Spatial Light Modulators (SLMs) have advanced the fields of complex and structured light. These Liquid-Crystal-on-Silicon (LCoS) based devices allow for the dynamic modulation of both the amplitude and phase of light. This tutorial-type talk will provide an overview of the working principle of Spatial Light Modulators (SLMs). We will first look at the mechanism as to how these devices operate, followed by how to setup your own SLM, as well as the motivation to calibrate these devices. We will look at how digital holograms can be generated, as well as some common problems that the user might encounter. Finally, we will discuss some applications which make use of SLMs.
In this work we generate optical fields whose polarisation structures not only rotate about the propagation axis, but can be tailored to accelerate, independently from their spatial profiles. Here we will demonstrate how this can be achieved with orthogonal, scalar fields, represented by weighted superpositions of oppositely charged Bessel beams, through path interference with a beam-splitter. In addition to their creation, we investigate various aspects of these generated modes, such as their angular accelerating Stokes vectors and optical current or intensity transport between various local positions within the field. Finally, we present a digital analogy to measure such fields in order to reconstruct their state of polarisation via Stokes polarimetry. undefined In this work we generate optical fields whose polarisation structures not only rotate about the propagation axis, but can be tailored to accelerate, independently from their spatial profiles. Here we will demonstrate how this can be achieved with orthogonal, scalar fields, represented by weighted superpositions of oppositely charged Bessel beams, through path interference with a beam-splitter. In addition to their creation, we investigate various aspects of these generated modes, such as their angular accelerating Stokes vectors and optical current or intensity transport between various local positions within the field. Finally, we present a digital analogy to measure such fields in order to reconstruct their state of polarisation via Stokes polarimetry.
In this work, Stokes polarimetery is used to extract the polarization structure of optical fields from only four measurements as opposed to the usual six measurements. Here, instead of using static polarization optics, we develop an all-digital technique by implementing a Polarization Grating (PG) which projects a mode into left- and right-circular states which are subsequently directed to a Digital Micromirror Device (DMD) which imparts a phase retardance for full polarization acquisition. We apply our approach in real-time to reconstruct the State of Polarization (SoP) and intra-modal phase of optical modes.
Current communication systems make use of polarization and wavelength multiplexing to increase transmission rates. To offer a further improvement, Orbital Angular Momentum (OAM) modes (or Laguerre-Gaussian modes) provide an infinite dimensional space. In this work, Laguerre-Gaussian modes are multiplexed and de-multiplexed by means of two Spatial Light Modulators (SLMs), making use of both their azimuthal and radial degrees of freedom. Due to the orthogonality of these modes, a modal decomposition technique is employed to detect the transmitted modes. Here we demonstrate this concept by transmitting an image over a 150 meter free-space link. The free-space link is also characterized in terms of its optical turbulence.
In the avid search for means to increase computational power in comparison to that which is currently available,
quantum walks (QWs) have become a promising option with derived quantum algorithms providing an associated speed
up compared to what is currently used for implementation in classical computers. It has additionally been shown that the
physical implementation of QWs will provide a successful computational basis for a quantum computer. It follows that
considerable drive for finding such means has been occurring over the 20+ years since its introduction with phenomena
such as electrons and photons being employed. Principal problems encountered with such quantum systems involve the
vulnerability to environmental influence as well as scalability of the systems. Here we outline how to perform the QW
due to interference characteristics inherent in the phenomenon, to mitigate these challenges. We utilize the properties of
vector beams to physically implement such a walk in orbital angular momentum space by manipulating polarization and
exploiting the non-separability of such beams.
Beams carrying orbital angular momentum (OAM) are ubiquitous in many experiments carried out today and cover a
wide range of research, from surface microstructure processing to optical tweezers and communications. It follows that
these beams are a significant factor in the outcome of these research areas. They are often generated through the use of
phase-only modulation with elements such as SLMs and q-plates due to the simplicity of the approach. Interesting
consequences result from this generation principal which include the introduction of radial modes as they propagate. We
experimentally demonstrate how this effects the distribution of power where a notable decrease in the desired
fundamental mode power occurs with higher OAM beams in addition to an expansion in the power across these radial
modes. This research additionally affirms their mathematical description as the recently introduced Hypergeometric-
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 implement digital holograms for the creation and detection of the spatial modes of light. We make use of modal decomposition theory to determine the numerous properties of light, from the modal content of laser beams to decoding the information stored in optical fields carrying orbital angular momentum. We demonstrate the versatility of these techniques to characterize both structured and vector fields with static and propagating optical fields. Finally, we show a holographic technique to realise a communication link using a densely packed spatial mode set where we experimentally multiplex and de-multiplex over 100 spatial modes.
