Abstract

An examination has been made of the influence of pump noise within a procedure for targeting laser dynamics. Specific attention is given to targeting Q-switched class B lasers to stable and unstable periodic orbits by means of a choice of the relative phase of the modulation and the instant of laser switch-on. When the phase space of a loss-modulated class B laser includes an unstable period-one orbit and two stable (antiphased) period-two orbits, noise causes a separatrix crossing, which results in switching between the two period-two orbits over a wide range of relative phases. It is shown here that in the regular targeting case pump noise is less important than intensity noise. However, pump noise is found to be of paramount importance in the case in which two possible targeting phases of the modulation are nearly degenerate. In this case of heteroclinic tangency pump noise induces additional crossings, which act transversally to the separatrix already at the initial stage of transients. By means of highest- (Nth-) passage-time distributions, trends in the relative impact of intensity and pump noises during the turn-on process are demonstrated.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. T. Arecchi, V. Degiorgio, and B. Querzola, Phys. Rev. Lett. 19, 1168 (1967); F. T. Arecchi and V. Degiorgio, Phys. Rev. A 3, 1108 (1971); F. T. Arecchi, in Noise in Nonlinear Dynamical Systems, F. Moss, L. Lugiato, and W. Schleich, eds. (Cambridge U. Press, Cambridge, UK, 1990), pp. 263–269.
    [CrossRef]
  2. P. Spano, A. D’Ottavi, A. Mecozzi, and B. Daino, Appl. Phys. Lett. 52, 2203 (1988); A. Mecozzi, P. Spano, A. D’Ottavi, and S. Piazzolla, Appl. Phys. Lett. 55, 769 (1989); A. G. Weber, W. Ronghan, E. H. Boettcher, M. Schell, and D. Bimberg, IEEE J. Quantum Electron. IEJQA7 28, 441 (1992).
    [CrossRef]
  3. K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, Dordrecht, The Netherlands, 1988); L. N. Langley and K. A. Shore, Opt. Lett. 18, 1432 (1993); C. R. Mirasso, P. Colet, and M. San Miguel, IEEE J. Quantum Electron. 29, 23 (1993).
    [CrossRef] [PubMed]
  4. A. Valle, M. A. Rodriguez, and C. R. Mirasso, Opt. Lett. 17, 1523 (1992); S. Balle, C. R. Mirasso, A. Sapia, and P. Spano, Appl. Phys. Lett. 63, 1721 (1993); M. San Miguel, in Laser Noise, R. Roy, ed., Proc. SPIE PSISDG 1376, 272 (1990).
    [CrossRef]
  5. S. E. Hodges, M. Munroe, W. Gadomski, J. Cooper, and M. G. Raymer, J. Opt. Soc. Am. B 14, 180 (1997); S. E. Hodges, M. Munroe, J. Cooper, and M. G. Raymer, J. Opt. Soc. Am. B 14, 191 (1997).
    [CrossRef]
  6. N. B. Abraham, P. Mandel, and L. M. Narducci, Progress in Optics, Vol. 25, E. Wolf, ed. (Elsevier, Amsterdam, 1988), p. 1.
  7. O. L. Gaiko, L. A. Kotomtseva, V. V. Nevdakh, L. N. Orlov, and A. M. Samson, Kvant. Elektron. (Moscow) 21, 655 (1994); [in English: Quantum Electron. 24, 603 (1994)].
    [CrossRef]
  8. F. Papoff, D. Dangoisse, E. Poitehanoteau, and P. Glorieux, Opt. Commun. 67, 358 (1988); R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, Phys. Rev. E 52, 4676 (1995).
    [CrossRef]
  9. L. A. Kotomtseva, A. V. Naumenko, A. M. Samson, and S. I. Turovets, Opt. Commun. 136, 335 (1997); European Quantum Electronics Conference (IEEE, New York, 1994), paper QThG41.
    [CrossRef]
  10. S. I. Turovets, A. Valle, and K. A. Shore, Phys. Rev. A 55, 2426 (1997).
    [CrossRef]
  11. A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  12. M. Ciofini, R. Meucci, P.-Y. Wang, and F. T. Arecchi, Europhys. Lett. 21, 735 (1993); M. Ciofini, A. Lapucci, R. Meucci, P. Y. Wang, and F. T. Arecchi, Phys. Rev. A 46, 5874 (1992).
    [CrossRef] [PubMed]
  13. C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1993).
  14. A. M. Samson and S. I. Turovets, Dokl. Akad. Nauk SSSR 31, 888 (1987).
  15. E. Ott, C. Greboggi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990); R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992).
    [CrossRef] [PubMed]
  16. E. Ott, Chaos in Dynamical Systems (Cambridge U. Press, Cambridge, UK, 1993), Chap. 8, pp. 277–283.
  17. J. R. Tredicce, N. B. Abraham, G. P. Puccioni, and F. T. Arecchi, Opt. Commun. 55, 131–134 (1985).
    [CrossRef]
  18. F. T. Arrechi and A. Politi, Phys. Rev. Lett. 45, 1219 (1980).
    [CrossRef]
  19. A. M. Samson and S. I. Turovets, preprint No. 438, 1986 (Institute of Physics, BSSR Academy of Sciences, Minsk); V. N. Chizhevsky and S. I. Turovets, Opt. Commun. 102, 175 (1993).
    [CrossRef]
  20. S. I. Turovets, National Academy of Sciences, Belarus (personal communication, 1997).
  21. S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
    [CrossRef] [PubMed]
  22. S. A. Akhmanov and M. A. Vorontsov, eds., New Physical Principles of Optical Signal Processing (Nauka, Moscow, 1990) (in Russian); S. A. Akhmanov, Yu. E. Diyakov, and A. S. Chirkin, Introduction in Statistical Electronics and Optics (Nauka, Moscow, 1981) (in Russian).
  23. A. W. Yu, G. P. Agrawal, and R. Roy, J. Stat. Phys. 54, 1223 (1989).
    [CrossRef]
  24. T. M. Shen, J. Lightwave Technol. 7, 1394 (1989).
    [CrossRef]
  25. P. Glorieux, C. Lepers, R. Corbalan, J. Cortit, and A. N. Pisarchik, Opt. Commun. 118, 309 (1995).
    [CrossRef]
  26. A. R. Bulsara, W. C. Schieve, and E. W. Jacobs, Phys. Rev. A 41, 668 (1990); W. C. Schieve and A. R. Bulsara, Phys. Rev. A 41, 1172 (1990).
    [CrossRef] [PubMed]

