Hamiltonian tools for the analysis of optical polarization control

Abstract

The study of the polarization dynamics of two counterpropagating beams in optical fibers has recently been the subject of a growing renewed interest, from both the theoretical and experimental points of view. This system exhibits a phenomenon of polarization attraction, which can be used to achieve a complete polarization of an initially unpolarized signal beam, almost without any loss of energy. Along the same way, an arbitrary polarization state of the signal beam can be controlled and converted into any other desired state of polarization, by adjusting the polarization state of the counterpropagating pump beam. These properties have been demonstrated in various different types of optical fibers, i.e., isotropic fibers, spun fibers, and telecommunication optical fibers. This article is aimed at providing a rather complete understanding of this phenomenon of polarization attraction on the basis of new mathematical techniques recently developed for the study of Hamiltonian singularities. In particular, we show the essential role that play the peculiar topological properties of singular tori in the process of polarization attraction. We provide here a pedagogical introduction to this geometric approach of Hamiltonian singularities and give a unified description of the polarization attraction phenomenon in various types of optical fiber systems.

A universal optical all-fiber omnipolarizer

“…Note that the finite size of the SOP spot can also be interpreted theoretically by the fact that the singularities lie on the boundary of the energy-momentum diagram (see Fig. 2 of the supplementary materials), so that convergence to the singularities cannot take place in an isotropic way, which limits the efficiency of the attraction process27. We remark that the polarization controller inserted into the reflective loop of Fig.…”

Optical flip–flop memory and data packet switching operation based on polarization bistability in a telecommunication optical fiber

“…The role of such stationary states has already been discussed in different works for the analysis of the conventional process of polarization attraction involving two injected beams [14][15][16]. It was shown that such systems exhibit Hamiltonian singularities, which play the role of attractors for the spatiotemporal dynamics [17].…”

“…As opposed to traditional polarizers, which are known to waste 50% of unpolarized light, Heebner et al proposed in 2000 a "universal polarizer" performing repolarization of unpolarized light with 100% efficiency [1]. Subsequently, this phenomenon of polarization attraction or polarization pulling has been the subject of growing interest in optical fiber systems, involving the Raman effect [2][3][4], Brillouin backscattering [5,6], parametric amplification [7,8], and the full-degenerate four-wave mixing process, also called cross-polarization rotation [9][10][11][12][13][14][15][16][17][18][19]. Note that, from a broader perspective, the recent works obtained in a counterpropagating configuration in telecommunication fibers are inherently based on a four-wave interaction, which has been the subject of pioneering studies in the past [20][21][22][23][24][25].…”

Nonlinear polarization effects in optical fibers: polarization attraction and modulation instability [Invited]

“…The availability of a relatively simple deterministic model for describing nonlinear lossless polarizers based on randomly birefringent telecom fibers provides a key tool for numerically estimating their performance. Moreover, the properties of steady-state solutions of the averaged polarization evolution equations may be described in terms of mathematical techniques developed for the study of Hamiltonian singularities [30]. Such approach has led to the interesting observation that polarization attraction is closely linked with the existence of singular tori or multidimensional separatrix solutions [31][32][33].…”