Abstract

We study pattern formation in a complex Swift–Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems submitted to a bichromatic injection when the instability is toward long (transverse) wavelengths. Applications include two-level lasers and photorefractive oscillators. Under such an injection, the original continuous phase symmetry of the system is replaced by a discrete one and phase bistability emerges. This leads to the spontaneous formation of phase-locked spatial structures, such as phase domains and dark-ring (phase) cavity solitons. The stability of the homogeneous solutions is studied, and numerical simulations are made covering all the dynamical regimes of the model, which turn out to be very rich. Derivations of the rocked complex Swift–Hohenberg equation, using multiple scale techniques, are given for the two-level laser and the photorefractive oscillator.

© 2018 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Hexagonal patterns in multistep optical parametric processes

Stefano Longhi
Opt. Lett. 26(10) 713-715 (2001)

Stable topological spatial solitons in optical parametric oscillators

Stefano Trillo, Marc Haelterman, and Adrian Sheppard
Opt. Lett. 22(13) 970-972 (1997)

Body-centered cubic dissipative crystal formation in a dispersive and diffractive optical parametric oscillator

M. Tlidi, D. Pieroux, and Paul Mandel
Opt. Lett. 28(18) 1698-1700 (2003)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (10)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (89)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription