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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

The modelling and calculation of some characteristic parameters of Er 3+ :LiNbO 3 optical waveguides

Niculae N. Puşcaş, I. Popescu

Published Feb 7, 2006• 0 citations
Publisher

Abstract

Based on the transmission spectra of Er3+-doped LiNbO3 optical waveguides in this paper we report some experimental and theoretical results concerning the evaluation of some spectroscopic parameters which characterize the above mentioned waveguides. The absorption experimental spectra were used to determine the homogeneous absorption and emission cross sections (utilising the density matrix formalism and the McCumber's theory and taking into account the Stark splitting of the levels), the oscillator strength of the absorption transition, the spontaneous emission probabilities, the radiative lifetime and the excitation energy in three regions of the optical spectrum: around 1550 nm, 980 nm and 550 nm, respectively. Also, we measured the rising and falling times and we calculated the homogeneous upconversion factor corresponding to the transition 4I15/2->4F7/2.

DOI
10.1117/12.675661

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Based on the transmission spectra of Er3+-doped LiNbO3 optical waveguides in this paper we report some experimental and theoretical results concerning the evaluation of some spectroscopic parameters which characterize the above mentioned waveguides. The absorption experimental spectra were used to determine the homogeneous absorption and emission cross sections (utilising the density matrix formalism and the McCumber's theory and taking into account the Stark splitting of the levels), the oscillator strength of the absorption transition, the spontaneous emission probabilities, the radiative lifetime and the excitation energy in three regions of the optical spectrum: around 1550 nm, 980 nm and 550 nm, respectively. Also, we measured the rising and falling times and we calculated the homogeneous upconversion factor corresponding to the transition 4I15/2->4F7/2.
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The polarization-dependent absorption and emission spectra of the 4113/2-4115/2 transition (A - 1.5 pm) in single crystal bulk Er:LiNbOs have been measured. Low-temperature (10 K) measurements of the Stark split energy levels of these two manifolds indicate at least two Er3+ sites. McCumber theory is applied to determine the Er:LiNb03 absorption and emission cross sections. These values are used to calculate the gain charac- teristics of Er:LiNbOs channel waveguides. Calculations indicate that a gain of 10 dB is achievable in a waveguide of several centimeters using -20-mW pump power.
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.
In this article, we report a theoretical study concerning some statistical parameters which characterize the single- and double-pass Er3+-doped Ti:LiNbO3 M-mode straight waveguides. For the derivation and the evaluation of the Fano factor, the statistical fluctuation and the spontaneous emission factor we used a quasi two-level model in the small gain approximation and the unsaturated regime. The simulation results show the evolution of these parameters under various pump regimes and waveguide lengths. The obtained results can be used for the design of complex rare earth-doped integrated circuits.
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.