The influence of phase aberrations on the beam quality factor of Hermite-Gauss beams is investigated. Analytical expressions of the beam quality factor of Hermite-Gauss beams due to astigmatism are derived. The results show that the width of the Hermite-Gauss beams is a significant parameter that determines how much each aberration affects the beam quality factor. This work will be beneficial and contribute to the design and development of high-power laser systems in various applications.
Spherical aberration is a common phase distortion that occurs in optical elements. An optical beam passing through an element that has spherical aberration will accrue a quartic phase term. Here, we provide an analytical analysis of the effect of the quartic phase on the beam quality factor of Laguerre-Gauss beams. We find that the beam radius is a critical parameter in determining the effect of the aberration on the quality of the laser beams.
KEYWORDS: Solid state lasers, Thermal lensing, Thermal optics, Beam diameter, Temperature distribution, Manufacturing, Refractive index, High power lasers
In this paper, we present a method for active control of thermally induced lensing in high-power lasers. We used thermal lensing to study the advantages of high-power lasers. Many delivery optics are sensitive to the thermally induced lens, which can change the focus position of the transmitted beam. To compensate for this, we used thermal lensing by pumping a crystal that had no absorption or amplification at the seed beam wavelength. By controlling the strength of the heat source, we demonstrate acute control of the focus position. Our modeling work is based on the finite-volume method (FVM) to analyse thermal effects in end-pumped solid-state crystals. This work has the potential to pave the way for active control of a thermally induced lens in high-powered laser-based applications.
Phase aberrations are ubiquitous in optical systems and can lead to the degradation of laser beam quality. The laser beam quality factor is an important parameter that can be used to determine the quality of a laser beam. In this work, we derive analytical expressions for the beam quality factor of Laguerre-Gaussian beams due to different types of astigmatism: 0° astigmatism, 45° astigmatism, x-triangular astigmatism, and y-triangular astigmatism. The results show that the beam waist radius is an important parameter in determining the effect of astigmatism on the beam quality factor of LG optical beams.
Flat-top or super-Gaussian beams have found applications in many diverse areas, particularly in laser materials processing. The creation of at-top beams requires an infinite spatial frequency spectrum and as at-top beams are not eigenmodes of the free space wave equation only approximations of at-top beams can be created. There exists a myriad of techniques to select such beams and while the majority these approaches can be efficient, these outputs are typically at a fixed plane and evolve to non-at beams beyond that plane. Methods to increase the depth of focus of at-top beams include the use of specially designed diffractive elements. These approaches hold well for larger beams, however, they are sensitive to the input beam size and the performance is drastically reduced for smaller beams. An attractive approach is the selection of propagation invariant vector at-top beams through the superposition of a Gaussian beam and a vortex beam of orthogonal polarizations. Such beams have been selected through Spatial Light Modulators (SLM) and hold a at plateau through the target plane of a convergent lens. The poor power handling capability of the SLM, however, restricts its application at higher powers. In this work we explore the amplification, through a single stage end-pumped amplifier, of vector at-top beams as selected through a Mach Zehnder interferometer. We demonstrate stable output properties and up to a 3x increased power output as compared to each beam in the corresponding superposition. This approach presents a useful advance in at-top beams for high power applications.
Master Oscillator Power Amplifier (MOPA) systems have garnered considerable interest to power scale low power seed beams (from the Master Oscillator) to higher powers. These systems are favourable to obtain the desired laser beam performance when additional optical elements such as Bragg gratings are required. These elements do not have to endure high optical intensities inside high-power oscillators and do not affect the beam quality or power efficiency. Power amplifiers consist of two primary architectures that include end-pumping and side-pumping. The latter offers greater amplification at the expense of increased thermally-induced beam distortions such as thermal lensing, while the former offers more controllable and efficient power scaling with a limit on the amplification potential. To date, the theoretical models describing the characteristics of end-pumped systems have been limited to two-dimensional crystal architectures with an approximation of the thermal lens as a two-dimensional element. In general, the optical pumping beam is over-simplified and does not reflect realworld spatial evolution over the entirety of the crystal rod length. These approximations hold for thin crystals operating under small-signal amplification, however, they are inaccurate for high signal amplification in long crystal rod geometries. In this work, we explore three-dimensional crystal rods in end-pumped configuration, using an in Infinitesimally sliced model, to study the amplification potential and thermal lens in end-pumped power amplifiers in greater detail while using beam shaping theory to model the pump beam transformation accurately over the length of the crystal. We verify our theoretical approach experimentally using a single amplifier stage in double-pass configuration for power scaling of Gaussian beams. We demonstrate over 95% correlation between our model and the corresponding experiment and show that this correlation extends over the small and high signal amplification regions. The improved model, experimental techniques and results outlined here will provide a valuable tool for advances towards optimizing high brightness amplifiers.
