Skip to content
naulon

No retraction, correction or concern found when last checked on Nov 1, 2026.

Reversing the pump dependence of a laser at an exceptional point

M. Brandstetter, M. Liertzer, C. Deutsch and 6 more

Nature Communications · 2014

doi:10.1038/ncomms5034

Abstract

When two resonant modes in a system with gain or loss coalesce in both their resonance position and their width, a so-called exceptional point occurs, which acts as a source of non-trivial physics in a diverse range of systems. Lasers provide a natural setting to study such non-Hermitian degeneracies, as they feature resonant modes and a gain material as their basic constituents. Here we show that exceptional points can be conveniently induced in a photonic molecule laser by a suitable variation of the applied pump. Using a pair of coupled microdisk quantum cascade lasers, we demonstrate that in the vicinity of these exceptional points the coupled laser shows a characteristic reversal of its pump dependence, including a strongly decreasing intensity of the emitted laser light for increasing pump power.

References 49

  1. 1.

    Berry M. V. Physics of nonhermitian degeneracies. Czechoslov. J. Phys. 54, 1039–1047 (2004 ).

    Not in our library

  2. 2.

    Rotter I. A non-Hermitian Hamilton operator and the physics of open quantum systems. J. Phys. Math. Theor. 42, 153001 (2009 ).

    Not in our library

  3. 3.

    Moiseyev N. Non-Hermitian Quantum Mechanics Cambridge University Press (2011 ).

    Not in our library

  4. 4.

    Heiss W. D. The physics of exceptional points. J. Phys. Math. Theor. 45, 444016 (2012 ).

    Not in our library

  5. 5.

    Chong Y. D. & Stone A. D. General linewidth formula for steady-state multimode lasing in arbitrary cavities. Phys. Rev. Lett. 109, 063902 (2012 ).

    Not in our library10.1103/physrevlett.109.063902

  6. 6.

    Longhi S. PT-symmetric laser absorber. Phys. Rev. A 82, 031801 (2010 ).

    Not in our library

  7. 7.

    Chong Y. D., Ge L. & Stone A. D. PT-symmetry breaking and laser-absorber modes in optical scattering systems. Phys. Rev. Lett. 106, 093902 (2011 ).

    Not in our library10.1103/physrevlett.106.093902

  8. 8.

    Gilary I., Mailybaev A. A. & Moiseyev N. Time-asymmetric quantum-state-exchange mechanism. Phys. Rev. A 88, 010102 (2013 ).

    Not in our library

  9. 9.

    Dietz B.. Exceptional points in a microwave billiard with time-reversal invariance violation. Phys. Rev. Lett. 106, 150403 (2011 ).

    Not in our library10.1103/physrevlett.106.150403

  10. 10.

    Lee S. B.. Observation of an exceptional point in a chaotic optical microcavity. Phys. Rev. Lett. 103, 134101 (2009 ).

    Not in our library10.1103/physrevlett.103.134101

  11. 11.

    Choi Y.. Quasieigenstate coalescence in an atom-cavity quantum composite. Phys. Rev. Lett. 104, 153601 (2010 ).

    Not in our library10.1103/physrevlett.104.153601

  12. 12.

    Wiersig J.. Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities. Phys. Rev. A 84, 023845 (2011 ).

    Not in our library

  13. 13.

    Brody D. C. & Graefe E.-M. Mixed-state evolution in the presence of gain and loss. Phys. Rev. Lett. 109, 230405 (2012 ).

    Not in our library10.1103/physrevlett.109.230405

  14. 14.

    Schomerus H. Quantum noise and self-sustained radiation of PT-symmetric systems. Phys. Rev. Lett. 104, 233601 (2010 ).

    Not in our library10.1103/physrevlett.104.233601

  15. 15.

    Bender C. M. & Boettcher S. Real spectra in non-hermitian hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998 ).

    Not in our library

  16. 16.

    El-Ganainy R., Makris K. G., Christodoulides D. N. & Musslimani Z. H. Theory of coupled optical PT-symmetric structures. Opt. Lett. 32, 2632 (2007 ).

    Not in our library10.1364/ol.32.002632

  17. 17.

    Guo A.. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009 ).

    Not in our library10.1103/physrevlett.103.093902

  18. 18.

    Rüter C. E.. Observation of parity–time symmetry in optics. Nat. Phys. 6, 192–195 (2010 ).

    Not in our library

  19. 19.

    Schindler J., Li A., Zheng M. C., Ellis F. M. & Kottos T. Experimental study of active LRC circuits with PT symmetries. Phys. Rev. A 84, 040101 (2011 ).

    Not in our library

  20. 20.

    Regensburger A.. Parity-time synthetic photonic lattices. Nature 488, 167–171 (2012 ).

    Not in our library10.1038/nature11298

  21. 21.

    Feng L.. Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies. Nat. Mater. 12, 108–113 (2013 ).

    Not in our library10.1038/nmat3495

  22. 22.

    Peng B.. Parity-time-symmetric whispering-gallery microcavities. Nat. Phys 10, 394–398 (2014 ).

    Not in our library

  23. 23.

