Experimental evidence for an optical spring

An optical spring effect has been observed in the motion of a Fabry-Pérot cavity suspended in the Low-Frequency Facility, R&D experiment of the VIRGO Collaboration. The experimental setup consists of a 1-cm-long cavity hanging from a mechanical isolation system, conceived to suppress seismic noise transmission to the optical components of the interferometer. The observed radiation pressure effect corresponds to an optical stiffness $k_{opt}$ ranging between $2.5\times {10}^4$ and $6.5\times {10}^4\mathrm{N}∕\mathrm{m}$. This paper reports several measurements of the mirror relative displacement carried out in different working conditions. The measured error signal spectra show broad resonances at frequencies compatible with the optomechanical system. In other runs cavity detuning oscillations have been observed at subhertz frequencies. In these cases the power spectrum of the control loop error signal exhibited a broad resonance with superimposed uniformly spaced peaks. These observations, validated by a simple model, prove that the fluctuations of the optical spring effect can become so large as to exhibit nonlinear features.

Figure 1

(Color online) Typical error signal power spectrum. The optical spring effect appears as a broad resonance at $\sim 80\mathrm{Hz}$.

Figure 2

(Color online) Schematic of the esperimental setup showing the optical layout, the control loop, and the acquisition system (DAQ) as seen from Filter 7. $\mathrm{Nd}:\mathrm{YAG}$ indicates a neodymium-doped yttrium aluminum garnet laser, EUM an electro-optic modulator, and PUL a polarizer.

Figure 3

(Color online) Power spectra of the error signal around optical spring peaks measured during three different runs. Scattered points have been computed by entering the respective static detunings in the mechanical model.

Figure 4

(Color online) Histogram of the closed-loop cavity detuning, indicating a large swinging at $0.37\mathrm{Hz}$ (bottom) and the $12.34\mathrm{Hz}$ mechanical resonance (top).

Figure 5

(Color online) High peaks due to the high nonlinearity of the optical spring evidenced by the swinging at $0.37\mathrm{Hz}$.