Abstract
Except for narrow-stripe edge-emitting semiconductor lasers, various types of laser structures have been proposed. They are proposed to compensate insufficient characteristics of narrow-stripe edge-emitting semiconductor lasers, however, those new types of devices intrinsically have unstable features even in their solitary oscillations. Also, the instability is greatly enhanced by the introduction of optical feedback and optical injection. We derive the rate equations for each semiconductor laser with a new structure and discuss its dynamic properties.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Acachihara H, Hess O, Abraham E (1993) Spatiotemporal chaos in broad-area semiconductor lasers. J Opt Soc Am B 10:658–665
Agrawal GP, Dutta NK (1993) Semiconductor lasers. Van Nostrand Reinhold, New York
Ahamed M, Yamada M (2002) Influence of instantaneous mode competition on the dynamics of semiconductor lasers. IEEE J Quantum Electron 38:682–693
Altés JB, Gatare I, Panajotov K, Thienpont H, Sciamanna M (2006) Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers. IEEE J Quantum Electron 42:198–207
Aoyama H, Tomida S, Shogenji R, Ohtsubo J (2011) Chaos dynamics in vertical-cavity surface-emitting semiconductor lasers with polarization-selected optical feedback. Opt Commun 284:1405–1411
Arteaga MA, Unold HJ, Ostermann JM, Michalzik R, Thienpont H, Panajotov K (2006) Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity—part II: experiments. IEEE J Quantum Electron 42:102–107
Asatuma T, Takiguchi Y, Frederico S, Furukawa A, Hirata S (2006) Successive phase change and stability of near-field patterns for broad-area laser diodes. SPIE Proc 6104:61040C
Barchanski A, Gensty T, Degen C, Fischer I, Elsäßer W (2003) Picosecond emission dynamics of vertical-cavity surface-emitting lasers: spatial, spectral, and polarization-resolved characterization. IEEE J Quantum Electron 39:850–858
Besnard P, Robert F, Charès ML, Stéphan GM (1997) Theoretical modeling of vertical-cavity surface-emitting lasers with polarized optical feedback. Phys Rev A 56:3191–3205
Besnard P, Charès ML, Stéphan G, Robert F (1999) Switching between polarized modes of a vertical-cavity surface-emitting laser by isotropic optical feedback. J Opt Soc Am B 16:1059–1064
Burkhard T, Ziegler MO, Fischer I, Elsäßer W (1999) Spatio-temporal dynamics of broad area semiconductor lasers and its characterization. Chaos, Solitons and Fractals 10:845–850
Carr TW, Erneux T (2001) Dimensionless rate equations and simple conditions for self-pulsing in laser diodes. IEEE J Quantum Electron 37:1171–1177
Danckaerta J, Naglera B, Alberta J, Panajotova K, Veretennicoff I, Erneux T (2002) Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers. Opt Commun 201:129–137
Degen C, Fischer I, Elsäßer W (1999) Transverse modes in oxide confined VCSELs: influence of pump profile, spatial hole burning, and thermal effects. Opt Express 5:38–47
Diehl R (2000) High-power diode laser, fundamentals, technology, applications. Springer-Verlarg, Berlin
Donovan K, Harrison P, Kelsall RW (2001) Self-consistent solutions to the intersubband rate equations in quantum cascade lasers: analysis of a GaAs/Al\(_{x}\)Ga\(_{1-x}\)As device. J Appl Phys 89:3084–3090
Erneux T, Viktorov EA, Mandel P (2007) Time scales and relaxation dynamics in quantum-dot lasers. Phys Rev A 76:023819-1–7
Erneux T, Viktorov EA, Kelleher B, Goulding D, Hegarty SP, Huyet G (2010) Optically injected quantum-dot lasers. Opt Lett 35: 937–939
Faist J, Capasso F, Sivco DL, Sirtori C, Hutchinson AL, Cho AY (1994) Quantum cascade laser. Science 264:553–556
Fischer I, Hess O, Elsäßer W, Göbel E (1996) Complex spatio-temporal dynamics in the near-field of broad-area semiconductor laser. EuroPhys Lett 35:579–584
Fujiwara N, Ohtsubo J (2004) Synchronization in chaotic vertical-cavity surface-emitting semiconductor lasers. SPIE Proc 5349:282–289
Fujiwara N, Takiguchi Y, Ohtsubo J (2003) Observation of low-frequency fluctuations in vertical-cavity surface-emitting lasers. Opt Lett 28:896–898
Fukushima T (2000) Analysis of resonator eigenmodes in symmetric quasistadium laser laser diodes. J Lightwave Technol 18:2208–2216
Fukushima T, Miyazaki H, Ando T, Tanaka T, Sakamoto T (2002) Nonlinear dynamics in directly modulated self-pulsating laser diodes with a highly doped saturable absorption layer. Jpn J Appl Phys 41 Part 1:117–124
Gaciu N, Gehrig E, Hess O (2007) Control of broad-area laser dynamics with delayed optical feedback. In: Schöll E, Schuster G (eds) Handbook of chaos control, Chap. 22. Wiley-VCH, Weinheim
Gatare I, Sciamanna M, Buesa J, Thienpont H, Panajotov K (2006) Nonlinear dynamics accompanying polarization switching in vertical-cavity surface-emitting lasers with orthogonal optical injection. Appl Phys Lett 88:101106-1–3
Gehrig E, Hess O (2003) Spatio-temporal dynamics and quantum fluctuations in semiconductor lasers. Springer-Verlag, Heidelberg
Gensty T, Elsäßer W (2005) Semiclassical model for the relative intensity noise of intersubband quantum cascade lasers. Opt Commun 256:171–183
Giudici M, Balle S, Ackemann T, Barland S, Tredicce JR (1999) Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model. J Opt Soc Am B 16:2114–2123
Gmachl C, Capasso F, Sivco DL, Cho AY (2001) Recent progress in quantum cascade lasers and applications. Rep Prog Phys 64:1533–1601
Goulding D, Hegarty SP, Rasskazov O, Melnik S, Hartnett M, Greene G, McInerney JG, Rachinskii D, Huyet1 G (2007) Excitability in a quantum dot semiconductor laser with optical injection. Phys Rev Lett 98:153903-1–4
Green RP, Xu JH, Mahler L, Tredicucci A, Beltram F, Giuliani G, Beere HE, Ritchie DA (2008) Linewidth enhancement factor of terahertz quantum cascade lasers. Appl Phys Lett 92:071106-1–071106-3
Grillot F, Veselinov K, Gioannini M, Montrosset I, Even J, Piron R, Homeyer E, Loualiche S (2009) Spectral analysis of 1.55-\(\mu \)m InAs-InP(113)B quantum-dot lasers based on a multipopulation rate equations model. IEEE J Quantum Electron 45:872–878
Haldar MK (2005) A simplified analysis of direct intensity modulation of quantum cascade lasers. IEEE J Quantum Electron 41:1349–1355
Hess O, Kuhn T (1996a) Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers I theoretical formulation. Phys Rev A 54:3347–3359
Hess O, Kuhn T (1996b) Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers II spatiotemporal dynamics. Phys Rev A 54:3360–3368
Hess O, Koch SW, Moloney JV (1995) Filamentation and beam propagation in broad-area semiconductor lasers. IEEE J Quantum Electron 31:35–43
Hodgson N, Weber H (1997) Optical resonators. Springer, London
Hong Y, Spencer PS, Shore KA (2004) Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback. Opt Lett 29:2151–2153
Hong Y, Ju R, Spencer PS, Shore KA (2005) Investigation of polarization bistability in vertical-cavity surface-emitting laser subjected to optical feedback. IEEE J Quantum Electron 41:619–624
Hugi A, Maulini R, Faist J (2010) External cavity quantum cascade laser. Semicond Sci Technol 25:083001-1–14
Hülsewede R, Sebastian J, Wenzel H, Beister G, Kanauer A, Erbert G (2001) Beam quality of high power 800 nm broad-area laser diodes with 1 and 2 mm large optical cavity structure. Opt Commun 192:69–75
Hurtado A, Quirce A, Valle A, Pesquera L, Adams MJ (2010) Nonlinear dynamics induced by parallel and orthogonal optical injection in 1550 nm vertical-cavity surface-emitting lasers (VCSELs). Opt Express 18:9423–9428
Huyet G, O’Brien D, Hegarty SP, McInerney JG, Uskov AV, Bimberg D, Ribbat C, Ustinov VM, Zhukov AE, Mikhrin SS, Kovsh AR, White JK, Hinzer K, SpringThorpe AJ (2004) Quantum dot semiconductor lasers with optical feedback. Phys Stat Sol (a) 201:345–352
Ikuma Y, Ohtsubo J (1998) Dynamics in a compound cavity semiconductor laser induced by small external-cavity-length change. IEEE J Quantum Electron 34:1240–1246
Jiang S, Pan Z, Dagenais M, Morgan RA, Kojima K (1993) High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers. Appl Phys Lett 63:3545–3547
