  We perform spatially dependent tuning of a GaInP photonic crystal cavity
using a continuous wave violet laser. Local tuning is obtained by laser heating
of the photonic crystal membrane. The cavity resonance shift is measured for
different pump positions and for two ambient gases: helium and nitrogen. We
find that the width of the temperature profile induced in the membrane depends
strongly on the thermal conductivity of the ambient gas. For He gas a narrow
spatial width of the temperature profile of 2.8 um is predicted and verified in
experiment.
