A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

The fact that light carries both linear and angular momentum is well-known to physicists. One application of the linear momentum of light is for optical tweezers, in which the refraction of a laser beam through a particle provides a reaction force that draws the particle towards the centre of the beam. The angular momentum of light can also be transfered to particles, causing them to spin. In fact, the angular momentum of light has two components that act through different mechanisms on various types of particle. This Review covers the creation of such beams and how their unusual intensity, polarization and phase structure has been put to use in the field of optical manipulation.

Tweezers with a twist

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

The induced nonlinear electric dipole and higher moments in an atomic system, irradiated simultaneously by two or three light waves, are calculated by quantum-mechanical perturbation theory. Terms quadratic and cubic in the field amplitudes are included. An important permutation symmetry relation for the nonlinear polarizability is derived and its frequency dependence is discussed. The nonlinear microscopic properties are related to an effective macroscopic nonlinear polarization, which may be incorporated into Maxwell's equations for an infinite, homogeneous, anisotropic, nonlinear, dielectric medium. Energy and power relationships are derived for the nonlinear dielectric which correspond to the Manley-Rowe relations in the theory of parametric amplifiers. Explicit solutions are obtained for the coupled amplitude equations, which describe the interaction between a plane light wave and its second harmonic or the interaction between three plane electromagnetic waves, which satisfy the energy relationship ${\ensuremath{\omega}}_{3}={\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$, and the approximate momentum relationship ${\mathrm{k}}_{3}={\mathrm{k}}_{1}+{\mathrm{k}}_{2}+\ensuremath{\Delta}\mathrm{k}$. Third-harmonic generation and interaction between more waves is mentioned. Applications of the theory to the dc and microwave Kerr effect, light modulation, harmonic generation, and parametric conversion are discussed.

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Interactions between Light Waves in a Nonlinear Dielectric

We introduce the concept of the perfect optical vortex whose dark hollow radius does not depend on the topological charge. It is shown analytically and experimentally that such a vortex can be approximately generated in the Fourier transforming optical system with a computer-controlled liquid-crystal spatial light modulator.

Generation of the "perfect" optical vortex using a liquid-crystal spatial light modulator

We have demonstrated a passively mode-locked diode end-pumped all-solid-state laser, which is composed of a Nd:Gd0.5Y0.5VO4 crystal and a folded cavity with a semiconductor saturable-absorber mirror grown by metal-organic chemical-vapor deposition. Stable cw mode locking with a 3.8-ps pulse duration at a repetition rate of 112 MHz was obtained. At 13.6 W of the incident pump power, a clean mode-locked fundamental-mode average output power of 3.9 W was achieved with an overall optical-to-optical efficiency of 29.0%, and the slope efficiency was 38.1%.

4-ps passively mode-locked Nd:Gd0.5Y0.5VO4 laser with a semiconductor saturable-absorber mirror.

An idea of an optimal annulus structure phase mask with helical wavefront is suggested; the resulting helical mode can be focused into a very clear optical vortex ring with the best contrast. Dependences of the optimal annulus width and the radius of the optical vortex ring on topological charge are found. The desired multi-optical vortices as the promising dynamic multi-optical tweezers are realized by extending our idea to the multi-annulus structure. Such multi-optical vortex rings allow carrying the same or different angular momentum flux in magnitude and direction. The idea offers flexibility and more dimensions for designing and producing the complicated optical vortices. For the Gaussian beam illumination, the optimal spot size, which ensures the high energy/power efficiency for generating the best contrast principal ring is also found.

Optimal annulus structures of optical vortices.

A cw laser-diode-pumped Yb-doped double-clad fiber laser operating in a hybrid Q-switched regime was demonstrated. The output pulses had a duration as short as 4.2 ns, a tunable wavelength range from 1080.8 to 1142.7 nm, and a linewidth of less than 0.05 nm. Maximum peak power of ∼175 kW and single-pulse energy of 1.57 mJ were obtained.

Tunable high-peak-power, high-energy hybrid Q-switched double-clad fiber laser

Quasi-phase matching facilitates the phase matching of any parametric interaction by setting an appropriately modulated period. We propose a dual-periodic structure that is used in the construction of a frequency-conversion device. For example, we have designed and fabricated such a dual-periodic structure in a LiTaO3 crystal. Using a fundamental source at 1.064 µm, we obtained ultraviolet radiation at 355 nm and green radiation at 532 nm simultaneously by frequency tripling and frequency doubling the fundamental source. Theoretically, this idea can be further extended to the design of a multiperiodic structure for achievement of more quasi-phase-matched processes in a single optical superlattice.

http://circuit.ucsd.edu/~zhaowei/Journals/JOSAB_NJU.pdf

Jing-Liang He

Papers

4-ps passively mode-locked Nd:Gd0.5Y0.5VO4 laser with a semiconductor saturable-absorber mirror.

Optimal annulus structures of optical vortices.

Tunable high-peak-power, high-energy hybrid Q-switched double-clad fiber laser

Engineering of a dual-periodic optical superlattice used in a coupled optical parametric interaction

Q-switched and mode-locked diode-pumped Nd:GdVO4 laser with low temperature GaAs saturable absorber