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Transverse patterns and length-scale selection in vertical-cavity surface-emitting lasers with a large square aperture

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Abstract

The length-scale selection in complex emission patterns spontaneously arising in broad-area vertical-cavity surface-emitting lasers is studied experimentally. The wavenumbers of individual tilted wave modes show a square-root-like dependence on the detuning between emission frequency and longitudinal cavity resonance, in accordance with theoretical expectations. The absolute values of the wavenumbers are in good qualitative agreement with calculations taking into account the reflection properties of the Bragg reflectors and dispersion.

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References

  1. Chow WW, Choquette KD, Crawford MH, Lear KL, Hadley GR (1997) IEEE J. Quantum Electron. 33:1810

    Article  ADS  Google Scholar 

  2. Willemsen MB, Khalid MUF, von Exter MP, Woerdman JP (1999) Phys. Rev. Lett. 82:4815

    Article  ADS  Google Scholar 

  3. Wiedenmann D, King R, Jung C, Jäger R, Michalzik R, Schnitzer P, Kicherer M, Ebeling KJ (1999) IEEE J. Sel. Top. Quantum Electron. 5:503

    Article  Google Scholar 

  4. Grabherr M, Miller M, Jäger R, Michalzik R, Martin U, Unold HJ, Ebeling KJ (1999) IEEE J. Sel. Top. Quantum Electron. 5:495

    Article  Google Scholar 

  5. Morgan RA, Kojima K, Mullally T, Guth GD, Focht MW, Leibenguth RE, Asom MT (1992) Appl. Phys. Lett. 61:1160

    Article  ADS  Google Scholar 

  6. Li H, Lucas TL, McInerney JG, Morgan RA (1994) Chaos Soliton. Fract. 4:1619

    Article  Google Scholar 

  7. Hegarty S, Huyet G, McInerney JG, Choquette KD (1999) Phys. Rev. Lett. 82:1434

    Article  ADS  Google Scholar 

  8. Hegarty S, Huyet G, Porta P, McInerney JG, Choquette KD, Geib KM, Hou HQ (1999) J. Opt. Soc. Am. B 16:2060

    ADS  Google Scholar 

  9. Huang KF, Chen YF, Lai HC, Lan YP (2002) Phys. Rev. Lett. 89:224102

    Article  PubMed  ADS  Google Scholar 

  10. Chen YF, Huang KF, Lai HC, Lan YP (2003) Phys. Rev. Lett. 90:053904

    Article  PubMed  ADS  Google Scholar 

  11. Lugiato LA, Lefever R (1987) Phys. Rev. Lett. 58:2209

    Article  PubMed  ADS  Google Scholar 

  12. Tlidi M, Georgiou M, Mandel P (1993) Phys. Rev. A 48:4605

    Article  PubMed  ADS  Google Scholar 

  13. Jakobsen PK, Moloney JV, Newell AC, Indik R (1992) Phys. Rev. A 45:8129

    Article  PubMed  ADS  Google Scholar 

  14. Firth WJ, Scroggie AJ (1994) Europhys. Lett. 26:521

    Article  ADS  Google Scholar 

  15. Lega J, Moloney J, Newell A (1994) Phys. Rev. Lett. 73:2978

    Article  PubMed  ADS  Google Scholar 

  16. Cross MC, Hohenberg PC (1993) Rev. Mod. Phys. 65:851

    Article  ADS  Google Scholar 

  17. Loiko NA, Babushkin IV (2001) J. Opt. B: Quantum S. O. 3:S234

    Article  Google Scholar 

  18. Ackemann T, Barland S, Tredicce JR, Cara M, Balle S, Jäger R, Grabherr PM, Miller M, Ebeling KJ (2000) Opt. Lett. 25:814