Jones RJ, Rees P, Spencer PS, Shore KA (2001) Chaos and synchronization of self-pulsating laser diodes. J Opt Soc Am B 18:166–172
Juang C, Chen MR, Juang J (1999) Nonlinear dynamics of self-pulsating laser diodes under external drive. Opt Lett 24:1346–1348
Juang C, Hwang TM, Juang J, Lin WW (2000) A synchronization scheme using self-pulsating laser diodes in optical chaotic communication. IEEE J Quantum Electron 36:300–304
Kuznetsov M, Tsang DZ, Walpole JN, Liau ZL, Ippen EP (1986) Chaotic pulsation of semiconductor lasers with proton-bombarded segment. In: Boyd RW, Raymer MG, Narducci LM (eds) Optical instabilities, Vol. 4. Cambridge University Press, Cambridge
Law JY, Agrawal GP (1997a) Effects of spatial hole burning on gain switching in vertical-cavity surface-emitting lasers. IEEE J Quantum Electron 33:462–468
Law JY, Agrawal GP (1997b) Mode-partition noise in vertical-cavity surface-emitting lasers. IEEE Photon Technol Lett 9:437–439
Law JY, Agrawal GP (1998) Feedback-induced chaos and intensity-noise enhancement in vertical-cavity surface-emitting lasers. J Opt Soc Am B 15:562–569
Levy G, Hardy AA (1997) Chaotic effects in flared lasers: a numerical analysis. IEEE J Quantum Electron 33:26–32
Li H, Iga K (2002) Vertical-cavity surface-emitting laser devices. Springer, Berlin
Li H, Lucas TL, McInerney JG, Wright MW, Morgan RA (1996) Injection locking dynamics of vertical cavity semiconductor lasers using conventional and phase conjugate injection. IEEE J Quantum Electron 32:22–235
Lim YL, Dean P, Nikolić M, Kliese R, Khanna SP, Lachab M, Valavanis A, Indjin D, Ikonić Z, Harrison P, Linfield EH, Davies AG, Wilson SJ, Rakić AD (2011) Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers. Appl Phys Lett 99:081108-1–3
Lüdge K (2011) Modeling quantum dot based laser devices. In: Lüdge K (ed) Nonlinear laser dynamics, Chap. 1. Wiley-VCH, Weinheim
Lüdge K, Schöll E (2009) Quantum-dot lasers-desynchronized nonlinear dynamics of electrons and holes. IEEE J Quantum Electron 45:1396–1401
Lüdge K, Bormann MJP, Malić E, Hövel P, Kuntz M, Bimberg D, Knorr A, Schöll E (2008) Turn-on dynamics and modulation response in semiconductor quantum dot lasers. Phys Rev B 78:035316-1–11
Lüdge K, Aust R, Fiol G, Stubenrauch M, Arsenijević D, Bimberg D, Schöll E (2010) Large-signal response of semiconductor quantum-dot lasers. IEEE J Quantum Electron 46:1755–1762
Luo GP, Peng C, Le HQ, Pei SS, Hwang WY, Ishaug B, Um J, Baillargeon JN, Lin CH (2001) Grating-tuned external-cavity quantum-cascade semiconductor lasers. Appl Phys Lett 78:2834–2836
Marciante JR, Agrawal GP (1998) Spatio-temporal characteristics of filamentation in broad-area semiconductor lasers: experimental results. IEEE Photon Technol Lett 10:54–56
Martín-Regalado J, van Tartwijk GHM, Balle S (1996a) Mode control and pattern stabilization in broad-area lasers by optical feedback. Phys Rev A 54:5386–5393
Martín-Regaldo J, Balle S, Abraham NB (1996b) Modeling spatio-temporal dynamics of gain-guided multistripe and broad-area lasers. IEE Proc Optoelectron 143:17–23
Martín-Regalado J, Prati JF, Abraham NB (1997) Polarization properties of vertical-cavity surface-emitting lasers. IEEE J Quantum Electron 33:765–783
Masoller C, Abraham NB (1999a) Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback. Phys Rev A 59:3021–3031
Masoller C, Abraham NB (1999b) Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate. Appl Phys Lett 74:1078–1080
Masoller C, Torre MS, Mandel P (2006) Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers. J Appl Phys 99:026108-1–3
Meng B, Wang QJ (2012) Theoretical investigation of injection-locked high modulation bandwidth quantum cascade lasers. Opt Express 20:1450–1464
Merbach D, Hess O, Herzel H, Schöll E (1995) Injection induced bifurcations of transverse spatiotemporal patterns in semiconductor arrays. Phys Rev E 52:1571–1578
Mirasso CR, van Tartwijk GHM, Hernández-García E, Lenstra D, Lynch S, Landais P, Phelan P, O’Gorman J, Elsäßer W (1999) Self-pulsating semiconductor lasers: theory and experiment. IEEE J Quantum Electron 35:764–770
