High-order nonlinear light–matter interactions in gases enable the generation of X-ray and attosecond light pulses, metrology and spectroscopy1. Optical nonlinearities in solid-state materials are particularly interesting for combining optical and electronic functions for high-bandwidth information processing2. Third-order nonlinear optical processes in silicon have been used to process optical signals with bandwidths greater than 1 GHz (ref. 2). However, fundamental physical processes for a silicon-based optical modulator in the terahertz bandwidth range have not yet been explored. Here, we demonstrate ultrafast phononic modulation of the optical index of silicon by irradiation with intense few-cycle femtosecond pulses. The anisotropic reflectivity modulation by the resonant Raman susceptibility at the fundamental frequency of the longitudinal optical phonon of silicon (15.6 THz) generates a frequency comb up to seventh order. All-optical >100 THz frequency comb generation is realized by harnessing the coherent atomic motion of the silicon crystalline lattice at its highest mechanical frequency.
Your institute does not have access to this article
Open Access articles citing this article.
Communications Physics Open Access 12 April 2021
Scientific Reports Open Access 29 August 2017
Nature Communications Open Access 01 June 2017
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Gohle, C. et al. A frequency comb in the extreme ultraviolet. Nature 436, 234–237 (2005).
Leuthold, J., Koos, C. & Freude, W. Nonlinear silicon photonics. Nature Photon. 4, 535–544 (2010).
Sokolov, A. V., Walker, D. R., Yavuz, D. D., Yin, G. Y. & Harris, S. E. Raman generation by phased and antiphased molecular states. Phys. Rev. Lett. 85, 562–565 (2000).
Suzuki, T., Hirai, M. & Katsuragawa, M. Octave-spanning Raman comb with carrier envelope offset control. Phys. Rev. Lett. 101, 243602 (2008).
Chan, H.-S. et al. Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics. Science 331, 1165–1168 (2011).
Baker, S., Walmsley, I. A., Tisch, J. W. G. & Marangos, J. P. Femtosecond to attosecond light pulses from a molecular modulator. Nature Photon. 5, 664–671 (2011).
Tom, H. W. K., Heinz, T. F. & Shen, Y. R. Second-harmonic reflection from silicon surfaces and its relation to structural symmetry. Phys. Rev. Lett. 51, 1983–1986 (1983).
Faisal, F. H. M., Kaminski, J. Z. & Saczuk, E. Photoemission and high-order harmonic generation from solid surfaces in intense laser fields. Phys. Rev. A 72, 023412 (2005).
Bisio, F., Nývlt, M., Franta, J., Petek, H. & Kirschner, J. Mechanisms of high-order perturbative photoemission from Cu(001). Phys. Rev. Lett. 96, 087601 (2006).
Renucci, J. B., Tyte, R. N. & Cardona, M. Resonant Raman scattering in silicon. Phys. Rev. B 11, 3885–3895 (1975).
Bartels, A., Dekorsy, T. & Kurz, H. Impulsive excitation of phonon-pair combination states by second-order Raman scattering. Phys. Rev. Lett. 84, 2981–2984 (2000).
Brennan C. J. & Nelson, K. A. Direct time-resolved measurement of anharmonic lattice vibrations in ferroelectric crystals. J. Chem. Phys. 107, 9691–9694 (1997).
Kuznetsov, A. V. & Stanton, C. J. Theory of coherent phonon oscillations in semiconductors. Phys. Rev. Lett. 73, 3243–3246 (1994).
Hase, M. & Kitajima, M. Interaction of coherent phonons with defects and elementary excitations. J. Phys. Condens. Matter 22, 073201 (2010).
Ishioka, K., Hase, M., Kitajima, M. & Petek, H. Coherent optical phonons in diamond. Appl. Phys. Lett. 89, 231916 (2006).
Cho, G. C., Kütt, W. & Kurz, H. Subpicosecond time-resolved coherent-phonon oscillations in GaAs. Phys. Rev. Lett. 65, 764–766 (1990).
Dekorsy, T., Cho, G. C. & Kurz, H. Coherent phonons in condensed media, in Light Scattering in Solids VIII, 76, Springer Topics in Applied Physics (Springer, 2000).
Sabbah, A. J. & Riffe, D. M. Femtosecond pump–probe reflectivity study of silicon carrier dynamics. Phys. Rev. B 66, 165217 (2002).
Hase, M., Kitajima, M., Constantinescu, A. M. & Petek, H. The birth of a quasiparticle observed in time–frequency space. Nature 426, 51–54 (2003).
Zeiger, H. J. et al. Theory for displacive excitation of coherent phonons. Phys. Rev. B 45, 768–778 (1992).
Ishioka, K. et al. Ultrafast electron–phonon decoupling in graphite. Phys. Rev. B 77, 121402(R) (2008).
Melnikov, A. et al. Coherent optical phonons and parametrically coupled magnons induced by femtosecond laser excitation of the Gd(0001) surface. Phys. Rev. Lett. 91, 227403 (2003).
Dhar, L., Rogers, J. A. & Nelson, K. A. Time-resolved vibrational spectroscopy in the impulsive limit. Chem. Rev. 94, 157–193 (1994).
Yan, Y.-X., Gamble, E. B. & Nelson, K. A. Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications. J. Chem. Phys. 83, 5391–5399 (1985).
Shank, C. V., Yen, R. & Hirlimann, C. Time-resolved reflectivity measurements of femtosecond-optical-pulse-induced phase transitions in silicon. Phys. Rev. Lett. 50, 454–457 (1983).
Pötz, W. & Vogl, P. Theory of optical–phonon deformation potentials in tetrahedral semiconductors. Phys. Rev. B 24, 2025–2037 (1981).
Kudryashov, S. I., Kandyla, M., Roeser, C. A. D. & Mazur, E. Intraband and interband optical deformation potentials in femtosecond-laser-excited α-Te. Phys. Rev. B 75, 085207 (2007).
Constantinescu, A. M. Carrier–LO Phonon Interactions in Si(001). PhD thesis, Univ. Pittsburgh (2010).
Riffe, D. M. & Sabbah, A. J. Coherent excitation of the optic phonon in Si: transiently stimulated Raman scattering with a finite-lifetime electronic excitation. Phys. Rev. B 76, 085207 (2007).
Aspens, D. E. & Studna, A. A. Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV. Phys. Rev. B 27, 985–1009 (1983).
The authors acknowledge M. Kitajima for stimulating discussions. This work was supported in part by the National Science Foundation (grant no. CHE-0650756).
The authors declare no competing financial interests.
About this article
Cite this article
Hase, M., Katsuragawa, M., Constantinescu, A. et al. Frequency comb generation at terahertz frequencies by coherent phonon excitation in silicon. Nature Photon 6, 243–247 (2012). https://doi.org/10.1038/nphoton.2012.35
Communications Physics (2021)
Nature Communications (2017)
Scientific Reports (2017)
Measurement of multimode coherent phonons in nanometric spaces in a homojunction-structured silicon light emitting diode
Applied Physics A (2014)