Laguerre-Gaussian Modes Research Articles

768-ary Laguerre-Gaussian-mode shift keying free-space optical communication based on convolutional neural networks.

Beyond orbital angular momentum of Laguerre-Gaussian (LG) modes, the radial index can also be exploited as information channel in free-space optical (FSO) communication to extend the communication capacity, resulting in the LG- shift keying (LG-SK) FSO communications. However, the recognition of radial index is critical and tough when the superposed high-order LG modes are disturbed by the atmospheric turbulences (ATs). In this paper, the convolutional neural network (CNN) is utilized to recognize both the azimuthal and radial index of superposed LG modes. We experimentally demonstrate the application of CNN model in a 10-meter 768-ary LG-SK FSO communication system at the AT of Cn2 = 1e-14 m-2/3. Based on the high recognition accuracy of the CNN model (>95%) in the scheme, a colorful image can be transmitted and the peak signal-to-noise ratio of the received image can exceed 35 dB. We anticipate that our results can stimulate further researches on the utilization of the potential applications of LG modes with non-zero radial index based on the artificial-intelligence-enhanced optoelectronic systems.

Performance analysis of free-space quantum key distribution using multiple spatial modes.

In the diffraction-limited near-field propagation regime, free-space optical quantum key distribution (QKD) systems can employ multiple spatial modes to improve their key rate. This improvement can be effected by means of high-dimensional QKD or by spatial-mode multiplexing of independent QKD channels, with the latter, in general, offering higher key rates. Here, we theoretically analyze spatial-mode-multiplexed, decoy-state BB84 whose transmitter mode set is either a collection of phase-tilted, flat-top focused beams (FBs) or the Laguerre-Gaussian (LG) modes. Although for vacuum propagation the FBs suffer a QKD rate penalty relative to the LG modes, their potential ease of implementation make them an attractive alternative. Moreover, in the presence of turbulence, the FB modes may outperform the LG modes.

Relevance of longitudinal fields of paraxial optical vortices

Longitudinal electromagnetic fields generally become comparable with the usually dominant transverse components in strongly focused, non-paraxial beams. For paraxial optical vortex modes it is highlighted here how their angular momentum properties produce longitudinal fields that in general must be accounted for. First-order longitudinal components of quantized Laguerre–Gaussian modes are derived and numerically studied with respect to the paraxial parameter, highlighting light-matter and spin-orbit interactions that stem from the longitudinal fields of paraxial beams in free space. New restrictions are cast on the validity of neglecting longitudinal fields for paraxial optical vortices interacting with atoms, molecules and other nanostructures.

Analysis of misaligned optical rotational Doppler effect by modal decomposition.

The optical rotational Doppler effect (RDE) is closely related to the unique orbital angular momentum (OAM) carried by optical vortex, whose topological charge means the mode of OAM. Compared with the coaxial incidence, the rotational Doppler frequency shift spectrum of a misaligned optical vortex (misaligned RDE) widens according to a certain law. In this paper, an OAM modal decomposition method of the misaligned optical RDE is proposed and the relative intensity of different OAM modes, namely the OAM spectrum, is derived based on an inner product computation. Analyses show that lateral displacements and angular deflections change the distribution of OAM modes relative to the rotation axis of the object. A misaligned Laguerre-Gaussian (LG) vortex can be represented as a specific combination of coaxial LG modes, and the difference between the topological charge of two adjacent modes is 1 or 2 with lateral displacements or angular deflections respectively. An experiment of misaligned optical RDE using a superimposed LG vortex is executed, and the obtained frequency shift spectrum with misaligned incidence expands into a set of discrete signals, which agrees well with the theoretical results. Moreover, we can get the rotation frequency of the object from an expanded frequency spectrum more quickly and accurately based on the difference between two adjacent signal peaks. The proposed method contributes to analyze the misaligned optical RDE comprehensively, which is significant in remote sensing and optical metrology.

Efficient vortex beam generation using gradient refractive-index microphase plates.