Mulet J, Balle S (2002) Spatio-temporal modeling of the optical properties of VCSELs in the presence of polarization effects. IEEE J Quantum Electron 38:291–305
Münkel M, Kaiser F, Hess O (1996) Spatio-temporal dynamics of multi-stripe semiconductor lasers with delayed optical feedback. Phys Lett A 222:67–75
Naumenko AV, Loiko NA, Sondermann M, Ackemann T (2003) Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector. Phys Rev A 68:033805-1–16
O’Brien D, Hegarty SP, Huyet G (2004) Sensitivity of quantum-dot semiconductor lasers to optical feedback. Opt Lett 29:1072–1074
Otto C, Lüdge K, Schöll E (2010) Modeling quantum dot lasers with optical feedback: sensitivity of bifurcation scenarios. Phys Stat Sol (b) 247:829–845
Petermann K (1988) Laser diode modulation and noise. Kluwer Academic, Dordrecht
Petitjean Y, Destic F, Mollier JC, Sirtori C (2011) Dynamic modeling of terahertz quantum cascade lasers. IEEE J Select Topics Quantum Electron 17:22–29
Rahman L, Winful H (1994) Nonlinear dynamics of semiconductor arrays: a mean field model. IEEE J Quantum Electron 30:1405–1406
Rana F, Ram RJ (2002) Current noise and photon noise in quantum cascade lasers. Phys Rev B 65:125313-1–26
Ryan A, Agrawal GP, Gray GR, Gage EC (1994) Optical feedback-induced chaos and its control in multimode semiconductor lasers. IEEE J Quantum Electron 30:668–679
Ryvkinn BS, Panajotov K, Avrutin EA, Veretennicoff I, Thienpont H (2004) Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers. J Appl Phys 96:6002–6007
San Miguel M, Feng Q, Moloney JV (1995) Light polarization dynamics in surface-emitting semiconductor lasers. Phys Rev A 52:1729–1740
Scalari G, Walther C, Fischer M, Terazzi R, Beere H, Ritchie D, Faist J (2009) THz and sub-THz quantum cascade lasers. Laser Photon Rev 3: 45–66
Scholz D, Braun H, Schwarz UT, Brüninghoff S, Queren D, Lell A, Strauss U (2008) Measurement and simulation of filamentation in (Al, In)GaN laser diodes. Opt Express 16:6846–6859
Sciamanna M, Panajotov K (2005) Two-mode injection locking in vertical-cavity surface-emitting lasers. Opt Lett 30:2903–2905
Sciamanna M, Panajotov K (2006) Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers. Phys Rev A 73:023811-1–17
Sciamanna M, Erneux T, Rogister F, Deparis O, Mégret P, Blondel M (2002a) Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers. Phys Rev A 65:041801-1–4
Sciamanna M, Rogister F, Deparis O, Mégret P, Blondel M, Erneux T (2002b) Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers. Opt Lett 27:261–263
Sciamanna M, Masoller C, Abraham NB, Rogister F, Mégret P, Blondel M (2003a) Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers. J Opt Soc Am B 20:37–39
Sciamanna M, Masoller C, Rogister F, Mégret P, Abraham NB, Blondel M (2003b) Fast pulsing dynamics of a vertical-cavity surface-emitting laser operating in the low-frequency fluctuation regime. Phys Rev A68:015805-1–4
Sciamanna M, Valle A, Mégret P, Blondel M, Panajotov K (2003c) Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers. Phys Rev E 68:016207-1–4
Shoji H, Nakata Y, Mukai K, Sugiyama Y, Sugawara M, Yokoyama N, Ishikawa H (1997) Lasing characteristics of self-formed quantum-dot lasers with multistacked dot layer. IEEE J Selct Topics Quantum Electron 3:188–195
Simmendinger C, Preißer D, Hess O (1999) Stabilization of chaotic spatiotemporal filamentation in large broad area lasers by spatially structured optical feedback. Opt Express 5:48–54
Sondermann M, Bohnet H, Ackemann T (2003) Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback. Phys Rev A 67:021802-1–4
Sugawara M (1999) Self-assembled InGaAs/GaAs quantum dots. Academic Press, San Diego
Tabaka A, Peil M, Sciamanna M, Fischer I, Elsäßer W, Thienpont H, Veretennicoff I, Panajotov K (2006) Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: pulse packages and polarization mode competition. Phys Rev A 73:013810-1–14
