Measurement of thermo-optic and coating Brownian noise in a novel coating design

Current gravitational wave detectors and other high precision instrumentation are limited by the optical quality and thermal noise properties of highly reflective dielectric optical coatings. This study characterizes a custom designed high reflectivity optical coating using silica and tantalum pentoxide ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi>SiO</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msub> </a:mrow> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mtext>Ta</c:mtext> <c:mn>2</c:mn> </c:msub> <c:msub> <c:mi mathvariant="normal">O</c:mi> <c:mn>5</c:mn> </c:msub> </c:math> ) on an ultralow-expansion glass substrate. This coating has been designed to have high thermal noise properties for a future experiment that aims to reduce the effect of Brownian coating noise. This paper presents, to our knowledge, the first measurement of thermo-optic noise for a <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:mrow> <f:msub> <f:mrow> <f:mi>SiO</f:mi> </f:mrow> <f:mrow> <f:mn>2</f:mn> </f:mrow> </f:msub> </f:mrow> <f:mo>:</f:mo> <f:msub> <f:mrow> <f:mtext>Ta</f:mtext> </f:mrow> <f:mrow> <f:mn>2</f:mn> </f:mrow> </f:msub> <f:msub> <f:mrow> <f:mi mathvariant="normal">O</f:mi> </f:mrow> <f:mrow> <f:mn>5</f:mn> </f:mrow> </f:msub> </f:mrow> </f:math> coating. We also present the coating design process of the unique coating and verify modeled coating properties, including transmission, absorption, Brownian coating noise, and thermo-optic noise. With a better understanding of thermo-optic noise and Brownian noise of unique coatings, the design process for optimizing optical coating for lower thermal noise can be better informed, such that the sensitivity of gravitational wave detectors and other precision instrumentation using highly reflective optical coatings is increased.