Formation of propagation invariant laser beams with anamorphic optical systems

Diode lasers are playing an increasingly important role in various applications, including pump sources for solid-state and fiber lasers, optical communications, printing systems, optical data storage, and electro-optical sensors. Compact package size, lower cost, and emission spectra from UV to IR, combined with conversion efficiencies in excess of 50% makes diode lasers a preferred choice over several other laser types. High-power diode laser beams are multimode, and can be described as an incoherent superposition of the limited number of individual lateral modes contained in the beam. The ability to shape and control the output beam characteristics of diode lasers requires establishing an accurate model of the multimode laser beam. We propose a general multimode laser beam model based on incoherent superposition of apodized Hermite-Gaussian modes to describe the spatial intensity distribution and propagation characteristics of the high-power diode laser beams. Free-space propagation characteristics of high power diode laser beams are compared with propagation characteristics of propagation invariant Hermite-Gaussian beams. Diffraction effects caused by micro-optics components will be presented, which show a significant impact on the intensity distributions of the individual lateral modes composing the beam, as well as on the multimode laser beam spatial distribution as a whole.

Control of the propagation properties of complex beams is desired for many applications. Here we present a novel method to generate propagation invariant shaped beams. Our method is based on a modified degenerate cavity (MDC) [1], [2], which has a huge number of degrees of freedom (300,000 modes in our system), that can be coupled and controlled. Specifically, the MDC allows direct access to both the x-space and k-space components of the laser beam. Accordingly, placing two amplitude masks, one in x-space and one in k-space, enables control of the output beam. Varying the geometric properties of the mask in x-space changes the shape of the output beam, and varying the geometric properties of the mask in k-space breaks the degeneracy between modes and forms spatial correlations (partial spatial coherence) in the output beam [1].

A tractor beam is a propagation invariant beam that pulls objects towards a light source. Here, an efficient tractor beam with improved stability is generated by illuminating a dielectric metasurface with a Gaussian beam.

In this work we present the numerical analysis of fully complex fields employing computer generated holograms, implemented with a commercial amplitude liquid-crystal spatial light modulator (SLM). The hologram transmittance is obtained by adding an appropriate bias function to the real cosine computer hologram of the encoded signal. For the purpose of this work, we consider an appropriated bias function for a modulator in which the amplitude transmittance is coupled with a phase modulation. This type of coupled phase appears in a commercial Twisted Nematic Liquid Crystal Display (TNLCD), configured to provide amplitude modulation, with only two polarizers as external components. This modulation curve was experimentally obtained and adjusted to a mathematical function. The numerical evaluation is done by calculating the signal to noise ratio of the reconstructed complex fields for the real modulation curve. Results show that for a good behavior for complex fields a constant bias function should be implemented. As a particular interesting case we generate propagation invariant complex beams with high accuracy and simplicity.

By applying a new method for aberration derivation to anamorphic systems made from cylindrical surfaces, we obtain a complete set of primary aberration coefficients. This set is in a form similar to the well-known Seidel aberrations for rotationally symmetrical optical systems (RSOS). The aberration coefficients include first-order quantities only. By tracing four nonskew paraxial marginal and chief rays in the two associated RSOS of the anamorphic system, the aberration coefficients can be derived.

The project was supported by the UK Engineering and Physical Sciences Research Council, RS MacDonald Charitable Trust, SULSA, and the St. Andrews 600th anniversary BRAINS appeal. K. D. is a Royal Society Wolfson Merit Award holder.

Propagation invariant hyperbolic beam, with and without optical vortex, is produced using Fourier-transform holography, which keeps its shape unchanged up to 45cm. Bessel function with arguments having hyperbolic locus are used to generate the mask.

We extend our work on the orthonormal polynomials for anamorphic imaging systems with rectangular pupils to those with circular pupils by the Gram-Schmidt orthogonalization. Based on the results obtained, we raise a question.

An original method is proposed to calculate the formation of specified far-field intensity distributions by a bimorph mirror in the case of initial transverse-multimode beams. The method is based on the Gerchberg—Saxton algorithm with replacement of the phase function in the plane of the control element by a function that takes into account both the intensity and phase distributions of each mode. The numerical results on the formation of a beam with the third-order super-Gaussian intensity distribution from beams composed of two or four lowest transverse modes are discussed. The experimental results on using the conventional Gerchberg—Saxton algorithm to form a desired intensity distribution from single-mode laser beams using a liquid-crystal modulator are presented.

