Conical Refraction Research Articles

Conical refraction of elastic waves in absorbing crystals

The absorption-induced acoustic-axis splitting in a viscoelastic crystal with an arbitrary anisotropy is considered. It is shown that after “switching on” absorption, the linear vector polarization field in the vicinity of the initial degeneracy point having an orientation singularity with the Poincare index n = ±1/2, transforms to a planar distribution of ellipses with two singularities n = ±1/4 corresponding to new axes. The local geometry of the slowness surface of elastic waves is studied in the vicinity of new degeneracy points and a self-intersection line connecting them. The absorption-induced transformation of the classical picture of conical refraction is studied. The ellipticity of waves at the edge of the self-intersection wedge in a narrow interval of propagation directions drastically changes from circular at the wedge ends to linear in the middle of the wedge. For the wave normal directed to an arbitrary point of this wedge, during movement of the displacement vector over the corresponding polarization ellipse, the wave ray velocity s runs over the same cone describing refraction in a crystal without absorption. In this case, the end of the vector moves along a universal ellipse whose plane is orthogonal to the acoustic axis for zero absorption. The areal velocity of this movement differs from the angular velocity of the displacement vector on the polarization ellipse only by a constant factor, being delayed by π/2 in phase. When the wave normal is localized at the edge of the wedge in its central region, the movement of vector s along the universal ellipse becomes drastically nonuniform and the refraction transforms from conical to wedge-like.

Conical refraction and formation of multiring focal image with Laguerre–Gauss light beams

For a light beam focused through a biaxial crystal along one of its optical axes, the effect of internal conical refraction in the crystal leads to the formation in the focal image plane of two bright rings separated by a dark ring. It is shown that, with circularly polarized Laguerre-Gauss LG(0)(ℓ) beams entering the crystal, this classical double-ring pattern is transformed into a multiring one consisting of ℓ+2 bright rings.

Frequency doubling with laser beams transformed by conical refraction in a biaxialcrystal

The second-harmonic generation with laser beams transformed by internal conicalrefraction in a biaxial crystal was studied in a cascaded two-crystal arrangement, wherethe biaxial crystal transformed the input Gaussian beam and another nonlinearcrystal was used for frequency doubling of the produced conical refraction pattern.Several specific second-harmonic beam profiles obtained for various positions of thenonlinear crystal along the beam propagation direction are considered and discussed.

Second-harmonic conical refraction: observation of free and forced harmonic waves

Observation of second-harmonic conical refraction in KTiOPO4 crystal is reported. Two second-harmonic conical patterns, namely forced and free harmonic waves, are identified and registered with exceptional clarity and level of details. The forced second-harmonic wave evolves into the characteristic ring intensity distribution while the free-harmonic wave gives a single ray direction, resulting in a spot.

Magnetic birefringence and conical refraction of elastic waves in antiferromagnetic α-Fe2O3

This paper reports on the results of an experimental investigation into the influence of linear magnetic birefringence of transverse elastic waves due to magnetoelastic interaction on the conical refraction of sound in antiferromagnetic α-Fe2O3. It has been found that, in a weakly ferromagnetic state, the incoming flux of the sound energy is separated into two fluxes corresponding to two normal modes of transverse vibrations in the sample. They propagate along the C 3 trigonal axis of this crystal with different phase velocities due to the linear magnetic birefringence of sound. It has been established that the angle of deviation (θη) from the C 3 axis for the group velocity of the normal mode of elastic vibrations, which does not interact with the magnetic subsystem, is determined by the internal conical refraction and does not depend on the magnitude of the magnetic field in the basal plane (H ⊥ C 3). It has also been shown that the angle of deviation (θξ) of the group velocity of the interacting mode of normal vibrations depends on the magnitude of the magnetic field and tends to θη at large values of H. The group velocity vectors lie in the same azimuth plane passing through the C 3 axis and deviate in opposite directions. The obtained results confirm the conclusions drawn from the theoretical description of the conical refraction of sound in antiferromagnets.

