Coupled longitudinal and transverse self-organization in lasers induced by transverse-mode locking
| Autor: | Didier Dangoisse, Pierre Glorieux, G. Slekys, Eric Louvergneaux |
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| Rok vydání: | 1998 |
| Předmět: | |
| Zdroj: | Scopus-Elsevier |
| ISSN: | 1094-1622 1050-2947 |
| DOI: | 10.1103/physreva.57.4899 |
| Popis: | The description of laser transverse patterns in terms of the empty cavity eigenmodes proved to be a successful method to interpret self-organization and spatiotemporal dynamics in lasers @1‐5#. Various cases of transverse dynamics involving low-order transverse-mode interactions, have shown that in the first approximation the dynamics arise from the frequency beating of the transverse modes @1,3‐5#. It has been shown that nonlinearity of the gain medium may lead to stationary patterns resulting from cooperative frequency locking @6#; due to their nonlinear coupling several transverse modes lock to a common optical frequency and particular phase differences are selected @7‐9#. In the resulting stationary pattern, amplitudes and relative phases of the interacting modes are determined by the minima of the generalized free energy of the system @10,11#. Different but equally possible locking phases between modes lead to a coexistence of various spatiotemporal behaviors of the pattern in which the locked modes, considered as nonlinear eigenmodes or supermodes @5#, continue to interact with the other modes. In this way, it has been pointed out that spatial multistability in lasers that may originate, for example, from transverse-mode locking, is promising for optical information processing applications like pattern recognition and associative memory @12,13#. In this paper we present experimental investigations on three-dimensional self-organization resulting from transverse-mode locking. We focus on the peculiarities of locking when the modes under consideration belong to different transverse order families. Up until now only transverse self-organization in the cross section perpendicular to the propagation axis has been investigated. Here, we consider propagation effects, including the third dimension that is often neglected in theoretical studies, by introduction of the mean-field approximation. Our experiments show that the transverse pattern of the beam strongly depends on the longitudinal coordinate and that the mean-field approximation becomes irrelevant in explaining most of the observed patterns. Empty cavity eigenmodes will be used to describe these patterns, since they were shown to provide a good basis in this problem @14#. More precisely, the pattern is developed on the eigenmodes of the empty cavity, and we neglect the changes in modal profiles due to nonlinear propagation effects. In this picture, we associate classical Gouy phase shifts to each of the cavity modes, and the nonlinearity arises from the coupling of the amplitudes of these modes via their common interactions with the active medium. This allows us to explain several features observed in the dynamics of transverse-mode locking; in particular, bistability and symmetry breaking between locked patterns with different spatial organization. We stress that this organization corresponds to combined longitudinal and transverse dependences. And this can be considered as an example of three-dimensional laser self-organization. This paper is organized in the following way. In the next section we recall the conditions in which the Gouy phase shift is relevant for the phase locking of transverse modes. The third section reports on the experimental setup. In the fourth one, we describe how mode locking selects stationary patterns and give the main characteristics of locking. Finally, the dynamics of a regime observed ~prelocking! just before locking, which lets us foresee the locking phase, is investigated in Sec. V. |
| Databáze: | OpenAIRE |
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