    Sun Y., Tan W., Li H., Li J. & Chen H. Experimental demonstration of a coherent perfect absorber with PT phase transition. Phys. Rev. Lett. 112, 143903 (2014 ).

    Not in our library10.1103/physrevlett.112.143903

  24. 24.

    Ambichl P.. Breaking of PT-symmetry in bounded and unbounded scattering systems. Phys. Rev. X 3, 41030 (2013 ).

    Not in our library

  25. 25.

    Persson E., Rotter I., Stöckmann H. J. & Barth M. Observation of resonance trapping in an open microwave cavity. Phys. Rev. Lett. 85, 2478–2481 (2000 ).

    Not in our library10.1103/physrevlett.85.2478

  26. 26.

    Wenzel H., Bandelow U., Wunsche H.-J. & Rehberg J. Mechanisms of fast self pulsations in two-section DFB lasers. IEEE J. Quantum Electron. 32, 69–78 (1996 ).

    Not in our library

  27. 27.

    Berry M. V. Mode degeneracies and the petermann excess-noise factor for unstable lasers. J. Mod. Opt. 50, 63–81 (2003 ).

    Not in our library

  28. 28.

    Liertzer M.. Pump-induced exceptional points in lasers. Phys. Rev. Lett. 108, 173901 (2012 ).

    Not in our library10.1103/physrevlett.108.173901

  29. 29.

    Türeci H. E., Ge L., Rotter S. & Stone A. D. Strong interactions in multimode random lasers. Science 320, 643–646 (2008 ).

    Not in our library10.1126/science.1155311

  30. 30.

    Fasching G.. Electrically controllable photonic molecule laser. Opt. Express 17, 20321–20326 (2009 ).

    Not in our library10.1364/oe.17.020321

  31. 31.

    Vahala K. Optical Microcavities World Scientific (2004 ).

    Not in our library

  32. 32.

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

    Not in our library10.1126/science.264.5158.553

  33. 33.

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

    Not in our library10.1038/417156a

  34. 34.

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

    Not in our library10.1038/nature06208

  35. 35.

    Chitsazi M.. Experimental observation of lasing shutdown via asymmetric gain. Phys. Rev. A 89, 043842 (2014 ).

    Not in our library

  36. 36.

    Mujagić E.. Two-dimensional broadband distributed-feedback quantum cascade laser arrays. Appl. Phys. Lett. 98, 141101 (2011 ).

    Not in our library

  37. 37.

    Wanke M. C.. Monolithically integrated solid-state terahertz transceivers. Nat. Photonics 4, 565–569 (2010 ).

    Not in our library

  38. 38.

    Benz A.. Terahertz active photonic crystals for condensed gas sensing. Sensors 11, 6003–6014 (2011 ).

    Not in our library10.3390/s110606003

  39. 39.

    Hugi A., Villares G., Blaser S., Liu H. C. & Faist J. Mid-infrared frequency comb based on a quantum cascade laser. Nature 492, 229–233 (2012 ).

    Not in our library10.1038/nature11620

  40. 40.

    Schwarz B.. Monolithically integrated mid-infrared quantum cascade laser and detector. Sensors 13, 2196–2205 (2013 ).

    Not in our library10.3390/sl30202196

  41. 41.

    Zhu J.. On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator. Nat. Photonics 4, 46–49 (2010 ).

    Not in our library

  42. 42.

    Gmachl C.. High-power directional emission from microlasers with chaotic resonators. Science 280, 1556–1564 (1998 ).

    Not in our library10.1126/science.280.5369.1556

  43. 43.

    Walther C., Scalari G., Amanti M. I., Beck M. & Faist J. Microcavity laser oscillating in a circuit-based resonator. Science 327, 1495–1497 (2010 ).

    Not in our library10.1126/science.1183167

  44. 44.

    Luo H.. Terahertz quantum-cascade lasers based on a three-well active module. Appl. Phys. Lett. 90, 041112 (2007 ).

    Not in our library

  45. 45.

    Williams B. S., Kumar S., Callebaut H., Hu Q. & Reno J. L. Terahertz quantum-cascade laser at λ≈100 μm using metal waveguide for mode confinement. Appl. Phys. Lett. 83, 2124 (2003 ).

    Not in our library

  46. 46.

    NGSolve Finite Element Library. at http://sourceforge.net/projects/ngsolve/.

    Not in our library

  47. 47.

    Ordal M. A.. Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared. Appl. Opt. 22, 1099–1119 (1983 ).

    Not in our library10.1364/ao.22.001099

  48. 48.

    Wiersig J. Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities. Phys. Rev. Lett. 97, 253901 (2006 ).

    Not in our library10.1103/physrevlett.97.253901

  49. 49.

    Benyoucef M., Shim J.-B., Wiersig J. & Schmidt O. G. Quality-factor enhancement of supermodes in coupled microdisks. Opt. Lett. 36, 1317–1319 (2011 ).

    Not in our library10.1364/ol.36.001317

Cited by papers we hold 3

Reads

Read by people on this page

None yet.

Checked or read by AI through naulon

None yet.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.

Are you an author?

Is this your paper?

Claim it to add your note and be paid when agents cite it. Free.