Transverse mode analysis of a laser beam by near- and far-field intensity measurements

Modal decomposition of complex optical fields using convolutional neural networks

Recent studies have shown convolutional neural networks (CNNs) can be trained to perform modal decomposition using intensity images of optical fields. A fundamental limitation of these techniques is that the modal phases cannot be uniquely calculated using a single intensity image. The knowledge of modal phases is crucial for wavefront sensing, alignment, and mode matching applications. Heterodyne imaging techniques can provide images of the transverse complex amplitude and phase profiles of laser beams at high resolutions and frame rates. In this work, we train a CNN to perform modal decomposition using simulated heterodyne images, allowing the complete modal phases to be predicted. This is, to our knowledge, the first machine learning decomposition scheme to utilize complex phase information to perform modal decomposition. We compare our network with a traditional overlap integral and center-of-mass centering algorithm and show that it is both less sensitive to beam centering and on average more accurate in our simulated images.

Transverse mode analysis for free-space laser beams using Bayesian analysis

Reliable and rapid assessment of the transverse mode quality of a free-space laser beam has a wide range of applications in laser development, research, and utilization. It has become even more important with recent advances in developing orbital angular momentum photon beams across a broad spectral region. In this work, a general modal analysis method for a free-space multimode laser beam has been developed based on Bayesian analysis. After transforming mode decomposition into a linear system problem, a Gaussian probabilistic model is used to find a closed-form solution. The method is found to be robust with the presence of Gaussian noise. Prior knowledge about the mode content can be incorporated into the method to improve the solution for situations when coherent disturbances or contamination are present in the laser beam. This method can be used to analyze the mode content for laser beams in different bases, such as Hermite-Gaussian (HG) modes and Laguerre-Gaussian (LG) modes. Three applications of this method are presented: a detailed modal analysis of the beam image from the incoherent intensity addition of HG modes and two examples of mode decomposition using the complex wavefront from the coherent superposition of HG and LG modes. The feasibility of this method is demonstrated using various simulation results. Based on digital images of a laser beam recorded without complex wavelength-limiting optics, in principle, this method can be used in a wide wavelength range from infrared to ultraviolet, and possibly x ray.

Fast modal analysis for Hermite-Gaussian beams via deep learning

The eigenmodes of Hermite-Gaussian (HG) beams emitting from solid-state lasers make up a complete and orthonormal basis, and they have gained increasing interest in recent years. Here, we demonstrate a deep learning-based mode decomposition (MD) scheme of HG beams for the first time, to the best of our knowledge. We utilize large amounts of simulated samples to train a convolutional neural network (CNN) and then use this trained CNN to perform MD. The results of simulated testing samples have shown that our scheme can achieve an averaged prediction error of 0.013 when six eigenmodes are involved. The scheme takes only about 23 ms to perform MD for one beam pattern, indicating promising real-time MD ability. When larger numbers of eigenmodes are involved, the method can also succeed with slightly larger prediction error. The robustness of the scheme is also investigated by adding noise to the input beam patterns, and the prediction error is smaller than 0.037 for heavily noisy patterns. This method offers a fast, economic, and robust way to acquire both the mode amplitude and phase information through a single-shot intensity image of HG beams, which will be beneficial to the beam shaping, beam quality evaluation, studies of resonator perturbations, and adaptive optics for resonators of solid-state lasers.

Comparative analysis of numerical methods for the mode analysis of laser beams

We present a comparative study of four numerical methods to detect the mode content of a laser beam from, at most, two intensity images. The techniques are compared regarding temporal effort, stability, and accuracy, using the example of three multimode optical fibers that differ in the number of supported modes.

Resolving spatial modes of lasers via matrix completion

We explain a technique that recovers the structure and the modal weights of spatial modes of lasers from a limited number of spatial coherence measurements. Our approach interpolates the unobserved spatial coherence measurements via the low-rank matrix completion algorithm based on nuclear norm minimization and then extracts the set of modes via singular value decomposition. Numerical examples are provided on a variety of lasers to demonstrate the effectiveness of the method, and it is shown that the proposed method can further reduce the number of measurements by a factor of 2 for a moderate data size.

Testosterone increases susceptibility to amebic liver abscess in mice and mediates inhibition of IFNγ secretion in natural killer T cells

Amebic liver abscess (ALA), a parasitic disease due to infection with the protozoan Entamoeba histolytica, occurs age and gender dependent with strong preferences for adult males. Using a mouse model for ALA with a similar male bias for the disease, we have investigated the role of female and male sexual hormones and provide evidence for a strong contribution of testosterone. Removal of testosterone by orchiectomy significantly reduced sizes of abscesses in male mice, while substitution of testosterone increased development of ALA in female mice. Activation of natural killer T (NKT) cells, which are known to be important for the control of ALA, is influenced by testosterone. Specifically activated NKT cells isolated from female mice produce more IFNγ compared to NKT cells derived from male mice. This high level production of IFNγ in female derived NKT cells was inhibited by testosterone substitution, while the IFNγ production in male derived NKT cells was increased by orchiectomy. Gender dependent differences were not a result of differences in the total number of NKT cells, but a result of a higher activation potential for the CD4(-) NKT cell subpopulation in female mice. Taken together, we conclude that the hormone status of the host, in particular the testosterone level, determines susceptibility to ALA at least in a mouse model of the disease.

Modal decomposition without a priori scale information

The modal decomposition of an arbitrary optical field may be done without regard to the spatial scale of the chosen basis functions, but this generally leads to a large number of modes in the expansion. While this may be considered as mathematically correct, it is not efficient and not physically representative of the underlying field. Here we demonstrate a modal decomposition approach that requires no a priori knowledge of the spatial scale of the modes, but nevertheless leads to an optimised modal expansion. We illustrate the power of the method by successfully decomposing beams from a diode-pumped solid state laser resonator into an optimised Laguerre-Gaussian mode set. Our experimental results, which are in agreement with theory, illustrate the versatility of the approach.

Azimuthal decomposition with digital holograms

We demonstrate a simple approach, using digital holograms, to perform a complete azimuthal decomposition of an optical field. Importantly, we use a set of basis functions that are not scale dependent so that unlike other methods, no knowledge of the initial field is required for the decomposition. We illustrate the power of the method by decomposing two examples: superpositions of Bessel beams and Hermite-Gaussian beams (off-axis vortex). From the measured decomposition we show reconstruction of the amplitude, phase and orbital angular momentum density of the field with a high degree of accuracy.

Eigenmode analysis of phased-coupled VCSEL arrays using spatial coherence measurements

We apply the modal coherence theory to evaluate the spatial mode structure of a 2×2 phase-coupled array of vertical cavity surface emitting lasers (VCSELs). The eigenmode structure is extracted for different pump currents by measuring the degree of spatial coherence of all VCSEL pairs in the array. The results reveal the impact of optical disorder and spatial hole burning on the modal discrimination. The approach is useful more generally for the evaluation of spatial mode content of other laser array.

Real-time determination of laser beam quality by modal decomposition

We present a real-time method to determine the beam propagation ratio M2 of laser beams. The all-optical measurement of modal amplitudes yields M2 parameters conform to the ISO standard method. The experimental technique is simple and fast, which allows to investigate laser beams under conditions inaccessible to other methods.

Laser beam quality and pointing measurement with an optical resonator

We present a compact diagnostic breadboard that is based on an optical ring resonator for measuring beam quality and pointing of single-frequency continuous wave lasers at a wavelength of 1064 nm. To determine the beam quality of the coherent test beam, this optical resonator is used to perform a mode decomposition into Hermite-Gaussian modes. For our laser system, a power fraction in the fundamental Gaussian mode of 97.2%+/-0.2% was measured. Residual misalignment and mis-mode-matching to the resonator as well as the astigmatism and/or ellipticity of the test beam have been determined. Numerical simulations showed that measurements of the M(2) factor and transversal intensity distribution are not suitable for determining this power fraction. To measure the beam pointing, the fundamental mode of the optical resonator was used as a stable reference. The pointing of the test beam was measured with the differential wave front sensing technique up to Fourier frequencies of 1 kHz with a sensitivity to relative pointing of /epsilon/=1x10(-6)/sqrt[Hz]. Pointing measurements with an alternative method were performed and showed good agreement.

Evaluation of the spatial coherence of a light beam through transverse intensity measurements

The problem of recovering the coherence features of a partially coherent quasi-monochromatic scalar optical source, starting solely from intensity measurements on the emitted beam, is addressed in the most general way, under the paraxial approximation. In particular, it is shown that on expanding the beam emitted by the source as a bundle of partially correlated Hermite-Gaussian beams, the correlation coefficients can be recovered, in principle, simply by performing scalar products between transverse intensity distributions and suitably defined functions.

Coherent-mode decomposition of partially polarized, partially coherent sources

It is shown that any partially polarized, partially coherent source can be expressed in terms of a suitable superposition of transverse coherent modes with orthogonal polarization states. Such modes are determined through the solution of a system of two coupled integral equations. An example, for which the modal decomposition is obtained in closed form in terms of fully linearly polarized Hermite Gaussian modes, is given.

Modal decomposition of partially coherent beams using the ambiguity function

Phase-space representations of optical beams such as the ambiguity function or the Wigner distribution function have recently gained considerable importance for the characterization of coherent and partially coherent beams. There is growing interest in beam properties such as the beam propagation factor and the coherence and phase information that can be extracted from these phase-space representations. A method is proposed to decompose a partially coherent beam into Hermite-Gaussian modes by using the ambiguity function. The modal weights and the possible phase relations of the Hermite-Gaussian modes are retrieved. The method can also be applied for the decomposition of the Wigner distribution function. Some examples are discussed in the scope of beam characterization.

Determining spatial modes of lasers with spatial coherence measurements

We explain a technique that extracts both the structure and the modal weights of spatial modes of lasers by analyzing the spatial coherence of the beam. This is the first time, to our knowledge, that an experimental method is being used to measure arbitrary forms of the spatial modes. We applied this method to an edge-emitting Fabry-Perot semiconductor laser with a stripe width of 5 mum and extracted fundamental and first-order lateral modes with relative power weights of 96.2% and 3.8%. There was a single transverse mode.

Evaluation of the modal structure of light beams composed of incoherent mixtures of Hermite-Gaussian modes

A new, to our knowledge, technique for determining the modal content of partially coherent beams that are made up of an incoherent superposition of Hermite-Gaussian modes is studied. The algorithm makes use of the intensity profile of the beam at an arbitrarily chosen transverse plane. Analytical derivations are presented for a Gaussian Schell-model source and flat-topped beams, as well as an analysis of their performances in the presence of experimental errors and noise. Numerical simulations are performed to test the accuracy and the stability of the recovery algorithm.

Intensity-based modal analysis of partially coherent beams with Hermite-Gaussian modes

Many partially coherent beams are made up of a superposition of mutually uncorrelated Hermite-Gaussian modes. We prove that knowledge of the transverse intensity profile of such a beam is sufficient for evaluating the weights of the modes in an exact way. Simulations indicate that the proposed method resists noise well.