An approximate solution has been presented for the single-input nonlinear optical directional coupler under the most commonly used condition: operating near the critical power. By introducing the approximation in previous step, a simplified integral equation has been obtained. It can be integrated as simple functions instead of elliptic functions. Numerical examples of our results have been given and compared with the exact solution and the approximate solution derived by A. T. Pham et al. Our results are more accurate than that of A. T. Pham et al.
Based on the theory of mode analysis, we present here a new method to calculate the absorption efficiency for the double-clad optical fibers. The ratio of the number of the absorbable modes to total number of guided modes is taken as absorption efficiency. Taking the radius of caustic surface as a threshold value, we can estimate whether or not an individual mode is absorbable. Results show that for a symmetric circular DCF, there is a large fraction of power which can never be absorbed and its absorption efficiency is low. Increasing the radius of RE-doped core can raise the absorption efficiency, but the single mode operation will be destroyed. For an offset core DCF, the high absorption efficiency can be achieved by increasing the offset distance. Also there exists an offset limit, beyond this the absorption efficiency reaches saturation. The result is that we can improve the absorption efficiency by increasing offset distance instead of the radius of fiber core. This conclusion is in principle consistent with precious 2-D ray optics methods.
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