Modal decomposition of Laguerre Gaussian beams with different radial orders using optical correlation technique

Measurement of the integer and fractional topological charge of optical vortex beams by using crossed blades

Measurement of the topological charge (TC) of vortex beams, including integer and fractional orbital angular momentum, is of great importance in diverse fields. Here we first investigate the diffraction patterns of a vortex beam from crossed blades with different opening angles and positionings on the beam by a simulation and experiment. Then the positions and opening angles of the crossed blades that are sensitive to the variation of TC are selected and characterized. We show that for a specific position of the crossed blades on the vortex beam, the integer TC can be measured directly by counting the bright spots in the diffraction pattern. Moreover, we show experimentally that for other positions of the crossed blades, by calculating the first-order moment of the intensity of the diffraction pattern, the integer TC between -10 and 10 can be obtained. In addition, this method is used to measure the fractional TC and, as an example, the TC measurement is demonstrated for a range between 1 and 2 with 0.1 steps. The result of the simulation and experiment shows good agreement.

Modal decomposition of an incoherent combined laser beam based on the combination of residual networks and a stochastic parallel gradient descent algorithm

With the increase of the superimposed eigenmodes number, the traditional numerical modal decomposition (MD) technique will inevitably suffer from ambiguity and local minima problems and thus is typically unsuitable for conducting modal decomposition of an incoherent combined laser beam. In this paper, we propose a novel, to the best of our knowledge, MD algorithm, named ResNet-SPGD, which combines the advantages of residual networks (ResNet) and stochastic parallel gradient descent (SPGD) algorithm. Via setting the modal mode coefficients obtained from the CNN model as the initial value of the SPGD algorithm, such algorithm shows an attractive solution to mitigate the problem of modal ambiguity. The proposed algorithm is preliminarily applied to the modal decomposition of an incoherent combined laser beam, and the feasibility is demonstrated via numerical simulations. Complete MD is performed with high accuracy, and the only cost is the sacrifice of some real-time capacity.

Measuring the squared amplitudes of the Laguerre-Gaussian beams via a single intensity frame

We propose the use of an intensity technique to decompose superpositions consisting of two, three, or four basis Laguerre-Gaussian (LG) modes, and measure the orbital angular momentum (OAM) of such superpositions. The mode generation and decomposition are both accomplished only on a 2f optical imaging system. We demonstrate numerically and experimentally that the squared amplitudes of superpositions can be determined by recording a single frame of the intensity distribution. This is accomplished by measuring the intensity along certain circles and solving a linear set of equations relating the sampled intensities to squared amplitudes. The accuracy of better than 98% for composite beams consisting of two, and about 90% for composite beams consisting of more than two basis modes are achieved. Finally, we report the value of the measured OAM of the superpositions with excellent accuracy regarding theoretical values, for small and large integer and non-integer OAM.

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.

Measuring the complex spectrum of orbital angular momentum and radial index with a single-pixel detector

Typical methods to decode a complex orbital-angular-momentum (OAM) spectrum suffer from issues such as a narrow OAM range, unstable interferometer, and long measuring time. In this Letter, we use a single-beam interferometer to measure the complex OAM spectrum with a single-pixel detector. The complex OAM spectrum ranging from -10 to 10 can be measured in 11 ms with the fidelity approach of 97.0%, experimentally. Our approach allows one to characterize an unknown coherent field with any complex basis, e.g., the Laguerre-Gaussian (LG) basis is used for radial index spectrum measurement. Furthermore, single-pixel complex amplitude imaging based on the LG spectrum acquisition is presented, and the advantages in resolution and flexibility are demonstrated.

Airy transform of Laguerre-Gaussian beams

Airy transform of Laguerre-Gaussian (LG) beams is investigated. As typical examples, the analytic expressions for the Airy transform of LG₀₁, LG₀₂, LG₁₁, and LG₁₂ modes are derived, which are special optical beams including the Airy and Airyprime functions. Based on these analytical expressions, the Airy transform of LG₀₁, LG₀₂, LG₁₁, and LG₁₂ modes are numerically and experimentally investigated, respectively. The effects of the control parameters α and β on the normalized intensity distribution of a Laguerre-Gaussian beam passing through Airy transform optical systems are investigated, respectively. It is found that the signs of the control parameters only affect the location of the beam spot, while the sizes of the control parameters will affect the characteristics of the beam spot. When the absolute values of the control parameters α and β decrease, the number of the side lobes in the beam spot, the beam spot size, and the Airy feature decrease, while the Laguerre-Gaussian characteristic is strengthened. By altering the control parameters α and β, the performance of these special optical beams is diversified. The experimental results are consistent with the theoretical simulations. The Airy transform of other Laguerre-Gaussian beams can be investigated in the same way. The properties of the Airy transform of Laguerre-Gaussian beams are well demonstrated. This research provides another approach to obtain special optical beams and expands the application of Laguerre-Gaussian beams.