Fade colour as function of angle in tikz

Question

I'm trying to create a tikz picture along the lines of

only with the blue colour fading out as it gets to the edge of the blue strip. Ideally, the blue bar should be fully blue in the middle (at the point (-1,0) to be precise), and white at the outer edges (the points (0,1) and (0,-1)).

The picture above was created as follows.

\documentclass{article}
\usepackage{tikz,xcolor}

\begin{document}
\begin{tikzpicture}
    \draw[line width=0.25cm, blue]  (90:1)  arc [start angle=90, end angle=270, radius=1];
    \draw[thick]                    (0,0)   circle [radius=1];
\end{tikzpicture}
\end{document}