The relationship between submillimeter (submm) dust emission polarization and near-infrared (NIR) $H$-band polarization produced by dust dichroic extinction was studied for the cold starless dense core FeSt 1-457. The distribution of polarization angles ($90^{circ}$-rotated for submm) and degrees were found to be very different between at submm and NIR wavelengths. The mean polarization angles for FeSt 1-457 at submm and NIR wavelengths are $132.1^{circ} pm 22.0^{circ}$ and $2.7^{circ} pm 16.2^{circ}$, respectively. The correlation between $P_H$ and $A_V$ was found to be linear from outermost regions to relatively dense line of sight of $A_V approx 25$ mag, indicating that NIR polarization reflects overall polarization (magnetic field) structure of the core at least in this density range. The flat $P_H/A_V$ versus $A_V$ correlations were confirmed, and the polarization efficiency was found to be comparable to the observational upper limit (Jones 1989). On the other hand, as reported by Alves et al., submm polarization degrees show clear linearly decreasing trend against $A_V$ from $A_V approx 20$ mag to the densest center ($A_V approx 41$ mag), appearing as polarization hole structure. The power law index for the $P_{rm submm}$ versus $A_V$ relationship was obtained to be $approx -1$, indicating that the alignment for the submm sensitive dust is lost. These very different polarization distributions at submm and NIR wavelengths suggest that (1) there is different radiation environment at these wavelengths or (2) submm-sensitive dust is localized or the combination of them.
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