richard.savage@LIGO.ORG - posted 06:36, Monday 25 August 2025 - last comment - 14:23, Wednesday 27 August 2025(86541)
Measurement of reflectivity of SPI beamsplitters
DriptaB, TonyS, RickS
Responding to a request from Jeff Kissel, we modified the Pcal measurement setup and used the standard Pcal analysis scripts to measure the reflectivity of two types of beamsplitters that have been procured for the SPI upgrade: 50/50 and 85/15 beamsplitters (two of each). Usually we are interested in the ratios of the responsivities of the two power sensors, but the same measurement results can be combined differently to yield the beamsplitter ratio.
NOTE: The Pcal system wavelength is 1047 nm, not 1064 nm.
The boxes containing the optics were labeled:
SPI PWR BS, 1064nm
50R:50T 45 DEG-Ppos
Batch 16075HA1
and
SPI PWR BS, 1064nm
85R:15T 45 DEG-Ppos
Batch 16075HA1
We measured two of each of the two beamsplitter types (50/50 and 85/15).
The measurement results are shown in the plots attached below. Note that HOP stands for "hundredth of a percent."
The measured reflectivities are:
50R/50T #1, two measuremetns: R = 0.4830 ± 0.002 %; R = 0.4830 ± 0.002 %
50R/50T #2: R = 0.4827. ± 0.002%
85R/15T #1 two measurements: R = 0.8624 ± 0.0005%; R = 0.8625 ± 0.0005 %
85R/15T #2: R = 0. ± 0.8599 ± 0.0004 %
Given the small specified wedges in the beamsplitter substrates, the ghost beams from the AR surface would likely pass through the entrance apertures on the power sensors (one inch diameter) and add to the received power in both reflection and transmission. However, the AR surface reflectivty appeared to be below the specified 0.1 %. We were not able to identify and measure the power in the beams reflecting from the AR surface. We will have another look when we break down the measurement setup.
Measurement setup and details:
We increased the Pcal Optical Follower Servo offset to give about 600 mW in each of the two output beams. We blocked one of the output beams and used the other beam for the beamsplitter measurements.
We aligned the laser steering mirror inside the transmitter module such that this beam propagates parallel to the table surface and along a row of holes in the optical table.
We found that the Pcal module output beam had some stray light of unknown origin outside the main beam (mostly three spots - see photo below) so we installed an aperture upstream at the Tx module output to block this stray light.
We installed a Karl Lambrect TFPC-12-1047nm thin film polarizing beamsplitter cube and aligned it such that the plane of the cube is parallel to the optical table surface. The Pcal Tx module output beams are nominally polarized paralllel to the surface of the optical table, but we installed this BS cube and carefully aligned it's plane of incidence to ensure that the polarization would be parallel to the plane of incidence of the beamsplitter to be tested.
We then installed the beamsplitter to be tested in the transmitted (polarized parallel to the surface of the table) beam and aligned it such that the plane of incidence is parallel to the optical table surface and the reflected beam is parallel to a row of holes on the optical table (45 deg. AOI, p-pol) and centered on the entrance aperture of one of the Pcal integrating spheres. The power incident on the beamsplitter was measured to be 570 mW.
The beams transmitted by the beamsplitter to be tested was reflected by a Pcal HR mirror (Precision Photonics / ATFilms Y1S-1025-45, Lot# WO22401, ITM100509, Run# 213472) and aligned to propagate along a row of holes and be centered on the entrance aperture of the second Pcal integrating sphere. The fractional power transmission of this HR mirror was measured twice to be: 3.2e-4 and 3.9 e-4. Average = 3.6e-4. We correct for this loss of power in the transmitted beam in the BS reflectivity calculations.
Images attached to this report
Non-image files attached to this report
Comments related to this report
J. Kissel, quoting R. Savage: A few extra explanatory words for the uninitiated on how this measurement works / how the results were derived: The uncertainties reported are the statistical variations for the measurements we made, highlighted in the attached plots. The authors have not attempted an assessment of potential systematic errors. I suspect that the largest sources of systematic error would likely result from - deviations of the incident polarization (as defined by the plane of incidence of the beamsplitter) from pure p-pol and - deviations of the Angle of Incdence from 45 deg. I also suspect that the errors we might have in this regard are much smaller than what you will have in the SPI installation given the much longer path lengths measured here vs. the SPI in-chamber setup. The next largest source of systematic errors might be - the temperature dependence of the reflectivity of the beamsplitters. We did not attempt to quantify this. We do measure, and correct for, the temperature dependence of the power sensor responsivities and their dark levels during the measurements. I suspect these will have a negligible impact on the measurement results reported for this effort. Regarding the measurement setup and math to derive the answers: The description of the responsivity ratio measurements given in D. Bhattacharjee et al., CQG 38.1 (2020): 015009 (P2000113) -- specifically the caption and text surrounding Figure 3 -- is the gist of the measurement method - simply replace "... the square root of the product of the ratios... replaced with "... the square root of the quotient of the ratios ..." from that caption. This yields the beamsplitter ratio, T/R, rather than the responsivity ratio of the two integrating sphere PDs that the PCAL team is after. (called \alpha_{W1W2} in the caption, but could also be any two responsivities, \alpha_{WG}, \alpha_{RW}, etc). Only - laser power variations that occur over the difference between times of recording the two power sensor outputs (less than 0.1 sec) - variations of the reflectivity of the BS or the responsivities of the two power sensors that occur over the time difference between measuring in the A-B and B-A configurations (less than 40 seconds) should impact the measurements. We record four time series: the output of both power sensors (in volts) and the temperatures (in volts) recorded by sensors on the circuit boards of both power sensors. The any temperature variation in the power sensor time series is normalized out, leaving two conditioned voltage time series for a given physical arrangement of PDs -- and thus are the (power) transmission, T, and (power) reflection, R, of the beam splitter (the A path's HR steering mirror -- that reflects light 90 [deg] to be parallel with the B path -- reflectivity is measured and taken into account as well -- see details below). The responsivity of these PCAL integration sphere + photodiode assemblies -- here we'll call them \rho_1 and \rho_2 -- is known to extremely high accuracy. Each data point you see in the plot is the ratio of [[ the BS ratio (T/R) resulting from one set of (two conditioned) time series when the sensors are in one configuration ]] and [[ a second BS Ratio (T/R) when PD positions have been swapped ]], i.e. accounting for - what was the T time series (from \rho_1 PD in the B position; the "A-B" configuration) becomes the R time series (from \rho_1 PD in the A Position; the "B-A" configuration). - what was the R time series (from \rho_2 PD in the A position; the "A-B" configuration) becomes the T time series (from \rho_2 PD in the B Position; the "B-A" configuration), and conversely So the math is T/R = sqrt { [(P x T x rho_1) / (P x R x rho_2)]_{A-B} / [(P x R x rho_1) / (P x T x rho_2)]_{B-A} } = sqrt{ (T/R)^2 } where again - P is the input power (in [W]), - R and T are the beam splitter reflectivity and transmission (in power; [W]), - \rho_1 and \rho_2 are the two different working standards, and - the subscript _{A-B} and _{B-A} are the answers in the two different physical configurations of the integrating spheres. Assuming no other loss or absorption, then the (power) reflectivity, R, displayed on the plots is R + T = 1 1 + T/R = 1/R R = 1 / (1 + T/R) As noted earlier, the powers (sensor outputs) for the transmitted path are multiplied by about 1.00035 to account for the transmissivity of the the HR mirror that reflects the transmitted beam to the power sensor.
