Averaged equations for injection locked semiconductor lasers
An averaging method valid for strongly nonlinear oscillators is used for the first time to describe the pulsating intensity regimes of semiconductor lasers subject to injection. Slow-time equations are derived which are valid for solutions of arbitrary amplitude. These averaged equations do not requ...
Saved in:
| Published in | Physica. D Vol. 161; no. 3; pp. 220 - 236 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
15.01.2002
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0167-2789 1872-8022 |
| DOI | 10.1016/S0167-2789(01)00375-X |
Cover
| Abstract | An averaging method valid for strongly nonlinear oscillators is used for the first time to describe the pulsating intensity regimes of semiconductor lasers subject to injection. Slow-time equations are derived which are valid for solutions of arbitrary amplitude. These averaged equations do not require the knowledge of a particular bifurcation point and are a good starting point for further analysis. Bifurcation points to periodic or quasiperiodic intensity oscillations are determined analytically by exploring certain limits of the parameters. Finally, we illustrate the strength and weakness of these expressions by comparing bifurcation diagrams obtained from the averaged equations and from the original laser equations. |
|---|---|
| AbstractList | An averaging method valid for strongly nonlinear oscillators is used for the first time to describe the pulsating intensity regimes of semiconductor lasers subject to injection. Slow-time equations are derived which are valid for solutions of arbitrary amplitude. These averaged equations do not require the knowledge of a particular bifurcation point and are a good starting point for further analysis. Bifurcation points to periodic or quasiperiodic intensity oscillations are determined analytically by exploring certain limits of the parameters. Finally, we illustrate the strength and weakness of these expressions by comparing bifurcation diagrams obtained from the averaged equations and from the original laser equations. |
| Author | Erneux, Thomas Nizette, Michel Kovanis, Vassilios Gavrielides, Athanasios |
| Author_xml | – sequence: 1 givenname: Michel surname: Nizette fullname: Nizette, Michel organization: Optique Nonlinéaire Théorique, Université Libre de Bruxelles, Bld. du Triomphe, Campus Plaine, C.P. 231, 1050 Bruxelles, Belgium – sequence: 2 givenname: Thomas surname: Erneux fullname: Erneux, Thomas email: terneux@ulb.ac.be organization: Optique Nonlinéaire Théorique, Université Libre de Bruxelles, Bld. du Triomphe, Campus Plaine, C.P. 231, 1050 Bruxelles, Belgium – sequence: 3 givenname: Athanasios surname: Gavrielides fullname: Gavrielides, Athanasios organization: Nonlinear Optics Group, Air Force Research Laboratory, 3550 Aberdeen Ave. SE, Kirtland AFB, Albuquerque, NM, 87117-5776, USA – sequence: 4 givenname: Vassilios surname: Kovanis fullname: Kovanis, Vassilios organization: Nonlinear Optics Group, Air Force Research Laboratory, 3550 Aberdeen Ave. SE, Kirtland AFB, Albuquerque, NM, 87117-5776, USA |
| BookMark | eNqFkM1LAzEQxYMo2Fb_BGGPelidfOwmRUFK8QsKHlToLWSTWUndbjTZFvzv3bbiwUsvMwxv3oP3G5LDNrRIyBmFSwq0vHrph8yZVONzoBcAXBb5_IAMqJIsV8DYIRn8vRyTYUoLAKCSywG5mawxmnd0GX6tTOdDm7I6xMy3C7SbM2uC_ejlhEtvQ-tWtuvlxiSM6YQc1aZJePq7R-Tt_u51-pjPnh-eppNZbjnILreFGQuuqoJbCVWtmCqVU4yOK1VUjgsFlAshHK-oAldWZcksLznWwgqD1vERKXa5NoaUItb6M_qlid-agt4g0FsEetNPA9VbBHre-67_-azvtiW7aHyz1327c2Nfbe0x6mQ9thadjz0b7YLfk_ADGO54UA |
