Tunable phase-only optical filters with a uniaxial crystal

A novel method of fabricating phase-only optical filters that is based on the properties of a uniaxial crystal is proposed. With these optical filters, the phase differences are tunable among the different filter zones. Many focal patterns can be obtained if these optical filters are placed in front of a lens; furthermore, these optical filters can also be used to make up for the distortions in fabrications in which they were used only as untunable optical filters.     

Photon tunneling in a uniaxial crystal film

A method for studying photon tunneling in uniaxial crystal films is presented. The complex refractive index and the complex angle of refraction of the evanescent wave in a crystal are calculated for the most general case. The reflectance and transmittance resulting from the tunneling effect in crystal films are discussed, and the relations among these coefficients and the optical parameters of crystal are found. These relations provide a theoretical basis for characterizing crystal films by means of photon tunneling.     

Rotational spin Hall effect in a uniaxial crystal

We have considered the propagation process of the phase-matched array of singular beams through a uniaxial crystal. We have revealed that local beams in the array are rotated when propagating. However the right and left rotations are unequal. There are at least two processes responsible for the array rotation: the interference of local beams and the spatial depolarization. The interference takes place in the vortex birth and annihilation events forming the symmetrical part of the rotation. The depolarization process contributes to the asymmetry of the rotation that is called the rotational spin Hall effect. It can be brought to light due to the difference between the envelopes of the dependences of the angular displacement on the inclination angle of the local beams or the crystal length reaching the value of some angular degree. The direction of the additional array rotation is exclusively defined by the handedness of the circular polarization in the initial beam array.     

Generation of optical vortices in spun multihelicoidal optical fibers

We have theoretically studied long-period spun l-helicoidal fibers and their ability to generate singular beams from regular ones. On the basis of perturbation theory in the presence of degeneracy, applied to the scalar waveguide equation, we obtained the structure of coupled modes of such fibers and their spectra. It is shown that the coupled modes consist of the fields, which taken separately bear topological charges that differ by l units. We have numerically studied the process of the passage of a Gaussian beam through such a fiber and demonstrated that long-period l-helicoidal fibers have the ability to change-in a certain wavelength range-the topological charge of the incoming Gaussian beam by l units, generating in this way charge-l optical vortex.     

Diffraction of combined optical vortices

The diffraction of light on the lens of a Gaussian beam past a uniaxial crystal is equivalent to the beam diffraction on a helicoidal phase grating of two partial beams with different curvatures of the wave front. This diffraction significantly distorts the Gaussian beam profile and an extended region with three beam waists is formed near the focal plane. The beam waist region can be rectified by varying the radii of the primary beam waist and the lens pupil.     

Ray equation for a spatially variable uniaxial crystal and its use in the optical design of liquid-crystal lenses

To be able to design optical systems (e.g., variable focus or zoom lenses) made from liquid-crystal devices, it is necessary to be able to ray trace in a birefringent medium where the angle of the optical axis is a function of position in the device. To our knowledge, the theory required to achieve this has not previously been published, and we derive a suitable algorithm and give some examples of its use.     

Tunneling selection of optical vortices

We have studied the process of separation of the dominant mode and guided vortices in a Y-shaped directional fiber beam splitter. It is shown that, under certain conditions, the dominant mode field is completely pumped to the second channel, leaving the optical vortex field in this channel unchanged. Based on such a splitter, a vortex fiber interferometer has been created and characterized with respect to linearity and temperature sensitivity.     

A few-mode optical fiber retaining optical vortices

The ability of an optical fiber with axial losses to selectively suppress the fundamental HE ₁₁ mode, as well as the TE and TM waveguide modes, and, simultaneously, to transmit optical vortices with almost zero energy losses is considered. The attenuation coefficients for the corresponding eigenmodes and vortices are determined. It is shown that such a fiber operates as a mode filter for the feeding beam.     

Double refraction of a Gaussian beam into a uniaxial crystal

For a linearly polarized three-dimensional Gaussian beam in air that is normally incident upon a plane interface with a uniaxial crystal with optic axis in an arbitrary direction, we present integral representations for the transmitted field suitable for asymptotic analysis and efficient numerical evaluation and derive analytical expressions for transmitted nontruncated Gaussian beams for the cases in which the incident beam is polarized parallel to the plane containing the optic axis and the interface normal and transverse to it. The general solution for an arbitrary polarization state of an incident Gaussian beam follows by superposition of these two solutions.     

Recognition of the interference spiral image in a fiber optical sensor employing optical vortices

Three methods of processing the image of an interference spiral formed in a fiber optical sensor employing optical vortices have been considered. It is established that a method based on recognition of the spiral image is most stable with respect to noises. Using this technique, it is possible to determine the angle of spiral rotation even when the visibility of the interference pattern decreases to 0.2. The passage from intensity measurements to determination of the geometric parameters of the image significantly increases the range of linearity of interferometric devices employing optical vortices.     

