A novel high resolution contactless technique for thermal field mapping and thermal conductivity determination: Two-Laser Raman Thermometry

We present a novel high resolution contactless technique for thermal conductivity determination and thermal field mapping based on creating a thermal distribution of phonons using a heating laser, while a second laser probes the local temperature through the spectral position of a Raman active mode. The spatial resolution can be as small as $300$ nm, whereas its temperature accuracy is $\pm 2$ K. We validate this technique investigating the thermal properties of three free-standing single crystalline Si membranes with thickness of 250, 1000, and 2000 nm. We show that for 2-dimensional materials such as free-standing membranes or thin films, and for small temperature gradients, the thermal field decays as $T(r) \propto ln(r)$ in the diffusive limit. The case of large temperature gradients within the membranes leads to an exponential decay of the thermal field, $T \propto exp[-A \cdot ln(r)]$. The results demonstrate the full potential of this new contactless method for quantitative determination of thermal properties. The range of materials to which this method is applicable reaches far beyond the here demonstrated case of Si, as the only requirement is the presence of a Raman active mode

Acoustic phonon propagation in ultra-thin Si membranes under biaxial stress field

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.We report on stress induced changes in the dispersion relations of acoustic phonons propagating in 27 nm thick single crystalline Si membranes. The static tensile stress (up to 0.3 GPa) acting on the Si membranes was achieved using an additional strain compensating silicon nitride frame. Dispersion relations of thermally activated hypersonic phonons were measured by means of Brillouin light scattering spectroscopy. The theory of Lamb wave propagation is developed for anisotropic materials subjected to an external static stress field. The dispersion relations were calculated using the elastic continuum approximation and taking into account the acousto-elastic effect. We find an excellent agreement between the theoretical and the experimental dispersion relations.The authors acknowledge financial support from the FP7 project MERGING (grant no. 309150); the Spanish MICINN projects nanoTHERM (grant no. CSD2010-0044) and TAPHOR (MAT2012-31392). JGB gratefully acknowledges support from the Spanish government through a Juan de la Cierva fellowship. MP and AS acknowledge funding from the Academy of Finland (grant no. 252598).Peer Reviewe

Optical and mechanical mode tuning in an optomechanical crystal with light-induced thermal effects

Under the terms of the Creative Commons Attribution (CC BY) license to their work.We report on the modification of the optical and mechanical properties of a silicon 1D optomechanical crystal cavity due to thermo-optic effects in a high phonon/photon population regime. The cavity heats up due to light absorption in a way that shifts the optical modes towards longer wavelengths and the mechanical modes to lower frequencies. By combining the experimental optical results with finite-difference time-domain simulations, we establish a direct relation between the observed wavelength drift and the actual effective temperature increase of the cavity. By assuming that the Young's modulus decreases accordingly to the temperature increase, we find a good agreement between the mechanical mode drift predicted using a finite element method and the experimental one.This work was supported by the EU through the project TAILPHOX (ICT-FP7-233883) and the ERC Advanced Grant SOULMAN (ERC-FP7-321122) and the Spanish projects TAPHOR (MAT2012-31392).Peer Reviewe

Slow light mediated by mode topological transitions in hyperbolic waveguides

We show that slow light in hyperbolic waveguides is linked to topological transitions in the dispersion diagram as the film thickness changes. The effect appears in symmetric planar structures with type II films, whose optical axis (OA) lies parallel to the waveguide interfaces. The transitions are mediated by elliptical mode branches that coalesce along the OA with anomalously ordered hyperbolic mode branches, resulting in a saddle point. When the thickness of the film increases further, the merged branch starts a transition to hyperbolic normally ordered modes propagating orthogonally to the OA. In this process, the saddle point transforms into a branch point featuring slow light for a broad range of thicknesses, and a new branch of ghost waves appears.Agència de Gestió d’Ajuts Universitaris i de Recerca (2017-SGR-1400); Ministerio de Economía y Competitividad (PGC2018-097035-B-I00, SEV-2015-0522); H2020 Marie Sklodowska-Curie Actions (GA665884); Fundación Cellex; Fundació Mir-Puig. National Science Foundation with a CAREER Grant No. ECCS-1749177.Award-winningPostprint (author's final draft

Engineering nanoscale hypersonic phonon transport

Controlling the vibrations in solids is crucial to tailor their mechanical properties and their interaction with light. Thermal vibrations represent a source of noise and dephasing for many physical processes at the quantum level. One strategy to avoid these vibrations is to structure a solid such that it possesses a phononic stop band, i.e., a frequency range over which there are no available mechanical modes. Here, we demonstrate the complete absence of mechanical vibrations at room temperature over a broad spectral window, with a 5.3 GHz wide band gap centered at 8.4 GHz in a patterned silicon nanostructure membrane measured using Brillouin light scattering spectroscopy. By constructing a line-defect waveguide, we directly measure GHz localized modes at room temperature. Our experimental results of thermally excited guided mechanical modes at GHz frequencies provides an eficient platform for photon-phonon integration with applications in optomechanics and signal processing transduction

Optical and mechanical mode tuning in an optomechanical crystal with light-induced thermal effects

[EN] We report on the modification of the optical and mechanical properties of a silicon 1D optomechanical crystal cavity due to thermo-optic effects in a high phonon/photon population regime. The cavity heats up due to light absorption in a way that shifts the optical modes towards longer wavelengths and the mechanical modes to lower frequencies. By combining the experimental optical results with finite-difference time-domain simulations, we establish a direct relation between the observed wavelength drift and the actual effective temperature increase of the cavity. By assuming that the Young's modulus decreases accordingly to the temperature increase, we find a good agreement between the mechanical mode drift predicted using a finite element method and the experimental one.This work was supported by the EU through the project TAILPHOX (ICT-FP7-233883) and the ERC Advanced Grant SOULMAN (ERC-FP7-321122) and the Spanish projects TAPHOR (MAT2012-31392). The authors thank A. Tredicucci for a critical reading of the manuscript and A. Pitanti for fruitful discussions.Navarro-Urrios, D.; Gomis-Bresco, J.; Capuj, NE.; Alzina, F.; Griol Barres, A.; Puerto Garcia, D.; Martínez Abietar, AJ.... (2014). Optical and mechanical mode tuning in an optomechanical crystal with light-induced thermal effects. Journal of Applied Physics. 116(9):93506-93510. https://doi.org/10.1063/1.4894623S93506935101169Kippenberg, T. J., & Vahala, K. J. (2008). Cavity Optomechanics: Back-Action at the Mesoscale. Science, 321(5893), 1172-1176. doi:10.1126/science.1156032Chan, J., Alegre, T. P. M., Safavi-Naeini, A. H., Hill, J. T., Krause, A., Gröblacher, S., … Painter, O. (2011). Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature, 478(7367), 89-92. doi:10.1038/nature10461Teufel, J. D., Donner, T., Li, D., Harlow, J. W., Allman, M. S., Cicak, K., … Simmonds, R. W. (2011). Sideband cooling of micromechanical motion to the quantum ground state. Nature, 475(7356), 359-363. doi:10.1038/nature10261Barclay, P. E., Srinivasan, K., & Painter, O. (2005). Nonlinear response of silicon photonic crystal micresonators excited via an integrated waveguide and fiber taper. Optics Express, 13(3), 801. doi:10.1364/opex.13.000801Ding, L., Senellart, P., Lemaitre, A., Ducci, S., Leo, G., & Favero, I. (2010). GaAs micro-nanodisks probed by a looped fiber taper for optomechanics applications. Nanophotonics III. doi:10.1117/12.853985Eichenfield, M., Michael, C. P., Perahia, R., & Painter, O. (2007). Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces. Nature Photonics, 1(7), 416-422. doi:10.1038/nphoton.2007.96Carmon, T., Yang, L., & Vahala, K. J. (2004). Dynamical thermal behavior and thermal self-stability of microcavities. Optics Express, 12(20), 4742. doi:10.1364/opex.12.004742Camacho, R. M., Chan, J., Eichenfield, M., & Painter, O. (2009). Characterization of radiation pressure and thermal effects in a nanoscale optomechanical cavity. Optics Express, 17(18), 15726. doi:10.1364/oe.17.015726Eichenfield, M., Chan, J., Camacho, R. M., Vahala, K. J., & Painter, O. (2009). Optomechanical crystals. Nature, 462(7269), 78-82. doi:10.1038/nature08524Oskooi, A. F., Roundy, D., Ibanescu, M., Bermel, P., Joannopoulos, J. D., & Johnson, S. G. (2010). Meep: A flexible free-software package for electromagnetic simulations by the FDTD method. Computer Physics Communications, 181(3), 687-702. doi:10.1016/j.cpc.2009.11.008Ding, L., Belacel, C., Ducci, S., Leo, G., & Favero, I. (2010). Ultralow loss single-mode silica tapers manufactured by a microheater. Applied Optics, 49(13), 2441. doi:10.1364/ao.49.002441J. Chan , Ph.D. dissertation, California Institute of Technology, Los Angeles, 2014.Priem, G., Dumon, P., Bogaerts, W., Van Thourhout, D., Morthier, G., & Baets, R. (2005). Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures. Optics Express, 13(23), 9623. doi:10.1364/opex.13.009623Liu, Y., & Tsang, H. K. (2007). Time dependent density of free carriers generated by two photon absorption in silicon waveguides. Applied Physics Letters, 90(21), 211105. doi:10.1063/1.2741611Johnson, J. A., Maznev, A. A., Cuffe, J., Eliason, J. K., Minnich, A. J., Kehoe, T., … Nelson, K. A. (2013). Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane. Physical Review Letters, 110(2). doi:10.1103/physrevlett.110.025901Hopkins, P. E., Reinke, C. M., Su, M. F., Olsson, R. H., Shaner, E. A., Leseman, Z. C., … El-Kady, I. (2011). Reduction in the Thermal Conductivity of Single Crystalline Silicon by Phononic Crystal Patterning. Nano Letters, 11(1), 107-112. doi:10.1021/nl102918qMarconnet, A. M., Asheghi, M., & Goodson, K. E. (2013). From the Casimir Limit to Phononic Crystals: 20 Years of Phonon Transport Studies Using Silicon-on-Insulator Technology. Journal of Heat Transfer, 135(6). doi:10.1115/1.4023577Jellison, G. E., & Burke, H. H. (1986). The temperature dependence of the refractive index of silicon at elevated temperatures at several laser wavelengths. Journal of Applied Physics, 60(2), 841-843. doi:10.1063/1.337386Xu, Q., & Lipson, M. (2006). Carrier-induced optical bistability in silicon ring resonators. Optics Letters, 31(3), 341. doi:10.1364/ol.31.000341Vanhellemont, J., & Simoen, E. (2007). Brother Silicon, Sister Germanium. Journal of The Electrochemical Society, 154(7), H572. doi:10.1149/1.2732221C. Bourgeois , E. Steinsland , N. Blanc , and N. F. de Rooij , in Proceedings of the 1997 IEEE International Frequency Control Symposium (1997), pp. 791–799

Generalized nonreciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering

Synthetic magnetism has been used to control charge neutral excitations for applications ranging from classical beam steering to quantum simulation. In optomechanics, radiation-pressure-induced parametric coupling between optical (photon) and mechanical (phonon) excitations may be used to break time-reversal symmetry, providing the prerequisite for synthetic magnetism. Here we design and fabricate a silicon optomechanical circuit with both optical and mechanical connectivity between two optomechanical cavities. Driving the two cavities with phase-correlated laser light results in a synthetic magnetic flux, which in combination with dissipative coupling to the mechanical bath, leads to nonreciprocal transport of photons with 35dB of isolation. Additionally, optical pumping with blue-detuned light manifests as a particle non-conserving interaction between photons and phonons, resulting in directional optical amplification of 12dB in the isolator through direction. These results indicate the feasibility of utilizing optomechanical circuits to create a more general class of nonreciprocal optical devices, and further, to enable novel topological phases for both light and sound on a microchip.Comment: 18 pages, 8 figures, 4 appendice