| CitedBy_id | crossref_primary_10_1103_PhysRevLett_115_203901 crossref_primary_10_1016_j_physrep_2005_06_003 crossref_primary_10_1088_0951_7715_18_3_010 crossref_primary_10_1109_JQE_2012_2222869 crossref_primary_10_1016_S0030_4018_02_02191_0 crossref_primary_10_1016_S0167_2789_02_00650_4 crossref_primary_10_1109_JSTQE_2021_3075645 |
| Cites_doi | 10.1103/PhysRevA.41.6470 10.1063/1.114591 10.1109/JQE.1985.1072760 10.1103/PhysRevA.47.736 10.1063/1.1397757 10.1016/0030-4018(94)90157-0 10.1016/S0030-4018(99)00603-3 10.1109/3.736105 10.1007/BF01325388 10.1109/3.89994 10.1016/S0030-4018(98)00584-7 10.1109/3.108 10.1063/1.111218 10.1007/978-1-4612-3968-0 10.1117/12.164762 10.1016/S0167-2789(97)00070-5 10.1137/0151058 10.1088/1355-5111/7/2/003 10.1103/PhysRevA.51.4181 10.1088/1355-5111/8/4/004 10.1007/978-1-4757-4213-8 10.1364/JOSAB.2.000173 10.1109/3.481870 10.1103/PhysRevE.58.4421 10.1109/68.623251 10.1109/3.511559 10.1117/12.356927 10.1088/1355-5111/9/5/009 10.1016/S0030-4018(96)00705-5 10.1142/S0218127401003693 10.1109/JQE.1982.1071632 10.1088/1355-5111/9/5/011 10.1016/S0030-4018(98)00434-9 10.1016/S0030-4018(00)00867-1 10.1103/PhysRevA.53.4372 |
| ContentType | Journal Article |
| Copyright | 2002 Elsevier Science B.V. |
| Copyright_xml | – notice: 2002 Elsevier Science B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/S0167-2789(01)00375-X |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Physics |
| EISSN | 1872-8022 |
| EndPage | 236 |
| ExternalDocumentID | 10_1016_S0167_2789_01_00375_X S016727890100375X |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 29O 4.4 457 4G. 5VS 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABFNM ABMAC ABNEU ABXDB ABYKQ ACAZW ACDAQ ACFVG ACGFS ACNCT ACNNM ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD AEBSH AEKER AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AIVDX AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BBWZM BKOJK BLXMC EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q GBLVA HMV HVGLF HZ~ H~9 IHE J1W K-O KOM M38 M41 MHUIS MO0 MVM N9A NDZJH O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SPD SPG SSQ SSW SSZ T5K TN5 TWZ WUQ XJT XPP YNT YYP ~02 ~G- AATTM AAXKI AAYWO AAYXX ABWVN ACRPL ADNMO ADVLN AEIPS AFJKZ AFXIZ AGCQF AGQPQ AGRNS AIIUN ANKPU APXCP BNPGV CITATION SSH |
| ID | FETCH-LOGICAL-c307t-c5a9438b53c70bf82868d8219b85bd348013444d3b180d6b662c363ef4c4aecd3 |
| IEDL.DBID | .~1 |
| ISSN | 0167-2789 |
| IngestDate | Tue Jul 01 03:25:25 EDT 2025 Thu Apr 24 23:09:23 EDT 2025 Fri Feb 23 02:32:42 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Averaged equations Injection locked semiconductor Hopf and torus bifurcations |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c307t-c5a9438b53c70bf82868d8219b85bd348013444d3b180d6b662c363ef4c4aecd3 |
| PageCount | 17 |
| ParticipantIDs | crossref_primary_10_1016_S0167_2789_01_00375_X crossref_citationtrail_10_1016_S0167_2789_01_00375_X elsevier_sciencedirect_doi_10_1016_S0167_2789_01_00375_X |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2002-01-15 |
| PublicationDateYYYYMMDD | 2002-01-15 |
| PublicationDate_xml | – month: 01 year: 2002 text: 2002-01-15 day: 15 |
| PublicationDecade | 2000 |
| PublicationTitle | Physica. D |
