We report on the development of elliptical, index tailored optical fibers for higher-order mode preservation for fiber-based, apertureless, internally illuminated scanning near-field optical microscopy (ai-SNOM). The fiber structure is simulated by the finite element method, showing large spreads of the effective indices for neighboring first higher-order modes. We demonstrate experimentally that due to this spread, the first higher-order modes do not couple, hence, the polarization is maintained, when the fiber is bent down to 1 cm radius. Further, we discuss the implications for ai-SNOM applications.