We show, both theoretically and experimentally, that it is possible to determine a nonuniform temperature distribution along a SNAP microresonator from a single measurement of its spectrum. In our experiment, we use a silica microcapillary containing a SNAP microresonator. The microcapillary is filled with water and locally heated with a moving heating source (light-pumped microfiber) introducing the temperature distribution parameterized as T(z)=T_0 exp(-|z-z_Q+iw|/L), where z is the coordinate along the microcapillary axis, z_Q is the heating source position, and w≪L is the width of the source. At each heating source position z_Q, we restore the parameters of this distribution from the SNAP microresonator spectrum. Our theoretical calculations are in a good agreement with the experimental data.
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