Radiation Pressure

Interferometric gravitational wave detectors make use of suspension systems to decouple mirrors from ground motion. Furthermore these interferometers operate with a very high circulating light power so that the radiation pressure from the reflected photons can significantly influence the mechanical behaviour of the mirrors. This leads to a very interesting coupling between the optical fields and the mirrors as mechanical oscillators, forming so-called optical springs. Optical springs and other radiation pressure effects can change the dynamics of an interferometer significantly, especially when considering transfer functions from mechanical motions to optical outputs.

It is important, as with any simulation tool, to understand the limits of the approximations made to allow radiation pressure effects to be implemented in Finesse. By nature, radiation pressure is proportional to the beam power, a non-linear relation in regards to the amplitude of the optical fields which is what Finesse computes. To linearise the physical equations described in the following sections the following assumptions are made:

  • The magnitude of any motion in the mirrors surface is much smaller than the wavelength of light, by default, 1064nm.

  • Therefore the optical sidebands created by such motion are also much smaller in magnitude than the magnitude of any carrier (laser or RF modulation) field.

  • That the frequency difference between carrier fields, laser fields and RF sidebands created with modulator components, are large in comparison to the frequencies of signals and of mechanical resonances of optics. This is required so that any beating between carriers fields does not cause significant radiation pressure effects.

It also follows that the maximum signal frequency must be less than half of the minimum frequency difference between carrier fields. If this frequency limit is exceeded, it is possible for the upper sidebands of one carrier field to become the lower sideband of another. This is not a scenario that the radiation pressure implementation of Finesse is designed to handle. Given that modulator frequencies are typically the order of MHz and radiation pressure effects are only of interest at low frequencies due to the mechanical susceptibility of a suspended object being \(\propto 1/f^{2}\), this should not be an issue that comes up frequently.