Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Frequency comb generation at terahertz frequencies by coherent phonon excitation in silicon

Abstract

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Schematic of refractive index modulation in silicon.
Figure 2: Coherent phonon oscillations.
Figure 3: Fourier transform spectrum obtained from the transient anisotropic reflectivity.

References

  1. Gohle, C. et al. A frequency comb in the extreme ultraviolet. Nature 436, 234–237 (2005).

    ADS  Article  Google Scholar 

  2. Leuthold, J., Koos, C. & Freude, W. Nonlinear silicon photonics. Nature Photon. 4, 535–544 (2010).

    ADS  Article  Google Scholar 

  3. 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).

    ADS  Article  Google Scholar 

  4. Suzuki, T., Hirai, M. & Katsuragawa, M. Octave-spanning Raman comb with carrier envelope offset control. Phys. Rev. Lett. 101, 243602 (2008).

    ADS  Article  Google Scholar 

  5. Chan, H.-S. et al. Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics. Science 331, 1165–1168 (2011).

    ADS  Article  Google Scholar 

  6. 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).

    ADS  Article  Google Scholar 

  7. 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).

    ADS  Article  Google Scholar 

  8. 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).

    ADS  Article  Google Scholar 

  9. 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).

    ADS  Article  Google Scholar 

  10. Renucci, J. B., Tyte, R. N. & Cardona, M. Resonant Raman scattering in silicon. Phys. Rev. B 11, 3885–3895 (1975).

    ADS  Article  Google Scholar 

  11. 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).

    ADS  Article  Google Scholar 

  12. Brennan C. J. & Nelson, K. A. Direct time-resolved measurement of anharmonic lattice vibrations in ferroelectric crystals. J. Chem. Phys. 107, 9691–9694 (1997).

    ADS  Article  Google Scholar 

  13. Kuznetsov, A. V. & Stanton, C. J. Theory of coherent phonon oscillations in semiconductors. Phys. Rev. Lett. 73, 3243–3246 (1994).

    ADS  Article  Google Scholar 

  14. Hase, M. & Kitajima, M. Interaction of coherent phonons with defects and elementary excitations. J. Phys. Condens. Matter 22, 073201 (2010).

    ADS  Article  Google Scholar 

  15. Ishioka, K., Hase, M., Kitajima, M. & Petek, H. Coherent optical phonons in diamond. Appl. Phys. Lett. 89, 231916 (2006).

    ADS  Article  Google Scholar 

  16. Cho, G. C., Kütt, W. & Kurz, H. Subpicosecond time-resolved coherent-phonon oscillations in GaAs. Phys. Rev. Lett. 65, 764–766 (1990).

    ADS  Article  Google Scholar 

  17. 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).

  18. Sabbah, A. J. & Riffe, D. M. Femtosecond pump–probe reflectivity study of silicon carrier dynamics. Phys. Rev. B 66, 165217 (2002).

    ADS  Article  Google Scholar 

  19. Hase, M., Kitajima, M., Constantinescu, A. M. & Petek, H. The birth of a quasiparticle observed in time–frequency space. Nature 426, 51–54 (2003).

    ADS  Article  Google Scholar 

  20. Zeiger, H. J. et al. Theory for displacive excitation of coherent phonons. Phys. Rev. B 45, 768–778 (1992).

    ADS  Article  Google Scholar 

  21. Ishioka, K. et al. Ultrafast electron–phonon decoupling in graphite. Phys. Rev. B 77, 121402(R) (2008).

    ADS  Article  Google Scholar 

  22. 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).

    ADS  Article  Google Scholar 

  23. Dhar, L., Rogers, J. A. & Nelson, K. A. Time-resolved vibrational spectroscopy in the impulsive limit. Chem. Rev. 94, 157–193 (1994).

    Article  Google Scholar 

  24. 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).

    ADS  Article  Google Scholar 

  25. 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).

    ADS  Article  Google Scholar 

  26. Pötz, W. & Vogl, P. Theory of optical–phonon deformation potentials in tetrahedral semiconductors. Phys. Rev. B 24, 2025–2037 (1981).

    ADS  Article  Google Scholar 

  27. 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).

    ADS  Article  Google Scholar 

  28. Constantinescu, A. M. Carrier–LO Phonon Interactions in Si(001). PhD thesis, Univ. Pittsburgh (2010).

  29. 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).

    ADS  Article  Google Scholar 

  30. 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).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge M. Kitajima for stimulating discussions. This work was supported in part by the National Science Foundation (grant no. CHE-0650756).

Author information

Authors and Affiliations

Authors

Contributions

M.H. and A.M.C. performed the experiments and analysed data. M.K. constructed the simulation model and M.H. carried out the model simulation. M.H., M.K. and H.P. discussed the results. M.H. and H.P. co-wrote the manuscript.

Corresponding authors

Correspondence to Muneaki Hase or Hrvoje Petek.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and Permissions

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2012.35

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing