Optical absorption of silicon nitride membranes at 1064 nm and at 1550 nm

Because of a low mechanical loss, thin films made of silicon nitride (${\mathrm{Si}}_3{\mathrm{N}}_4$) are interesting for fundamental research and development in the field of gravitational-wave detection. ${\mathrm{Si}}_3{\mathrm{N}}_4$ membranes allow for the characterization of quantum radiation pressure noise (RPN), which will be a limiting noise source in gravitational-wave detectors of the second and third generations. Furthermore, ${\mathrm{Si}}_3{\mathrm{N}}_4$ is an interesting material for possible thermal noise reduction in highly reflective mirror coatings. For both applications, the optical absorption of ${\mathrm{Si}}_3{\mathrm{N}}_4$ needs to be low. This paper presents absorption measurements on low-stress ${\mathrm{Si}}_3{\mathrm{N}}_4$ membranes showing an absorption a factor of 7 lower at 1550 nm than at 1064 nm resulting in an estimated 2 times higher sensitivity in RPN experiments at the higher wavelength and making ${\mathrm{Si}}_3{\mathrm{N}}_4$ an interesting material for highly reflective multimaterial mirror coatings at 1550 nm.

Figure 1

Photo of a LPCVD ${\mathrm{Si}}_3{\mathrm{N}}_4$ membrane fabricated by Norcada [9]: A silicon substrate was coated with ${\mathrm{Si}}_3{\mathrm{N}}_4$ and a $5\mathrm{mm}\times 5\mathrm{mm}$ window was etched into the silicon substrate to produce the ${\mathrm{Si}}_3{\mathrm{N}}_4$ membrane.

Figure 2

(a) Brewster’s angle for ${\mathrm{Si}}_3{\mathrm{N}}_4$ is at 65° (minimum of pink line), independent from the thickness of the substrate. At this angle the $p$-polarized pump light is transmitted. Because of an etalon effect, the $2\mu \mathrm{m}$ thick ${\mathrm{Si}}_3{\mathrm{N}}_4$ membrane transmits most of the incident laser power at an angle of incidence of 50°, at which the $s$-polarized probe light is transmitted. (b) Probe beam (1620 nm) and pump beam (1550 nm/1064 nm) are crossing at an angle of about 14° inside the membrane. (c) Typical absorption measurement at 1550 nm using PCI. Absorption signal (purple line): The membrane position is scanned along the direction of the pump beam and reaches a maximum of 226 ppm in the beam crossing point. Phase signal (green line): The phase response to the amplitude modulation of the pump beam is $-42°$.

Figure 3

Experimental setup for indirect absorption measurements via cavity round-trip loss: The membrane was positioned at Brewster’s angle inside the cavity to minimize loss $P_{\mathrm{out}}$ due to reflected light.The cavity length was periodically modulated and the resulting cavity resonance peaks were detected using a photodiode in reflection, the signal being separated from the incident beam with a Faraday rotator (FR).

Figure 4

(a) Reflected resonance peaks at 1064 nm without membrane: measured peak, blue dots; simulated peak, orange line. (b) Fitted resonance peaks for the cavity without membrane (orange line), and for membranes different in thickness. The impedance mismatch of the overcoupled cavity decreases with increasing absorption loss due to increasing membrane thickness.

Figure 5

The pink line shows the prediction of the absorption at 1064 nm made in [6] based on $k=1.5\times {10}^{-4}$ [8]. Geometric effects associated with the position of the membrane relative to standing wave nodes or antinodes in the cavity are not relevant in our case due to the use of Brewster’s angle. The black dots present the experimental results from the cavity measurements work at 1064 nm and the green triangle results at 1550 nm. The results from the PCI measurements are shown by the blue dot (1064 nm) and the purple triangle (1550 nm). The dashed red and dotted green lines extrapolate the PCI results indicating a lower limit for the absorption.

Figure 6

Example for a measurement of $N_{\mathrm{FSR}}$: The yellow curve shows the PZT modulation voltage ($=\mathrm{ramp}$ signal), and the light blue curve shows a PDH signal. The ratio of the modulation range (black dashed lines) and the separation of the sidebands ($=2\times$ the sideband frequency ${\nu }_{\mathrm{SB}}$, red dashed lines) multiplied with the sideband separation and divided by the free spectral range (FSR) of the cavity provides the number of free spectral ranges $N_{\mathrm{FSR}}$ scanned per ramp side.

Figure 7

(a) Schematic of a HR coating stack, which consists of 18 bilayers of ${\mathrm{SiO}}_2$ (blue) and $\mathrm{Ti}:{\mathrm{Ta}}_2{\mathrm{O}}_5$ (green) on a cSi (grey) substrate. The blue line shows the normalized electric field intensity (EFI) inside the coating. (b) Schematic of a four-material coating identical in reflectivity, in which the outermost 4 bilayers are made of ${\mathrm{SiO}}_2$ and $\mathrm{Ti}:{\mathrm{Ta}}_2{\mathrm{O}}_5$, while in the following 4 bilayers $\mathrm{Ti}:{\mathrm{Ta}}_2{\mathrm{O}}_5$ is replaced by ${\mathrm{Si}}_3{\mathrm{N}}_4$ (yellow) as a high index material. The lowest 7 bilayers are made of ${\mathrm{Si}}_3{\mathrm{N}}_4$ and aSi (pink) with ${\mathrm{Si}}_3{\mathrm{N}}_4$ being the low index material.

Figure 8

Schematic of the ${\mathrm{Si}}_3{\mathrm{N}}_4$ membrane (yellow) and the incident and reflected laser beams (red lines).