<p>Einstein Telescope (ET) is expected to achieve sensitivity improvements exceeding an order of magnitude compared to current gravitational-wave detectors. The rigorous characterization in optical birefringence of materials and coatings has become a critical task for next-generation detectors, especially since this birefringence is generally spatially non-uniform. A highly sensitive optical polarimeter has been developed at the Department of Physics and Earth Sciences of the University of Ferrara and INFN - Ferrara Section, Italy, aimed at performing two-dimensional birefringence mapping of substrates. In this paper we describe the design and working principle of the system and present results for crystalline silicon, a candidate material for substrates in the low-frequency interferometers of ET. We find that the birefringence is <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\lesssim 10^{-7}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>≲</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> for commercially available samples and is position dependent in the silicon (100)-oriented samples, with variations in both magnitude and axis orientation. We also measure the intrinsic birefringence of the (110) surface: <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\Delta n^{(110)}=-(1.50\pm 0.15)\times 10^{-6}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>n</mi> <mrow> <mo stretchy="false">(</mo> <mn>110</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <mo>-</mo> <mrow> <mo stretchy="false">(</mo> <mn>1.50</mn> <mo>±</mo> <mn>0.15</mn> <mo stretchy="false">)</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> @ <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\lambda =1550$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo>=</mo> <mn>1550</mn> </mrow> </math></EquationSource> </InlineEquation> nm. Implications for the performance of gravitational-wave interferometers are discussed.</p>

Apparatus for the measurement of birefringence maps of optical materials: the case of crystalline silicon for Einstein Telescope

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2025年10月25日

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Alina Mariana Soflau,
Federico Della Valle,
Francesco Cescato,
Giovanni Di Domenico,
Aurélie Max Mailliet,
Lorenzo Malagutti,
Emilio Mariotti,
Andrea Mazzolari,
Marco Romagnoni,
Guido Zavattini

摘要

Einstein Telescope (ET) is expected to achieve sensitivity improvements exceeding an order of magnitude compared to current gravitational-wave detectors. The rigorous characterization in optical birefringence of materials and coatings has become a critical task for next-generation detectors, especially since this birefringence is generally spatially non-uniform. A highly sensitive optical polarimeter has been developed at the Department of Physics and Earth Sciences of the University of Ferrara and INFN - Ferrara Section, Italy, aimed at performing two-dimensional birefringence mapping of substrates. In this paper we describe the design and working principle of the system and present results for crystalline silicon, a candidate material for substrates in the low-frequency interferometers of ET. We find that the birefringence is $\lesssim 10^{-7}$ $≲ 10^{- 7}$ for commercially available samples and is position dependent in the silicon (100)-oriented samples, with variations in both magnitude and axis orientation. We also measure the intrinsic birefringence of the (110) surface: $\Delta n^{(110)}=-(1.50\pm 0.15)\times 10^{-6}$ $Δ n^{(110)} = - (1.50 \pm 0.15) \times 10^{- 6}$ @ $\lambda =1550$ $λ = 1550$ nm. Implications for the performance of gravitational-wave interferometers are discussed.