The creation and annihilation of optical vortices using cascade conical diffraction

Internal conical diffraction produces a superposition of orthogonally polarised zero- and first-order Bessel like beams from an incident circularly polarised Gaussian beam. For right-circularly polarised light, the first-order beam has an optical vortex of charge -1. Upon propagation of the first-order beam through a second biaxial crystal, a process which is termed cascade conical refraction, the generated beam is a superposition of orthogonally polarised fields of charge 0 and -1 or 0 and -2. This spin to orbital angular momentum conversion provides a new method for the generation and annihilation of optical vortices in an all-optical arrangement that is solely dependent on the incident polarisation and vortex handedness.

Improving directivity of laser beams by employing the effect of conical refraction in biaxial crystals

The far-field pattern of Gaussian beams transformed by conical refraction in biaxial crystal is analyzed. It is shown that one of the two outgoing beam components acquires, under certain conditions, a profile with a dominating central peak. The width of this peak can be made significantly smaller than the width of the parent diffraction-limited Gaussian beam at the same propagation distance. The formation of such structurally-stable sub-diffraction beam core improves the beam directivity. Another component is a charge-one optical vortex, that forms the annular shell of the beam and carries the rest of the beam power.

Biaxial crystal as a versatile mode converter

The extreme versatility of the internal conical refraction in biaxial crystals in thetransformation of Gaussian laser beams is demonstrated and discussed. By means ofsimple variations in the focusing and polarization of the input beam, various beamconfigurations like Bessel–Gauss, Hermite–Gauss, Laguerre–Gauss, and othersare shown to be produced from a lowest-order Gaussian beam passed through abiaxial crystal along one of its optical axes. Further transformations of the beamprofile and formation of more complex light patterns were obtained in a cascadedscheme, when the beam was passed consecutively through two crystals. Theseobservations, together with the known ability of conical refraction to form a variety ofother complex light structures, demonstrate the unique properties of the effectin manipulations with the amplitude, phase, and polarization of light beams.

Laser with simultaneous Gaussian and conical refraction outputs

We report a double-sided two-mirror neodymium-doped KGd(WO4)2/Nd:KGW conical refraction laser which produces a linearly polarised output from the flat output coupler and a cone-refracted output from the curved output coupler. The linearly polarised output had a polarisation extinction ratio of 20:1 with a Gaussian beam profile and a measured M2=1. The unpolarised output had the intensity and polarisation distribution corresponding to a cone-refracted Gaussian beam with extinction ratio of 2.7:1.

Antiferromagnetic conical refraction of elastic waves in hematite

Conical refraction, which is due to the renormalization of the elastic moduli by the effective magnetoelastic interaction and depends on the static magnetic field, has been experimentally observed in an α-Fe2O3 trigonal easy-plane antiferromagnet in addition to the usual internal conical refraction of transverse elastic waves propagating along the trigonal C3 axis. It has been shown that the deviation angle θη of the energy flux from the C3 axis at the internal conical refraction is independent of the magnetic field applied in the basal plane (H ⊥ C3) and is a constant determined by the ratio of the elastic moduli C14 and C44. The deviation angle of the energy flux at the antiferromagnetic conical refraction increases with the magnetic field and approaches the value θη at large H values. The results are well described by the theory of this phenomenon developed by E.A. Turov and confirm its basic conclusions.

Second-harmonic conical refraction in GUHP

A comparison of linear and second-harmonic conical refractions inguanylurea(1 +) hydrogen phosphite (GUHP) single crystal is reported. The favorable material properties ofGUHP allowed us to observe well resolved second-harmonic conical refraction ringsincluding the Poggendorff division. Study of the refraction patterns confirmed that thespatial distributions of the electromagnetic field behind the sample compare well in thelinear and quadratic cases.

Conical refraction Nd:KGd(WO_4)_2 laser

In 1832 Hamilton predicted conical refraction, concluding that if a beam propagates along an optic axis of a biaxial crystal, a hollow cone of light will emerge. Nearly two centuries on, cascade conical refraction involving multiple crystals has not been investigated. We empirically investigate a unique two-crystal configuration, and use this to demonstrate an ultra-efficient conical refraction Nd:KGd(WO(4))(2) laser providing multi-watt output with excellent beam quality independent of resonator design with a slope efficiency close to the theoretical maximum, offering a new route for power and brightness-scaling in solid-state bulk lasers.

