The accurate knowledge of the rare-earth spectroscopic parameters is fundamental for the design of both fiber and integrated active devices. The lifetimes, the branching ratios, the up-conversion, the cross-relaxation, the energy transfer coefficients of the rare-earths must be preliminarily identified before the design. The particle swarm optimization (PSO) is an efficient global search approach; when applied to rare-earth-doped host materials and devices, it permits the rare-earth spectroscopic characterization starting from optical gain measurements. The model for the peculiar case of a SiO2 - SnO2 : Er3+ glass ceramic system is illustrated. Two different, direct and indirect, pumping schemes are considered for the rare-earth spectroscopic characterization. In the direct pumping scheme, a pump at 378 nm wavelength is used to excite the erbium ions. The SnO2 does not take part in the excitation process. On the contrary, in the indirect pumping scheme the SnO2 is involved by exploiting the absorption band around 307 nm wavelength via a proper pump. In this case, the energy transfer between the SnO2 and the Er3+ ions occurs during the amplification process. The fabricated SiO2 - SnO2 : Er3+ glass ceramic slab waveguide is simulated via a finite element method (FEM) code and a homemade code is used to solve the rate equations. In order to identify the value of the SnO2-Er3+ energy transfer coefficient, the ratio between the two simulated optical gains at 1533 nm wavelength, with the direct and indirect pumping schemes, is compared with the ratio between the two emission intensity measurements.
The theoretical model of rare earth doped optical devices based on the rate equations and the power propagation equations can be employed for recovering, via an indirect approach, the rare earth spectroscopic parameters. As an example, the model for an erbium doped silica-tin dioxide, SiO2 - SnO2 : Er3+, glass ceramic waveguide is considered. Two different pumping schemes are employed to excite the erbium ions, the direct pumping at 378 nm and the indirect pumping at 307 nm via the tin dioxide. The achievable optical gain per unit length at 1533 nm is then evaluated for both pumping cases. The ratio between the two simulated optical gains is compared with the emission intensity measurements to estimate the value of the SnO2-Er3+ energy transfer coefficient. The particle swarm optimization algorithm is applied in order to find the SiO2 - SnO2 : Er3+ glass ceramic spectroscopic parameters which properly match the simulated optical gains ratio with the experimentally measured emission ratios. In the same way, the pump power coupled in the glass ceramic waveguide is also recovered. The SnO2-Er3+ energy transfer coefficient is estimated to be about 6.1 × 10-22 m3/s.
The paper illustrates both review and original simulation results obtained via the modelling of different set-ups based on optical microresonators for applications in optical sensing, lasing and spectroscopy. Passive microbubbles and microspheres coupled via long period fiber gratings (LPGs) and tapered fibers are designed and/or constructed for sensing of biological fluids in the near infrared (NIR) wavelength range. Rare earth doped chalcogenide glass integrated microdisks are designed for active sensing in the medium infrared (MIR) wavelength range. A home-made numerical code modelling the optical coupling and the active behavior via rate equations of ion population is employed for a realistic design, by taking into account the most important active phenomena in rare earths, such as the absorption rates, the stimulated emission rates, the amplified spontaneous emission, the lifetime and branching ratios, the ion-ion energy transfers and the excited state absorption. Optical coupling is obtained by employing ridge waveguides, for micro-disks, and tapered fibers, for microspheres and microbubbles. Different dopant rare earths as Erbium (Er3+) and Praseodymium (Pr3+) are considered.
A Dy3+-doped ZBLAN fiber amplifier based on an in-band pumped configuration is designed and optimized via an evolutionary approach. In the proposed model, the rate equations are coupled with the power propagation equations for the pump and signal beams. The complete amplifier model allows the definition of the fitness function to be optimized. Realistic values for optical and spectroscopic parameters are considered. For a fiber with dopant concentration of 2000 ppm, by employing an input pump power of 1 W at 2.72 μm wavelength, an optical gain of about 15.56 dB at 2.95 μm wavelength is obtained.
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