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Temporal cavity soliton (CS) emerges as a balance between dispersion, nonlinearity, external pump source and total losses occurring within an optical cavity. In this work, we assume the pump loss into account as the pump field propagates within the circular trajectory of the cavity. We study how the CS evolves under the effect of pump depletion. The dynamics of intra-cavity field can be evaluated numerically with the help of spatio-temporal Lugiato-Lefever equation (LLE). Here, we consider whispering gallery mode (WGM) CaF2 resonator of radius 2.5 mm for the simulation purpose. Initial pump power has been selected such that it always remain on the lower branch of the optically bistable region under decay. A linear pump loss coefficient αloss = 10−3 has been imposed on the external pump source. For this specific pump loss coefficient, we observe that generated cavity soliton undergoes in a non-uniform decay. For finding the occurrence of this transition from stable to unstable regime, phase of CS has been evaluated. A spiral pattern in the phase-space diagram dictates the formation of a stable cavity soliton. Unstable soliton regime begins when the phase becomes negative and that happens when external pump undergoes some threshold value regulated by loss coefficient.
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