All-polarization beamsplitters for interferometer applications

Optical beamsplitters with similar properties for orthogonal, linear polarization modes are required for realizing polarization-based speed meter schemes to reduce backaction noise in gravitational-wave interferometers. In this paper, we investigate two beamsplitter coatings obtained from Laseroptik GmbH and Optoman on a best-effort basis that aim for a 50/50 power splitting ratio and equal overall phase shift for two orthogonal, linear polarization modes interacting with the optic. We show that while Laseroptik GmbH opted for coating stack with 22 alternating layers of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>Ta</a:mi><a:mn>2</a:mn></a:msub><a:msub><a:mi mathvariant="normal">O</a:mi><a:mn>5</a:mn></a:msub></a:mrow></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>SiO</c:mi><c:mn>2</c:mn></c:msub></c:math>, Optoman produced a much thinner coating made of five <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>SiO</d:mi><d:mn>2</d:mn></d:msub></d:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>SiO</e:mi><e:mi>x</e:mi></e:msub></e:math> (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mn>0</f:mn><f:mo>&lt;</f:mo><f:mi>x</f:mi><f:mo>&lt;</f:mo><f:mn>2</f:mn></f:mrow></f:math>) layers. With these strategies, the Laseroptik coating achieves an equal power reflectivity of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mn>51</g:mn><g:mo>%</g:mo></g:mrow></g:math> at <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msup><h:mn>46</h:mn><h:mo>∘</h:mo></h:msup></h:math> angle of incidence and zero phase shift between both polarizations at <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mn>44</i:mn><i:mo>.</i:mo><i:msup><i:mn>25</i:mn><i:mo>∘</i:mo></i:msup></i:mrow></i:math> angle of incidence. The Optoman coating achieves power reflectivities of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mn>49</j:mn><j:mo>%</j:mo></j:mrow></j:math> for <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi>s</k:mi></k:mrow></k:math> polarization and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mn>51</l:mn><l:mo>%</l:mo></l:mrow></l:math> for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>p</m:mi></m:math> polarization with a differential phase shift around <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:msup><n:mn>5</n:mn><n:mo>∘</n:mo></n:msup></n:math> largely independent of the angle of incidence.