General design principle for structured light lasers.

Using custom laser cavities to produce as the output some desired structured light field has seen tremendous advances lately, but there is no universal approach to designing such cavities for arbitrarily defined field structures within the cavity, e.g., at both the output and gain ends. Here we outline a general design approach for structured light from lasers which allows us to specify the required cavity for any selected structured light fields at both ends. We verify the approach by numerical simulation as well as by an unwrapped cavity experiment. The power of this approach is that the cavity can be designed to maximise the overlap with the available pump for higher powers, minimise thermal effects for higher brightness, and at the same time output a desired structured light field that may differ substantially from the gain-end profile. These benefits make this work appeal to the large laser communities interested in cavities for high brightness and/or customized output beams.

Extended focus depth for Gaussian beam using binary phase diffractive optical elements.

A novel technique to improve the focus depth of a Gaussian beam is presented in this paper. The improvement is based on two-step beam shaping using a cascade of binary phase diffractive optical elements (BPDOEs). The first BPDOE transforms the incident Gaussian beam into a high-order radial Laguerre-Gaussian beam (LGp0). Then the second BPDOE rectifies the obtained LGp0 beam and gives rise to a quasi-Gaussian one in the focal plane of a converging lens. This resulting quasi-Gaussian beam exhibits a lower divergence and larger focus depth compared to the pure Gaussian beam having the same beam waist. These results open new possibilities in laser beam manufacturing and micromachining, and in applications that need an extended focus depth.

Doughnut laser beam as an incoherent superposition of two petal beams.

Laguerre-Gaussian beams with a nonzero azimuthal index are known to carry orbital angular momentum (OAM), and are routinely created external to laser cavities. The few reports of obtaining such beams from laser cavities suffer from inconclusive evidence of the real electromagnetic field. In this Letter we revisit this question and show that an observed doughnut beam from a laser cavity may not be a pure Laguerre-Gaussian azimuthal mode but can be an incoherent sum of petal modes, which do not carry OAM. We point out the requirements for future analysis of such fields from laser resonators.

Tuneable Gaussian to flat-top resonator by amplitude beam shaping.

We outline a simple laser cavity comprising an opaque ring and a circular aperture that is capable of producing spatially tuneable laser modes, from a Gaussian beam to a Flat-top beam. The tuneability is achieved by varying the diameter of the aperture and thus requires no realignment of the cavity. We demonstrate this principle using a digital laser with an intra-cavity spatial light modulator, and confirm the predicted properties of the resonator experimentally.

Exciting higher-order radial Laguerre-Gaussian modes in a diode-pumped solid-state laser resonator.

In this paper we experimentally demonstrate the intracavity generation of selected Laguerre-Gaussian modes of variable radial order, from 0 to 5. Our technique requires only an amplitude mask made up of absorbing rings to be placed inside the cavity, with the ring radii selected to coincide with the zeros of the desired Laguerre-Gaussian mode. We demonstrate high mode purity and a mode volume proportional to the order of the mode. Our results suggest a possible route to high brightness diode-pumped solid-state laser sources.

Reconstruction-free sensitive wavefront sensor based on continuous position sensitive detectors.

We propose a new device that is able to perform highly sensitive wavefront measurements based on the use of continuous position sensitive detectors and without resorting to any reconstruction process. We demonstrate experimentally its ability to measure small wavefront distortions through the characterization of pump-induced refractive index changes in laser material. In addition, it is shown using computer-generated holograms that this device can detect phase discontinuities as well as improve the quality of sharp phase variations measurements. Results are compared to reference Shack-Hartmann measurements, and dramatic enhancements are obtained.

Spatial properties of coaxial superposition of two coherent Gaussian beams.

In this paper, we explore theoretically and experimentally the laser beam shaping ability resulting from the coaxial superposition of two coherent Gaussian beams (GBs). This technique is classified under interferometric laser beam shaping techniques contrasting with the usual ones based on diffraction. The experimental setup does not involve the use of some two-wave interferometer but uses a spatial light modulator for the generation of the necessary interference term. This allows one to avoid the thermal drift occurring in interferometers and gives a total flexibility of the key parameter setting the beam transformation. In particular, we demonstrate the reshaping of a GB into a bottle beam or top-hat beam in the focal plane of a focusing lens.

Baryscan: a sensitive and user-friendly alternative to Z scan for weak nonlinearities measurements.

A new and efficient technique for measuring weak optical nonlinearities is reported. Like Z scan, its implementation is basic, both experimentally and theoretically, but leads to an improved sensitivity of λ/5.104, which represents, to date, one of the highest observed enhancements. With this technique, which is based upon the use of a position sensitive detector, nonlinear properties are deduced by monitoring the barycentric position of a truncated pump-probe laser beam as the sample is moved along the optical axis. The technique is experimentally validated by measuring the pump-induced refractive index change and the underlying polarizability variation resulting from the excitation of the Cr(3+) ions in ruby.

Transverse superresolution technique involving rectified Laguerre-Gaussian LG(p)° beams.

