Uri Levy

Parallel transmission of images through single optical fibers

The characteristics and limits of parallel transmission of two-dimensional imagery through single optical fibers are reviewed, and methods for overcoming the inherent smearing that occurs at the output are discussed. These solutions include: a) control of the fibers refractive index profile; b) incorporation of complex filters; and c) encoding the information at the input and decoding the output after transmission.

Weakly diverging to tightly focused Gaussian beams: a single set of analytic expressions

Analytic expressions describing all vector components of Gaussian beams, linearly polarized as well as radially polarized, are presented. These simple expressions, to high powers in divergence angle, were derived from a single-component vector potential. The vector potential itself, as in the 1979 work of Davis [Phys. Rev. A19, 1177 (1979)PLRAAN1050-294710.1103/PhysRevA.22.1159], was approximated by the first two terms of an infinite series solution of the Helmholtz equation. The expressions presented here were formulated to emphasize the dependence of the amplitude of the various field components on the beams divergence angle. We show that the amplitude of the axial component of a linearly polarized Gaussian beam scales as the divergence angle squared, whereas the amplitude of the cross-polarized component of a linearly polarized Gaussian beam scales as the divergence angle to the fourth power. Weakly diverging Gaussian beams as well as strongly focused Gaussian beams can be described by exactly the same set of mathematical expressions, up to normalization constant. For a strongly focused linearly polarized Gaussian beam, the ellipticity of the dominant electric field component, typically calculated by the Debye-Wolf integral, is reproduced. For yet higher accuracy, terms with higher powers in divergence angle are presented, but the inclusion of these terms is limited to low divergence angles and short axial distances.

Modal treatment of an optical fiber with a modified hyperbolic secant index distribution

The hyperbolic secant index distribution is known to be optimal for a two-dimensional waveguide, in the sense that all guided modes propagate at the same group velocity. We solve the three-dimensional wave equation for a slightly modified hyperbolic secant index profile. By calculating the propagation constants of the guided modes we can estimate the impulse response of the fiber. We show that in the hyperbolic secant fiber the effective pulse broadening is twelve times smaller than in the parabolic profile, and somewhat narrower than that produced by the optimal a-power profile.

Free-space nonperpendicular electric-magnetic fields.

The electric and magnetic components of an electromagnetic wave in free space are believed by many to be perpendicular to each other. We outline a procedure by which electromagnetic potentials are constructed, and we derive free-space nonperpendicular electric-magnetic fields from these potentials. We show, for example, that in free-space Bessel-related fields, at a small region near the origin, the angle between these components spans a range of 7°-173°, that is, they are far from being perpendicular. This can be contrasted with plane waves, where, following the same procedure, we verify that the electric field strength (E(x,y,z,t)) and the magnetic flux density (B(x,y,z,t)) are indeed perpendicular to each other and to the direction of propagation.

Weakly diverging to tightly focused Gaussian beams: a single set of analytic expressions: continuation—symmetric beams

The always diverging-converging laser beams, more rigorously referred to as Gaussian beams, are part of many physical and electro-optical systems. Obviously, a single set of analytic expressions describing these beams in a large span of divergence-convergence angles at the focal plane, and at any distance away from the focal plane, will prove very handy. We have recently published three such analytic sets, one set for linearly polarized beams and two sets for radially polarized beams. However, our published analytic set for linearly polarized beams describes nonsymmetric electric-magnetic field components. Specifically, the strong transverse magnetic field component does not become elliptic at very large divergence angles as it should be, and the other transverse magnetic component, indeed very weak, is missing altogether. Here we present an analytic set of expressions symmetrically describing linearly polarized Gaussian beams. The symmetry applies to the x-electric y-magnetic components and vice versa and to the two electric-magnetic z-components. An important property of the presented set of expressions is power conservation. That is, the electromagnetic power crossing a plane transverse to the propagation direction in a unit time is conserved. Power conservation assures beam description accuracy at any axial distance. The presented analytic expressions, although not strictly satisfying Maxwells equations, describe Gaussian beams with very reasonable accuracy from low divergence angles up to divergence angles as large as 0.8 rad in a medium with refractive index of 1.5, i.e., up to a NA of 1.1. These expressions should then readily assist in the design of practically all laser-related systems and in the research of diverse physics and electro-optic fields.

Second and third harmonic waves excited by focused Gaussian beams.

Harmonic generation by tightly-focused Gaussian beams is finding important applications, primarily in nonlinear microscopy. It is often naively assumed that the nonlinear signal is generated predominantly in the focal region. However, the intensity of Gaussian-excited electromagnetic harmonic waves is sensitive to the excitation geometry and to the phase matching condition, and may depend on quite an extended region of the material away from the focal plane. Here we solve analytically the amplitude integral for second harmonic and third harmonic waves and study the generated harmonic intensities vs. focal-plane position within the material. We find that maximum intensity for positive wave-vector mismatch values, for both second harmonic and third harmonic waves, is achieved when the fundamental Gaussian is focused few Rayleigh lengths beyond the front surface. Harmonic-generation theory predicts strong intensity oscillations with thickness if the material is very thin. We reproduced these intensity oscillations in glass slabs pumped at 1550nm. From the oscillations of the 517nm third-harmonic waves with slab thickness we estimate the wave-vector mismatch in a Soda-lime glass as Δk(H)= -0.249μm(-1).