Traditional optical communication systems optimize multiplexing in polarization and wavelength both trans- mitted in fiber and free-space to attain high bandwidth data communication. Yet despite these technologies, we are expected to reach a bandwidth ceiling in the near future. Communications using orbital angular momentum (OAM) carrying modes offers infinite dimensional states, providing means to increase link capacity by multiplexing spatially overlapping modes in both the azimuthal and radial degrees of freedom. OAM modes are multiplexed and de-multiplexed by the use of spatial light modulators (SLM). Implementation of complex amplitude modulation is employed on laser beams phase and amplitude to generate Laguerre-Gaussian (LG) modes. Modal decomposition is employed to detect these modes due to their orthogonality as they propagate in space. We demonstrate data transfer by sending images as a proof-of concept in a lab-based scheme. We demonstrate the creation and detection of OAM modes in the mid-IR region as a precursor to a mid-IR free-space communication link.
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.
Current optical communication technologies are predicted to face a bandwidth capacity limit in the near future. The nature of the limitation is fundamental rather than technological and is set by nonlinearities in optical fibers. One solution, suggested over 30 years ago, comprises the use of spatial modes of light as information carriers. Along this direction, light beams endowed with orbital angular momentum (OAM) have been demonstrated as potential information carriers in both, free space and fibres. However, recent studies suggest that purely OAM modes does not increase the bandwidth of optical communication systems. In fact, in all work to date, only the azimuthal component of transverse spatial modes has been used. Crucially, all transverse spatial modes require two degrees of freedom to be described; in the context of Laguerre-Gaussian (LGp`) beams these are azimuthal (l) and radial (p), the former responsible for OAM. Here, we demonstrate a technique where both degrees of freedom of LG modes are used as information carrier over free space. We transfer images encoded using 100 spatial modes in three wavelengths as our basis, and employ a spatial demultiplexing scheme that detects all 100 modes simultaneously. Our scheme is a hybrid of MIMO and SMM, and serves as a proof-of-principle demonstration. The cross-talk between the modes is small and independent of whether OAM modes are used or not.
Significant interest has been devoted to tailoring optical fields that transversely accelerate during propagation in the form of Airy, Weber and Mathieu beams. In this work, we introduce a new type of optical field that exhibits controlled angular acceleration during propagation which is achieved by superpositions of Bessel beams with non-canonical phase functions. We demonstrate these angular accelerating fields by modulating the phase and amplitude of a supercontinuum source with the use of a phase-only spatial light modulator (SLM). We illustrate that by considering only the first diffraction order when the SLM is encoded with a blazed grating, the SLM is capable of tailoring the spatial profile of broadband sources without any wavelength dependence. By digitally simulating free-space propagation on the SLM, we compare the effects of real and digital propagation on the angular rotation rates of the resulting optical fields for various wavelengths. The development of controlled angular accelerating optical fields will be useful in areas such as particle manipulation, plasma control, material processing and non-linear optics.
We experimentally demonstrate an information encoding protocol using the two degrees of freedom of Laguerre Gaussian modes having different radial and azimuthal components. A novel method, based on digital holography, for information encoding and decoding using different data transmission scenarios is presented. The effects of the atmospheric turbulence introduced in free space communication is discussed as well.
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.
A long-standing question in optics has been to efficiently measure the phase (or wavefront) of an optical field. This has led to numerous publications and commercial devices such as phase shift interferometry, wavefront reconstruction via modal decomposition and Shack-Hartmann wavefront sensors. In this work we develop a new technique to extract the phase which in contrast to previously mentioned methods is based on polarization (or Stokes) measurements. We outline a simple, all-digital approach using only a spatial light modulator and a polarization grating to exploit the amplitude and phase relationship between the orthogonal states of polarization to determine the phase of an optical field. We implement this technique to reconstruct the phase of static and propagating optical vortices.
In this work we construct coherent superpositions of Gaussian and vortex modes which can be described to occupy the complex-plane. We demonstrate how these fields can be experimentally constructed in a digital, controllable manner with a spatial light modulator. Once these fields have been generated we illustrate, with three separate techniques, how the constituent components of these fields can be extracted, namely by measuring the intensity of the field at two adjacent points; performing a modal decomposition and a new digital Stokes measurement.