Twisted light carrying orbital angular momentum (OAM) has given rise to many developments ranging from optical manipulation to optical communications. Generating twisted light from solid-state lasers was initially achieved by amplitude and dynamic phase control, and more recently by manipulating the geometric phase of light. These lasers have been limited to generate superposition of OAM modes as well as scalar modes with OAM ℓ = 10. Here we incorporate a metasurface device into a visible solid-state laser to control the angular momentum of light by arbitrary spin-to-orbit coupling. We demonstrate the generation of pure Laguerre Gaussian modes with OAM up to ℓ = 100. Modal decomposition measurements of the output beams reveal the higher purity of the generated modes can reach up to 96% for ℓ = 1 and 88% for ℓ = 100. our approach offers a new route for high brightness OAM states at the source.
The use of beams carrying orbital angular momentum (OAM) has become ubiquitous and topical in a variety of research fields. More recently, there has been a growing interest in exotic OAM carrying beams with spatially variant polarisation, so called Poincaré sphere beams. Structuring these beams at the source gives rise to compact solutions for a myriad of applications, from laser materials processing to microscopy. Here we present a visible laser that control's the angular momentum of light by arbitrary spin-orbit (SO) momentum conversion using novel metasurface devices. Further, we outline how to generate high purity OAM states in a deterministic manner with charge up to 100. Finally, we demonstrate the generation of symmetric and non-symmetric vector vortex beams from the same source with a large OAM differential between modes of up to 90. The performance and versatility in design of our approach offers a route to control light's angular momentum at the source.
The Higher order Poincar´e sphere (HOPS) is generally used to describe scalar and vector orbital angular momentum modes. These modes have found many applications to date; however, they are limited to low power levels. It has thus become topical to consider amplification of such structured light modes. Here, we study the purity of the HOPS beams in a master oscillator power amplifier configuration using recently developed characterization tools through birefringent and non-birefringent amplifiers. We outline a general theory for this problem where we consider both gain and vector perspectives, and confirm our theory by experiment.
Additive manufacturing applications, in areas such as aerospace and medicine, are limited due to the lack of process stability and quality management. In particular, geometrical inaccuracies and the presence of mechanical defects hinder repeatability of the process1. A great disadvantage of AM is that verifying the quality of AM produced parts are mainly done after part fabrication which does not allow the operator to act upon defects observed during the actual build. To break into industries with very high quality standards, an important issue to be addressed is in-situ quality control during a build2, 3. If defects on a new powder layer can be detected before laser melting occurs, a new layer may be suitably recoated or the process can be paused for user controlled rectification. The work which will be presented here is focused on image based process monitoring of a powder bed additive manufacturing system using a shadow casting method. As a proof of principle, a few main defects during recoating will be identified and analyzed to establish the severity and possible impact of the defects on metal powder consolidation. Preliminary results of defects identified before and after material consolidation will be shown. For this, a software package is in development to automatically detect defects. This is aimed towards developing a system which in the future will contribute to quality assurance.
Fractals are mathematical series that exhibit replicating patterns at every scale. If the repeated patterns are identical at every scale, the fractal is termed self-similar. Fractals have found their way into applications such as communication and cosmology. Theoretical simulations showed that the eigenmodes of unstable laser resonators possess a fractal character, in contrast with the well-known stable-cavity eigenmodes. Unstable laser resonators have a special plane, called self-conjugate, in which the eigenmodes not only have the same pattern, but are also magnified copies of themselves. Here, we show a novel optical resonator that is capable of generating eigenmodes with self-similar fractal features. Our novel resonator is considered as an analogue to both the monitor-insidemonitor effect and monitor-outside-monitor effects. The fractal feature is proved by finding a typical image of the eigenstate at different scales. More quantitatively, we measured the pattern dimension which had a non-integer value, as is characteristic of self-similar fractals.
Mathematical self-similar fractals manifest identical replicated patterns at every scale. Recently, fractals have found their way into a myriad of applications. In optics, it has been shown that manipulation of unstable resonator parameters such as cavity length, curvatures of mirrors, the design of aperture and its transverse position can reveal self-similar fractal patterns in the resonators eigenmodes. Here, we present a novel laser resonator that can generate self-similar fractal output modes. This resonator has a special plane termed self-conjugate, during each round trip inside the cavity, is imaged upon itself with either a magnification or demagnification depending on the direction of beam propagation inside the cavity. By imaging an aperture placed in the self-conjugate plane inside the cavity, we qualitatively show the fractal behaviour occurring at various scales which, are given by powers of the magnification at the self-conjugate plane. We computed the fractal dimension of the patterns we generated and obtained non-integer values, as is expected for fractals.