1997

S. I. Turovets, A. Valle, and K. A. Shore, Phys. Rev. A 55, 2426 (1997).
[CrossRef]

1995

P. Glorieux, C. Lepers, R. Corbalan, J. Cortit, and A. N. Pisarchik, Opt. Commun. 118, 309 (1995).
[CrossRef]

1994

S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
[CrossRef] [PubMed]

1989

A. W. Yu, G. P. Agrawal, and R. Roy, J. Stat. Phys. 54, 1223 (1989).
[CrossRef]

T. M. Shen, J. Lightwave Technol. 7, 1394 (1989).
[CrossRef]

1987

A. M. Samson and S. I. Turovets, Dokl. Akad. Nauk SSSR 31, 888 (1987).

1985

J. R. Tredicce, N. B. Abraham, G. P. Puccioni, and F. T. Arecchi, Opt. Commun. 55, 131–134 (1985).
[CrossRef]

1980

F. T. Arrechi and A. Politi, Phys. Rev. Lett. 45, 1219 (1980).
[CrossRef]

Abraham, N. B.

S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
[CrossRef] [PubMed]

J. R. Tredicce, N. B. Abraham, G. P. Puccioni, and F. T. Arecchi, Opt. Commun. 55, 131–134 (1985).
[CrossRef]

Agrawal, G. P.

A. W. Yu, G. P. Agrawal, and R. Roy, J. Stat. Phys. 54, 1223 (1989).
[CrossRef]

Alvarez, R.

