## About possibility of bistable dynamics in lasers with single-mode cavities |

JOSA B, Vol. 30, Issue 1, pp. 79-86 (2013)

http://dx.doi.org/10.1364/JOSAB.30.000079

Enhanced HTML Acrobat PDF (403 KB)

### Abstract

A previously unknown mechanism of bistable behavior in lasers with single-mode cavities is proposed and analyzed. It is shown that if losses in a cavity exhibit nonmonotonic dependence on frequency, the equation for stationary lasing frequencies can have multiple solutions even in single-mode cavities. In such a case, a system can generate one of several lasing outputs characterized by different frequencies and intensities. All these potential lasing states are stable at the same pumping level, and the choice between them is determined by initial conditions. The latter can be, in principle, controlled by seeding pulses. This mechanism does not depend on such nonlinear effects responsible for most known types of bistability as saturable absorption or cross saturation. An example of a cavity structure, in which such a mechanism can be realized, is presented. Standard lasing equations fail to describe dynamical behavior of such systems; therefore a generalized approach treating dynamic of lasing frequency and intensity on equal footing is developed.

© 2012 Optical Society of America

**OCIS Codes**

(140.3430) Lasers and laser optics : Laser theory

(140.3570) Lasers and laser optics : Lasers, single-mode

(190.1450) Nonlinear optics : Bistability

(130.4815) Integrated optics : Optical switching devices

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: October 3, 2012

Revised Manuscript: October 29, 2012

Manuscript Accepted: October 30, 2012

Published: December 6, 2012

**Citation**

Vladimir Shuvayev, Vinod Menon, Alexander Lisyansky, and Lev Deych, "About possibility of bistable dynamics in lasers with single-mode cavities," J. Opt. Soc. Am. B **30**, 79-86 (2013)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-1-79

Sort: Year | Journal | Reset

### References

- C. M. Bowden, M. Ciftan, and H. R. Robl, Optical Bistability (Plenum, 1981).
- P. Mandel, Theoretical Problems in Cavity Nonlinear Optics (Cambridge University, 1997).
- K. Otsuka, Nonlinear Dynamics in Optical Complex Systems (Kluwer, 1999).
- N. N. Rosanov, Spatial Hysteresis and Optical Patterns(Springer, 2002).
- H. Kawaguchi, Bistabilities and Nonlinearities in Laser Diodes (Artech House, 1994).
- H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).
- A. T. Rosenberger, L. A. Orozco, and H. J. Kimble, “Observation of absorptive bistability with 2-level atoms in a ring cavity,” Phys. Rev. A 28, 2569–2572 (1983). [CrossRef]
- A. Joshi and M. Xiao, “Optical multistability in three-level atoms inside an optical ring cavity,” Phys. Rev. Lett. 91, 143904 (2003). [CrossRef]
- A. J. Vanwonderen and L. G. Suttorp, “Dispersive optical bistability in a nonideal Fabry–Perot cavity. 1. Stability analysis of the Maxwell–Bloch equations,” Z. Phys. B 83, 135–142 (1991).
- T. Vivero, J. M. Rivas-Moscoso, A. P. Gonzalez-Marcos, and J. A. Martin-Pereda, “Dispersive optical bistability in quantum wells with logarithmic gain,” IEEE J. Quantum Electron. 46, 1184–1190 (2010). [CrossRef]
- H. A. Batarfi, “Dispersive switching in bistable models,” J. Nonlinear Opt. Phys. 17, 265–273 (2008). [CrossRef]
- S. T. Dembinski, A. Kossakowski, L. A. Lugiato, and P. Mandel, “Semi-classical and quantum-theory of bistability in lasers containing saturable absorbers 2,” Phys. Rev. A 18, 1145–1151 (1978). [CrossRef]
- L. A. Lugiato, P. Mandel, S. T. Dembinski, and A. Kossakowski, “Semi-classical and quantum theories of bistability in lasers containing saturable absorbers,” Phys. Rev. A 18, 238–254 (1978). [CrossRef]
- H. Kawaguchi, “Optical bistability and chaos in a semiconductor-laser with a saturable absorber,” Appl. Phys. Lett. 45, 1264–1266 (1984). [CrossRef]
- E. Arimondo, D. Dangoisse, C. Gabbanini, E. Menchi, and F. Papoff, “Dynamic behavior of bistability in a laser with a saturable absorber,” J. Opt. Soc. Am. B 4, 892–899 (1987). [CrossRef]
- J. M. Oh and D. H. Lee, “Strong optical bistability in a simple L-band tunable erbium-doped fiber ring laser,” IEEE J. Quantum Electron. 40, 374–377 (2004). [CrossRef]
- L. Guidoni, R. Mannella, V. Isaia, P. Verkerk, and E. Arimondo, “Stochastic resonance in a laser with saturable absorber,” Nuovo Cimento D 17, 803–810 (1995). [CrossRef]
- S. Djabi, H. Boudoukha, and M. Djabi, “Optical bistability in a laser containing a saturable absorber,” Ann. Phys. 32, 63–65 (2007). [CrossRef]
- C. Masoller, M. Oria, and R. Vilaseca, “Modeling a semiconductor laser with an intracavity atomic absorber,” Phys. Rev. A 80, 013830 (2009). [CrossRef]
- S. Ishii and T. Baba, “Bistable lasing in twin microdisk photonic molecules,” Appl. Phys. Lett. 87, 181102 (2005). [CrossRef]
- A. V. Naumenko, N. A. Loiko, and T. Ackemann, “Analysis of bistability conditions between lasing and nonlasing states for a vertical-cavity surface-emitting laser with frequency-selective optical feedback using an envelope approximation,” Phys. Rev. A 76, 023802 (2007). [CrossRef]
- B. Farias, T. P. de Silans, M. Chevrollier, and M. Oria, “Frequency bistability of a semiconductor laser under a frequency-dependent feedback,” Phys. Rev. Lett. 94, 173902 (2005). [CrossRef]
- H. E. Tureci, A. D. Stone, L. Ge, S. Rotter, and R. J. Tandy, “Ab initio self-consistent laser theory and random lasers,” Nonlinearity 22, C1–C18 (2009). [CrossRef]
- L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010). [CrossRef]
- L. Ge, Y. D. Chong, S. Rotter, H. E. Tureci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 023820 (2011). [CrossRef]
- M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Tureci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012). [CrossRef]
- M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics(Addison-Wesley, 1974).
- A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000). [CrossRef]
- O. Zaitsev and L. Deych, “Diagrammatic semiclassical laser theory,” Phys. Rev. A 81, 023822 (2010). [CrossRef]
- A. E. Siegman, Lasers (University Science, 1986).
- H. E. Tureci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006). [CrossRef]
- H. E. Tureci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007). [CrossRef]
- H. E. Tureci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008). [CrossRef]
- K. Staliunas and V. J. Sánchez Morcillo, Transverse Patterns in Nonlinear Optical Resonators (Springer, 2003).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.