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European Quantum Electronics Conference (EQEC)

Spontaneous pattern formation in an absorptive system

W. J. Firth, Andrew J. Scroggie

Published Aug 24, 2005• 0 citations
Publisher

Abstract

We present analytical and numerical results indicating pattern formation in a purely absorptive medium, namely a resonantly-excited two-level system in a ring cavity. Pattern formation occurs when the cavity is mistuned such that the optical wavelength exceeds that of the nearby cavity mode. But then off-axis or tilted waves can exactly fit the cavity, and this determines the dominant transverse wave vector of the pattern. >

DOI
10.1109/eqec.1994.698056

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Spontaneous pattern formation in an absorptive system

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We present analytical and numerical results indicating pattern formation in a purely absorptive medium, namely a resonantly-excited two-level system in a ring cavity. Pattern formation occurs when the cavity is mistuned such that the optical wavelength exceeds that of the nearby cavity mode. But then off-axis or "tilted" waves can exactly fit the cavity, and this determines the dominant transverse wave vector of the pattern.>

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We present analytical and numerical results indicating pattern formation in a purely absorptive medium, namely a resonantly-excited two-level system in a ring cavity. Pattern formation occurs when the cavity is mistuned such that the optical wavelength exceeds that of the nearby cavity mode. But then off-axis or tilted waves can exactly fit the cavity, and this determines the dominant transverse wave vector of the pattern. >
The development of spontaneous stationary equilibrium patterns induced by the injection of a laser pump field into a purely absorptive two-level atomic sodium vapour ring cavity is investigated by means of various weakly non-linear stability analyses applied to the appropriate governing evolution equation for this optical phenomenon. In the quasi-equilibrium limit for its atomic variables, the mathematical system modelling that phenomenon can be reduced to a single modified Swift–Hohenberg non-linear partial differential time-evolution equation describing the intracavity field on an unbounded 2D spatial domain. Diffraction of radiation can induce transverse patterns consisting of stripes, squares and hexagonal arrays of bright spots or honeycombs in an initially uniform plane-wave configuration. Then, these theoretical predictions are compared with both relevant experimental evidence and existing numerical simulations from some recent non-linear optical pattern formation studies.
Pattern formation near threshold in large-aspect-ratio, single-longitudinal-mode, two-level lasers with plane mirrors under the action of a weak injected plane-wave field resonant with the atomic transition frequency and tilted with respect to the laser cavity axis is analytically investigated in terms of the amplitude equations for the system. It is shown that, when the laser emission occurs off-axis, the appearance of resonances among the injected signal field and the unstable emerging tilted waves drastically changes the pattern selection properties of the free-running laser. As a result new transverse patterns, which include singly and doubly periodic stripes and undulating hexagons, may be stabilized by the injected signal. These patterns arise from the superposition of the forced mode with either one, two, or three traveling waves on the critical circle of the free-running laser. This is a distinctive feature from similar structures more commonly found in passive optical systems, where complex patterns always arise as a superposition of standing waves. The stability properties of the various patterns and their selection rules are analytically investigated within the amplitude equations.
We discuss a novel type of optical instability, which leads to the spontaneous formation of a stationary spatial structure, instead of to the onset of oscillations or pulsations. A passive system is contained in an optical cavity, to which we add two lateral mirrors. Under appropriate conditions, diffraction of radiation can induce the onset of a transverse-stripe structure in an initially uniform plane-wave field configuration. In this paper, we consider the case of a homogeneously broadened two-level system. The model on which our analysis is based is derived from the Maxwell-Bloch equations in the paraxial approximation, using the mean-field limit and assuming a large Fresnel number. We show that, with respect to the bistability parameter C, the threshold of the spatial instability coincides with the bistability threshold for absorptive, resonant optical bistability. The spatial instability requires, however, a detuned configuration and can arise both in the absence and presence of bistability. In the latter case, it can occur both in the lower and in the upper branch of the steady-state curve. The instability is caused by competition between different transverse modes, which realize a situation of spatial coexistence, different from the state of temporal coexistence which characterizes the spontaneous oscillations that arise from the previously known multimode instabilities. Finally, we discuss some points relevant for an experimental observation of this phenomenon.
We study the kinetics of transverse pattern formation in a passive ring cavity containing two-level atoms. Parameters are chosen such that the Turing instabilities are on the upper and lower branches of a bistable domain and close to the limit points, so that the interaction between the long-wavelength modes includes the homogeneous mode. This leads to the formation of a localized structure which connects the two stable branches of the homogeneous bistable solution. The kinetics of this pattern formation is described by simple scaling laws.