S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
[CrossRef] [PubMed]

Arecchi, F. T.

J. R. Tredicce, N. B. Abraham, G. P. Puccioni, and F. T. Arecchi, Opt. Commun. 55, 131–134 (1985).
[CrossRef]

Arrechi, F. T.

F. T. Arrechi and A. Politi, Phys. Rev. Lett. 45, 1219 (1980).
[CrossRef]

Balle, S.

S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
[CrossRef] [PubMed]

Corbalan, R.

P. Glorieux, C. Lepers, R. Corbalan, J. Cortit, and A. N. Pisarchik, Opt. Commun. 118, 309 (1995).
[CrossRef]

Cortit, J.

P. Glorieux, C. Lepers, R. Corbalan, J. Cortit, and A. N. Pisarchik, Opt. Commun. 118, 309 (1995).
[CrossRef]

D’Angelo, E. J.

S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
[CrossRef] [PubMed]

Gambhir, A.

S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
[CrossRef] [PubMed]

Glorieux, P.

P. Glorieux, C. Lepers, R. Corbalan, J. Cortit, and A. N. Pisarchik, Opt. Commun. 118, 309 (1995).
[CrossRef]

Lepers, C.

P. Glorieux, C. Lepers, R. Corbalan, J. Cortit, and A. N. Pisarchik, Opt. Commun. 118, 309 (1995).
[CrossRef]

Pisarchik, A. N.

P. Glorieux, C. Lepers, R. Corbalan, J. Cortit, and A. N. Pisarchik, Opt. Commun. 118, 309 (1995).
[CrossRef]

Politi, A.

F. T. Arrechi and A. Politi, Phys. Rev. Lett. 45, 1219 (1980).
[CrossRef]

Puccioni, G. P.

J. R. Tredicce, N. B. Abraham, G. P. Puccioni, and F. T. Arecchi, Opt. Commun. 55, 131–134 (1985).
[CrossRef]

Roy, R.

S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
[CrossRef] [PubMed]

A. W. Yu, G. P. Agrawal, and R. Roy, J. Stat. Phys. 54, 1223 (1989).
[CrossRef]

Samson, A. M.

A. M. Samson and S. I. Turovets, Dokl. Akad. Nauk SSSR 31, 888 (1987).

San Miguel, M.

S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
[CrossRef] [PubMed]

Shen, T. M.

T. M. Shen, J. Lightwave Technol. 7, 1394 (1989).
[CrossRef]

Shore, K. A.

S. I. Turovets, A. Valle, and K. A. Shore, Phys. Rev. A 55, 2426 (1997).
[CrossRef]

Thornburg, K. S.

S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
[CrossRef] [PubMed]

Tredicce, J. R.

S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
[CrossRef] [PubMed]

J. R. Tredicce, N. B. Abraham, G. P. Puccioni, and F. T. Arecchi, Opt. Commun. 55, 131–134 (1985).
[CrossRef]

Turovets, S. I.

S. I. Turovets, A. Valle, and K. A. Shore, Phys. Rev. A 55, 2426 (1997).
[CrossRef]

A. M. Samson and S. I. Turovets, Dokl. Akad. Nauk SSSR 31, 888 (1987).

Valle, A.

S. I. Turovets, A. Valle, and K. A. Shore, Phys. Rev. A 55, 2426 (1997).
[CrossRef]

Yu, A. W.

A. W. Yu, G. P. Agrawal, and R. Roy, J. Stat. Phys. 54, 1223 (1989).
[CrossRef]

Dokl. Akad. Nauk SSSR

A. M. Samson and S. I. Turovets, Dokl. Akad. Nauk SSSR 31, 888 (1987).

J. Lightwave Technol.

T. M. Shen, J. Lightwave Technol. 7, 1394 (1989).
[CrossRef]

J. Stat. Phys.

A. W. Yu, G. P. Agrawal, and R. Roy, J. Stat. Phys. 54, 1223 (1989).
[CrossRef]

Opt. Commun.