Vortex beams were theoretically demonstrated by patterning a fiber facet with $N$-segment microphase plates. By changing the aluminum oxynitride material composition of each segment, gradient refractive-index phase plates (GRPs) were designed and introduced a ${{2}}\pi l$ azimuthal optical phase difference. The gradient index profile was able to convert a fiber Gaussian mode to a Laguerre-Gaussian mode with varieties of topological charge $l$. A three-dimensional finite-difference time-domain method was applied to calculate the near-field optical phase maps and the far-field beam profiles projected from the micro-GRPs. A uniform vortex beam with a symmetrical doughnut shape was obtained by optimizing the GRPs' radii and the number of segments. The micro-GRPs enabled flat optical components for efficient vortex beam generation.

Modal conversion of transverse mode-locked laser beams

The conversion of transverse mode-locked (TML) laser beams from a Hermite-Gaussian (HG) to a Laguerre-Gaussian (LG) mode set using a cylindrical lens mode converter was demonstrated experimentally. By changing the spatial symmetry of the beams new spatio-temporal dynamics for TML lasers were enabled. In particular, the fast linear motion of an oscillating laser spot, generated by a TML laser based on HG modes, was translated into the circular motion of a TML laser beam based on LG modes. The mode conversion was demonstrated successfully for different average mode orders. Apart from an average ellipticity of about 6%, the converted beam profiles remained circular over the propagation from the near- into the far-field. The remaining ellipticity seemed to be introduced by astigmatism of the incident HG TML beam, which could be compensated before conversion. Due to their radial symmetry and high scanning speed TML laser beams based on LG modes are well suited for precision applications like STED or Minflux microscopy.

A New Type of Shape-Invariant Beams with Structured Coherence: Laguerre-Christoffel-Darboux Beams

A new class of sources presenting structured coherence properties is introduced and analyzed. They are obtained as the incoherent superposition of coherent Laguerre-Gaussian modes with suitable coefficients. This ensures that the shape of the intensity profile and the spatial coherence features of the propagated beams are invariant during paraxial approximation. A simple analytical expression is obtained for the cross-spectral density of the sources of this class, regardless of the number of superposed modes. Properties of these sources are analyzed and described by several examples.

High-quality reconstruction of an optical image by an efficient Laguerre-Gaussian mode decomposition method

We propose and experimentally demonstrate an optical image reconstruction in the Laguerre-Gaussian (LG) domain. Because LG mode features circular symmetry, it has unique advantages to decompose an image with rotational symmetry. In the experiment, we realize a high-fidelity reconstruction of an optical image by using about 104 LG modes. In the proposed configuration, the radial sampling points are much fewer than those in the existing methods, which can significantly improve the efficiency. Furthermore, we show azimuthal image noise reduction through LG domain filtering. Our results open a door for LG-mode based optical image processing.

ML-Based Identification of Structured Light Schemes under Free Space Jamming Threats for Secure FSO-Based Applications

This paper exploits for the first time the use of machine learning (ML) based techniques to identify complex structured light patterns under free space optics (FSO) jamming attacks for secure FSO-based applications. Five M-ary modulation schemes, construed using Laguerre and Hermite Gaussian (LG and HG) mode families, were used in this investigation. These include 8-ary LG, 8-ary superposition-LG, 16-ary HG, 16-ary LG and superposition-LG, and 32-ary LG and superposition-LG and HG formats. The work was conducted using experimental demonstrations for two different jammer positions. The convolutional neural network (CNN)-based ML method was utilized to differentiate between the stressed mode patterns. The experimental results show a 100% recognition accuracy for 8-ary LG, 8-ary superposition-LG, and 16-ary HG at 1, −2, and −2 dB signal-to-jammer ratios (SJR), respectively. For SJR values < 0 dB, the standard LG modes are the most affected by jamming and are not recommended for data transmission in such an environment. Besides, the accuracy of determining the jammer direction of arrival was investigated using CNN and a simpler classifier based on linear discriminant analysis (LDA). The results show that advanced networks (e.g., CNN) are required to achieve reliable performance of 100% direction determination accuracy, at −5 dB SJR, as opposed to 97%, at 2 dB SJR, for a simple LDA classifier.

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.

Optical grinder: sorting of trapped particles by orbital angular momentum.

