G. Ropars

A depolarizer as a possible precise sunstone for Viking navigation by polarized skylight

Viking navigation from Norway to America in the northern latitudes remains a mystery for physicists, historians and archaeologists. Polarimetric methods using absorbing dichroic crystals as polarizers to detect a hidden Sun direction using the polarized skylight have led to controversies. Indeed, these techniques may lack in sensitivity, especially when the degree of polarization is low. Here, we demonstrate theoretically and experimentally that using the transparent common Iceland spar as a depolarizer, the Vikings could have performed a precise navigation under different conditions. Indeed, when simply rotated, such a birefringent crystal can completely depolarize, at the so-called isotropy point, any partially polarized state of light, allowing us to guess the direction of the Sun. By equalizing the intensities of the ordinary and extraordinary beams at the isotropy point, we show that the Sun direction can be determined easily, thanks to a simple sensitive differential two-image observation. A precision of a few degrees could be reached even under dark crepuscular conditions. The exciting recent discovery of such an Iceland spar in the Alderney Elizabethan ship that sank two centuries before the introduction of the polarization of light in optics may support the use of the calcite crystal for navigation purposes.

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.

Experimental evidence of single round-trip oscillation in polarization self-modulated vertical-cavity surface emitting lasers

The polarizations and frequencies of the two eigenstates of a vertical cavity surface emitting laser with an external cavity containing a quarter-wave plate are theoretically and experimentally analyzed. It is shown that the polarizations of these eigenstates are fixed by the neutral axes of the quarter-wave plate. The optical pulses at a frequency equal to a half of the free spectral range of the external cavity, observed through a linear polarizer, are due to beats between the two eigenstates. All these features show that such polarization self-modulated lasers oscillate in a single round trip.

The inhibition mechanism in polarization bistable semiconductor lasers

The polarization bistability between TE 00 and TM 00 eigenstates in InGaAsP/InP lasers is shown to be due to the mode inhibition mechanism. A theoretical analysis shows that the switching is governed by two current-dependent competing terms. One term represents the self-stabilization for the existing lasing mode to resist the onset of a new mode. The other term is the gain recovering term of the nonlasing mode. The major contribution to the latter is the relative current dependence of the TE and TM gains. By making proper assumptions for the device parameters based on experimental data, the observed hysteresis loops have been successfully modeled. The conditions for the existence of polarization bistability are discussed.

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.

Polarization slaving mechanisms in vectorial bistable lasers

The basic mechanisms of external all-optical control of polarization bistabilities are isolated in one- and two-frequency systems. Induced rotation and induced inhibition mechanisms by vectorial injection in lasers are theoretically predicted and experimentally shown in both systems. The sensitivity of the vectorial systems leads to subfemtojoule switching energies, which correspond to the theoretical threshold values. A reduction by four orders of magnitude compared to the lowest energy demonstrated in scalar passive systems is obtained.

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.

Dark zone in the centre of the Arago-Poisson diffraction spot of a helical laser beam.

We report on the diffraction of non-zero Laguerre Gaussian laser beams by an opaque disk. We observe a tiny circular dark zone at the centre of the usual Arago-Poisson diffraction bright spot. For such non-diffracting dark hollow beams, we have measured diameters as small as 20 μm on distances of the order of ten metres, without focalization. Diameters depend on the diffracting object size and on the topological charge of the input Laguerre Gaussian beam. These results are in good agreement with theoretical considerations. Potential applications are then discussed.

Direct monitoring of the coupling constant in vectorial lasers

The partial separation of two laser eigenstates is used to differentially modulate their net gains, hence permitting to demonstrate a simple method to measure the coupling constant C in bistable vectorial lasers. The same experimental setup works equally well for weak coupling. A good agreement between theoretical and experimental values is obtained in both cases. Moreover, the method is applied to the case of external cavity VCSELs used in optical clocking experiments.

Polarization dragging in injected lasers

The vectorial injection locking of a slave laser by a linearly polarized master laser is theoretically and experimentally investigated, taking the nature and the stability of the eigenstates of the slave laser into account. It is proved that the behavior of the polarization, intensity, and frequency of the slave laser can be described by four nonlinear coupled differential equations, for lasers in which population inversion remains quite constant. In particular, it is shown that the stability of the eigenstates of the slave laser plays a dramatic role in the response of this laser to injection. Isotropic slave lasers are shown to follow adiabatically the polarization of the master laser in the frequency locking range. Loss anisotropic slave lasers exhibit a specific Adler tongue behavior and can support the transfer of the polarization of the master laser only along their eigenstates. Phase anisotropic slave lasers are shown to exhibit two bistable or simultaneous Adler curves and to offer new possibilities of all-optical command. In all of these cases, a good agreement is obtained between theory and experiment and the study of polarization throws light on the physics of injection locking. >