Basic elliptical Gaussian wave and beam in a uniaxial crystal

Electromagnetic beams in a uniaxial crystal are treated with emphasis on the extraordinary mode. A virtual source that generates a basic elliptical Gaussian wave propagating obliquely to the optic axis is identified. An exact expression is obtained for this basic elliptical Gaussian wave that simplifies to the corresponding basic elliptical Gaussian beam in the appropriate limit. In the direction of amplitude propagation, the paraxial result becomes identical to the exact result and the sum of all the nonparaxial contributions vanish. The characteristics of the basic elliptical Gaussian beam are illustrated with a numerical example. From the spectral representation of the basic Gaussian wave, the first three orders of nonparaxial corrections for the basic elliptical Gaussian beam are determined. The nonparaxial results reduce correctly to those of the fundamental Gaussian beam in an isotropic medium.     

Evolution properties of a twisted Gaussian Schell-model beam in a uniaxial crystal

Paraxial propagation of a linearly polarised twisted Gaussian Schell-model (TGSM) beam in a uniaxial crystal is investigated. With the help of a tensor method, an analytical formula for the cross-spectral density (CSD) of a TGSM beam propagating in a uniaxial crystal orthogonal to the optical axis is derived. The evolution properties of the intensity distribution, the coherence widths and the twist factor of a TGSM beam in a uniaxial crystal are illustrated numerically. It is shown that the TGSM beam becomes an anisotropic TGSM beam in a uniaxial crystal and its evolution properties are closely related with its initial coherence, twist factor and the parameters of the crystal. The uniaxial crystal provides an effective way for modulating the properties of a TGSM beam, which will be useful in some applications, such as free-space optical communications and nonlinear optics, where a partially coherent beam with controlled beam profile and twist factor is required.     

Transmission of a two-dimensional Gaussian beam into a uniaxial crystal.

We study the transmission of a two-dimensional (2-D) TM Gaussian beam through a plane interface between an isotropic medium (e.g., air) and a uniaxially anisotropic crystal. The optic axis of the crystal is taken to be in the plane of incidence but is arbitrarily oriented relative to the interface normal. We show that, in the paraxial approximation, a nontruncated transmitted 2-D TM Gaussian beam inside a uniaxial crystal can be expressed in a form similar to that of a scalar Gaussian beam that propagates in a homogeneous medium. We also show that the transmitted beam corresponding to an incident 2-D TM Gaussian beam with its main propagation direction along the interface normal is tilted inside the crystal by the same angle as is the transmitted axial ray that corresponds to a normally incident ray.     

Paraxial wave equation for the extraordinary-mode beam in a uniaxial crystal

With reference to the analysis contained in J. Opt. Soc. Am. 73, 920 (1983), certain comments on and clarifications of the paraxial wave equation pertaining to the extraordinary-mode beam propagating obliquely to the optic axis in a uniform uniaxial crystal are presented.     

Focusing of radially and azimuthally polarized beams through a uniaxial crystal

We calculated and measured the difference between focal positions of radially and azimuthally polarized beams after passing through a uniaxial crystal. Calculations were carried out on the basis of the ray optics and the vector diffraction theory. The results of the calculations were in good agreement with those of the experiment. In addition, we discussed the polarization selection in a hemispherical laser cavity that was used for the generation of a radially polarized beam by use of the birefringence of a c-cut Nd:YVO4 laser crystal [Opt. Lett. 31, 2151 (2006)]. The stability range of the laser cavity length for the generation of a radially polarized beam was also in good agreement with the differences mentioned above.     

Statistical properties of a radially polarized twisted Gaussian Schell-model beam in a uniaxial crystal

We derive the analytical formulas for the elements of the cross-spectral density matrix of a radially polarized partially coherent beam with a twist phase named radially polarized twisted Gaussian Schell-model (RPTGSM) beam propagating in a uniaxial crystal, and explore the statistical properties, such as the intensity distribution, the degree of polarization (DOP) and the state of polarization (SOP) of such beam in a uniaxial crystal with the help of the derived formulas. It is found that the statistical properties of a RPTGSM beam are closely related with the twist phase and the anisotropy of the uniaxial crystal, e.g. the twist phase leads to the rotation of the intensity, DOP and SOP distributions, and the anisotropy of the uniaxial crystal leads to the asymmetry distributions of these statistical properties. Our results will be useful for designing light field with prescribed intensity, DOP and SOP distributions, and may be useful in optical manipulations and free-space optical communications.     

Diffraction characteristics with various polarizations of overlapping holographic gratings in a uniaxial crystal

By the Riemann method, a coupled wave model is derived for the ordinary-to-ordinary (OO) and extraordinary-to-extraordinary (EE) Bragg diffraction of a Gaussian beam by overlapping holographic gratings in a uniaxial crystal. The computer simulation is used to discuss the relations among the diffraction efficiency, the index modulation, the wavelength sensitivity, the angular sensitivity, and the the widths of the recording and reading beams. The characteristics of EE and OO diffraction in a uniaxial crystal are found to be remarkably different. The simulation shows that EE diffraction may exhibit far higher diffraction efficiency than does OO diffraction for very low index modulation with the same hologram size, for example, nearly 90% when the size is 8.2 x 10(-5).     

Fine structure of “white” optical vortices in crystals

Representation of a perturbed optical vortex past a uniaxial crystal and a polarization filter on the complex plane and the orbital Poincaré sphere was experimentally and theoretically studied. It is shown that the main properties of a polychromatic optical vortex are adequately described using eight experimentally measured quantities, including four orbital and four spin Stokes parameters of a singular beam.