An overview of the work done within the Mathematical Optics group at the CSIR’s National Laser Centre will be presented. We will focus on our work done in laser beam shaping with the use of digital holograms for the generation of superimposed optical fields which carry orbital angular momentum (OAM) and the development of OAM measurement techniques. Since OAM offers a potentially infinite-dimensional state space, much interest has been generated in its measurement for higher-dimensional quantum information processing to be realised. We generate superpositions of higher-order Bessel beams and show that even though we can create a field which carries no overall OAM, we can still witness an angular rotation in the intensity profile of the beam. We also develop a new OAM measurement technique by means of digital holograms.
We encode mutually unbiased bases (MUBs) using the higher-dimensional orbital angular momentum (OAM) degree of freedom and illustrate how these states are encoded on a phase-only spatial light modulator (SLM). We perform (d - 1)- mutual unbiased measurements in both a classical prepare and measure scheme and on entangled photon pairs for dimensions ranging from d = 2 to 5. The calculated average error rate, mutual information and secret key rate show an increase in information capacity as well as higher generation rates as the dimension increases.
We demonstrate how to create non-diffracting vector Bessel beams by implementing a spatial light modulator (SLM) to generate scalar Bessel beams which are then converted into vector fields by the use of an azimuthally-varying birefringent plate, known as a q-plate. The orbital angular momentum (OAM) of these generated beams is measured by performing a modal decomposition on each of the beam’s polarization components. This is achieved by separating the circular polarization components through a polarization grating (PG) before performing the modal decomposition. We investigate both single charged Bessel beams as well as superpositions and the results are in good agreement with theory.
We experimentally generate non-diffracting vector vortex beams by using a Spatial Light Modulator (SLM) and an azimuthal birefringent plate (q-plate). The SLM generates scalar Bessel beams and the q-plate converts them to vector vortex beams. Both single order Bessel beam and superposition cases are studied. The polarization and the azimuthal modes of the generated beams are analyzed. The results of modal decompositions on polarization components are in good agreement with theory. We demonstrate that the generated beams have cylindrical polarization and carry polarization dependent Orbital Angular Momentum (OAM).
In this work we will present two techniques for the measurement of superimposed higher-order Bessel beams. In the first technique we will outline a simple approach using only a spatial light modulator and a Fourier transforming lens to decompose the OAM spectrum of an optical field. We test this approach on symmetric and non-symmetric superpositions of non-diffracting higher-order Bessel beams. Our second procedure consists of two refractive optical elements which perform a Cartesian to log-polar coordinate transformation, translating helically phased beams into a transverse phase gradient. By introducing two cylindrical lenses we can focus each of the azimuthal modes associated with each Bessel beam to a different lateral position in the Fourier plane, while separating the radial wave-vectors in the image-plane.
SLMs used for spatial modulation of lasers are often used in conjunction with very narrow bandwidth laser
light where diffractive dispersion could be approximated as a constant. It is known that diffractive dispersion
is inversely proportional to wavelength and this effect can be compensated for depending on the optical set-up.
SLMs use birefringent liquid crystal (LC) pixels each with an adjustable refractive index at a specific polarization.
The range of the adjustable refractive index is wavelength dependent. This adds an additional SLM dependent
dispersion. Note that we distinguish between diffractive dispersion and SLM dependent dispersion. SLMs are
therefore calibrated in order to have linearly adjustable phase retardation of light incident on the pixels between
zero and two pi for a specific wavelength. It is therefore unavoidable when using the same SLM, to do beam
shaping of a source which emits multiple wavelengths or a wide bandwidth, that the device will not modulate
all wavelengths between zero and two pi. We numerically and experimentally investigate the effect of SLM
dependent dispersion on spatial modulation of light incident on a 2D SLM. We further discuss why it is possible
to modulate multiple wavelengths between zero and two pi despite SLM dependent dispersion.
Although many techniques are efficient at measuring optical orbital angular momentum (OAM), they do not allow one to
obtain a quantitative measurement for the OAM density across an optical field and instead only measure its global OAM.
Numerous publications have demonstrated the transfer of local OAM to trapped particles by illustrating that particles
trapped at different radial positions in an optical field rotate at different rotation rates. Measuring these rotation rates to
quantitatively extract the OAM density is not only an indirect measurement but also a complicated experiment to
execute. In this work we theoretically calculate and experimentally measure the OAM density of light, for both
symmetric and non-symmetric optical fields. We outline a simple approach using only a spatial light modulator and a
Fourier transforming lens to measure the OAM spectrum of an optical field and we test the approach on superimposed non-diffracting higher-order Bessel beams. We obtain quantitative measurements for the OAM density as a function of the radial position in the optical field for both symmetric and non-symmetric superpositions, illustrating good agreement with the theoretical prediction. The ability to measure the OAM distribution of optical fields has relevance in optical tweezing, and quantum information and processing.
