Audio-band coating thermal noise measurement for Advanced LIGO with a multimode optical resonator

In modern high precision optical instruments, such as in gravitational wave detectors or frequency references, thermally induced fluctuations in the reflective coatings can be a limiting noise source. This noise, known as coating thermal noise, can be reduced by choosing materials with low mechanical loss. Examination of new materials becomes a necessity in order to further minimize the coating thermal noise and thus improve sensitivity of next generation instruments. We present a novel approach to directly measure coating thermal noise using a high finesse folded cavity in which multiple Hermite-Gaussian modes coresonate. This method is used to probe surface fluctuations on the order ${10}^{-17}\mathrm{m}/\sqrt{\mathrm{Hz}}$ in the frequency range 30–400 Hz. We applied this technique to measure thermal noise and loss angle of the coating used in Advanced LIGO.

Figure 1

At the heart of this experimental work is a high-finesse optical cavity which resonates three distinct fields: a horizontally polarized Gaussian TEM00 mode, and two vertically polarized Hermite-Gaussian modes, TEM02 and TEM20 [22]. The primary advantage of using multiple resonant fields in a high-finesse cavity is that all of these fields share the same sensitivity to changes in cavity length and laser frequency. On the other hand, each mode samples a different part of the coating, and thus the coating thermal noise seen by each of the resonant modes is largely independent. Since this experiment measures the difference between the resonant frequencies of the TEM02 and TEM20 modes, ideally all cavity length noises cancel leaving only the desired coating thermal noise.

Figure 2

While the multimode approach can be applied to any optical cavity, this experiment benefits greatly from a folded geometry. Among the numerous advantages of this geometry are the use of a flat high-reflectivity sample mirror, and the ability to change the size of the beam on the sample mirror without changing the optical modes resonant in the cavity. The inset image shows the TEM20 and TEM02 modes, highlighting the fact that they overlap only in a small central area and otherwise sample distinct regions of the coating.

Figure 3

The experimental setup for the multimode measurement involves a Nd:YAG laser (far left) and an in-vacuum high-finesse cavity (far right). In order to avoid multiple lasers, and the multiple sources of frequency and intensity noise they would introduce, a single laser beam is split into three paths, two of which are shifted in frequency (with AOMs), and each of which is independently phase modulated at its own radio frequency (with EOMs). The laser frequency is controlled to lock the TEM00 mode to the cavity length while the TEM02 and TEM20 modes are locked to the cavity by controlling their frequency differences with respect to the laser frequency. The primary output of the experiment is the difference between the TEM02 and TEM20 resonant frequencies (labeled BEAT NOTE), changes in which are dominated by the coating thermal noise of the sample.

Figure 4

The delay line discriminator method for CTN readout. The conversion of frequency fluctuations imprinted on the beat note to corresponding phase fluctuations is obtained with the delay line and subsequently converted to a voltage signal on the phase detector. Ports rf REF and rf IN add in quadrature. The $\pi /2$ phase lag between both rf ports sets the phase detector to the best linear response for the measured phase fluctuations.

Figure 5

Block diagram of control loops for the TEM00 mode. All of the important noise sources are indicated as ${\delta }_i$, and each loop component with nonzero gain value is marked with $G_i$. The TEM00 mode is locked to the cavity length using PDH in reflection. An additional 204 kHz loop is used to reduce frequency noise related to the locking scheme of $\mathrm{TEM}20/02$ modes. More detail in text.

Figure 6

Block diagram of the $\mathrm{TEM}02/20$ control loop. Both modes are frequency locked to the cavity with VCOs using PDH in transmission. An additional 102 kHz loop is used to control intensity noise at the PDH modulation frequency.

Figure 7

Stored energy distribution and stress concentration as a result of an applied pressure field on the coating surface. For reference we also show TEM00 results. It is worth noting that the differential intensity profile corresponding to $\mathrm{TEM}20/02$ causes zero net-stress at the rim of the sample mirror. Thus this multimode CTN measurement technique is insensitive to the losses associated with mirror clamps.

Figure 8

Counterpropagating beams on the folding mirror cause an interference pattern imprinted on the resonating modes. The fringe pattern can affect the sensitivity to coating thermal noise. For a cavity folding angle of 17.2 deg (Table 2) the fringe separation is $1.8\mu \mathrm{m}$. The figure shows the stress in the coating in the z-direction as a result of an applied pressure profile $p_{\text{fringe}}$. The coating is only affected by the fringe down to the depth of $1.6\mu \mathrm{m}$ below which the stress becomes uniform. For our folded cavity the correction factor $C_{\text{fringe}}=0.98$ is only slightly different from unity, indicating that this effect has little impact on our results.

Figure 9

The measurement result for an Advanced LIGO ETM coating witness sample. In the range 30–400 Hz the largest noise contributions comes from coating thermal noise with a characteristic $1/\sqrt{f}$ slope and a white sensing noise. Most of the sharp features are from the 60 Hz mains.