Tachikawa T, Takimoto S, Shogenji R, Ohtsubo J (2010) Dynamics of broad-area semiconductor lasers with short optical feedback. IEEE J Quantum Electron 46:140–149
Takiguchi Y, Asatsuma T, Hirata S (2006) Effect of the threshold reduction on a catastrophic optical mirror damage in broad-area semiconductor lasers with optical feedback. SPIE Proc 6104:61040X
Takimoto S, Tachikawa T, Shogenji R, Ohtsubo J (2009) Control of spatio-temporal dynamics of broad-area semiconductor lasers by strong optical injection. IEEE Photon Technol Lett 21:1051–1053
Tang X, van der Ziel JP, Chang B, Johnson R, Tatum JA (1997) Observation of bistability in GaAs quantum-well vertical-cavity surface-emitting lasers. IEEE J Quantum Electron 33:927–932
Totschnig G, Winter F, Pustogov V, Faist J, Müller A (2002) Mid-infrared external-cavity quantum-cascade laser. Opt Lett 27:1788–1800
Tronciu VZ, Yamada M, Ohno T, Ito S, Kawakami T, Taneya M (2003) Self-pulsation in an InGaN laser—theory and experiment. IEEE J Quantum Electron 39:1509–1514
Valle A, Gatare I, Panajotov K, Sciamanna M (2007) Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection. IEEE J Quantum Electron 43:322–333
Valle A, Sarma J, Shore KA (1995a) Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes. IEEE J Quantum Electron 31:1423–1431
Valle A, Sarma J, Shore KA (1995b) Dynamics of transverse competition in vertical cavity surface emitting laser diodes. Opt Commun 115:297–302
van Tartwijk GHM, San Miguel M (1996) Optical feedback on self-pulsating semiconductor lasers. IEEE J Quantum Electron 32:1191–1202
Viktorov EA, Mandel P, O’Driscoll I, Carroll O, Huyet G, Houlihan J, Tanguy Y (2006) Low-frequency fluctuations in two-state quantum dot lasers. Opt Lett 31:2302–2304
Von Lehmen AC, Florez LT, Stoffel NG (1991) Dynamics, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers. IEEE J Quantum Electron 27:1402–1409
von Staden J, Gensty T, Elsäßer W, Giuliani G, Mann C (2006) Measurements of the \(\alpha \) factor of a distributed-feedback quantum cascade laser by an optical feedback self-mixing technique. Opt Lett 31:2574–2576
Winful HG (1992) Instability threshold for an array of coupled semiconductor lasers. Phys Rev A 46:6093–6094
Winful HG, Chen YC, Liu JM (1986) Frequency locking, quasiperiodicity, and chaos in modulated self-pulsating semiconductor lasers. Appl Phys Lett 48:616–618
Winful HG, Rahman L (1990) Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers. Phys Rev Lett 65:1575–1578
Wójcika AK, Belyanin A, Yu N, Diehl L, Capasso F (2010) Nonlinear coupling of transverse modes in quantum cascade lasers. Opt Eng 49:111114-1–10
Wójcik AK, Yu N, Capasso F, Belyanin A (2011a) Nonlinear optical interactions of laser modes in quantum cascade lasers. J Modern Opt 58:727–742
Wójcika AK, Yu N, Diehl L, Capasso F, Belyanin A (2011b) Self-synchronization of laser modes and multistability in quantum cascade lasers. Phys Rev Lett 106:133902-1–4
Yamada M (1993) A theoretical analysis of self-sustained pulsation phenomena in narrow-stripe semiconductor lasers. IEEE J Quantum Electron 29:1330–1336
Yamada M (1996) Theoretical analysis of noise-reduction effects in semiconductor lasers with help of self-sustained pulsation phenomena. J Appl Phys 79:61–71
Yamada M (1998a) Computer simulation of feedback induced noise in semiconductor lasers operating with self-sustained pulsation. IEICE Trans Electron E81-C:768–780
Yamada M (1998b) A theoretical analysis of quantum noise in semiconductor leasers operating with self-sustained pulsation. IEICE Trans Electron E81-C:290–298
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ohtsubo, J. (2013). Instability and Chaos in Various Laser Structures. In: Semiconductor Lasers. Springer Series in Optical Sciences, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30147-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-30147-6_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30146-9
Online ISBN: 978-3-642-30147-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)