Reduction of higher order mode generation in large scale gravitational wave interferometers by central heating residual aberration correction

Imperfect cavity mirrors in the arms of an interferometric gravitational-wave (GW) detector can result in the generation of unwanted higher order modes that are close to or at resonance in the cavity. This can lead to many undesirable effects such as increased round-trip losses or degraded contrast defect. Polishing mirrors to fulfill the requirements of 2nd generation GW interferometers is extremely challenging. For the use of LG33 modes in 3rd generation detectors it would be necessary to improve polishing by an order of magnitude. In this article we present a novel technique for the in situ correction of cavity mirror surface figures by central heating residual aberration correction. This system targets and corrects specific features of the mirror surface figure such as to reduce scattering from the fundamental cavity mode to specific higher order modes by more than an order of magnitude. We demonstrate, by simulation, the feasibility of such a system and give examples of its application to 2nd and 3rd generation GW interferometers.

Figure 1

Schematic optical design of Virgo.

Figure 2

(a) Typical power spectral density (PSD) of AdV grade mirrors. (b) Example mirror map randomly generated from PSD. Color scale in nm.

Figure 3

(a) Higher order modes 8 and 9 content in reflected beam for different end mirror radii of curvature. (b) Round-trip losses. Peaks in round-trip losses correspond to peaks in HOM content in the cavity mode.

Figure 4

Suppression of scattering into HOM 8 and 9 by correcting input mirror map. (a) Original randomly generated mirror map. (b) Optimal correction to cancel the 8th and 9th order HOM’s, where Zernikes up to order 40 were used. (c) Corrected mirror map. Color scale in nm.

Figure 5

Comparison of mirror map PSD before and after correction for input and end mirrors. (a) Input mirror map. Dip in spatial frequency at $20{\mathrm{m}}^{-1}$. (b) End mirror map. Dip in spatial frequency at $16{\mathrm{m}}^{-1}$.

Figure 6

Comparison of original and corrected mirror maps in arm cavity (a) Higher order mode 8 and 9 content in reflected beam for different end mirror radii of curvature. (b) Round-trip-losses.

Figure 7

Schematic design of CHRAC.

Figure 8

Monte carlo simulation of infrared radiation emitted from a $3\times 3$ array of black-body heat sources, for which 5 pixels are switched on. (a) Heat pattern directly after heater array (b) Heat pattern of the image projected onto the surface of the cavity mirror.

Figure 9

Calculation used to estimate power absorbed in cavity mirror. (a) Spectrum plots for emissivity of alumina, absorption of cavity mirror substrate (fused silica) and blackbody emission for a blackbody temperature of 500 degrees C. (b) Product of three spectra in 9a resulting in spectrum of absorbed power for a heat source at 500 degrees C. Peak wavelength is just above 5 microns.

Figure 10

Calculated intensity absorbed by the cavity mirror for a blackbody heater with varying temperature.

Figure 11

Finite element simulation of a projected square of $1\times 1{\mathrm{cm}}^2$ yielding an absorbed intensity of $10\mathrm{mW}/{\mathrm{cm}}^2$. (a) Mirror surface temperature distribution. Color scale in degrees Celsius. Ambient temperature of 26.85 degrees Celsius. (b) Change in surface figure. Color scale in nm.

Figure 12

Validation of adaptive optics approach to finding CHRAC actuator powers to correct mirror surface figure. (a) Target correction map to be generated by CHRAC. Color scale in nm. (b) Actuator power to be absorbed by mirror. Color scale in mW. (c) Reconstructed correction map from optical influence matrix and derived actuator powers. Color scale in nm. (d) Surface figure obtained using actuator powers of Fig. 12b in Ansys simulation. Color scale in nm.

Figure 13

Suppression of scattering of LG33 mode into other 9th order modes by correcting input mirror map. (a) Original randomly generated mirror map. (b) Optimal correction to cancel scattering into other 9th order modes. (c) Corrected mirror map. Color scale in nm.

Figure 14

Intensity distribution of beam reflected from simulated arm cavity. (a) Using original mirror maps. 79.0% in the LG33 mode (b) Using corrected mirror maps. More than 99.9% in the LG33 mode. Color scale in $\mathrm{W}/{\mathrm{m}}^2$.