Self-sustained photothermal oscillations in high-finesse Fabry-Perot microcavities

We report the experimental investigation of a regime of microscopic Fabry-Perot resonators in which competing light-induced forces—photothermal expansion and photothermal refraction—acting oppositely and on different timescales lead to self-sustained persistent oscillations. Previously concealed as ordinary thermo-optic bistability—a common feature in low-loss resonator physics—these dynamics are visible as fast pulsations in cavity transmission or reflection measurements at sufficiently high time resolution. Their underlying mathematical description is shared by many slow-fast phenomena in chemistry, biology, and neuroscience. Our observations are relevant in particular to microcavity applications in atom optics and cavity quantum electrodynamics, even in nominally rigid structures that have not undergone lithography.

Figure 1

(a) Transmission of microcavity as its length is being varied at a rate of 8.8 $\mathrm{pm}/\mu \mathrm{s}$ by PZTs, for a set of laser input powers $P_{\mathrm{in}}$. In the left (right) traces, the length is being increased (decreased). (b) Zoomed view into the right traces of panel (a).

Figure 2

Zoomed view of the oscillatory regions of the $P_{\mathrm{in}}=22\mathrm{mW}$ up-ramp data of Fig. 1. The Roman numerals indicate the starting time of each trace (offset vertically for clarity) in relation to the representation in Fig. 1.

Figure 3

(a) Contour plot of the stationary temperature ($t\to \infty$) on the mirror surface (left) and on the $x=0$ cross-sectional plane (right), obtained from a numerical solution of the heat diffusion equation for $P_{\mathrm{circ}}=100$ W. The inset shows the temperature along the $z$ axis. (b) On-axis temperature as a function of time at the surface (left) and $4\mu \mathrm{m}$ beneath the surface (right).

Figure 4

Circulating power [Eq. (9)] computed numerically from the solution of the differential Eqs. (7) and (8) for three different input laser powers. A PZT scan rate of 8.8 $\mathrm{pm}/\mu \mathrm{s}$ as in the data of Fig. 1 was assumed, as well as $B_s=18\mathrm{pm}/\mathrm{W}, B_f=-0.9\mathrm{pm}/\mathrm{W}, {\tau }_s=4\mu \mathrm{s}$, and ${\tau }_f=0.15\mu \mathrm{s}$. (a) The cavity length is increasing and $L_0=400$ pm. (b) The cavity length is decreasing and $L_0=-400\mathrm{pm}$. Traces are offset vertically by 60 W for clarity.

Figure 5

(a) Zoomed view of the trace at $P_{\mathrm{in}}=20\mathrm{mW}$ relative to time $t=110\mu \mathrm{s}$ as indicated by the arrow in Fig. 4. (b) Time-dependent cavity-length change associated with photothermal expansion. (c) Time-dependent cavity-length change associated with photothermal refraction. (d) Time-dependent cavity-length change associated with both photothermal expansion and photothermal refraction. The horizontal dashed line indicates the location of the resonance.

Figure 6

(a) Experimental cavity transmission as a function of time for an initial displacement from resonance of approximately one half linewidth, for $P_{\mathrm{in}}=10\mathrm{mW}$ (the cavity length is not scanned). (b) Same as in panel (a) but for an initial displacement from resonance of approximately 1/10 of a linewidth. (c) Phase-space plot (time derivative of cavity transmission vs cavity transmission) for the same conditions as in panel (a) but based on data covering a total time of $10\mu \mathrm{s}$. (d) Phase-space plot for the same conditions as in panel (b) but based on data covering a total time of $40\mu \mathrm{s}$.