Nonlinear dynamics and chaos in an optomechanical beam

[EN] Optical nonlinearities, such as thermo-optic mechanisms and free-carrier dispersion, are often considered unwelcome effects in silicon-based resonators and, more specifically, optomechanical cavities, since they affect, for instance, the relative detuning between an optical resonance and the excitation laser. Here, we exploit these nonlinearities and their intercoupling with the mechanical degrees of freedom of a silicon optomechanical nanobeam to unveil a rich set of fundamentally different complex dynamics. By smoothly changing the parameters of the excitation laser we demonstrate accurate control to activate two-and four-dimensional limit cycles, a period-doubling route and a six-dimensional chaos. In addition, by scanning the laser parameters in opposite senses we demonstrate bistability and hysteresis between two-and four-dimensional limit cycles, between different coherent mechanical states and between four-dimensional limit cycles and chaos. Our findings open new routes towards exploiting silicon-based optomechanical photonic crystals as a versatile building block to be used in neurocomputational networks and for chaos-based applications.This work was supported by the European Comission project PHENOMEN (H2020-EU-713450), the Spanish Severo Ochoa Excellence program and the MINECO project PHENTOM (FIS2015-70862-P). DNU, PDG and MFC gratefully acknowledge the support of a Ramon y Cajal postdoctoral fellowship (RYC-2014-15392), a Beatriu de Pinos postdoctoral fellowship (BP-DGR 2015 (B) and a Severo Ochoa studentship, respectively. We would like to acknowledge Jose C. Sabina de Lis, J.M. Plata Suarez, A. Trifonova and C. Masoller for fruitful discussions.Navarro-Urrios, D.; Capuj, NE.; Colombano, MF.; García, PD.; Sledzinska, M.; Alzina, F.; Griol Barres, A.... (2017). Nonlinear dynamics and chaos in an optomechanical beam. Nature Communications. 8. https://doi.org/10.1038/ncomms14965S8Strogatz, S. H. 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Dynamical back-action at 5.5 GHz in a corrugated optomechanical beam

