Optical Waveguide Theory

Vector modes are spatial modes that have spatially inhomogeneous states of polarization, such as, radial and azimuthal polarization. In this work, the spatially inhomogeneous states of polarization of vector modes are used to increase the transmission data rate of free-space optical communication via mode division multiplexing. A mode (de)multiplexer for vector modes based on a liquid crystal q-plate is introduced. As a proof of principle, four vector modes each carrying a 20-Gbit/s quadrature phase shift keying signal (aggregate 80 Gbit/s) on a single wavelength channel (λ∼1550  nm) were transmitted ∼1  m over the lab table with <−16.4  dB mode crosstalk. Bit error rates for all vector modes were measured at the 7% forward error correction threshold with power penalties <3.41  dB.

4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer

We describe the polarization topology of the vector beams emerging from a patterned birefringent liquid crystal plate with a topological charge q at its center (q-plate). The polarization topological structures for different q-plates and different input polarization states have been studied experimentally by measuring the Stokes parameters point-by-point in the beam transverse plane. Furthermore, we used a tuned q=1/2-plate to generate cylindrical vector beams with radial or azimuthal polarizations, with the possibility of switching dynamically between these two cases by simply changing the linear polarization of the input beam.

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Polarization pattern of vector vortex beams generated by q-plates with different topological charges

In this work, it is experimentally demonstrated that the nonseparability of vector beams (e.g., radial and azimuthal polarization) can be used to encode information for optical communication. By exploiting the nonseparability of a vector beam's space and polarization degrees of freedom using conventional wave plates, it is shown that 2 bits of information can be encoded when applying the identity and three Pauli operators to its polarization degree of freedom. It is also shown that vector beams can be efficiently decoded with as low as 2.7% cross talk using a Mach-Zehnder interferometer that exploits a higher-order Pancharatnam-Berry phase and liquid crystal q-plates.

Using the nonseparability of vector beams to encode information for optical communication

We utilize the interaction of tightly focused ultrashort pulses with transparent media to imprint their local polarization in the focal region. In particular, we demonstrate that this technique allows for a subwavelength resolution diagnostic of complex polarization states including the presence of the longitudinal component of the electric field. Moreover, we demonstrate the first ever material ablation with the longitudinal electric field of femtosecond pulses.

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Revealing local field structure of focused ultrashort pulses.

We have studied the effect of the spin-orbit interaction on generation and conversion of optical vortices in multihelicoidal fibers, that is, the fibers possessing a multihelical refractive index profile. On the basis of a fully analytical approach we have obtained the spectra of coupled modes and their structure. Specifically, we have established selection rules, under which the spin-orbit interaction mediates the conversion of optical vortices into vortices with the topological charge changed by $\ifmmode\pm\else\textpm\fi{}(\ensuremath{\ell}\ifmmode\pm\else\textpm\fi{}2)$, $\ensuremath{\ell}$ being the number of helical branches in refractive index distribution. Also, we have shown that the spin-orbit interaction can lead to generation of radially and azimuthally polarized TE and TM modes from optical vortices. We have also demonstrated that if such generation is mediated by a scalar-type perturbation of the fiber's form, it is possible only for weakly deformed fibers. For strongly deformed fibers such perturbation can result only in generation of vortices with zero total angular momentum. Additionally, we have studied the possibility of polarization control over the orbital angular momentum of the generated state in such a system.

Spin-orbit-interaction-induced generation of optical vortices in multihelicoidal fibers

We theoretically study generation and conversion of optical vortices (OVs) in long-period helical core fibers (HCFs) produced by drawing from a perform with an eccentric core. Solving scalar waveguide equation in the helical coordinates we demonstrate that in such fibers topologically induced corrections to scalar propagation constants lead to convergence of spectral curves. At their intersection points a resonance coupling takes place between the fundamental and the vortex modes, as well as the coupling between OVs, whose topological charges differ by unity. This coupling leads to energy exchange between the coupled modes, which is manifested either in conversion of the input fundamental mode into an OV or transformation of an OV into the OV with higher by 1 (or lower, depending on core's helicity) value of the topological charge. This effect can be used for creation of all-fiber generators of singular beams from regular input beams. We also study effect of ellipticity of the core's form on transformation properties of HCFs and show that this leads to splitting of resonance fiber's parameters, at which conversion of left and right circularly polarized input regular beams into OVs occurs. We prove that in long-period HCFs one can neglect this effect due to reduction of polarization mode dispersion in twisted fibers.

Generation and conversion of optical vortices in long-period helical core optical fibers

We investigate the structure of the higher order modes in uniformly twisted weakly guiding strongly elliptical optical fibres. An analytical solution of the vector wave equation for this problem is presented based on the effective reduction of a twisted fibre equation to a straight fibre one. On the basis of the perturbation theory the structure of the higher order elliptical screw modes and polarization corrections to the scalar propagation constant are found as functions of the pitch value and the fibre parameters. It is demonstrated that at a certain rate of twisting the l = 1 modes of such fibres are presented by two pairs of almost pure arbitrary polarized optical vortices. The orbital angular momentum of the l = 1 modes is studied as a function of pitch.

Optical vortices and the higher order modes of twisted strongly elliptical optical fibres

We have experimentally and theoretically shown that the circularly polarized beam bearing singly charged optical vortex propagating through a uniaxial crystal can be split after focusing into the radially and azimuthally polarized beams in vicinity of the focal area provided that the polarization handedness and the vortex topological charge have opposite signs. Quality of the polarization structure can reach unity.

Natural shaping of the cylindrically polarized beams

We study the field generated in the outer space by the superposition of modes of a regular circular monomode fiber array. It is shown that a supermode of the fiber array generates a discrete optical vortex; the formula for the topological charge of the vortex is obtained depending on the order of the supermode and the number of fibers in the array. The orbital angular momentum carried by an arbitrary superposition of supermodes is shown to equal the weighted sum of partial angular momenta of supermodes. It is shown that for certain combinations of supermodes the angular momentum comprises along with its intrinsic part also the extrinsic constituent. For such combinations precession of the angular momentum about the propagation axis is demonstrated. It is demonstrated that by combining supermodes one can generate in the array stable regularly rotating linear azimuthons. By creating a phased excitation of certain groups of fibers in the array one can control the global soliton-like motion of the excited domain.

C N Alexeyev

Papers

Spin-orbit-interaction-induced generation of optical vortices in multihelicoidal fibers

Generation and conversion of optical vortices in long-period helical core optical fibers

Optical vortices and the higher order modes of twisted strongly elliptical optical fibres

Natural shaping of the cylindrically polarized beams

Linear azimuthons in circular fiber arrays and optical angular momentum of discrete optical vortices