A promising technique has been proposed recently [Opt. Commun. 284, 1331 (2011), Opt. Commun. 284, 4107 (2011)] for breaking the diffraction limit of light. This technique consists of transforming a symmetrical Laguerre-Gaussian LG(p)° beam into a near-Gaussian beam at the focal plane of a thin converging lens thanks to a binary diffractive optical element (DOE) having a transmittance alternatively equal to -1 or +1, transversely. The effect of the DOE is to convert the alternately out-of-phase rings of the LG(p)° beam into a unified phase front. The benefits of the rectified beam at the lens focal plane are a short Rayleigh range, which is very useful for many laser applications, and a focal volume much smaller than that obtained with a Gaussian beam. In this paper, we demonstrate numerically that the central lobe's radius of the rectified beam at the lens focal plane depends exclusively on the dimensionless radial intensity vanishing factor of the incident beam. Consequently, this value can be easily predicted.

Variant of the method of Fox and Li dedicated to intracavity laser beam shaping.

We present a variant of the method of Fox and Li [Bell Syst. Tech. J. 40, 453 (1961); Proc. IEEE 51, 80 (1963)] dedicated to intracavity laser beam shaping for resonators containing an arbitrary number of amplitude and phase diffractive optics. Contrary to Fox and Li, the starting point is the desired field. The latter is injected into the usual sequence of lenses representing just a single round trip, and the optimization process iterates until the input and the output fields match as much as possible. We illustrate this technique by deriving a simple model for generating single cylindrical TEM(p0) modes, thanks to a π-phase plate placed inside a plano-concave cavity. The experimental validation attests an excellent agreement with numerical predictions.

Modeling the propagation of apertured high-order Laguerre-Gaussian beams by a user-friendly version of the mode expansion method.

The mode expansion method (MEM) models the propagation of an apertured beam by expressing the diffracted field as a finite series of Laguerre-Gaussian or Hermite-Gaussian modes. An optimal expansion parameter set (beam waist of the modes and its location) reduces the number of modes, which is difficult to derive, especially for high-order incident beams. We propose a user-friendly version of the MEM in which the expansion parameter set and the suitable number of modes are simply deduced from the approximation of the apertured incident beam.

Cascades of pi-phase plates: a transparent diffractive focusing system.

Typically, refractive lenses are used to focus rays of light, but an alternative way can be found by exploiting diffraction of light. It is well known that cascades of hard-edge apertures are able to focus light but with the great drawback of absorption losses. In this paper, we demonstrate that replacing hard-edge apertures with pi-phase plates within a cascade greatly improves the focusing of collimated Gaussian beams. In addition, we propose a simple model to design this cascade, in particular to find the locations and the radii of the different optics once the focal length has been chosen. This model deduced from numerical simulation is useful for sizing cascades consisting of a high number of components and characterized by a strong focusing ability, without requiring a time-consuming optimization process.

Properties of a laser cavity containing an absorbing ring.

This paper considers the transverse optical properties of an absorbing ring when it is lighted by a symmetrical Laguerre-Gauss beam TEM(p0). It is demonstrated that the insertion of an opaque ring having adequate size inside a diaphragmed laser cavity is able to improve greatly (rate of about 100%) the discrimination between the TEM(00) and the TEM(10) modes, while keeping the diffraction losses unchanged or even decreased.

Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method.

A variant of the Gaussian beam expansion method consists in expanding the Bessel function J0 appearing in the Fresnel-Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre-Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization-computation directly. We propose another solution consisting in expanding J0 onto a set of collimated Laguerre-Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively.

Beam-shaping longitudinal range of a binary diffractive optical element.

An experimental and theoretical investigation of laser beam shaping using a simple binary diffractive optic is presented. Beam tailoring has been characterized by the experimental determination of two relevant parameters: beam propagation factor M(2) and the beam-shaping longitudinal range, which represents the propagating distance for which the tailored beam remains nearly unchanged.

Simple interferometric technique for generation of a radially polarized light beam.

We present a theoretical and experimental investigation of an interferometric technique for converting a linearly polarized Gaussian beam into a radially polarized doughnut beam. The experimental setup accomplishes the coherent summation of two orthogonally polarized TEM01 and TEM10 beams that are obtained from the transformation of a TEM00 beam by use of a simple binary diffractive optical element. We have shown that the degree of radial polarization is maximum at a given distance from the interferometer output port that depends on the diameter of the incident beam at the interferometer input port.

Improvement of the self-Q-switching behavior of a Cr:LiSrAlF6 laser by use of binary diffractive optics.

It has been shown experimentally and theoretically that Q-switching behavior is possible in a flashlamp-pumped Cr-doped LiSrAlF6 (Cr3+:LiSAF) laser that consists only of two mirrors, a laser crystal, and a diaphragm. We demonstrate that insertion into a laser of a binary diffractive optical element can speed up the dynamics of the self-Q-switched laser such that the output pulse is shortened (from 60 to 33 ns) and its energy is increased (from 36 to 54 mJ). The self-Q-switching behavior of the laser has the ability to produce a laser pulse with a duration that one can adjust continuously from 60 to 700 ns just by opening the diaphragm.