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We present a formalism to compute Brownian thermal noise in functional optical surfaces such as grating reflectors, photonic crystal slabs or complex metamaterials. Such computations are based on a specific readout variable, typically a surface integral of a dielectric interface displacement weighed by a form factor. This paper shows how to relate this form factor to Maxwells stress tensor computed on all interfaces of the moving surface. As an example, we examine Brownian thermal noise in monolithic T-shape grating reflectors. The previous computations by Heinert et al. [Heinert et al., PRD 88 (2013)] utilizing a simplified readout form factor produced estimates of thermal noise that are tens of percent higher than those of the exact analysis in the present paper. The relation between the form factor and Maxwells stress tensor implies a close correlation between the optical properties of functional optical surfaces and thermal noise.
We present a joint theoretical and experimental characterization of thermo-refractive noise in high quality factor ($Q$), small mode volume ($V$) optical microcavities. Analogous to well-studied stability limits imposed by Brownian motion in macrosco
Gratings and holograms are patterned surfaces that tailor optical signals by diffraction. Despite their long history, variants with remarkable functionalities continue to be discovered. Further advances could exploit Fourier optics, which specifies t
Thermal frequency fluctuations in optical cavities limit the sensitivity of precision experiments ranging from gravitational wave observatories to optical atomic clocks. Conventional modeling of these noises assumes a linear response of the optical f
Thermal noise generally greatly exceeds quantum noise in optomechanical devices unless the mechanical frequency is very high or the thermodynamic temperature is very low. This paper addresses the design concept for a novel optomechanical device capab
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