Microchip lasers are the most compact (~1mm3) and the simplest diode pumped solid state lasers The mirrors of the optical cavity are directly deposited on the polished faces of a thin (-1mm) laser material. They are fabricated using collective fabrication processes allowing a low cost mass production. A microchip laser has a typical size of 1×1×0.5 mm3. It is very reliable and simple to use. The microchip laser is a kind of optical transformer which transforms a poor quality laser diode beam to a diffraction limited TEM00 and single frequency laser beam Moreover, by active or passive Q-switching , very short pulses (-0.4 to 2 ns) with very high peak power (0.5 to 50 kW) can be obtained. Standard wavelengths are: 1μm or 1.3μm with Nd doped materials such as YAG, YVO4, LMA, etc.; 1.5μm with Er and Yb co-doped phosphate glass; 2μm with Tm doped materials. The laser threshold is generally low, i.e as low as 9mW for 1.5μm microchip laser with a slope efficiency of 38%. Passively Q-switched Nd:YAG microchip laser can be fabricated using a novel process. A thin film (~30-50μm) of Cr4+:YAG, which is a saturable absorber at 1064nm, is epitaxially grown on 25mm diameter and 0.5 to 1mm thick Nd:YAG subtrates. The absorption coefficient of the epitaxial thin film saturable absorber is ~20-25 cm-1, about five times higher than the bulk Cr4+:YAG. The saturable absorption is adjusted by polishing the thin film. This process has the advantage to keep the monolithic structure of the microchip laser without any optical interface between the active and passive materials, and allows a great flexibility for the design of Q-switched lasers. Typical pulse energies are between 0.5 to 5μJ using low power diode pumps, and the pulse width is 0.4 to 2ns. Repetition rates as high 100kHz have been obtained. The pulse energy, width and peak power are independant of the pump power, which acts only on the pulse repetition rate which increases linearly with the diode pump power. The plane-parallel Fabry-Perot cavity of the microchip laser is optically stabilized by thermal effects due to the heating by the pump power. The laser mode is also defined by thermal effects. In order to avoid this problem, stable plano-concave optical cavities are fabricated using photolithography and ion beam etching technologies such as used currently in microelectronics. Small microlenses with 100-200μm in diameter and 1μm thick are directly fabricated with a collective process on laser materials such as Nd:YAG or Er,Yb:glass. The microlense acts as a concave micromirror for the microchip laser cavity, with a radius of curvature of few mm, so that the cavity is optically stable and the laser mode is well defined. The laser threshold is drastically reduced, i.e. less than 2mW incident pump power in CW mode Moreover, this technology allows also the fabrication of micro-optical components, such as microlenses on silica substrates, which can be used for the fabrication of optical microsystems including microchip lasers. For exemple such microlenses are used for the fiber coupling of a stable cavity microchip laser. The low cost, the re lability, the excellent beam quality and the high peak power of the microchip lasers are very useful for several industrial applications such as: time of flight range finding; micro-marking of materials; compact green laser for alignment; injection locking; etc.

The temporal and spatial structures of turbulent liquid phase (water) in pipelines were investigated. Two cases were considered one single liquid phase flow at 80 l/m, second slugy part of slug flow by introducing gas (compressed air) at 60 l/m while keeping liquid flow rate same. Particle image velocimetry (PIV) was used for quantitative measurement of two-dimensional instantaneous velocity of liquid phase. The overall effect of coherent structures on the dynamics of flow in liquid phase for both cases were studied by proper orthogonal decomposition (POD). POD technique was able to identify the structures and characterize them. Spatial and temporal modes were achieved for both cases. The dynamics of flow structure were quite changed with the introduction of gas phase for case II. For case I, the first two spatial modes contained 40% of the energy while for case II only first spatial contained the maximum energy. FFT analysis of temporal modes showed that the first temporal mode for case I has frequency 4.617 while for case II the first temporal mode has frequency 4.64Hz.

This paper discusses the novel adaptive optical closed loop system with water-cooled bimorph mirror as a wavefront corrector to compensate for the aberrations of high-power CW laser beam. Shack-Hartmann wavefront sensor is used as an element for feedback control. Comparison of phase conjugation and modified hill-climbing technique is shown.

A method suggested for the formation of non-Gaussian laser beams is based on the use of a multilayer dielectric exit mirror with its transmission dependent smoothly on the coordinates. A technique for the fabrication of such mirrors by half-shadow evaporation in vacuum is described. Fabrication of mirrors with a transmission minimum on the laser resonator axis is reported. Various intensity distributions (including one which is nearly uniform) are obtained. It is shown that for mirrors of this kind the TEM01 mode is loaded more strongly than the TEM00 mode, which ensures a higher mode stability than in the case of a laser with homogeneous mirrors.

Laser-beam shaping and suppression of beam self-focusing in high-peak-power Nd:glass laser systems are discussed. The role of Fresnel diffraction at apertures at the laser facility as the source of dangerous spatial scales for small-scale self-focusing is illustrated. Methods of the formation of super-Gaussian laser beams for suppressing diffraction ripples on the beam profile and their self-focusing are presented. A brief outline of self-focusing as the primary nonlinear optical process limiting the brightness of Nd:glass laser installations is given. Methods for self-focusing suppression are presented.KeywordsNonlinear MediumBeam ShapingLawrence Livermore National LaboratoryGlass LaserFresnel DiffractionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The approach of forming light beams with a spatial spectrum in the form of polymorphic curves based on the application of the Whittaker integral is studied numerically. The detailed modeling results and the influence of various parameters on regarded beams are investigated.