We customize a transversely structured, tunable light landscape on the basis of orbital angular momentum (OAM)-carrying beams for the purpose of advanced optical manipulation. Combining Laguerre-Gaussian (LG) modes with helical phase fronts of opposite OAM handedness, counter-rotating transfer of OAM is enabled in a concentric intensity structure, creating a dynamic "grinding" scenario on dielectric microparticles. We demonstrate the ability to trap and rotate silica spheres of various sizes and exploit the light fields' feature to spatially separate trapped objects by their size. We show the adaptability of the light field depending on the chosen LG mode indices, allowing on-demand tuning of the trapping potential and sorting criteria. The versatility of our approach for biomedical application is examined by spatial discriminating yeast cells and silica spheres of distinct diameter.

Digital analysis of a speckle pattern of chaotic mode composition and restoration of a regular intensity pattern after a multimode fiber

A process of mode matching in a chaotic speckle pattern without a reference beam responsible for the formation of a holographic grating was studied experimentally and theoretically. Our approach was based on measuring the amplitudes and phases of the Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes in a speckle pattern formed by the radiation of a multimode gradient fiber. The speckle pattern was formed in a hologram of a spatial light modulator using a multimode gradient fiber model while taking into account the mode and polarization dispersion, as well as random phase jumps of each eigenmode. We managed to match 210 modes of the speckle pattern and restore not only the original pattern, but also each structured LG mode and the entire chain of HG eigenmodes.

Orbital angular momentum of generalized cosine Gaussian beams with an infinite number of screw dislocations

We study a novel family of mth-order cosine Gaussian optical vortex beams with an infinite (but countable) number of screw dislocations, each with the topological charge m. An expression is derived for the normalized-to-power orbital angular momentum (OAM) of such beams. The OAM is shown to increase quadratically with the order m. The transverse intensity distributions of such beams consists of two light spots residing on a straight line orthogonal to the straight line with points of phase singularity. The OAM-spectrum of such beams is almost symmetric and the order (topological charge) of the central harmonic in this spectrum is approximately equal to the normalized OAM of the beam. Each such beam is a superposition of an infinite number of the single-ringed Laguerre-Gaussian modes with only even and nonnegative azimuthal indices. Such rotating two-petal beams can be used for increasing the longitudinal resolution in the optical microscopy.

Fractional-order-Bessel Fourier-invariant optical vortices

A new set of vortex rotationally symmetric Bessel beams is investigated, which are Fourier-invariant and have low sidelobes, in contrast to all the other known Bessel beams. Complex amplitudes in the source plane and in the far field are obtained analytically. These beams are of finite energy (and thus physically realizable for the topological charge exceeding 4), but they do not have the Gaussian envelope. In the initial plane and in the Fraunhofer diffraction area, their complex amplitude is proportional to the Bessel function of a fractional order (odd integer number divided by 6), although the vortex itself is of an integer order. Compared to the zero-radial-index Laguerre–Gaussian modes, such beams have smaller inner dark spot. Such beams can be generated by a spatial light modulator and applied in data transmission, interferometry, trapping of metallic particles.

Rotational Doppler effect detection by LG beams with a nonzero radial index.

The capability to detect the rotational speed of non-cooperative targets in a long distance is a difficult problem to be solved. In recent years, vortex light provides a feasible solution for the measurement of rotational speed for its spiral phase and the orbital angular momentum. Laguerre-Gaussian (LG) mode, as the typical vortex beam, has been widely employed in rotational Doppler effect (RDE) experiments. Here, we show that the nonzero radial index LG beam not only has a specific physical meaning but also can enhance the light intensity and the amplitude of RDE frequency signal relative to a zero radial index LG beam. To this end, we theoretically analyze the reason of intensity enhancement of a nonzero radial index beam and verify the conclusion in a variable control experiment. Our study provides a new aspect of LG beams that can be considered in rotational speed detection based on RDE. It may produce an improvement of the detection range of rotating targets in practical applications.

Coupling light to higher order transverse modes of a near-concentric optical cavity.

Optical cavities in the near-concentric regime have near-degenerate transverse modes; the tight focusing transverse modes in this regime enable strong coupling with atoms. These features provide an interesting platform to explore multi-mode interaction between atoms and light. Here, we use a spatial light modulator (SLM) to shape the phase of an incoming light beam to match several Laguerre-Gaussian (LG) modes of a near-concentric optical cavity. We demonstrate coupling efficiency close to the theoretical prediction for single LG modes and well-defined combinations of them, limited mainly by imperfections in the cavity alignment.