A procedure to efficiently sort orbital angular momentum (OAM) states of light, by performing a Cartesian to log-polar
coordinate transformation which translates helically phased beams into a transverse phase gradient, currently exists1. We
implement this mode transformer, which comprises of two custom refractive optical elements2, to efficiently sort Bessel
beams carrying OAM. Introducing two cylindrical lenses, allows the focusing of each of the input OAM Bessel states to
a different lateral position in the Fourier plane and separates the radial wave-vectors in the image-plane. We demonstrate
the concept by separating over forty OAM states and radial wave-vectors.
We present a novel technique to measure the orbital angular momentum (OAM) density of light. The technique is based on modal decomposition, enabling the complete reconstruction of optical fields, including the reconstruction of the beams Poynting vector and the OAM density distribution. The modal decomposition is performed using a computer-generated hologram (CGH), which allows fast and accurate measurement of the mode spectrum. The CGH encodes the modes of interest, whose powers and relative phase differences are measured from the far-field diffraction pattern of the illuminating optical field with the hologram transmission function. In combination with a classical measurement of Stokes parameters, including a polarizer and a quarter-wave plate in front of the hologram, the polarization state of each mode is measured. As a consequence, any arbitrary vector field can be reconstructed, including amplitude, phase, and polarization. Having all information on the optical field, the Poynting vector and the OAM density can be calculated directly.
We applied our method to beams emerging from optical fibers, which allows us to investigate arbitrary coherent superposition of fiber modes with complexly shaped intensity and polarization distributions. The excitation of certain mode mixtures is done by appropriate input coupling and using diffractive phase masks to shape the input beam and hence enhance the excitation efficiency of distinct modes. The accuracy of the achieved results is verified by comparing the reconstructed with the directly measured beam intensity, revealing excellent agreement.
By using digital holograms, we present a simple technique for performing a complete azimuthal decomposition of an
arbitrary laser mode. The match-filter, used to perform the azimuthal decomposition, is bounded by an annular ring,
allowing us to conduct a scale-independent decomposition on our selected mode. This technique therefore requires no
prior knowledge of the mode structure, the mode phases, or the amplitude distribution. A basis comprising of the angular
harmonics is used to express the spatial distribution of the selected mode in terms of spatially dependant coefficients. We
use this to infer directly from the measured weightings of the azimuthally decomposed modes and their phase-delay
measurements, the intensity of the selected field, its phase, and its orbital angular momentum (OAM) density. We
illustrate the concept by executing a full decomposition of two examples: a superposition of two Bessel beams, with
relative phase differences, and an off-axis vortex mode. We show a reconstruction of the amplitude, phase and OAM
density of these fields with a high degree of accuracy.
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.
We experimentally generated superpositions of higher-order Bessel beams that possess no global orbital angular momentum (OAM), yet exhibit an angular rotation in their intensity profile as the field propagates. The digital holograms encoded on a spatial light modulator (SLM), used for generating such fields, consist of two annular rings of unequal radial wave-vectors where each ring is encoded with an azimuthal mode of equal order but opposite charge. We present experimentally measured angular rotation rates for some example superposition fields, which are shown to be in good agreement with that predicted theoretically. Introducing a second SLM and a Fourier transforming lens, we demonstrate a simple approach to perform an azimuthal decomposition of our generated optical fields. Bounding the match-filter to an annular ring, of varying radius, we are able to perform a scale-independent azimuthal decomposition of our initial field. From the measured weightings of the azimuthally decomposed modes we show reconstruction of the cross-sectional intensity profile and OAM density of our initial field.
In this report we theoretically calculate and experimentally measure the OAM density of a coherent superposition of both
symmetric and non-symmetric non-diffracting Bessel beams. Although the intensity pattern of the superimposed field
rotates at a fixed angular velocity (which is due to the differing wave-vectors of the component fields), we show that the
magnitude and direction of the OAM is dependent on the radial position within the field. We outline a simple approach
using only a spatial light modulator to measure the OAM density for a superposition of non-diffracting Bessel beams.
Our quantitative measurements are in good agreement with predicted values.
In this paper we present a mechanism for the generation of the superposition of higher-order Bessel beams, which
implements a ring slit aperture and spatial light modulator (SLM). Our experimental technique is also adapted to
generate nondiffracting speckle fields. We report on illuminating a ring slit aperture with light which has an azimuthal
phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the
phase dependence of the light illuminating the ring slit aperture is random, a nondiffracting speckle field is produced.
The experimentally produced fields are in good agreement with those calculated theoretically.