| PublicationYear | 2002 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Petitbon, Gallion, Debarge, Chabran (BIB5) 1988; 24 Bourland, Haberman, Kath (BIB34) 1991; 51 Wieczorek, Krauskopf, Lenstra (BIB24) 2000; 183 Simpson, Liu, Gavrielides, Kovanis, Alsing (BIB14) 1994; 26 Zimmermann, Natiello, Solari (BIB20) 1997; 109 Kovanis, Erneux, Gavrielides (BIB28) 1999; 159 Kovanis, Gavrielides, Simpson, Liu (BIB16) 1995; 67 Braza, Erneux (BIB18) 1989; 41 J. Kevorkian, J.D. Cole, Multiple Scale and Singular Perturbation Methods, Applied Mathematical Sciences, Vol. 114, Springer, New York, 1996. Y. Yamamoto, Coherence, Amplification and Quant. Effects in Semiconductor Lasers, Wiley/Interscience, New York, 1991. Tredicce, Arrechi, Lippi, Puccioni (BIB1) 1985; 2 Oppo, Politi (BIB37) 1985; 59 Wieczorek, Krauskopf, Lenstra (BIB23) 1999; 172 Gavrielides, Kovanis, Erneux (BIB38) 1997; 136 Annovazzi-Lodi, Sciré, Sorel, Donati (BIB12) 1998; 34 M. Nizette, T. Erneux, A. Gavrielides, V. Kovanis, Injection locked semiconductor laser dynamics from large to small detunings, in: P. Blood, A. Ishibashi, M. Osinski (Eds.), Physics and Simulations of Optoelectronic Devices VII, Proc. SPIE 3625 (1999) 679–691. Solari, Oppo (BIB19) 1994; 111 Simpson, Liu, Gavrielides (BIB8) 1996; 32 De Jagher, van der Graaf, Lenstra (BIB36) 1996; 8 Simpson, Liu, Huang, Tai (BIB2) 1997; 9 Krauskopf, van der Graaf, Lenstra (BIB39) 1997; 9 Yeung, Strogatz (BIB25) 1998; 58 S.H. Strogatz, Nonlinear Dynamics and Chaos, Addison-Wesley, New York, 1994. Li, Lukas, McInerney, Wright, Morgan (BIB9) 1996; 32 N.M. Krylov, N.N. Bogoliubov, Introduction to Nonlinear Mechanics, Princeton University Press, Princeton, NJ, 1957. Erneux, Kovanis, Gavrielides, Alsing (BIB27) 1996; 53 Liu, Chen, Meng, Simpson (BIB7) 1997; 9 C. Mayol, M.A. Natiello, M.G. Zimmermann, Resonance structure in a weakly detuned laser with injected signal, Int. J. Bifurcation Chaos 11 (2001) 2587–2605. M.G. Zimmermann, M.A. Natiello, H.G. Solari, Global bifurcations in a laser with injected signal: beyond Adler’s approximation, Chaos 11 (2001) 500–513. Simpson, Lui, Gavrielides, Kovanis, Alsing (BIB15) 1995; 51 Lenstra, van Tartwijk, van der Graaf, De Jagher (BIB11) 1993; 2039 P.G. Drazin, Nonlinear Systems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Oxford, 1992. Lee, Pang, Park, Lee (BIB13) 1993; 47 Hui, D’Ottavi, Mecozzi, Spano (BIB17) 1991; 27 van Tartwijk, Lenstra (BIB10) 1995; 7 Krauskopf, Tollenaar, Lenstra (BIB22) 1998; 156 Mogensen, Olesen, Jacobsen (BIB6) 1985; 21 J. Kevorkian, J.D. Cole, Perturbation Methods in Applied Mathematics, Applied Mathematical Sciences, Vol. 34, Springer, New York, 1981. Lang (BIB4) 1982; 18 Zimmermann (10.1016/S0167-2789(01)00375-X_BIB20) 1997; 109 Erneux (10.1016/S0167-2789(01)00375-X_BIB27) 1996; 53 Oppo (10.1016/S0167-2789(01)00375-X_BIB37) 1985; 59 10.1016/S0167-2789(01)00375-X_BIB3 Petitbon (10.1016/S0167-2789(01)00375-X_BIB5) 1988; 24 Li (10.1016/S0167-2789(01)00375-X_BIB9) 1996; 32 Solari (10.1016/S0167-2789(01)00375-X_BIB19) 1994; 111 Wieczorek (10.1016/S0167-2789(01)00375-X_BIB23) 1999; 172 Lang (10.1016/S0167-2789(01)00375-X_BIB4) 1982; 18 Simpson (10.1016/S0167-2789(01)00375-X_BIB15) 1995; 51 Lee (10.1016/S0167-2789(01)00375-X_BIB13) 1993; 47 10.1016/S0167-2789(01)00375-X_BIB35 Kovanis (10.1016/S0167-2789(01)00375-X_BIB16) 1995; 67 10.1016/S0167-2789(01)00375-X_BIB21 van Tartwijk (10.1016/S0167-2789(01)00375-X_BIB10) 1995; 7 Kovanis (10.1016/S0167-2789(01)00375-X_BIB28) 1999; 159 Mogensen (10.1016/S0167-2789(01)00375-X_BIB6) 1985; 21 Annovazzi-Lodi (10.1016/S0167-2789(01)00375-X_BIB12) 1998; 34 De Jagher (10.1016/S0167-2789(01)00375-X_BIB36) 1996; 8 Simpson (10.1016/S0167-2789(01)00375-X_BIB14) 1994; 26 Tredicce (10.1016/S0167-2789(01)00375-X_BIB1) 1985; 2 Lenstra (10.1016/S0167-2789(01)00375-X_BIB11) 1993; 2039 Simpson (10.1016/S0167-2789(01)00375-X_BIB8) 1996; 32 Liu (10.1016/S0167-2789(01)00375-X_BIB7) 