Abstract
Esaki and Tsu’s superlattice1, made by alternating two different semiconductor materials, was the first one-dimensional artificial crystal that demonstrated the ability to tailor semiconductor properties. One motivation of this work was the realization of the Bloch oscillator2,3 and the use of its particular dispersive optical gain4,5 to achieve a tuneable source of electromagnetic radiation. However, these superlattices were electrically unstable in the steady state6. Fortunately, because it is based on scattering-assisted transitions, this particular gain does not arise only in superlattices, but also more generally in semiconductor heterostructures7,8 such as quantum cascade lasers9 (QCLs), where the electrical stability can be controlled10. Here, we show the unambiguous spectral signature of Bloch gain in a special QCL designed to enhance the latter by exhibiting laser action in the condition of weak to vanishing population inversion.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to the full article PDF.
USD 39.95
Prices may be subject to local taxes which are calculated during checkout




Similar content being viewed by others
References
Esaki, L. & Tsu, R. Superlattice and negative differential conductivity in semiconductors. IBM J. Res. Develop. 14, 61–65 (1970).
Bloch, F. Uber die quantenmechhanik der elektronen in kristallgittern. Z. Phys. 52, 555–600 (1928).
Zener, C. A theory of the electrical breakdown of solid dielectrics. Proc. R. Soc. A 145, 523–529 (1934).
Ktitorov, S. A., Simin, G. S. & Sindalovskii, V. Y. Bragg reflections and the high-frequency conductivity of an electronic solid-state plasma. Fiz. tverd. Tela. 13, 2230–2233 (1971).
Ignatov, A. A. & Romanov, Y. A. Nonlinear electromagnetic properties of semiconductors with a superlattice. Phys. Status Solidi B 73, 327–333 (1976).
Choi, K. K., Levine, B. F., Malik, R. J., Walker, J. & Bethea, C. G. Periodic negative conductance by sequential resonant tunneling through an expanding high-field superlattice domain. Phys. Rev. B 35, 4172–4175 (1987).
Willenberg, H., Döhler, G. H. & Faist, J. Intersubband gain in a Bloch oscillator and quantum cascade laser. Phys. Rev. B 67, 085315 (2003).
Wacker, A. Gain in quantum cascade lasers and superlattices: A quantum transport theory. Phys. Rev. B 66, 085326 (2002).
Faist, J. et al. Quantum cascade laser. Science 264, 553–556 (1994).
Sirtori, C. et al. Resonant tunneling in quantum cascade lasers. IEEE J. Quantum Electron. 34, 1722–1729 (1998).
Feldmann, J. et al. Optical investigation of Bloch oscillations in a semiconductor superlattice. Phys. Rev. B 46, 7252–7255 (1992).
Waschke, C. et al. Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice. Phys. Rev. Lett. 70, 3319–3322 (1993).
Sekine, N. & Hirakawa, K. Dispersive terahertz gain of a nonclassical oscillator: Bloch oscillation in semiconductor superlattices. Phys. Rev. Lett. 94, 057408–057412 (2005).
Unterrainer, K. et al. Inverse Bloch oscillator: Strong terahertz-photocurrent resonances at the Bloch frequency. Phys. Rev. Lett. 76, 2973–2976 (1996).
Savvidis, P., Kolasa, B., Lee, G. & Allen, S. Resonant crossover of terahertz loss to the gain of a Bloch oscillating inas/alsb superlattice. Phys. Rev. Lett. 92, 196802 (2004).
Imamoglu, A. & Ram, R. J. Semiconductor lasers without population inversion. Opt. Lett. 19, 1744–1746 (1994).
Faist, J. et al. Quantum cascade lasers without intersubband population inversion. Phys. Rev. Lett. 76, 411–414 (1996).
Gorfinkel, V., Luryi, S. & Gelmont, B. Theory of gain spectra for quantum cascade lasers and temperature dependence of their characteristics at low and moderate carrier concentrations. IEEE J. Quantum Electron. 32, 1995–2003 (1996).
Sirtori, C. et al. Mid-infrared (8.5 μm) semiconductor lasers operating at room temperature. IEEE Photon. Technol. Lett. 9, 294–296 (1997).
Barbieri, S. et al. Gain measurements on gaas-based quantum cascade lasers using a two-section cavity technique. IEEE J. Quantum Electron. 36, 736–741 (2000).
Kazarinov, R. F. & Suris, R. A. Electric and electromagnetic properties of semiconductors with a superlattice. Sov. Phys. Semicond. 6, 120–131 (1972).
Acknowledgements
This work was supported by the Swiss National Science Foundation and the National Center of Competence in Research, Quantum Photonics.
Author information
Authors and Affiliations
Contributions
The structures were designed by J.F. and grown by M.G. and N.H. using molecular beam epitaxy. T.G. fabricated the samples, worked on the measurement technique and measured the samples together with N.S. The theoretical work and the gain calculations were done by R.T. who also wrote the manuscript together with J.F., the head of the group in which the work was carried out.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Rights and permissions
About this article
Cite this article
Terazzi, R., Gresch, T., Giovannini, M. et al. Bloch gain in quantum cascade lasers. Nature Phys 3, 329–333 (2007). https://doi.org/10.1038/nphys577
Received:
Accepted:
Published:
Issue date:
DOI: https://doi.org/10.1038/nphys577
This article is cited by
-
Enhanced photoluminescence from porous silicon nanowire arrays
Nanoscale Research Letters (2013)
-
High k-space lasing in a dual-wavelength quantum cascade laser
Nature Photonics (2009)
-
Lasing high in k-space
Nature Photonics (2009)
-
A round-up of recent papers in the field of photonics published by the physical sciences division of the Nature Publishing Group
Nature Photonics (2007)
-
Coexistence of gain and absorption
Nature Physics (2007)