The use of beams carrying orbital angular momentum (OAM) has become ubiquitous and topical in a variety of research fields. More recently, there has been a growing interest in exotic OAM carrying beams with spatially variant polarization, so called Poincare sphere beams, with the well known cylindrical vector beams (CVBs) a particular example; for example, they can be used to obtain tighter focus in applications ranging from optical trapping and tweezing, to laser material processing. Here we outline how to generate such beams in a deterministic manner directly from a solid state laser by employing intra-cavity geometric phase control. Further, we show how to detect and quantify such beams and introduce a new beam quality factor for vector beams. Finally, we consider the effects of amplification on the quality of such beams. We show that the amplification process can be used to maintain, degrade or improve the overall quality of vector beams.
Vector beams that carrying orbital angular momentum (OAM) have become ubiquitous and topical in a variety of research fields. The quality of such beams usually degrades while propagating in space. Here, we report a noval technique to improve the quality of vector beams by amplifying these beams through birefringent amplifier. We demonstrated this experimentally over the different orientation of the amplifier to reach enhancement in the quality of maximum 20% of that for the incident beam.
We present an experimental technique to generate partially coherent vortex beams with an arbitrary azimuthal index using only a spatial light modulator. Our approach is based on digitally simulating the intrinsic randomness of broadband light passing through a spiral phase plate. We illustrate the versatility of the technique by generating partially coherent beams with different coherence lengths and orbital angular momentum content, without any moving optical device. Consequently, we study its cross-correlation function in a wavefront folding interferometer. The comparison with theoretical predictions yields excellent agreement.
We show how one can determine the various properties of light, from the modal content of laser beams to decoding the information stored in optical fields carrying orbital angular momentum, by performing a modal decomposition. Although the modal decomposition of light has been known for a long time, applied mostly to pattern recognition, we illustrate how this technique can be implemented with the use of liquid-crystal displays. We show experimentally how liquid crystal displays can be used to infer the intensity, phase, wavefront, Poynting vector, and orbital angular momentum density of unknown optical fields. This measurement technique makes use of a single spatial light modulator (liquid crystal display), a Fourier transforming lens and detector (CCD or photo-diode). Such a diagnostic tool is extremely relevant to the real-time analysis of solid-state and fibre laser systems as well as mode division multiplexing as an emerging technology in optical communication.
We investigate the selection of a flat-top beam and a Gaussian beam inside a laser cavity on opposing mirrors. The concept is tested external to the laser cavity in a single pass and double pass regime where the latter mimics a single round trip in the laser. We implement this intra-cavity selection through the use of two 16 level diffractive optical elements. We consider a solid-state diode side-pumped laser resonator in a typical commercial laser configuration that consists of two planar mirrors where the DOEs are positioned at the mirrors. We out couple the Gaussian and flat-top distributions and we show that we improve the brightness of the laser with active mode control. We also demonstrate that the quality of the beam transformations determine the brightness improvement.
In this paper we experimentally demonstrate the measurement of thermally induced lensing, using a Shack-Hartmann wavefront sensor. We measured the thermally induced lens from the coefficient of defocus aberration using a Shack-Hartmann wavefront sensor (SHWFS). As a calibration technique, we infer the focal length of standard lenses probed by a collimated Gaussian beam of wavelength 633 nm. The technique was applied to an Nd:YAG crystal that is actively pumped by a diode laser operating at 808 nm. The results were compared to the results obtained by changing the properties of the end-pumped solid-state laser resonator operating at 1064 nm, where the length of an unstable plane-parallel laser resonator cavity is varied, and the laser output power was measured.
Higher-order Laguerre–Gaussian beams with zero radial index and nonzero azimuthal index are known to carry orbital angular momentum (OAM), and they are routinely created external and internal to laser cavities. Previous reports on the generation of such modes from laser cavities suffer from inconclusive evidence of the real electromagnetic field. In this paper we demonstrate a simple method of selectively generating higher-order doughnut modes using a digital laser and we 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 also demonstrate a method that could be used for future analysis of such fields from laser resonators.