1997; 9 10.1016/S0167-2789(01)00375-X_BIB29 Braza (10.1016/S0167-2789(01)00375-X_BIB18) 1989; 41 Wieczorek (10.1016/S0167-2789(01)00375-X_BIB24) 2000; 183 10.1016/S0167-2789(01)00375-X_BIB26 10.1016/S0167-2789(01)00375-X_BIB32 Krauskopf (10.1016/S0167-2789(01)00375-X_BIB22) 1998; 156 10.1016/S0167-2789(01)00375-X_BIB31 Gavrielides (10.1016/S0167-2789(01)00375-X_BIB38) 1997; 136 Krauskopf (10.1016/S0167-2789(01)00375-X_BIB39) 1997; 9 10.1016/S0167-2789(01)00375-X_BIB33 Yeung (10.1016/S0167-2789(01)00375-X_BIB25) 1998; 58 Hui (10.1016/S0167-2789(01)00375-X_BIB17) 1991; 27 10.1016/S0167-2789(01)00375-X_BIB30 Simpson (10.1016/S0167-2789(01)00375-X_BIB2) 1997; 9 Bourland (10.1016/S0167-2789(01)00375-X_BIB34) 1991; 51 |
| References_xml | – volume: 34 start-page: 2350 year: 1998 end-page: 2357 ident: BIB12 article-title: Dynamic behavior and locking of a semiconductor laser subjected to external injection publication-title: IEEE J. Quant. Electr. – volume: 2 start-page: 173 year: 1985 end-page: 183 ident: BIB1 article-title: Instabilities in lasers with an injected signal publication-title: JOSA B – volume: 156 start-page: 158 year: 1998 end-page: 169 ident: BIB22 article-title: Tori and their bifurcations in an optically injected semiconductor laser publication-title: Opt. Commun. – reference: Y. Yamamoto, Coherence, Amplification and Quant. Effects in Semiconductor Lasers, Wiley/Interscience, New York, 1991. – volume: 9 start-page: 1325 year: 1997 ident: BIB7 article-title: Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking publication-title: IEEE Photon. Technol. Lett. – volume: 59 start-page: 111 year: 1985 end-page: 115 ident: BIB37 article-title: Toda potentials in laser equations publication-title: Z. Phys. B – reference: N.M. Krylov, N.N. Bogoliubov, Introduction to Nonlinear Mechanics, Princeton University Press, Princeton, NJ, 1957. – volume: 58 start-page: 4421 year: 1998 end-page: 4435 ident: BIB25 article-title: Nonlinear dynamics of a solid-state laser with injection publication-title: Phys. Rev. E – volume: 67 start-page: 2780 year: 1995 end-page: 2782 ident: BIB16 article-title: Instabilities and chaos in optically injected semiconductor lasers publication-title: Appl. Phys. Lett. – volume: 21 start-page: 784 year: 1985 end-page: 793 ident: BIB6 article-title: Locking conditions and stability properties for a semiconductor laser with external light injection publication-title: IEEE J. Quant. Electr. – reference: J. Kevorkian, J.D. Cole, Multiple Scale and Singular Perturbation Methods, Applied Mathematical Sciences, Vol. 114, Springer, New York, 1996. – volume: 111 start-page: 173 year: 1994 end-page: 190 ident: BIB19 article-title: Laser with injected signal: perturbation of an invariant circle publication-title: Opt. Commun. – volume: 51 start-page: 1150 year: 1991 end-page: 1167 ident: BIB34 article-title: Averaging methods for the phase shift of arbitrarily perturbed strongly nonlinear oscillators with an application to capture publication-title: SIAM J. Appl. Math. – volume: 32 start-page: 227 year: 1996 end-page: 235 ident: BIB9 article-title: Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection publication-title: IEEE J. Quant. Electr. QE – volume: 27 start-page: 1688 year: 1991 end-page: 1695 ident: BIB17 article-title: Injection locking in distributed feedback semiconductor lasers publication-title: IEEE J. Quant. Electron. QE – volume: 172 start-page: 279 year: 1999 end-page: 295 ident: BIB23 article-title: A unifying view of bifurcations in a semiconductor laser subject