  We present a theoretical and experimental analysis of nonlinear thermo-optic
effects in suspended chalcogenide glass nanobeam cavities. We measure the power
dependent resonance peaks and characterise the dynamic nonlinear thermo-optic
response of the cavity under modulated light input. Several distinct nonlinear
characteristics are identified, including a modified spectral response
containing periodic fringes, a critical wavelength jump and saturated time
delay for modulation frequency faster than the thermal characteristic time. We
reveal that the coupling to a parasitic Fabry-Perot cavity enables isolated
thermal equilibrium states resulting in the discontinuous thermo-optic critical
point.