P. Glorieux, C. Lepers, R. Corbalan, J. Cortit, and A. N. Pisarchik, Opt. Commun. 118, 309 (1995).
[CrossRef]

J. R. Tredicce, N. B. Abraham, G. P. Puccioni, and F. T. Arecchi, Opt. Commun. 55, 131–134 (1985).
[CrossRef]

Phys. Rev. A

S. I. Turovets, A. Valle, and K. A. Shore, Phys. Rev. A 55, 2426 (1997).
[CrossRef]

Phys. Rev. Lett.

F. T. Arrechi and A. Politi, Phys. Rev. Lett. 45, 1219 (1980).
[CrossRef]

S. Balle, M. San Miguel, N. B. Abraham, J. R. Tredicce, R. Alvarez, E. J. D’Angelo, A. Gambhir, K. S. Thornburg, and R. Roy, Phys. Rev. Lett. 72, 3510 (1994).
[CrossRef] [PubMed]

Other

S. A. Akhmanov and M. A. Vorontsov, eds., New Physical Principles of Optical Signal Processing (Nauka, Moscow, 1990) (in Russian); S. A. Akhmanov, Yu. E. Diyakov, and A. S. Chirkin, Introduction in Statistical Electronics and Optics (Nauka, Moscow, 1981) (in Russian).

E. Ott, C. Greboggi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990); R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

E. Ott, Chaos in Dynamical Systems (Cambridge U. Press, Cambridge, UK, 1993), Chap. 8, pp. 277–283.

A. R. Bulsara, W. C. Schieve, and E. W. Jacobs, Phys. Rev. A 41, 668 (1990); W. C. Schieve and A. R. Bulsara, Phys. Rev. A 41, 1172 (1990).
[CrossRef] [PubMed]

A. M. Samson and S. I. Turovets, preprint No. 438, 1986 (Institute of Physics, BSSR Academy of Sciences, Minsk); V. N. Chizhevsky and S. I. Turovets, Opt. Commun. 102, 175 (1993).
[CrossRef]

S. I. Turovets, National Academy of Sciences, Belarus (personal communication, 1997).

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

M. Ciofini, R. Meucci, P.-Y. Wang, and F. T. Arecchi, Europhys. Lett. 21, 735 (1993); M. Ciofini, A. Lapucci, R. Meucci, P. Y. Wang, and F. T. Arecchi, Phys. Rev. A 46, 5874 (1992).
[CrossRef] [PubMed]

C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1993).

F. T. Arecchi, V. Degiorgio, and B. Querzola, Phys. Rev. Lett. 19, 1168 (1967); F. T. Arecchi and V. Degiorgio, Phys. Rev. A 3, 1108 (1971); F. T. Arecchi, in Noise in Nonlinear Dynamical Systems, F. Moss, L. Lugiato, and W. Schleich, eds. (Cambridge U. Press, Cambridge, UK, 1990), pp. 263–269.
[CrossRef]

P. Spano, A. D’Ottavi, A. Mecozzi, and B. Daino, Appl. Phys. Lett. 52, 2203 (1988); A. Mecozzi, P. Spano, A. D’Ottavi, and S. Piazzolla, Appl. Phys. Lett. 55, 769 (1989); A. G. Weber, W. Ronghan, E. H. Boettcher, M. Schell, and D. Bimberg, IEEE J. Quantum Electron. IEJQA7 28, 441 (1992).
[CrossRef]

K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, Dordrecht, The Netherlands, 1988); L. N. Langley and K. A. Shore, Opt. Lett. 18, 1432 (1993); C. R. Mirasso, P. Colet, and M. San Miguel, IEEE J. Quantum Electron. 29, 23 (1993).
[CrossRef] [PubMed]

A. Valle, M. A. Rodriguez, and C. R. Mirasso, Opt. Lett. 17, 1523 (1992); S. Balle, C. R. Mirasso, A. Sapia, and P. Spano, Appl. Phys. Lett. 63, 1721 (1993); M. San Miguel, in Laser Noise, R. Roy, ed., Proc. SPIE PSISDG 1376, 272 (1990).
[CrossRef]

S. E. Hodges, M. Munroe, W. Gadomski, J. Cooper, and M. G. Raymer, J. Opt. Soc. Am. B 14, 180 (1997); S. E. Hodges, M. Munroe, J. Cooper, and M. G. Raymer, J. Opt. Soc. Am. B 14, 191 (1997).
[CrossRef]

N. B. Abraham, P. Mandel, and L. M. Narducci, Progress in Optics, Vol. 25, E. Wolf, ed. (Elsevier, Amsterdam, 1988), p. 1.