to optical injection publication-title: Opt. Commun. – volume: 2039 start-page: 11 year: 1993 end-page: 22 ident: BIB11 article-title: Multi-wave mixing dynamics in a diode laser publication-title: Chaos Opt. SPIE – volume: 183 start-page: 215 year: 2000 end-page: 226 ident: BIB24 article-title: Mechanisms for multistability in a semiconductor laser with optical injection publication-title: Opt. Commun. – reference: M.G. Zimmermann, M.A. Natiello, H.G. Solari, Global bifurcations in a laser with injected signal: beyond Adler’s approximation, Chaos 11 (2001) 500–513. – volume: 53 start-page: 4372 year: 1996 end-page: 4380 ident: BIB27 article-title: Mechanism for period doubling bifurcation in a semiconductor laser subject to optical injection publication-title: Phys. Rev. A – reference: P.G. Drazin, Nonlinear Systems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Oxford, 1992. – reference: S.H. Strogatz, Nonlinear Dynamics and Chaos, Addison-Wesley, New York, 1994. – volume: 136 start-page: 253 year: 1997 end-page: 256 ident: BIB38 article-title: Analytical stability boundaries for a semiconductor laser subject to optical injection publication-title: Opt. Commun. – reference: C. Mayol, M.A. Natiello, M.G. Zimmermann, Resonance structure in a weakly detuned laser with injected signal, Int. J. Bifurcation Chaos 11 (2001) 2587–2605. – volume: 24 start-page: 148 year: 1988 end-page: 154 ident: BIB5 article-title: Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser publication-title: IEEE J. Quant. Electr. – volume: 18 start-page: 976 year: 1982 end-page: 983 ident: BIB4 article-title: Injection locking properties of a semiconductor laser publication-title: IEEE J. Quant. Electr. – volume: 47 start-page: 736 year: 1993 end-page: 739 ident: BIB13 article-title: Bistability and chaos in an injection-locked semiconductor laser publication-title: Phys. Rev. A – volume: 9 start-page: 765 year: 1997 end-page: 784 ident: BIB2 article-title: Nonlinear dynamics induced by external optical injection in semiconductor lasers publication-title: Quant. Semiclass. Optics – reference: J. Kevorkian, J.D. Cole, Perturbation Methods in Applied Mathematics, Applied Mathematical Sciences, Vol. 34, Springer, New York, 1981. – volume: 32 start-page: 1456 year: 1996 end-page: 1468 ident: BIB8 article-title: Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection publication-title: IEEE J. Quant. Electron. – volume: 7 start-page: 87 year: 1995 end-page: 143 ident: BIB10 article-title: Semiconductor lasers with optical injection and feedback publication-title: Quant. Semiclass. Opt. – volume: 51 start-page: 4181 year: 1995 end-page: 4185 ident: BIB15 article-title: Period-doubling cascades and chaos in a semiconductor laser with optical injection publication-title: Phys. Rev. A – volume: 8 start-page: 805 year: 1996 end-page: 822 ident: BIB36 article-title: Relaxation-oscillation phenomena in an injection-locked semiconductor laser publication-title: Quant. Semiclass. Opt. – volume: 109 start-page: 293 year: 1997 end-page: 314 ident: BIB20 article-title: Sil’nikov-saddle-node interaction near a codimension-2 bifurcation: laser with injected signal publication-title: Physica D – volume: 9 start-page: 797 year: 1997 end-page: 809 ident: BIB39 article-title: Bifurcations of relaxation oscillations in an optically injected diode laser publication-title: Quant. Semiclass. Opt. – volume: 26 start-page: 3539 year: 1994 end-page: 3541 ident: BIB14 article-title: Period-doubling route to chaos in a semiconductor laser subject to