R. M. Herman

Production and uses of diffractionless beams

It is proposed to obtain intense optical fields, whose form shows little change in size over long paths, through the use of either conical lenses or spherical lenses showing spherical aberration together with a single projecting lens. The conical lens is shown to produce fields whose transverse structure is given by a zero-order Bessel function J0, while the spherical aberrating lens produces (real or virtual) J0-like transverse structures, provided that the central portion of the aberrating lens is occluded. In all cases projection gives a J0 real-image optical structure. Intensity, size of the transverse structure, and range considerations are developed, and some aspects of optimization are discussed. A negative aberrating lens gives a long range of nearly constant size in the image field, and a universal expression is presented to describe the image size as a function of image distance for this case. Projection with an aberrating projection lens is shown to improve the constancy of the final J0 pattern size dramatically. Typical photographic results are included for beams generated by using a low-power He–Ne laser. Brief considerations of practical uses of diffractionless beams are presented.

Apodization of diffractionless beams

Coatings with graded transmission, placed near the rims of conical lenses and perhaps other axicons, provide apodization that removes the axial intensity variations in Bessel-type optical beams.

Diffraction and focusing of Gaussian beams

Methods for the measurement of the waist size and position for Gaussian beams are summarized. An alternative method is given which would apply to pulsed systems. The general theory of diffraction of Gaussian beams is developed which provides a new method for the location of the beam waist. These methods which use hole gratings are employed to demonstrate their feasibility using a small cw source.

High-efficiency diffractionless beams of constant size and intensity

Design considerations are presented for pairs of spherically aberrating elements that produce diffractionless beams of high efficiency and nearly constant size and intensity over specified ranges of axial position. An approximate design, assuming an aberration quadratic in radial ray positions, is followed by a final lens (mirror) specification that is verified through meridional ray tracing. This then provides an accurate determination of beam characteristics. Examples are presented that represent a variety of applications. As a design aid, a simple prescription is given for generating families of substantially different Bessel-like beams from any given pair of elements under small changes in element separation. Pattern sizes and ranges are compared with those of Gaussian beams, shadow lengths are examined for Bessel-type beams, and beam efficiencies are fully analyzed.

Bessel-like beams modulated by arbitrary radial functions

An approximate method for determining the radial and axial intensity of a Bessel-like beam is presented for the general case in which a radial Bessel distribution of any order is modulated by an arbitrary function. For Bessel-Gauss, generalized Bessel-Gauss, and Bessel-super-Gauss beams, this simple approximation yields results that are very close to the exact values, while they are exact for Bessel beams. A practical beam that can be generated with a combination of simple lenses is also analyzed and illustrated.

Rayleigh range and the M 2 factor for Bessel–Gauss beams

The M(2) factor of Bessel-Gauss beams derived by Borghi and Santarsiero [Opt. Lett. 22, 262-264 (1997)] is shown to predict the e(-2) axial position rather than the half-intensity position of the on-axis intensity as the Rayleigh range divided byM(2) for large values of k(t)w(0). For small values of k(t)w(0), the half-intensity axial position of the J(0) Bessel-Gauss beam is the Rayleigh range divided by M(2). Also, the ratio of the half-intensity lengths of J(0) Bessel-Gauss and comparable Gaussian beams having the same radial size of their central regions is shown to be M(2)/1.3. For equal input powers and largek(t)w(0), the values of peak intensity times effective range for J(0)Bessel-Gauss beams is a constant and is a factor of 1.3 larger than the corresponding product for the comparable simple Gaussianbeam.

Nonlinear reflection properties of germanium associated with thermal effects

Thermal excitations on a germanium surface under simultaneous irradiation by two monochromatic optical beams, one strong and one weak, are predicted as functions of the angular separation and frequency difference between the beams, their relative polarization, their intensities, and pulse durations. Nonlinear optical reflection for Q-switched ruby laser pulses is then described. Weak reflected and diffracted beam intensities show tendencies in which the former is preferentially enhanced for a downshifted weak beam frequency, while the latter depends only on the shift magnitude. Both are suppressed for large shifts or large angular separations between input beams.

Hole gratings for laser damage testing

The use of hole gratings in small-spot laser damage testing is discussed. If the intensity loss due to the transmission of the grating and due to the production of several spots can be tolerated, a hole grating is shown to increase the ease of establishing a damage threshold by the production of spots with a wide range of intensities whose ratios are well understood. It allows the investigation of defect-related damage since several regions are illuminated with equal intensities, and it permits the investigation of the effects of several closely spaced simultaneous illuminations. Several types of arrays of circles and ellipses are investigated, and the effects of hole size, hole spacing, hole shape, and elliptical hole orientation are discussed. The effects of apertures of the grating are also discussed. Two methods of suppression of diffraction spots lying outside the Airy disk are described and illustrated which utilize distributions of either circular hole sizes or of elliptical hole orientations. Two arrays are used in damage tests of metal surfaces to illustrate their use.

Unified Impact Theory for Velocity-Changing Effects and Speed Dependencies in Neutral Species Lineshapes

A dipole correlation function which incorporates velocity-changing (motional narrowing) effects and the effects of speed-dependent Lorentz relaxation rates into otherwise Voigt profile correlation functions is developed, based partly upon previous work by the author. For the first time simple closed expressions, which lend themselves to elementary calculation beginning only with the relevant parts of intermolecular interaction energies, are developed for the cubic time-dependent term within the exponent describing the decay of the correlation function. This term is of first order in perturber number density, as are the Lorentz parameters, and is complex, thereby allowing for narrowing, changing in shape and asymmetry in the line profile. “Soft” and “hard” collisions play no explicit role, though both are variously present for each line. Quartic time dependencies are also discussed, though they are thought to be negligible in nonhydrogen molecular spectroscopy. Finally, some comments are added about a relevant technique for hydrogen spectra.

Propagation and focusing of Bessel–Gauss, generalized Bessel–Gauss, and modified Bessel–Gauss beams

The propagation of Bessel-Gauss, generalized Bessel-Gauss, and modified Bessel-Gauss beams, for which the exact form of the optical fields is known, is analyzed according to the approximate theory developed previously by the authors [J. Opt. Soc. Am. 17, 1021 (2000)]. Approximations are developed for the fields themselves that are highly accurate and yet are simple in their form and physical description. A set of simple equations is developed, which directly give the parameters describing an image beam following passage through a perfect lens of focal length f, starting with any of the above-mentioned object beams. Ray propagation for these types of beams is described, and it is specifically noted that the intensity maxima do not follow straight paths, while the auxiliary F(rho, z) function in fact does follow straight paths.