Monolithic microchip lasers consist of a thin slice of laser crystal where the cavity mirrors are deposited directly onto the end faces. While this property makes such lasers very compact and robust, it prohibits the use of intracavity laser beam shaping techniques to produce complex light fields. We overcome this limitation and demonstrate the selection of complex light fields in the form of vector-vortex beams directly from a monolithic microchip laser. We employ pump reshaping and a thermal gradient across the crystal surface to control both the intensity and polarization profile of the output mode. In particular, we show laser oscillation on a superposition of Laguerre–Gaussian modes of zero radial and nonzero azimuthal index in both the scalar and vector regimes. Such complex light fields created directly from the source could find applications in fiber injection, materials processing and in simulating quantum processes.
A great number of laser applications need in place of the usual Gaussian beam a flat-top intensity profile in the focal plane of a focusing lens. In general the transformation of the laser beam from the Gaussian to the flat-top shape is made by a diffractive beam shaping technique. It is worthwhile to note that this transformation occurs in the vicinity of the focal plane. If a flat top laser beam keeping its shape during propagation is needed then this can be obtained by a weighted incoherent mixing of LG00 and LG01 eigenmodes. Here, we consider the generation of these two transverse modes by a solid-state laser axially pumped by a laser diode. The idea is to design the laser cavity so as to make identical the losses of LG00 and LG01 modes. To reach this objective we have used two techniques. The first one called as diffractive lies to insert an adequate amplitude mask inside the cavity. The second one called as interferometric consisted to couple the laser to an external cavity. It is important to note that LG00 and LG01 modes are not spatially in concurrence, i.e. the peak of the LG00 appears in the dip of the LG01 mode. As a result, the energy extraction from the amplifying medium is improved increasing thus the laser slope efficiency. Theory and experimental verifications have been done for the diffractive and interferometric techniques allowing the generation of a flat-top laser beam keeping its shape from the near-field to the far-field.
KEYWORDS: Holograms, Digital holography, Multiplexing, Wavefronts, Spatial light modulators, Modes of laser operation, Optical communications, Data transmission, Single mode fibers, Signal detection
High-capacity data transmission has been implemented using single channel optical systems. This technique is limited and soon it will be unable to fulfill the growing needs for higher bit rate data transmission. Hence multi-mode transmission has been recently given attention as a potential solution to the current problems. In this context, we demonstrate a method of multiplexing laser modes using spatial light modulators (SLMs). In our proposed technique, we use Laguerre Gaussian (LG) modes, which form a complete basis set; hence multi-mode masks can be created by taking a linear combination of the LG modes. Since LG modes are characterised by two degrees of freedom, the azimuthal index ` and radial index ρ, this allows for multi-dimensional states. There are however some experimental challenges which include the sensitivity of the setup to misalignment, that leads to mode-coupling. It is also important that the injected modes ha a uniform power spectrum so that are weighted equally. The size of the multi-modes is highly dependent on the resolution of the SLM.
We analyze the effect of atmospheric turbulence on the propagation of multiplexed Laguerre Gaussian modes. We present a method to multiplex Laguerre Gaussian modes using digital holograms and decompose the resulting field after encountering a laboratory simulated atmospheric turbulence. The proposed technique makes use of a single spatial light modulator for the generation of superimposed beam and a second spatial light modulator and a CCD camera for the modal decomposition. The obtained results demonstrate how sensitive the Laguerre Gaussian beams are to atmospheric distortions.
Optics and photonics research in Africa has gradually grown in the past ten years with a very active optical community involved in state-of-the-art research. Despite relatively low resources, optics research in the continent is competitive with many international benchmarks and has had a significant impact within the African continent. In the past five years, a group of dynamic students have developed the student chapter network from Tunisia to South Africa. The first student chapters of the optical society of America (OSA) and the international society for optics and photonics (SPIE) were established in South Africa (in the Council for Scientific and Industrial Research (CSIR) and in the University of Stellenbosch), followed by a chapter in Tunisia (Engineering school of communications of Tunis, Sup’Com). In this paper, we will present the major activities of the student chapters of Tunisia and South Africa, and how they are promoting optics and photonics in Africa.
We explore an intra-cavity beam shaping approach to generate a Gaussian distribution by the metamorphosis of a Gaussian beam into a flat-top distribution on opposing mirrors. The concept is tested external to the cavity through the use of two spatial light modulators (SLM), where the first SLM is used to transform a collimated Gaussian into a flat-top distribution and the second SLM is encoded with the conjugate phase of the flat-top for conversion back to a Gaussian. We implement this intra-cavity selection through the use of two optical elements of the refractive variant that are designed from the phase profiles addressed to the SLMs. We consider a solid-state diode side-pumped laser resonator that consists of two planar mirrors where the refractive optics are positioned at the mirrors. We out couple the Gaussian and show that the output beam size is comparable with the theoretical predictions and that we have an increase in optical brightness when compared to the cavity without any optics.
