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IEEE Journal of Quantum Electronics

Theoretical modeling of optical amplification in Er-doped Ti:LiNbO/sub 3/ waveguides

M. Dinand, W. Sohler

Published May 1, 1994• 100 citations
Publisher

Abstract

An accurate theoretical analysis is presented describing optical amplification in Er-diffused Ti:LiNbO/sub 3/ channel waveguides. It follows as far as possible the theory already developed for Er-doped fibers. As optical pumping around /spl lambda//sub p//spl ap/1.48 /spl mu/m is considered, a quasi-two-level model for the Er/sup 3+/ ions is used with wavelength-dependent cross sections. The optical gain in the 1.53 /spl mu/m>

DOI
10.1109/3.303692

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An accurate theoretical analysis is presented describing optical amplification in Er-diffused Ti:LiNbO/sub 3/ channel waveguides. It follows as far as possible the theory already developed for Er-doped fibers. As optical pumping around /spl lambda//sub p//spl ap/1.48 /spl mu/m is considered, a quasi-two-level model for the Er/sup 3+/ ions is used with wavelength-dependent cross sections. The optical gain in the 1.53 /spl mu/m>
In this paper it is presented a theoretical evaluation of the following important amplifier parameters: the output mean photon number, the standard deviation, the Fano factor, the statistical fluctuation and the spontaneous emission factor for single and double pass configuration, and for forward and backward pumping schemes in quasi two level optical waveguide amplifiers. The theoretical model used to evaluate the noise characterization of an Er3+-doped Ti:LiNbO3 waveguide amplifiers is based on the photon statistics master equation of the linear amplifier, closely related with EDFA model and has been modified to account for the effects of the host material. One considered a quasi two level system model and one neglected ESA due to the considered pumping wavelength. The interaction of the pump and signal photons with Er3+ ions in LiNbO3 can be described using the rate equations. The simulations were performed using the small gain approximation in Er3+:Ti:LiNbO3 optical waveguides. The pump was supposed in the 1480 nm range and the signal having (lambda) equals 1530 nm. The evaluation of the above mentioned parameters vs. wavelength, pump powers, etc. were also performed and commented.
In the small gain approximation and the unsaturated regime in this paper we report some original results concerning the evaluation of the Fano factor, statistical fluctuation and spontaneous emission factor which characterize the photon statistics on the number of excited modes, dopant concentration and power pumping in the single and double pass Er3+ - doped LiNbO, straight waveguide amplifiers pumped near 1484 nm using erfc, Gaussian and constant profile of the Er3+ ions in LiNbO, crystal. We demonstrated that for 50 mW input pump power the Poisson photon statistics are maintained in the above mentioned amplifiers for concentrations of the Er ions smaller than l026 m-3 and also high gains and low noise figures are achievable. The obtained results can be used for the design of optoelectronic integrated circuits.
A study of the complex atomic susceptibility of erbium-doped fiber amplifiers operating near the 1.53- mu m transition (/sup 4/I/sub 13/2/-/sup 4/I/sub 15/2/) developed from a semiclassical theoretical description is presented. Expressions for the emission cross section sigma /sub e/( lambda ) and absorption cross section sigma /sub a/( lambda ) of erbium:glass as a quasi-three-level laser system with Stark-split sublevel manifolds are derived. The results are used to calculate the cross sections of aluminosilicate erbium-doped fibers at low temperatures (T=4.2, 77 K) and at room temperature. It is demonstrated that an expression for the gain coefficient of the fiber amplifier can be derived from the expression of the susceptibility. Using Kramers-Kronig relations, an expression for the refractive index change in the fiber is derived. The theoretical spectral gain profile of the fiber amplifier and concurrent refractive index changes are analyzed for different pumping regimes.>
A novel measurement system provides determination of pump induced phase shifts in erbium doped fibers with an accuracy of /spl sim//spl pi//20. Using this system, a systematical analysis of the pump induced modulation of the refractive index and dispersions for a signal at 1550 nm and a pump at 980 nm is reported. The analysis contains measurements of pump induced refractive index changes as function of wavelength, pump power, and doping concentration. A model taking account of the contribution to the refractive index changes from optical transitions between /sup 4/I/sub 15/2/ states and /sup 4/I/sub 13/2/ states in Er/sup 3+/ yields good agreement to experimental results apart from a wavelength independent offset. The offset is interpreted to originate from high energetic optical transitions. The results show that for a large refractive index modulation, a short and highly doped fiber should be used with limited amplified spontaneous emission effect. In optical communication systems comprising erbium doped fiber amplifiers, a tradeoff between dispersion and amplification must be made.