    Article  ADS  Google Scholar 

  19. Bortolozzo U, Villoresi P, Ramazza PL (2001) Phys. Rev. Lett. 87:274102

    Article  PubMed  ADS  Google Scholar 

  20. Esteban-Martin A, Garcia J, Roldán E, Taranenko VB, de Valcárcel GJ, Weiss CO (2004) Phys. Rev. A 69:033816

    Article  ADS  Google Scholar 

  21. von Exter MP, von Doorn AKJ, Woerdman JP (1997) Phys. Rev. A 56:845

    Article  ADS  Google Scholar 

  22. Hess O (1998) Opt. Express 2:424

    Article  ADS  Google Scholar 

  23. Rössler T, Indik RA, Harkness GK, Moloney JV (1998) Phys. Rev. A 58:3279

    Article  ADS  Google Scholar 

  24. Fischer I, Hess O, Elsäßer W, Göbel E (1997) Europhys. Lett. 35:579

    Article  ADS  Google Scholar 

  25. Barchanski A, Gensty T, Degen C, Fischer I, Elsäßer W (2003) IEEE J. Quantum Electron. 39:850

    Article  ADS  Google Scholar 

  26. Ning L, Hu Y, Ecke RE, Ahlers G (1993) Phys. Rev. Lett. 71:2216

    Article  PubMed  ADS  Google Scholar 

  27. Gluckman BJ, Marq P, Bridger J, Gollub JP (1993) Phys. Rev. Lett. 71:2034

    Article  PubMed  ADS  Google Scholar 

  28. Farjas J, Hennequin D, Dangoisse D, Glorieux P (1998) Phys. Rev. A 57:580

    Article  ADS  Google Scholar 

  29. Siegman AE (1986) Lasers. University Science Books, Mill Valley, CA

    Google Scholar 

  30. Ackemann T, Grosse-Nobis W, Lippi GL (2001) Opt. Commun. 189:5

    Article  ADS  Google Scholar 

  31. Newell AC, Moloney JV (1992) Nonlinear Optics. Addison-Wesley, Redwood City, CA

    Google Scholar 

  32. Hadley GR (1995) Opt. Lett. 20:1483

    Article  ADS  Google Scholar 

  33. Coldren LA, Corzine SW (1995) Diode Lasers and Photonic Integrated Circuits. Wiley, New York

    Google Scholar 

  34. Debernardi P (2001) Phys. Rev. A 63:1

    Article  Google Scholar 

  35. Debernardi P, Bava GP, Degen C, Fischer I, Elsäßer W (2002) IEEE J. Quantum Electron. 38:73

    Article  ADS  Google Scholar 

  36. K.F. Huang, personal communication (2004)

  37. E.F. Schubert, http://www.rpi.edu/simschubert/Educational%20resources/Materials%20-%20refractive%20index%20and%20extinction%20coefficient.pdf

  38. Adachi S (1985) J. Appl. Phys. 58:R1

    Article  ADS  Google Scholar 

  39. J.V. Moloney, personal communication (2001)

  40. Babic DI, Chung Y, Dagli N, Bowers JE (1993) IEEE J. Quantum Electron. 29:1950

    Article  ADS  Google Scholar 

  41. Babic DI, Corzine SW (1992) IEEE J. Quantum Electron. 28:514

    Article  ADS  Google Scholar 

  42. K.J. Ebeling, in Semiconductor Quantum Optoelectronics: From Quantum Physics to Smart Devices, ed. by Miller A, Ebrahimzadeh M, Finlayson DM (SUSSP Publications and Institute of Physics Publishing, Bristol, 1999), pp 295–338

    Google Scholar 

  43. D’Alessandro G, Firth WJ (1991) Phys. Rev. Lett. 66:2597

    Article  PubMed  ADS  Google Scholar 

  44. Ackemann T, Lange W (2001) Appl. Phys. B 72:21

    ADS  Google Scholar 

  45. Firth WJ, Pare C (1990) Opt. Lett. 13:1096

    ADS  Google Scholar 

Download references

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Correspondence to T. Ackemann.

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PACS

42.60.Jf; 42.65.Sf; 42.55.Sa; 42.55.Px

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Schulz-Ruhtenberg, M., Babushkin, I., Loiko, N. et al. Transverse patterns and length-scale selection in vertical-cavity surface-emitting lasers with a large square aperture. Appl. Phys. B 81, 945–953 (2005). https://doi.org/10.1007/s00340-005-2012-1

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  • DOI: https://doi.org/10.1007/s00340-005-2012-1

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