Simplified gain calculation in erbium-doped LiNbO 3 waveguides

Abstract

The combination of excellent electro-optical, acousto-optical and non-linear optical properties makes lithium niobate (LiNbO₃) an attractive host material for integrated optical components such as electro-optical modulators, acousto-optically tunable wavelength filters and Bragg gratings. In the last few years Erbium doped LiNbO₃ waveguide optical amplifiers (EDWA's) have attracted increasing interest. The combination of the amplifying properties of erbium with the excellent acousto-optical and electro-optical properties of the waveguide substrate LiNbO₃ allows the development of a whole class of new waveguide devices of higher functionality. The optical gain achievable in Ti:Er:LiNbO₃ waveguides by optical pumping could compensate or even over compensate these scattering, absorption and insertion losses leading to "zero loss" devices with net optical gain. The different types of lasers and amplifiers can be combined with other active and passive devices on the same substrate to form integrated optical circuits (IOC's) for a variety of applications in optical communications, sensing, signal processing and measurement techniques. The analysis of Er-doped diffused channel waveguides is, hence, required for design of amplifying integrated optical circuits in order to optimize the performance of these gain devices. The coupled differential equations, which govern the evolution of, pump power (1484nm), signal power (1485 to 1600nm) and amplified spontaneous emission, involve integrals which depend explicitly on the modal fields at the pump and signal wavelength in the diffused channel waveguide. In general, it is not possible to obtain analytical forms for the modal fields and propagation constant, hence, to obtain them various approximate or numerical methods (BPM, finite difference or finite element) are used. In this paper the modal field profiles obtained by the variational analysis are further approximated to an appropriately chosen Gaussian function, which leads to analytical forms of coupled differential equations with no integrals for the calculation of gain and ASE characteristics of the amplifying waveguide. Thus, computations are simplified and computation time is also reduced.