Optically active mechanical modes of tapered optical fibers

Abstract

Tapered optical fibers with a nanofiber waist are widely used tools for efficient coupling of light to photonic devices or quantum emitters via the nanofiber's evanescent field. In order to ensure wellcontrolled coupling, the phase and polarization of the nanofiber guided light field have to be stable. Here, we show that in typical tapered optical fibers these quantities exhibit high-frequency thermal fluctuations. They originate from high-Q torsional oscillations that opto-mechanically couple to the nanofiber-guided light. We present a simple ab-initio theoretical model that quantitatively explains the torsional mode spectrum and that can be used to design tapered optical fibers with tailored mechanical properties.PACS numbers: 46.40.Ff, 62.25.Fg, 78.67.Uh Tapered optical fibers with a subwavelength-diameter waist (TOFs) feature a strong evanescent field in the waist region and are widely used to efficiently interface light and matter or to couple light into photonic devices, such as micro-resonators or photonic crystals. These applications rely on the stability of the phase and polarization of the nanofiber guided light field as well as on the position of the nanofiber. Achieving this stability is all the more challenging in a high vacuum environment where the mechanical damping due to the surrounding gas is negligible. Here, we experimentally demonstrate that under these conditions torsional mechanical modes exhibit surprisingly high quality factors and lead to resonantly enhanced vibrations that modulate the phase and polarization of the optical mode via the strain-optic effect. Based on an analytic model as well as on experimental measurements, we show that the commonly used exponential radius profile confines a subset of the torsional mechanical modes to the nanofiber section, leading to the high Q-factors.From a mechanical point of view, a TOF is a slender cylinder with varying cross-section. Torsional waves in such a structures can be described by a one-dimensional wave equation which has been treated comprehensively in the literature [1,2]. In case of the mechanical modes considered here, their wavelength is much larger than the largest cross-section of the TOF so that no higher order angular and radial modes exist (slender rod approximation). Furthermore, the radius variations occurring in the TOF profile are sufficiently shallow to assume plane wavefronts that are perpendicular to the fiber axis. Under these conditions, the torsional motion can be described by a Webster-type wave equation where φ(t, z) is the angular displacement amplitude as function of time t and axial position along the fiber z and ∂ x = ∂/∂x with x = t, z. The torsional wave velocity is radius independent and given by c t = G/ρ = (3680 ± 130) m/s, where G = (30 ± 2) GPa is the shear modulus and ρ = (2210 ± 10) kg/m 3 is the mass density of silica [3][4][5]. The third term of the wave equation takes the radius profile of the cylinder, a(z), into account via the polar angular moment of inertia I p (z) = π ρ a(z) 4 /2.Using a sepa...

Experimental stress–strain analysis of tapered silica optical fibers with nanofiber waist

“…For all data presented in this work, including these for TOFs with only 160 nm waist radius, the measured forceelongation relationships are well explained assuming the macroscopic values of Young's modulus and of the nonlinearity parameter α. Recent experiments have observed that also other macroscopic material parameters remain valid for systems with wavelength-scale dimensions [28]. This holds promising perspectives for, e.g., the precise the design of the mechanical and optical properties of miniaturized photonic components as well as for fundamental studies with optical nanofibers.…”

Photon and phonon spectral functions for continuum quantum optomechanics

“…Inspite of the fact that photons show low damping rates, where waveguide photon leaks can be neglicted, phonon decoherence and losses are of big influence and put limitations on coherent performance of these components. Phonon dissipation in nanostructure are mainly due to geometric disorder, mechanical contacts and thermal noise [19][20][21], and can strongly influence phonon cooling senarios [13]. Photon and phonon dissipations introduce a big challenge for the future of photonic and phononic efficiency in nanostructures.…”

Optical Nanofibers

“…One contribution comes from elastic scattering events of the far-detuned trapping beams Grimm et al (2000), a wellknown effect in dipole traps. A less familiar contribution comes from torsional modes of the ONF Wuttke et al (2013). The torsional modes couple to the polarization of all the guided fields.…”

“…The frequencies of these modes are densely populated and they are close enough to the trapping frequencies (∼ 200 kHz) to consider parametric heating of the atoms as particularly strong mechanisms for losses. Torsional modes have been measured and characterized Wuttke et al (2013), and even optically excited Fatemi et al (2016);Fenton et al (2016). However, it is necessary to suppress them or increase their frequencies to prevent direct and parametric heating of the atoms.…”