B. Ya. Zel’dovich

Physical effects in optical fields with nonzero average cube, 〈E 3 〉 ≠ 0

We discuss some physical effects that take place in multifrequency light fields with a nonzero average cube of the electric field, 〈E3〉 ≠ 0. We calculated the polar asymmetry in electron emission that is due to interference between two-photon ionization by the fundamental radiation (ω) and one-photon ionization by the second-harmonic (2ω) wave. The expression for the quasi-static force, which acts on electrons and is proportional to the average cube of the light field, is derived.

Wave propagation in a guiding structure: one step beyond the paraxial approximation

Propagation of electromagnetic waves is considered for a medium with (x, y)-dependent locally isotropic dielectric and magnetic susceptibilities ∊ik = ∊(x, y)δik and μik = μ(x, y)δik, i.e., for a waveguide. In the paraxial approximation the polarization is disconnected from the propagation. We have developed a self-consistent theory of the postparaxial corrections. It allows, in particular, for the description of intrafiber geometrical rotation of polarization and its inverse phenomenon, the optical Magnus effect, which are both determined by the profile of refractive index n=∊μ only and constitute spin–orbit interaction of a photon. The birefringence splitting of linearly polarized modes or meridional rays on the other hand, turns out to be dependent on the gradients of impedance ρ=μ/∊, the quadrupole part of spin–orbit interaction. An important point of the theory is a transformation of field variables such that the z-propagation operator becomes Hermitian, in analogy with the transitions from a full relativistic Dirac equation to the Schrodinger–Pauli equation with spin–orbital corrections. A theoretical explanation is given for the phenomenon previously observed in experiment: preservation of circular polarization by an axially symmetric step-profile multimode fiber and depolarization of an input linearly polarized wave by the same fiber.

Recording a static hologram with laser beams of different frequencies in photorefractive crystals

A mechanism for recording a static hologram in photorefractive Bi12TiO20 crystal by a moving interference pattern is studied theoretically and experimentally. The mechanism is the result of detection of the pattern by the phase-locked ac field that is applied to the crystal, and the field’s frequency is much greater than the inverse response time of the hologram.

Stabilization of the speckle pattern of a multimode fiber undergoing bending

The propagation of light in a multimode optical fiber waveguide results in speckle, a complicated mapping of the input field onto the output field. The speckle pattern changes as the fiber undergoes twists and bends. We show theoretically and demonstrate experimentally that changes in the mapping caused by bends in one region of the fiber can be compensated with bends applied along a fixed region of the fiber. In this way the output speckle pattern of the fiber can be stabilized. In this method it is supposed that the modes evolve adiabatically without intermixing and that the analytical dependence of perturbed propagation eigenvalues of the modes follows R(-2) behavior, where R is the local value of bend radius.

Use of skew rays in multimode fibers to generate speckle field with nonzero vorticity

Beams at the output of an axially symmetric multimode fiber were produced with mostly positive or negative values of angular index m through skew illumination of the input end of the fiber. In this way rays with predominantly positive or negative helicity were excited inside the fiber. The output cw speckle field at the wavelength lambda = 632.8 nm contained large densities N(+) and N(-) of wave-front dislocations, or optical vortices, of both positive and negative sign. Vorticity was defined as V = N(+) - N(-) , was expressed analytically through the Wigner function of the field, and was found experimentally to be in good agreement with theory.

BRIEFING: beam reconstruction by iteration of an electromagnetic field with an induced nonlinearity gauge

Measurement of the local intensity and phase distributions in the small focal waist of a laser beam with the use of a thin nonlinear-optical layer is discussed. We suggested and tested in a computer experiment the beam reconstruction by iteration of an electromagnetic field with an induced nonlinear gauge (BRIEFING) algorithm, which allows one to extract the absolute intensity (in watts per square centimeter) and phase distributions from two intensity patterns in the far-field zone: with and without nonlinearity.

Higher-dimensionality caustics owing to competing reorientation of a liquid crystal by laser beams

Formation of hyperbolic umbilic caustics is observed experimentally in the far-field zone as a result of self- and mutual-phase modulation of laser beams by means of competing reorientation of a nematic liquid crystal. The interference pattern reveals maximum response for an unusually small (≈5°) angle of light refraction into the cell. It is thus demonstrated that higher-order diffraction catastrophes can be induced and controlled by nonlinear optical processes.

Nondegenerate two-wave interaction in a photorefractive crystal in an external detecting field

A hologram recording mechanism in photorefractive Bi(12)TiO(20) crystal by different-frequency laser beams in an ac field is studied. The frequency difference between the beams is essentially more than the reverse of the response time of the hologram.

Recording of a stationary photorefractive grating in an external ac field by rapidly modulated beams

A mechanism for recording a static hologram in a photorefractive crystal in an externally applied ac field is investigated. One beam is rapidly modulated, and the interference pattern is moving. The frequency of modulation coincides with the frequency of the externally applied ac field and strongly exceeds the inverse buildup time. Both phase and amplitude modulations are investigated theoretically and experimentally. The experiment was performed in a Bi12TiO20 crystal.

Phase properties of χ(2) gratings in glass

A new method for the measurement of the phase shift between second-harmonic light generated by a bulk glass and the injected second-harmonic seed is presented. A linearly polarized pump and a second-harmonic seed with noncollinear polarizations were used for preparation of cerium-doped lead-silica glass. Independence of the phase shift from the angle between the polarizations of the recording waves is demonstrated, and a phase shift value close to 90 degrees is observed, i.e., the X((2)) grating was in phase with the real ?E(EE)?.