D. Heinert

Comparison of the temperature dependence of the mechanical dissipation in thin films of Ta2O5 and Ta2O5 doped with TiO2

Here we report the first results comparing the temperature dependence of the mechanical dissipation in thin films of Ta_2O_5 and Ta_2O_5 doped with TiO_2, of a type suitable for use in the multilayer optical coatings for advanced gravitational wave detectors. The results indicate that doping Ta_2O_5 with TiO_2 can significantly alter the distribution of activation energies associated with the low-temperature dissipation peak.

Calculation of thermal noise in grating reflectors

Grating reflectors have been repeatedly discussed to improve the noise performance of metrological applications due to the reduction or absence of any coating material. So far, however, no quantitative estimate on the thermal noise of these reflective structures exists. In this work we present a theoretical calculation of a grating reflector’s noise. We further apply it to a proposed third generation gravitational wave detector. Depending on the grating geometry, the grating material, and the temperature, we obtain a thermal noise decrease by up to a factor of 10 compared to conventional dielectric mirrors. Thus the use of grating reflectors can substantially improve the noise performance in metrological applications.

Measurement of the mechanical loss of prototype GaP/AlGaP crystalline coatings for future gravitational wave detectors

Thermal noise associated with the dielectric optical coatings used to form the mirrors of interferometric gravitational wave detectors is expected to be an important limit to the sensitivity of future detectors. Improvements in detector performance are likely to require coating materials of lower mechanical dissipation. Typically, current coatings use multiple alternating layers of ion-beam-sputtered amorphous silica and tantalum pentoxide (doped with titania). We present here measurements of the mechanical dissipation of promising alternative crystalline coatings that use multi-layers of single crystal gallium phosphide (GaP) and aluminium gallium phosphide (AlGaP) that are epitaxially grown and lattice matched to a silicon substrate. Analysis shows that the dissipation of the crystalline coating materials appears to be significantly lower than that of the currently used amorphous coatings, potentially enabling a reduction of coating thermal noise in future gravitational wave detectors.

Reduction of coating thermal noise by using an etalon

Reduction of coating thermal noise is a key issue in precise measurements like a gravitational-wave detector, where each mirror is coated by a few tens of dielectric layers to achieve high reflectivity while the noise level increases with the number of layers. One way to realize the reduction is mechanical separation of the first few layers from the rest. Using an etalon with a few layers on the front and more on the back surface is a way to realize such a system. We perform a noise analysis of an etalon using the Fluctuation–dissipation theorem with probes on both sides.

Acoustic losses in a thick quartz plate at low temperatures

We have shown that thermoelastic losses give the significant contribution to the total mechanical damping in the low loss quartz even for the bulk samples if the thickness of the sample is smaller than other dimensions. We have developed a model that describes experimental data of mechanical losses in a round quartz plate with the diameter 7.48 cm and the thickness 1.2 cm at temperatures 5–25 K in the range of eigenfrequencies 11–300 kHz. The model takes into account both the contribution of thermoelastic losses and the contribution due to the interaction of the acoustic wave with thermal phonons (Akhieser damping). Thermoelastic processes determine losses below 120 kHz. At larger eigenfrequencies, the Akhieser damping dominates.

Brownian thermal noise in functional optical surfaces

We present a formalism to compute Brownian thermal noise in functional optical surfaces such as grating reflectors, photonic crystal slabs or complex metamaterials. Such computations are based on a specific readout variable, typically a surface integral of a dielectric interface displacement weighed by a form factor. This paper shows how to relate this form factor to Maxwells stress tensor computed on all interfaces of the moving surface. As an example, we examine Brownian thermal noise in monolithic T-shape grating reflectors. The previous computations by Heinert et al. [Heinert et al., PRD 88 (2013)] utilizing a simplified readout form factor produced estimates of thermal noise that are tens of percent higher than those of the exact analysis in the present paper. The relation between the form factor and Maxwells stress tensor implies a close correlation between the optical properties of functional optical surfaces and thermal noise.

Reducing thermal noise in future gravitational wave detectors by employing Khalili etalons

Reduction of thermal noise in dielectric mirror coatings is a key issue for the sensitivity improvement in the second and third generation interferometric gravitational wave detectors. Replacing an end mirror of the interferometer by an anti-resonant cavity (a so-called Khalili cavity) has been proposed to realize the reduction of the overall thermal noise level. In this article we show that the use of a Khalili etalon, which requires less hardware than a Khalili cavity, yields still a significant reduction of thermal noise. We identify the optimum distribution of coating layers on the front and rear surfaces of the etalon and compare the total noise budget with a conventional mirror. In addition we briefly discuss advantages and disadvantages of the Khalili etalon compared with the Khalili cavity in terms of technical aspects, such as interferometric length control and thermal lensing.

Measurement of the optical absorption of bulk silicon at cryogenic temperature and the implication for the Einstein Telescope

We report in this article on the measurement of the optical absorption of moderately doped crystalline silicon samples at 1550 nm, which is a candidate material for the main optics of the low temperature interferometer of the Einstein Telescope (ET). We observe a nearly constant absorption from room temperature down to cryogenic temperatures for two silicon samples presenting an optical absorption of 0.029 cm−1 and 780 ppm cm−1, both crystals doped with boron. This is in contradiction to what was assumed previously—a negligible optical absorption at low temperature due to the carrier freezeout. As the main consequence, if the silicon intrinsic absorption can not be lowered, the cross section of the mirror suspension of the ET must be increased to be able to carry away the excess heat generated by the partially absorbed laser beam during the operation of the interferometer.

Mechanical losses in low loss materials studied by cryogenic resonant acoustic spectroscopy of bulk materials (CRA spectroscopy)

The capability to measure Q factors at cryogenic temperatures enhances the ability to study relaxation processes in solids. Here we present a high-precision cryogenic setup with the ability to measure Q factors of at least 10(9). This level of sensitivity offers new potential for analyzing relaxation processes in solids and for correlating mode shape and relaxation strength. Our improved method of mechanical spectroscopy, cryogenic resonant acoustic spectroscopy of bulk materials, is verified by identifying relaxation processes in low-loss quartz crystals. For the first time, we observe additional damping peaks. The mechanical Q factors of different modes of cylindrical crystalline quartz substrates were measured from 300 down to 6 K. Resonant modes with frequencies between 10 and 325 kHz were excited without contact to the substrates and the ring down of the amplitudes was recorded using an interferometric vibration readout.

Mechanical Spectroscopy of Silicon as a Low Loss Material for High Precision Mechanical and Optical Experiments

The paper summarises systematic studies of the mechanical loss of crystalline silicon at low temperatures from 300 to 5 K. Thermo-elastic loss is discussed as a main contribution in thin samples. A numerical method based on a finite element analysis is presented to determine the thermo-elastic loss of arbitrarily shaped samples. Additionally, mechanical loss associated with oxygen is investigated in Czochralski grown silicon bulk samples. The process has the activation energy of about 168 meV. An orientation dependency of the loss is observed. The lowest loss reported in this paper was achieved with a cylindrical bulk sample having a diameter of 110 mm and a length of 200 mm at around 5 K and a resonant frequency of about 22.3 kHz.