[EN] We report on the optomechanical properties of a breathing mechanical mode oscillating at 5.5 GHz in a 1D corrugated Si nanobeam. This mode has an experimental single-particle optomechanical coupling rate of vertical bar g(o, OM)vertical bar= 1.8 MHz (vertical bar g(o, OM)vertical bar/2 pi=0.3 MHz) and shows strong dynamical back-action effects at room temperature. The geometrical flexibility of the unit-cell would lend itself to further engineering of the cavity region to localize the mode within the full phononic band-gap present at 4 GHz while keeping high go, OM values. This would lead to longer lifetimes at cryogenic temperatures, due to the suppression of acoustic leakage.This work was supported by the EU through the FP7 project TAILPHOX (ICT-FP7-233883) and the ERC Advanced Grant SOULMAN (ERC-FP7-321122) and the Spanish projects TAPHOR (MAT2012-31392). D.N-U and J.G-B acknowledge support in the form of postdoctoral fellowships from the Catalan (Beatriu de Pinos) and the Spanish (Juan de la Cierva) governments, respectively.Navarro-Urrios, D.; Gomis-Bresco, J.; El-Jallal, S.; Oudich, M.; Pitanti, A.; Capuj, N.; Tredicucci, A.... (2014). Dynamical back-action at 5.5 GHz in a corrugated optomechanical beam. AIP Advances. 4(12). https://doi.org/10.1063/1.4902171S412Aspelmeyer, M., Kippenberg, T. J., & Marquardt, F. (Eds.). (2014). Cavity Optomechanics. doi:10.1007/978-3-642-55312-7Kippenberg, T. J., Rokhsari, H., Carmon, T., Scherer, A., & Vahala, K. J. (2005). Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity. Physical Review Letters, 95(3). doi:10.1103/physrevlett.95.033901Hossein-Zadeh, M., Rokhsari, H., Hajimiri, A., & Vahala, K. J. (2006). Characterization of a radiation-pressure-driven micromechanical oscillator. Physical Review A, 74(2). doi:10.1103/physreva.74.023813Eichenfield, M., Chan, J., Camacho, R. M., Vahala, K. J., & Painter, O. (2009). Optomechanical crystals. Nature, 462(7269), 78-82. doi:10.1038/nature08524Pennec, Y., Laude, V., Papanikolaou, N., Djafari-Rouhani, B., Oudich, M., El Jallal, S., … Martínez, A. (2014). Modeling light-sound interaction in nanoscale cavities and waveguides. Nanophotonics, 3(6). doi:10.1515/nanoph-2014-0004Chan, J., Alegre, T. P. M., Safavi-Naeini, A. H., Hill, J. T., Krause, A., Gröblacher, S., … Painter, O. (2011). Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature, 478(7367), 89-92. doi:10.1038/nature10461Safavi-Naeini, A. H., Alegre, T. P. M., Chan, J., Eichenfield, M., Winger, M., Lin, Q., … Painter, O. (2011). Electromagnetically induced transparency and slow light with optomechanics. Nature, 472(7341), 69-73. doi:10.1038/nature09933Pennec, Y., Rouhani, B. D., Li, C., Escalante, J. M., Martinez, A., Benchabane, S., … Papanikolaou, N. (2011). Band gaps and cavity modes in dual phononic and photonic strip waveguides. AIP Advances, 1(4), 041901. doi:10.1063/1.3675799Gomis-Bresco, J., Navarro-Urrios, D., Oudich, M., El-Jallal, S., Griol, A., Puerto, D., … Torres, C. M. S. (2014). A one-dimensional optomechanical crystal with a complete phononic band gap. Nature Communications, 5(1). doi:10.1038/ncomms5452Oudich, M., El-Jallal, S., Pennec, Y., Djafari-Rouhani, B., Gomis-Bresco, J., Navarro-Urrios, D., … Makhoute, A. (2014). Optomechanic interaction in a corrugated phoxonic nanobeam cavity. Physical Review B, 89(24). doi:10.1103/physrevb.89.245122Chan, J., Safavi-Naeini, A. H., Hill, J. T., Meenehan, S., & Painter, O. (2012). Optimized optomechanical crystal cavity with acoustic radiation shield. Applied Physics Letters, 101(8), 081115. doi:10.1063/1.4747726Safavi-Naeini, A. H., Hill, J. T., Meenehan, S., Chan, J., Gröblacher, S., & Painter, O. (2014). Two-Dimensional Phononic-Photonic Band Gap Optomechanical Crystal Cavity. Physical Review Letters, 112(15). doi:10.1103/physrevlett.112.153603Johnson, S. G., Ibanescu, M., Skorobogatiy, M. A., Weisberg, O., Joannopoulos, J. D., & Fink, Y. (2002). Perturbation theory for Maxwell’s equations with shifting material boundaries. Physical Review E, 65(6). doi:10.1103/physreve.65.066611Navarro-Urrios, D., Gomis-Bresco, J., Capuj, N. E., Alzina, F., Griol, A., Puerto, D., … Sotomayor-Torres, C. M. (2014). Optical and mechanical mode tuning in an optomechanical crystal with light-induced thermal effects. Journal of Applied Physics, 116(9), 093506. doi:10.1063/1.4894623Barclay, P. E., Srinivasan, K., & Painter, O. (2005). Nonlinear response of silicon photonic crystal micresonators excited via an integrated waveguide and fiber taper. Optics Express, 13(3), 801. doi:10.1364/opex.13.000801J. Chan, Ph.D. thesis, California Institute of Technology, Los Angeles, 2014.Gorodetsky, M. L., Schliesser, A., Anetsberger, G., Deleglise, S., & Kippenberg, T. J. (2010). Determination of the vacuum optomechanical coupling rate using frequency noise calibration. Optics Express, 18(22), 23236. doi:10.1364/oe.18.02323