晶体锥折射空心光束的位相差及偏振特性

Based on the principle of hollow ring achieved by conical refraction effect in biaxial crystal,the formula of phase difference distribution between every point and the minimal point in the hollow ring are deduced,and the regularity of phase difference distribution is obtained by means of simulations.The continuity in the circumference of polarization direction variation of each point in the hollow ring is proved.In the experiment,un-polarized He-Ne laser is adopted to perpendicular radiate KNbO3 crystal,then polarization characteristic of hollow beams achieved by conical refraction effect in biaxial crystal is tested.The result of theoretical analysis agrees well with experiment.

Analogies between the torque-free motion of a rigid body about a fixed point and light propagation in anisotropic media

An apparently unnoticed analogy between the torque-free motion of a rotating rigid body about a fixed point and the propagation of light in anisotropic media is stated. First, a new plane construction for visualizing this torque-free motion is proposed. This method uses an intrinsic representation alternative to angular momentum and independent of the modulus of angular velocity \U0001d6da. The equivalence between this plane construction and the well-known Poinsot's three-dimensional graphical procedure is also shown. From this equivalence, analogies have been found between the general plane wave equation (relation of dispersion) in anisotropic media and basic equations of torque-free motion of a rigid body about a fixed point. These analogies allow reciprocal transfer of results between optics and mechanics and, as an example, reinterpretation of the internal conical refraction phenomenon in biaxial media is carried out. This paper is intended as an interdisciplinary application of analogies for students and teachers in the context of intermediate physics courses at university level.

On Conical Refraction in Hexagonal and Cubic Media

The occurrence of conical refraction in hexagonal and in cubic elastic media is investigated by the method of localizations. This is accomplished by generalizing the Atiyah–Bott–Gårding theory from the scalar case to hyperbolic square systems of linear partial differential systems with constant coefficients.

The fundamental matrix of the system of linear elastodynamics in hexagonal media. Solution to the problem of conical refraction

An explicit integral representation by single definite integrals of the fundamental matrix (Green's tensor) of the time-dependent system of hexagonal elastic media is derived. Thereby the problem of internal conical refraction in such media is solved.

Polarization-tunable Yb:KGW laser based on internal conical refraction

Using internal conical refraction, we demonstrate an Yb:KGW laser where the polarization state can be arbitrarily altered without any additional cavity components. The extinction ratio can also be altered between 1:1 and 40:1. The maximum output power achieved was 8.6 W at a slope efficiency of 60.5% with respect to incident pump power. This equals the power performance of a standard Yb:KGW laser used for reference.

Conical refraction: Experiments and large-scale demonstrations

Results of experiments on internal and external conical refraction on a rhombic sulfur single crystal are presented. A high-transmission optical scheme is suggested with light focusing on the crystal surface which allows two fringes of internal conical refraction ∼1 m in diameter to be observed in laser radiation. Two fringes of external conical refraction with unique polarization state are first observed, and conditions of light energy concentration along the biradial are discussed. The focusing power of a plane-parallel biaxial crystal plate is measured.

Walk-off near optic axes of spatially dispersive media of fluorite symmetry: the case of conical points

Experimental evidence of the influence of the so-called intrinsic birefringence of fluorite in 2001 has revived interest in spatial dispersion effects, whereby the index surface of fluorite and crystals with the same symmetry shows seven optic axes, of which four intersect this surface at pairs of conical points. Nevertheless it has been shown that conical internal refraction never happens—so near all the optic axes the walk-off angle is small. I provide first-order expansions of the walk-off angles near the two types of optic axes. For those associated with conical points the result is striking: near them the walk-off angle, far from being greater than near the other optic axes, is much smaller because its first-order approximation is null! This result could become useful for the correction of birefringence effects in lenses designed for the vacuum ultraviolet, where fluorite is one of the very few materials available.

Formation of radial and azimuthal polarization of light

This paper discusses a method of obtaining and controlling radial and azimuthal polarization of light beams on the basis of conical refraction and electrooptics. An optical diagram of such a polarization converter is described, and a mathematical transformation of the phase of the orthogonal polarizations is considered.