Spectral broadening of 112 mJ, 1.3 ps pulses at 5 kHz in a LG10 multipass cell with compressibility to 37 fs

The first-order helical Laguerre–Gaussian mode (also called donut mode) is used to improve the energy throughput of nonlinear spectral broadening in gas-filled multipass cells. The method proposed in this Letter enables, for the first time to the best of our knowledge, the nonlinear spectral broadening of pulses with energies beyond 100 mJ and is suitable for an average power of more than 500 W while conserving an excellent spatio-spectral homogeneity of ∼ 98 % and a Gaussian-like focus profile. Additionally compressibility from 1.3 ps to 37 fs is demonstrated.

Hybrid WDM and Optical-CDMA over Multi-Mode Fiber Transmission System based on Optical Vortex

The optical vortex has recently attracted scholars to implement it in optical tweezers, microscopy, optical communications, quantum information processing, optical trapping, and laser machining. Optical vortex beam applied classically that can be transferred to the transverse amplitude of a heralded single-photon, and optical vortex possesses a helical wavefront and carries orbital angular momentum. In this study, Optical vortex is applied in optical-CDMA (optical code-division multiple-access) in conjunction with WDM (wavelength division multiplexing). This mechanism aims to increase the capacity and security in optical communication significantly. The implementation of Laguerre-Gaussian (LG) modes with optical vortex based on one dimension zero cross-correlation (ZCC) code shows that mode coupling reduces effectively. Consequently, a positive increase in channel performance and response. Accordingly, the LG modes based on the 1D-ZCC code are investigated and propagated over multi-mode fiber (MMF) based on an optical vortex, which also substantially reduces channel effects. Consequently, all these attributes combined will result in a hybrid WDM-Optical-CDMA with an optical vortex system over MMF.

Digital sorting of laser beams by radial number: degenerate and non-degenerate states

We have created and tested a computer sorting method of Laguerre-Gauss (LG) radial modes with permanent topological charge arising from the perturbation of both single LG beams and their composition using a diaphragm with different radius R. The method based on computer analysis of the intensity moments. We considered two types of perturbed beams: single LG beam and complex LG beams with different radial number included in an integral array. The diaphragm acts on LG beam in such a way that when the radius of the diaphragm decreases, a set of secondary LG modes with different radial indices, which are characterized by different mode spectra, arise. Reconstructed spectrum using digital processing allows one to reconstruct the real LG modes and calculate the measure of uncertainty arising under the action of a disturbance, using the concept of information entropy. The calculations performed showed that the correlation degree of the measured disturbed beams is about 0.94. It was also found that the perturbation of a complex beam leads to the appearance of a degenerate spectrum in amplitudes, since one spectral line corresponds to a whole set of modes with different radial indices. To detect the spectrum, it was required to know M keys, which are the spectra of the amplitudes of nondegenerate perturbed beams in our experiment, degree of correlation was also 0.94.

Design of a Hybrid WDMA-Optical-CDMA over Multi-Mode Fiber Transmission System based on LG Modes for Short Haul-Local Area Network

Various optical communication technologies use Optical-Code Division Multiple Access (Optical-CDMA) as a channel access technique, which allows transmission of different users simultaneously over the optical communication channel. Therefore, Optical-CDMA permits free undue interference transmission of several users. Whereas Wavelength-division multiple access (WDMA) is a technique that can be implemented on how the optical channel can be divided into subchannels. This paper proposes a Hybrid WDMA-Optical-CDMA over multi-mode fiber (MMF) transmission system for short haul-local area network. The WDMA system is carried out by using four Laguerre-Gaussian (LG) modes that operate over four main wavelengths (1551 nm, 1550 nm, 1549 nm and 1548 nm). Additionally, the Optical-CDMA system is carried out by using one dimension Zero Cross-Correlation (ZCC) code to overcome multiple access interference (MAI) between the four ZCC codes. The performance of our system is evaluated based on eye diagrams, Q-Factor and bit-error rates (BER) measurements.