Albert Le Floch

Nonlinear polarization dynamics in anisotropic lasers

Abstract Instabilities are observed in the polarization of lasers with controlled anisotropies when double external dynamics are induced by both static and time periodic nonlinear Faraday effects, revealing two kinds of behavior: (i) in lasers with loss anisotropy, quasiperiodicity and Arnold tongues are exhibited and (ii) in lasers with phase anisotropy, additional period-doubling and intermittency occur. These different behaviors are in agreement with models in which the atomic variables are adiabatically eliminated.

The polarization sense in human vision

Unlike humans, numerous animals are differentially sensitive to the vector orientation of linearly polarized light. However as early as 1844 Haidinger noted that weak blue-yellow brushes appear, centered on the fovea, when the sky is observed through a slowly rotating polarizer. Different models have been proposed to try to understand this phenomenon, but the precise mechanism remains unknown and the polarization unexploited. We suggest that when Fresnels laws are applied to the unguided oblique rays, that the cylindrical geometry of the blue cones in the fovea along with their distribution induces an extrinsic dichroism and could explain why the human eye is sensitive to polarization. We have constructed an artificial eye model system using the same laws and were able to photograph the appearance of entoptic-like blue-dark brushes, confirming the observations and our mathematical simulations. Moreover, our in vivo and in vitro tests show that in addition to the usual 3s fading time measured using a stationary stimulus, there exists for this entoptic image a short extra creating and erasing time of about 0.1s, using a dynamical stimulus. We have also found that, surprisingly, the rotating pattern is more regular and symmetrical with one of our two eyes around a more circular blue cone-free area, the dominant eye. Our results suggest that the polarization sense can provide important information in many areas that remain to be explored.

The sixteenth century Alderney crystal: a calcite as an efficient reference optical compass?

The crystal recently discovered in the 1592 sunken Elizabethan ship is shown to be an Iceland spar. We report that two main phenomena, with opposite effects, explain the good conservation and the evolution of this relatively fragile calcite crystal. We demonstrate that the Ca2+–Mg2+ ion exchanges in such a crystal immersed in sea water play a crucial role by limiting the solubility, strengthening the mechanical properties of the calcite, while the sand abrasion alters the crystal by inducing roughness of its surface. Although both phenomena have reduced the transparency of the Alderney calcite crystal, we demonstrate that Alderney-like crystals could really have been used as an accurate optical sun compass as an aid to ancient navigation, when the Sun was hidden by clouds or below the horizon. To avoid the possibility of large magnetic errors, not understood before 1600, an optical compass could have helped in providing the sailors with an absolute reference. An Alderney-like crystal permits the observer to follow the azimuth of the Sun, far below the horizon, with an accuracy as great as ±1°. The evolution of the Alderney crystal lends hope for identifying other calcite crystals in Viking shipwrecks, burials or settlements.

Sensitive dichroism measurements using eigenstate decay times

The optical decay times associated with the eigenstates of an anisotropic cavity are measured. This leads to a simple differential method for isolating the linear (or circular) dichroism in either optical or atomic systems.

A simple method to measure the lifetime of excited levels of rare earth ions: application to erbium ions in fluorophosphate glasses

Abstract A resonant technique, based on the sinusoidal modulation of the pump beam intensity, is demonstrated in the case of the precise measurement of the lifetime of the 4 I 13 2 level of erbium ions in fluorophosphate hosts. This intensity modulation is obtained via a rotation of the polarization of the pump beam. The large signal-to-noise ratio enables the use of low pump power and apparent lifetime shortenings due to ion-ion energy transfer processes and to amplification of spontaneous emission are circumvented. A parallel ith decay times deduced from usual fluorescence decay measurements is performed. Extension of the method to the spectroscopy of other rare-earth ions is discussed.

Vectorial bistability and simultaneity of the two helicoidal stationary eigenstates of a ring laser

Abstract The dynamics of the two helicoidal stationary eigenstates of a ring laser is investigated. It is experimentally shown that the choice of the isotopic composition of the HeNe gas discharge allows a control of the coupling constant of the two eigenstates. Vectorial bistability and vectorial simultaneity of the two eigenstates are observed and interpreted in the framework of a Landau potential model.

The sunstone and polarised skylight: ancient Viking navigational tools?

Although the polarisation of the light was discovered at the beginning of the nineteenth century, the Vikings could have used the polarised light around the tenth century in their navigation to America, using a ‘sunstone’ evoked in the Icelandic Sagas. Indeed, the birefringence of the Iceland spar (calcite), a common crystal in Scandinavia, permits a simple observation of the axis of polarisation of the skylight at the zenith. From this, it is possible to guess the azimuth of a hidden Sun below the horizon, for instance. The high sensitivity of the differential method provided by the ordinary and extraordinary beams of calcite at its so-called isotropy point is about two orders higher than that of the best dichroic polariser and permits to reach an accuracy of  ±1° for the Sun azimuth (at sunrise and sunset). Unfortunately, due to the relative fragility of calcite, only the so-called Alderney crystal was discovered on board a 16th ancient ship. Curiously, beyond its use as a sunstone by the Vikings, during these last millennia calcite has led to the discovery of the polarisation of the light itself by Malus and is currently being used to detect the atmospheres of exoplanets. Moreover, the differential method for the light polarisation detection is widely used in the animal world.

Goos–Hänchen effect in the dynamics of laser eigenstates

A theoretical model is developed to predict the behavior of the TE and TM eigenstates of a laser when the Goos–Hanchen effect associated with a total internal reflection inserted inside the laser cavity is taken into account. The generalized Jones matrix describing the internal reflection on a plane interface is determined, and the dynamics of the linearly polarized eigenstates around the critical angle is investigated both theoretically and experimentally. Moreover, the strong coupling between the TE and TM eigenstates is shown to provide a direct visualization of the Goos–Hanchen lateral shift.

Ring-laser gyro with spatially resolved eigenstates

The spatial resolution of laser eigenstates is applied to ring geometry. A bidirectional optical diode based on the Faraday effect and nonreciprocal intracavity losses is theoretically and experimentally investigated. This novel optical diode combined with spatial separation provides a biased gyro with no lock-in band.

Measurement of residual reflectivities using the two eigenstates of a passive cavity

A sensitive differential method is described for isolating from other losses the residual reflectivity of an antireflection coating deposited on a quarterwave plate. Insertion of such a plate into a passive cavity reveals two eigenstates related to its axis, which may be by nature simultaneously resonant and antiresonant. The ratio between the two corresponding output intensities depends on the residual reflectivity of the plate and is moreover enhanced by the resonator. A residual reflectivity resolution of 10 ppm with a relatively low cavity finesse of 70 is achieved, and the possibility of measuring separately the losses from the coating and the substrate, using a half-coated quarterwave plate, is developed. We discuss the performances of our experimental setup and possible improvements and extensions of the method, in particular to isotropic components.