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/10.1063/1.489462393506935101169Kippenberg, 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