optical injection publication-title: Appl. Phys. Lett. – volume: 159 start-page: 177 year: 1999 end-page: 183 ident: BIB28 article-title: Largely detuned injection-locked semiconductor lasers publication-title: Opt. Commun. – reference: M. Nizette, T. Erneux, A. Gavrielides, V. Kovanis, Injection locked semiconductor laser dynamics from large to small detunings, in: P. Blood, A. Ishibashi, M. Osinski (Eds.), Physics and Simulations of Optoelectronic Devices VII, Proc. SPIE 3625 (1999) 679–691. – volume: 41 start-page: 6470 year: 1989 end-page: 6479 ident: BIB18 article-title: Constant phase, phase drift, and phase entrainment in lasers with an injected signal publication-title: Phys. Rev. A – volume: 41 start-page: 6470 year: 1989 ident: 10.1016/S0167-2789(01)00375-X_BIB18 article-title: Constant phase, phase drift, and phase entrainment in lasers with an injected signal publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.41.6470 – volume: 67 start-page: 2780 year: 1995 ident: 10.1016/S0167-2789(01)00375-X_BIB16 article-title: Instabilities and chaos in optically injected semiconductor lasers publication-title: Appl. Phys. Lett. doi: 10.1063/1.114591 – volume: 21 start-page: 784 year: 1985 ident: 10.1016/S0167-2789(01)00375-X_BIB6 article-title: Locking conditions and stability properties for a semiconductor laser with external light injection publication-title: IEEE J. Quant. Electr. doi: 10.1109/JQE.1985.1072760 – volume: 47 start-page: 736 year: 1993 ident: 10.1016/S0167-2789(01)00375-X_BIB13 article-title: Bistability and chaos in an injection-locked semiconductor laser publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.47.736 – ident: 10.1016/S0167-2789(01)00375-X_BIB21 doi: 10.1063/1.1397757 – volume: 111 start-page: 173 year: 1994 ident: 10.1016/S0167-2789(01)00375-X_BIB19 article-title: Laser with injected signal: perturbation of an invariant circle publication-title: Opt. Commun. doi: 10.1016/0030-4018(94)90157-0 – volume: 172 start-page: 279 year: 1999 ident: 10.1016/S0167-2789(01)00375-X_BIB23 article-title: A unifying view of bifurcations in a semiconductor laser subject to optical injection publication-title: Opt. Commun. doi: 10.1016/S0030-4018(99)00603-3 – volume: 34 start-page: 2350 year: 1998 ident: 10.1016/S0167-2789(01)00375-X_BIB12 article-title: Dynamic behavior and locking of a semiconductor laser subjected to external injection publication-title: IEEE J. Quant. Electr. doi: 10.1109/3.736105 – volume: 59 start-page: 111 year: 1985 ident: 10.1016/S0167-2789(01)00375-X_BIB37 article-title: Toda potentials in laser equations publication-title: Z. Phys. B doi: 10.1007/BF01325388 – volume: 27 start-page: 1688 year: 1991 ident: 10.1016/S0167-2789(01)00375-X_BIB17 article-title: Injection locking in distributed feedback semiconductor lasers publication-title: IEEE J. Quant. Electron. QE doi: 10.1109/3.89994 – volume: 159 start-page: 177 year: 1999 ident: 10.1016/S0167-2789(01)00375-X_BIB28 article-title: Largely detuned injection-locked semiconductor lasers publication-title: Opt. Commun. doi: 10.1016/S0030-4018(98)00584-7 – volume: 24 start-page: 148 year: 1988 ident: 10.1016/S0167-2789(01)00375-X_BIB5 article-title: Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser publication-title: IEEE J. Quant. Electr. doi: 10.1109/3.108 – volume: 26 start-page: 3539 year: 1994 ident: 10.1016/S0167-2789(01)00375-X_BIB14 article-title: Period-doubling route to chaos in a semiconductor laser subject to optical injection publication-title: Appl. Phys. Lett. doi: 10.1063/1.111218 – ident: 