In optics, and specifically lasers, a Gaussian beam is a beam of electromagnetic radiation having a transverse electrical field which is described by a Gaussian function. The Inventors are aware of the present practice of generating a Gaussian beam in an optical resonator of a laser apparatus by suppressing or filtering higher order modes to leave only the lowest (or fundamental) order mode of the optical resonator. The suppressing of the higher order modes necessarily introduces a loss into the laser. Accordingly, a Gaussian beam is generated at the expense of energy.
Typically, amplitude elements rather than phase elements are used to suppress the higher order Hermite-Gaussian and Laguerre-Gaussian modes because all of the modes in the optical resonator have the same phase and differ only by a constant.
Lasers which emit Gaussian beams are sought after for many applications. Thus, on account of the thermal losses of such lasers, laser manufacturers offer either lower energy lasers or lasers which are pumped very hard to compensate for the losses. Such pumping of the lasers can introduce other problems, such as thermal problems.
The Inventors desire a lossless or low loss laser capable of emitting a Gaussian beam by the use of phase-only optical elements.
The Inventors are also aware that there are many applications where a laser beam with an intensity profile that is as flat as possible is desirable, particularly in laser materials processing. Flat-top-like beams (FTBs) may include super-Gaussian beams of high order, Fermi-Dirac beams, top-hat beams and flat-top beams. Such beams have the characteristic of a sharp intensity gradient at the edges of the beam with a nearly constant intensity in the central region of the beam, resembling a top-hat profile.
The methods of producing such flat-top-like beams can be divided into two classes, namely extra- and intra-cavity beam shaping. Extra-cavity (external) beam shaping can be achieved by manipulating the output beam from a laser with suitably chosen amplitude and/or phase elements, and has been extensively reviewed to date [1]. Unfortunately, amplitude beam shaping results in unavoidable losses, while reshaping the beam by phase-only elements suffers from sensitivity to environmental perturbations, and is very dependent on the incoming field parameters.
The second method of producing such beam intensity profiles, intra-cavity beam shaping, is based on generating a FTB directly as the cavity output mode. There are advantages to this, not the least of which is the potential for higher energy extraction from the laser due to a larger mode volume, as well as an output field that can be changed in size by conventional imaging without the need for special optics in the delivery path. Unfortunately, such laser beams are not solutions to the eigenmode equations of optical resonators with spherical curvature mirrors, and thus cannot be achieved (at least not as a single mode) from conventional optical resonator designs.
The key problem is how to calculate the required non-spherical curvature mirrors of the resonator in order to obtain a desired output field. One method to do this is to reverse propagate the desired field at the output coupler side of the resonator to the opposite mirror, and then calculate a suitable mirror surface that will create a conjugate field to propagate back. This will ensure that the desired field is resonant. This method was first proposed by Belanger and Pare [2-4], and is further referred to as the reverse propagation technique. It was shown that the intra-cavity element could be defined such that a particular field distribution would be the lowest loss mode, opening the way to intra-cavity beam shaping by so-called graded-phase mirrors. This principle has been applied to solid state lasers [5], and extended by inclusion of an additional internal phase plate for improving the discrimination of undesired higher order modes [6]. However, in general this approach does not lead to closed form solutions for the required mirror phases.
The Inventors also aim to find an approach which yields simple expressions for calculating the mirror surfaces. This approach is contrasted with the reverse propagating technique for calculating suitable graded-phase mirrors.