We explore an interferometric beam shaping technique that considers the coaxial superposition of two Gaussian beams. This technique is traditionally implemented in a Mach-Zehnder interferometer; however, to avoid phase shift drift due to vibrations and thermal effects we employ amplitude and phase modulation with a spatial light modulator (SLM) to achieve the beam shaping. We consider two Gaussian beams of equal but opposite curvature that possess the same phase and width incident on a focusing lens. At the plane of the lens we obtain a multi-ringed beam with a central intensity maximum which develops into a multi-ringed beam with a central null at the focal plane of the lens. The interesting feature of this beam is that it possesses two focal spots on either side of the focal plane of the lens. We investigate obstructing the beam at the focal plane of the lens and by carefully selecting the free parameters we obtain an unobstructed second focus while the equivalent Gaussian beam is sufficiently obstructed.
We introduce the correlation filter method for measuring the modal power spectrum of multi-mode beams. The method is based on an optical filter performing the integral relation of correlation. This filter is realized as a computer-generated hologram with a specifically designed transmission function based on the spatial distribution of the set of modes under test. The beam that is illuminating the hologram is generating a diffraction pattern containing information about modal amplitudes and intermodal phase differences. We will show that a simple single-shot intensity measurement is sufficient to gain the information about modal amplitudes and phases from the diffraction pattern which result in the ability to reconstruct the optical field under test. Beside a detailed presentation of the measurement process, the setup and the design of the correlation filters, the major advantage of the method, the ability to perform real-time measurements is introduced. As a test system, we investigate the guided modes of a few mode multi-mode fiber and show fast changing modal coupling processes. Thereby, we show measurement results of online-monitoring the reconstructed optical field of the beam under test.
Modal decomposition of optical fields as a concept has been in existence for many decades, yet despite its clear
applications to laser beam analysis it has nevertheless remained a seldom used tool. With the commercialization of
liquid crystal devices, digital holography as an enabling tool has become accessible to all, and with it modal
decomposition has come of age. Here we outline the basic principles of modal decomposition of laser beams with digital holograms, and review recent results on the modal decomposition of arbitrary optical fields. We show how to use the information to infer the intensity, phase, wavefront, Poynting vector and orbital angular momentum density of the light. In particular, we show how to achieve optimal modal decomposition even in the absence of key information about the field, such as its scale and wavefront. We demonstrate the techniques on optical fields from fibers, diode-pumped solidstate lasers, and structured light by laser beam shaping.
Phase-only spatial light modulators are now ubiquitous tools in modern optics laboratories, and are often used to
generate so-called structured light. In this work we outline the use of a phase-only spatial light modulator to achieve full complex amplitude modulation of the light, i.e., in amplitude and phase. We outline the theoretical concept, and then illustrate its use with the example of the laser beam shaping of Gaussian beams into flat-top beams. We quantify the performance of this approach for the creation of such fields, and compare the results to conventional lossless approaches to flat-top beam generation.
In this paper we explore vortex beams and in particular the generation of single LG0l modes and superpositions thereof.
Vortex beams carry orbital angular momentum (OAM) and this intrinsic property makes them prevalent in transferring
this OAM to matter and to be used in quantum information processing. We explore an extra-cavity and intra-cavity
approach in LG0l mode generation respectively. The outputs of a Porro-prism resonator are represented by "petals" and
we show that through a full modal decomposition, the "petal" fields are a superposition of two LG0l modes.
A method of decomposing a dual-directional laser beam into a forward propagating field and a backward propagating
field for an apertured plano-concave cavity is presented. An intra-cavity aperture is a simple method of laser beam
shaping as higher-order transverse modes are discriminated. Two fundamental resonator theories, namely, Fox-Li and
Laguerre-Gaussian decomposition are used in the determination of the respective beam profiles at a specific plane. A
preliminary set-up is characterized for Gaussian propagation in an attempt to verify that the cavity is viable. A
comparison of experimental data with the theories is presented.
An experimental approach in generating Petal-like transverse modes, which are similar to what is seen in porro-prism
resonators, has been successfully demonstrated. We hypothesize that the petal-like structures are generated from a
coherent superposition of Laguerre-Gaussian modes of zero radial order and opposite azimuthal order. To verify this
hypothesis, visually based comparisons such as petal peak to peak diameter and the angle between adjacent petals are
drawn between experimental data and simulated data. The beam quality factor of the Petal-like transverse modes and an
inner product interaction is also experimentally compared to numerical results.
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