10.1016/S0167-2789(01)00375-X_BIB35 doi: 10.1007/978-1-4612-3968-0 – volume: 2039 start-page: 11 year: 1993 ident: 10.1016/S0167-2789(01)00375-X_BIB11 article-title: Multi-wave mixing dynamics in a diode laser publication-title: Chaos Opt. SPIE doi: 10.1117/12.164762 – volume: 109 start-page: 293 year: 1997 ident: 10.1016/S0167-2789(01)00375-X_BIB20 article-title: Sil’nikov-saddle-node interaction near a codimension-2 bifurcation: laser with injected signal publication-title: Physica D doi: 10.1016/S0167-2789(97)00070-5 – ident: 10.1016/S0167-2789(01)00375-X_BIB31 – volume: 51 start-page: 1150 year: 1991 ident: 10.1016/S0167-2789(01)00375-X_BIB34 article-title: Averaging methods for the phase shift of arbitrarily perturbed strongly nonlinear oscillators with an application to capture publication-title: SIAM J. Appl. Math. doi: 10.1137/0151058 – volume: 7 start-page: 87 year: 1995 ident: 10.1016/S0167-2789(01)00375-X_BIB10 article-title: Semiconductor lasers with optical injection and feedback publication-title: Quant. Semiclass. Opt. doi: 10.1088/1355-5111/7/2/003 – volume: 51 start-page: 4181 year: 1995 ident: 10.1016/S0167-2789(01)00375-X_BIB15 article-title: Period-doubling cascades and chaos in a semiconductor laser with optical injection publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.51.4181 – volume: 8 start-page: 805 year: 1996 ident: 10.1016/S0167-2789(01)00375-X_BIB36 article-title: Relaxation-oscillation phenomena in an injection-locked semiconductor laser publication-title: Quant. Semiclass. Opt. doi: 10.1088/1355-5111/8/4/004 – ident: 10.1016/S0167-2789(01)00375-X_BIB33 doi: 10.1007/978-1-4757-4213-8 – volume: 2 start-page: 173 year: 1985 ident: 10.1016/S0167-2789(01)00375-X_BIB1 article-title: Instabilities in lasers with an injected signal publication-title: JOSA B doi: 10.1364/JOSAB.2.000173 – volume: 32 start-page: 227 year: 1996 ident: 10.1016/S0167-2789(01)00375-X_BIB9 article-title: Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection publication-title: IEEE J. Quant. Electr. QE doi: 10.1109/3.481870 – volume: 58 start-page: 4421 year: 1998 ident: 10.1016/S0167-2789(01)00375-X_BIB25 article-title: Nonlinear dynamics of a solid-state laser with injection publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.58.4421 – volume: 9 start-page: 1325 year: 1997 ident: 10.1016/S0167-2789(01)00375-X_BIB7 article-title: Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking publication-title: IEEE Photon. Technol. Lett. doi: 10.1109/68.623251 – volume: 32 start-page: 1456 year: 1996 ident: 10.1016/S0167-2789(01)00375-X_BIB8 article-title: Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection publication-title: IEEE J. Quant. Electron. doi: 10.1109/3.511559 – ident: 10.1016/S0167-2789(01)00375-X_BIB29 doi: 10.1117/12.356927 – volume: 9 start-page: 765 year: 1997 ident: 10.1016/S0167-2789(01)00375-X_BIB2 article-title: Nonlinear dynamics induced by external optical injection in semiconductor lasers publication-title: Quant. Semiclass. Optics doi: 10.1088/1355-5111/9/5/009 – volume: 136 start-page: 253 year: 1997 ident: 10.1016/S0167-2789(01)00375-X_BIB38 article-title: Analytical stability boundaries for a semiconductor laser subject to optical injection publication-title: Opt. Commun. doi: 10.1016/S0030-4018(96)00705-5 – ident: 10.1016/S0167-2789(01)00375-X_BIB26 doi: 10.1142/S0218127401003693 – ident: 10.1016/S0167-2789(01)00375-X_BIB32 – ident: 10.1016/S0167-2789(01)00375-X_BIB30 – volume: 18 start-page: 976 year: 1982 ident: 10.1016/S0167-2789(01)00375-X_BIB4 