O. L. Gaiko, L. A. Kotomtseva, V. V. Nevdakh, L. N. Orlov, and A. M. Samson, Kvant. Elektron. (Moscow) 21, 655 (1994); [in English: Quantum Electron. 24, 603 (1994)].
[CrossRef]

F. Papoff, D. Dangoisse, E. Poitehanoteau, and P. Glorieux, Opt. Commun. 67, 358 (1988); R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, Phys. Rev. E 52, 4676 (1995).
[CrossRef]

L. A. Kotomtseva, A. V. Naumenko, A. M. Samson, and S. I. Turovets, Opt. Commun. 136, 335 (1997); European Quantum Electronics Conference (IEEE, New York, 1994), paper QThG41.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Transient time versus modulator phase in the Q-switching regime: deterministic case, i.e., without Langevin noise (solid curve), spontaneous (+), population (□), and both (⋄) Langevin terms included; variance of the transient time for three latter cases: short-dashed, long-dashed, and dotted curves, correspondingly. Modulation frequency ω/[v(y0 -1)]1/2=2, modulation depth m=0.1, pump parameter y0 =2, and hold-off ratio k=4. Noise strengths: β1=4 ×10-8 and β2=10-6.

Fig. 2
Fig. 2

Same as in Fig. 1, but for the degenerate case {an even number of the targeting peaks, ω/[v(y0-1)]1/2=1.95}. Near the degenerate peak averaging was performed over 4000 simulations.

Fig. 3
Fig. 3

(a) Global stochastic Poincare section and (b)–(d) its enlargements. Stochastic iterates of an initial thermalized cloud when both noises are included are shown by dots, rhomboids for (b)–(d) purely spontaneous noise, and pluses for purely pump noise (b)–(d). The separatrix in the deterministic limit is plotted by (a) open circles and (b)–(d) by solid lines. (b) Outset of the laser off-state is shown by a dashed line. Filled circles and filled square are 2T-periodic stable orbits and the unstable T-periodic orbit, respectively.

Fig. 4
Fig. 4

First four passage time distribution functions in the case when only [(a), (c)] the population or [(b), (d)] the spontaneous Langevin term is taken into account for the modulator phase [(a), (b)] 0.28×2π and [(c), (d)] 0.8×2π. All other parameters are as in Fig. 1. Time is normalized to the modulation period. The reference value of u is 1.63.  

Fig. 5
Fig. 5

First four passage time distribution functions in the case when only (a) spontaneous or (b) pump noise is taken into account for the modulator phase 0.55×2π. All other parameters are as in Fig. 2. Time is normalized to the modulation period. The reference value of u is 1.63. These distributions were computed using 104 simulations.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

dn/dt=[KN-γc(t)]n+Rsp+Fn(t),
dN/dt=rp-2KNn-γ2N+RN(t),
Rsp=βγradN2,
Fn(t)=(2Rspn)1/2ξ(t),ξ(t)ξ(s)=δ(t-s),
ξ(t)=0,
RN(t)=(R)1/2ζ(t),ζ(t)ζ(s)=δ(t-s),
ζ(t)=0,
du/dτ=v[y-k(τ)-m cos(ωτ+φ)]u+rsp+(2rspu)1/2ξ(τ),
dy/dτ=y0-(1+u)y+(δ)1/2ζ(τ),
u0ϖq[v(y0-1)]-1/2 sin(ϖτ)/[ust+Δu(τ)][1-Δu1cos(ϖτ+Δφ1)]β2[v(y0-1)]-1/2×cos(ϖτ)10-7,

Metrics