We present a simple method based on the soliton perturbative theory to design microwires of non-uniform diameter profiles. In contrast to previous methods, the one presented here relies on minimizing the soliton perturbation by third order dispersion (TOD) while taking into account the change of the soliton local duration along the microwire. The method leads to a design that maximizes the soliton self-frequency shift in non-uniform microwires. The microwire design comprises a unique dispersion profile such that a wavelength-shifting soliton experiences only weak perturbations from the TOD and avoids shedding its energy into the dispersive waves. The TOD perturbation is quantified with an analytic expression $\epsilon$ that is kept below a threshold value, thus keeping a soliton weakly perturbed by TOD in every position within the microwire. Numerical simulations are conducted to check the validity of the method. We consider a fundamental soliton centered at a wavelength of 2000 nm propagating in As<sub>2</sub>Se<sub>3</sub> microwires of length as short as 10 cm. The results show that optimized non-uniform diameter profile allows the tuning of the self-frequency shifted soliton over a spectral range of 860 nm.
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