article-title: Injection locking properties of a semiconductor laser publication-title: IEEE J. Quant. Electr. doi: 10.1109/JQE.1982.1071632 – volume: 9 start-page: 797 year: 1997 ident: 10.1016/S0167-2789(01)00375-X_BIB39 article-title: Bifurcations of relaxation oscillations in an optically injected diode laser publication-title: Quant. Semiclass. Opt. doi: 10.1088/1355-5111/9/5/011 – volume: 156 start-page: 158 year: 1998 ident: 10.1016/S0167-2789(01)00375-X_BIB22 article-title: Tori and their bifurcations in an optically injected semiconductor laser publication-title: Opt. Commun. doi: 10.1016/S0030-4018(98)00434-9 – volume: 183 start-page: 215 year: 2000 ident: 10.1016/S0167-2789(01)00375-X_BIB24 article-title: Mechanisms for multistability in a semiconductor laser with optical injection publication-title: Opt. Commun. doi: 10.1016/S0030-4018(00)00867-1 – ident: 10.1016/S0167-2789(01)00375-X_BIB3 – volume: 53 start-page: 4372 year: 1996 ident: 10.1016/S0167-2789(01)00375-X_BIB27 article-title: Mechanism for period doubling bifurcation in a semiconductor laser subject to optical injection publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.53.4372 |
| SSID | ssj0001737 |
| Score | 1.6818098 |
| Snippet | An averaging method valid for strongly nonlinear oscillators is used for the first time to describe the pulsating intensity regimes of semiconductor lasers... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 220 |
| SubjectTerms | Averaged equations Hopf and torus bifurcations Injection locked semiconductor |
| Title | Averaged equations for injection locked semiconductor lasers |
| URI | https://dx.doi.org/10.1016/S0167-2789(01)00375-X |
| Volume | 161 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1NSwMxEB2KIuhBtCrWj7IHD3pIuzHZTQpeSrFUxV60sLeQr4WqbKutV3-7SXZrK4iCtyXZCcsw-_IOb94AnClFicwNRq4YCKJMKiS1e8qtwUxzZmwQY94P08GI3mZJVoPeohfGyyor7C8xPaB1tdKustmejsftBy-gD32cOAxyzXwHO2W-1lsfS5kHZqVvpvf39m8vu3jKE8LieYwvwiEo-_l-Wrlz-juwXZHFqFt-zy7UbFGHrRULwTpsBAmnnu3BVddVpUMHE9nX0r97FjlGGo2LpyC3KiJ3bz277ZnXw08Kb_Tqth17dgxwH0b968feAFWzEZB2f-Uc6UR2KOEqIZrFKvfN4NxwBz-KJ8oQbwpDKKWGKMxjk6o0vdQkJTanmkqrDTmAtWJS2EOIrCONOWYcE8upwVp2tJRUMqrSpEMT1gC6yIjQlXG4n1_xIlYUYikTPpEixiIkUmQNaH2FTUvnjL8C-CLd4lsJCIfuv4ce_T_0GDbDgJcYI5ycwNr87d2eOp4xV81QSE1Y797cDYafx4zL6w |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LSwMxEB58IOpBfGJ97sGDHtZuTHaTghcpSn31osLeQl4LVdlWW6_-difZrVYQBW8hyYRlmP1mDt98A3CgNaOqsCTGYKAx40rHyuCqcJZwI7h1gYx52806D-wqT_MpaI97YTytssb-CtMDWtc7zdqbzUGv17zzBPrQx0nCINd8GmZZigsM6uP3L54H4ZVwphf49te_2niqJ8LmYUKOwitx_nOCmkg6F8uwVFeL0Vn1QSsw5cpVWJzQEFyFucDhNMM1OD3DsER4sJF7qQS8hxGWpFGvfAx8qzLCxPWEx0NPiO-XXukVj7F8xhJwHR4uzu_bnbgejhAb_C1HsUlVi1GhU2p4ogvfDS6sQPzRItWWelUYyhizVBOR2Exn2YmhGXUFM0w5Y-kGzJT90m1C5LBqLAgXhDrBLDGqZZRiijOdpS2W8gawsUekqZXD_QCLZzlBEcu49I6UCZHBkTJvwPGn2aCSzvjLQIzdLb_FgER4_9106_-m-zDfub-9kTeX3ettWAjTXhISk3QHZkavb24Xi46R3gtB9QGzis1- |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Averaged+equations+for+injection+locked+semiconductor+lasers&rft.jtitle=Physica.+D&rft.au=Nizette%2C+Michel&rft.au=Erneux%2C+Thomas&rft.au=Gavrielides%2C+Athanasios&rft.au=Kovanis%2C+Vassilios&rft.date=2002-01-15&rft.issn=0167-2789&rft.volume=161&rft.issue=3-4&rft.spage=220&rft.epage=236&rft_id=info:doi/10.1016%2FS0167-2789%2801%2900375-X&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_S0167_2789_01_00375_X |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0167-2789&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0167-2789&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0167-2789&client=summon |