Complete nonlinear polarization control in an optical fiber system.

International audience; We consider the counterpropagating interaction of a signal and a pump beam in an isotropic optical fiber. On the basis of recently developed mathematical techniques, we show that an arbitrary state of polarization of the signal beam can be converted into any other desired state of polarization. On the other hand, an unpolarized signal beam may be repolarized into two specific states of polarization, without loss of energy. Both processes of repolarization and polarization conversion may be controlled by adjusting the polarization state of the backward pump.

Manifestation of Hamiltonian Monodromy in Nonlinear Wave Systems

International audience; We show that the concept of dynamical monodromy plays a natural fundamental role in the spatiotemporal dynamics of counterpropagating nonlinear wave systems. By means of an adiabatic change of the boundary conditions imposed to the wave system, we show that Hamiltonian monodromy manifests itself through the spontaneous formation of a topological phase singularity (2 - or -phase defect) in the nonlinear waves. This manifestation of dynamical Hamiltonian monodromy is illustrated by generic nonlinear wave models. In particular, we predict that its measurement can be realized in a direct way in the framework of a nonlinear optics experiment.

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

We report the experimental observation of bistability and hysteresis phenomena of the polarization signal in a telecommunication optical fiber. This process occurs in a counterpropagating configuration in which the optical beam nonlinearly interacts with its own Bragg-reflected replica at the fiber output. The proof of principle of optical flip–flop memory and 10  Gbit/s routing operation is also reported based on this polarization bistability. Finally, we also provide a general physical understanding of this behavior on the basis of a geometrical analysis of an effective model of the dynamics. Good quantitative agreement between theory and experiment is obtained.

Time-optimal control of spin-1/2 particles with dissipative and generalized radiation-damping effects

We analyze the time-optimal control of spin-1/2 particles with bounded field amplitudes in the presence of dissipative and radiation damping effects. Using tools of geometric optimal control theory, we determine different optimal syntheses for specific values of the system parameters. We show the nontrivial role of the effective radiation damping effect on the optimal control law.

Understanding the global structure of two-level quantum systems with relaxation: Vector fields organized through the magic plane and the steady-state ellipsoid

Hamiltonian tools for the analysis of optical polarization control

Import JabRef; International audience; 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 demonstrate…

Optical flip-flop memory and routing operation based on polarization bistability in optical fiber

A polarization bistability and hysteresis cycle phenomenon is demonstrated in optical fibers thanks to a counter-propagating four-wave mixing interaction. Based on this process, we successfully report the proof-of-principle of an optical flip-flop memory and a 10-Gbit/s routing operation.

Optimal control of the signal-to-noise ratio per unit time of a spin 1/2 particle: The crusher gradient and the radiation damping cases

We show to which extent the signal to noise ratio per unit time of a spin 1/2 particle can be maximized. We consider a cyclic repetition of experiments made of a measurement followed by a radio-frequency magnetic field excitation of the system, in the case of unbounded amplitude. In the periodic regime, the objective of the control problem is to design the initial state of the system and the pulse sequence which leads to the best signal to noise performance. We focus on two specific issues relevant in nuclear magnetic resonance, the crusher gradient and the radiation damping cases. Optimal control techniques are used to solve this non-standard control problem. We discuss the optimality of t…

Connection between optimal control theory and adiabatic-passage techniques in quantum systems

This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from the Pontryagin Maximum Principle. In a three-level quantum system, we show that the Stimulated Raman Adiabatic Passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.

Simultaneous time-optimal control of the inversion of two spin-12particles

We analyze the simultaneous time-optimal control of two-spin systems. The two noncoupled spins, which differ in the value of their chemical offsets, are controlled by the same magnetic fields. Using an appropriate rotating frame, we restrict the study to the case of opposite shifts. We then show that the optimal solution of the inversion problem in a rotating frame is composed of a pulse sequence of maximum intensity and is similar to the optimal solution for inverting only one spin by using a nonresonant control field in the laboratory frame. An example is implemented experimentally using nuclear magnetic resonance techniques.

Optimal control of the inversion of two spins in Nuclear Magnetic Resonance

International audience; We investigate the optimal control of the inversion of two spin 1/2 particles in Nuclear Magnetic Resonance. The two spins, which differ by their resonance offset, are controlled by the same radio frequency magnetic field. Using the Pontryagin Maximum Principle, we compute the optimal control sequence which allows to reach the target state in a given time, while minimizing the energy of the magnetic field. A comparison with the time-optimal solution for bounded control amplitude realizing the same control in the same time is made. An experimental illustration is done using techniques of Nuclear Magnetic Resonance.

Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension

International audience; We analyze the role of soliton solutions and Hamiltonian singularities in the dynamics of counterpropagating waves in a medium of finite spatial extension. The soliton solution can become unstable due to the finite extension of the system. We show that the spatiotemporal dynamics then relaxes toward a Hamiltonian singular state of a nature different than that of the soliton state. This phenomenon can be explained through a geometrical analysis of the singularities of the stationary Hamiltonian system.

Line of polarization attraction in highly birefringent optical fibers

We investigate the phenomenon of polarization attraction in a highly birefringent fiber. This polarization process originates from the nonlinear interaction of two counter-propagating beams. We show that all polarization states of the forward (signal) beam are attracted toward a specific line of polarization states on the surface of the Poincare sphere, whose characteristics are determined by the polarization state of the injected backward (pump) beam. This phenomenon of polarization attraction takes place without any loss of energy for the signal beam. The stability of different stationary solutions is also discussed through intensive numerical simulations. On the basis of mathematical tec…

A universal optical all-fiber omnipolarizer

International audience; Wherever the polarization properties of a light beam are of concern, polarizers and polarizing beamsplitters (PBS) are indispensable devices in linear-, nonlinear- and quantum-optical schemes. By the very nature of their operation principle, transformation of incoming unpolarized or partially polarized beams through these devices introduces large intensity variations in the fully polarized outcoming beam(s). Such intensity fluctuations are often detrimental, particularly when light is post-processed by nonlinear crystals or other polarization-sensitive optic elements. Here we demonstrate the unexpected capability of light to self-organize its own state-of-polarizatio…

Polarization control in spun and telecommunication optical fibers

International audience; We consider the counterpropagating interaction of a signal and a pump beam in a spun fiber and in a randomly birefringent fiber, the latter being relevant to optical telecommunication systems. On the basis of a geometrical analysis of the Hamiltonian singularities of the system, we provide a complete understanding of the phenomenon of polarization attraction in these two systems, which allows to achieve a control of the polarization state of the signal beam by adjusting the polarization of the pump. In spun fibers, all polarization states of the signal beam are attracted toward a specific line of polarization states on the Poincaré sphere, whose characteristics are d…