Phase-resolved measurements of stimulated emission in a laser


Lasers are usually described by their output frequency and intensity. However, laser operation is an inherently nonlinear process. Knowledge about the dynamic behaviour of lasers is thus of great importance for detailed understanding of laser operation and for improvement in performance for applications. Of particular interest is the time domain within the coherence time of the optical transition. This time is determined by the oscillation period of the laser radiation and thus is very short. Rigorous quantum mechanical models1,2 predict interesting effects like quantum beats, lasing without inversion, and photon echo processes. As these models are based on quantum coherence and interference, knowledge of the phase within the optical cycle is of particular interest. Laser radiation has so far been measured using intensity detectors, which are sensitive to the square of the electric field. Therefore information about the sign and phase of the laser radiation is lost. Here we use an electro-optic detection scheme to measure the amplitude and phase of stimulated radiation, and correlate this radiation directly with an input probing pulse. We have applied this technique to semiconductor quantum cascade lasers, which are coherent sources operating at frequencies between the optical (>100 THz) and electronic (<0.5 THz) ranges3. In addition to the phase information, we can also determine the spectral gain, the bias dependence of this gain, and obtain an insight into the evolution of the laser field.

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Figure 1: Terahertz time-domain spectroscopy of a THz-QCL.
Figure 2: Fourier transform of the transmission signal modulated by the THz-QCL.
Figure 3: Build-up of the electric field oscillations phase-locked to the external source.
Figure 4: Bias current characteristics of the THz QCL.


  1. 1

    Scully, M. O. & Lamb, W. E. Quantum theory of an optical maser. I. General theory. Phys. Rev. 159, 208–226 (1967)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Haken, H. Cooperative phenomena in systems far from thermal equilibrium and in nonphysical systems. Rev. Mod. Phys. 47, 67–121 (1975)

    ADS  MathSciNet  Article  Google Scholar 

  3. 3

    Faist, J. et al. Quantum cascade laser. Science 264, 553–556 (1994)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Bennet, W. R. Hole burning effect in a He-Ne optical maser. Phys. Rev. 126, 580–593 (1962)

    ADS  Article  Google Scholar 

  5. 5

    Rigrod, W. W. Gain saturation and output power of optical masers. J. Appl. Phys. 34, 2602–2609 (1963)

    ADS  Article  Google Scholar 

  6. 6

    Osgood, R., Eppers, W. & Nichols, E. An investigation of the high-power CO laser. IEEE J. Quant. Electron. QE-6, 145–154 (1970)

    ADS  Article  Google Scholar 

  7. 7

    Crowe, W. & Ahearn, W. F. Semiconductor laser amplifier. IEEE J. Quant. Electron. QE-2, 283–289 (1966)

    ADS  Article  Google Scholar 

  8. 8

    Diels, J.-C. & Rudolph, W. Ultrashort Laser Pulse Phenomena: Fundamentals, Technique, and Applications on a Femtosecond Time Scale (Academic, San Diego, 1996)

    Google Scholar 

  9. 9

    Wu, Q. & Zhang, X.-C. Ultrafast electro-optic field sensor. Appl. Phys. Lett. 68, 1604–1606 (1996)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Huber, R. et al. How many-particle interactions develop after ultrafast excitation of an electron-hole plasma. Nature 414, 286–289 (2001)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Huber, R., Kaindl, R. A., Schmid, B. A. & Chemla, D. S. Broadband terahertz study of excitonic resonances in the high-density regime in GaAs/Al x Ga1–x As quantum wells. Phys. Rev. B 72, 161314 (2005)

    ADS  Article  Google Scholar 

  12. 12

    Huber, R. et al. Stimulated terahertz emission from intraexcitonic transitions in Cu2O. Phys. Rev. Lett. 96, 017402 (2006)

    ADS  Article  Google Scholar 

  13. 13

    Koehler, R. et al. Terahertz semiconductor-heterostructure laser. Nature 417, 156–159 (2002)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Walther, C., Scalari, G., Faist, J., Beere, H. & Ritchie, D. Low frequency terahertz quantum cascade laser operating from 1.6 to 1.8 THz. Appl. Phys. Lett. 89, 231121 (2006)

    ADS  Article  Google Scholar 

  15. 15

    Taflove, A. Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 1995)

    Google Scholar 

  16. 16

    Ziolkowski, R. W., Arnold, J. M. & Gogny, D. M. Ultrafast pulse interactions with two-level atom. Phys. Rev. A 52, 3082–3094 (1995)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Kröll, J. et al. Longitudinal spatial hole burning in terahertz quantum cascade lasers. Appl. Phys. Lett. (in the press)

  18. 18

    Faist, J., Capasso, F., Sirtori, C., Sivco, D. L. & Cho, A. Y. in Intersubband Transitions in Quantum Wells: Physics and Device Applications II (eds Liu, H. C. & Capasso, F.) 1–83 (Academic, London, 2000)

    Google Scholar 

  19. 19

    Alton, J. et al. Buried waveguides in terahertz quantum cascade lasers based on two-dimensional plasmon modes. Appl. Phys. Lett. 86, 071109 (2005)

    ADS  Article  Google Scholar 

  20. 20

    Barbieri, S. et al. 2.9 THz quantum cascade lasers operating up to 70 K in continuous wave. Appl. Phys. Lett. 85, 1674–1676 (2004)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Kohen, S., Williams, B. & Hu, Q. Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators. J. Appl. Phys. 97, 053106 (2005)

    ADS  Article  Google Scholar 

  22. 22

    Baltuska, A. et al. Attosecond control of electronic processes by intensive light fields. Nature 421, 611–615 (2003)

    ADS  CAS  Article  Google Scholar 

  23. 23

    Nuss, M. C. & Orenstein, J. in Millimeter and Submillimeter Wave Spectroscopy of Solids (ed. Gruener, G.) Ch. 2 (Springer, Berlin, 1998)

    Google Scholar 

  24. 24

    Zhang, X.-C., Hu, B. B., Darrow, J. T. & Auston, D. H. Generation of femtosecond electromagnetic pulses from semiconductor surfaces. Appl. Phys. Lett. 56, 1011–1013 (1990)

    ADS  CAS  Article  Google Scholar 

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We are grateful to D. P. Kelly for comments on the presentation of the manuscript. We acknowledge financial support from the European Commission under the Integrated Project TeraNova funded by the IST directorate, and from the Austrian Science Fond (FWF) under the project Advanced Light Sources (ADLIS).

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Correspondence to Karl Unterrainer.

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The authors declare no competing financial interests.

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Kröll, J., Darmo, J., Dhillon, S. et al. Phase-resolved measurements of stimulated emission in a laser. Nature 449, 698–701 (2007).

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