them into solid microlenses. Various microlenses, having a geometrical diameter from 20 to 140 µm with F/1.0 to F/11.0, were successfully produced by controlling the volume and viscosity of the polymer resin and their wettability to the substrate. Their uniformity in a microlens array was measured to be within ±1% in diameter and ±3 µm in pitch. Hybrid integration of an ink-jetted microlens with a wire-bonded vertical-cavity surface-emitting laser (VCSEL) was also demonstrated. When an inkjetted microlens (45-µm diameter, F/2.0) was formed on the aperture of an 850-nm VCSEL, the coupling efficiency into a single-mode fiber was 4 dB higher than without the microlens.

We study Friedmann-Robertson-Walker cosmological models with matter content composed of two perfect fluids ρ 1 and ρ 2 , with barotropic pressure densities p 1 /ρ 1 = ω 1 = const and p 2 /ρ 2 = ω 2 = const, where one of the energy densities is given by ρ 1 = C 1 a α + C 2 a β , with C 1 , C 2 , α and β taking constant values. We solve the field equations by using the conservation equation without breaking it into two interacting parts with the help of a coupling interacting term Q. Nevertheless, with the found solution may be associated an interacting term Q, and then a number of cosmological interacting models studied in the literature correspond to particular cases of our cosmological model. Specifically those models having constant coupling parametersα,β and interacting terms given by Q =αHρ DM , Q =αHρ DE , Q =αH(ρ DM + ρ DE ) and Q =αHρ DM +βHρ DE , where ρ DM and ρ DE are the energy densities of dark matter and dark energy respectively. The studied set of solutions contains a class of cosmological models presenting a scaling behavior at early and at late times. On the other hand the two-fluid cosmological models considered in this paper also permit a three fluid interpretation which is also discussed. In this reinterpretation, for flat Friedmann-Robertson-Walker cosmologies, the requirement of positivity of energy densities of the dark matter and dark energy components allows the state parameter of dark energy to be in the range −1.37 ω DE < −1/3.