Modal decomposition without a priori scale information

Contribution to the Improvement of the Correlation Filter Method for Modal Analysis with a Spatial Light Modulator

Modal decomposition of light is essential to study its propagation properties in waveguides and photonic devices. Modal analysis can be carried out by implementing a computer-generated hologram acting as a match filter in a spatial light modulator. In this work, a series of aspects to be taken into account in order to get the most out of this method are presented, aiming to provide useful operational procedures. First of all, a method for filter size adjustment based on the standard fiber LP-mode symmetry is presented. The influence of the mode normalization in the complex amplitude encoding-inherent noise is then investigated. Finally, a robust method to measure the phase difference between modes is proposed. These procedures are tested by wavefront reconstruction in a conventional few-mode fiber.

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.

Modal analysis of structured light with spatial light modulators: a practical tutorial

A quantitative analysis of optical fields is essential, particularly when the light is structured in some desired manner, or when there is perhaps an undesired structure that must be corrected for. A ubiquitous procedure in the optical community is that of optical mode projections-a modal analysis of light-for the unveiling of amplitude and phase information of a light field. When correctly performed, all the salient features of the field can be deduced with high fidelity, including its orbital angular momentum, vectorial properties, wavefront, and Poynting vector. Here, we present a practical tutorial on how to perform an efficient and effective optical modal decomposition, with emphasis on holographic approaches using spatial light modulators, highlighting the care required at each step of the process.

Maximum coupling efficiency to an optical resonator based on the Laguerre-Gauss decomposition of a beam

We present a new numerical method to calculate the optimum lens transformation to implement on a monochromatic laser beam path, in order to maximize its coupling to the fundamental Gaussian mode of a resonator or to a single-mode optical fiber whose mode can be described as Gaussian to a good approximation. This method relies on a useful mathematical relation on Laguerre-Gauss modes of different waists and reduces in the end to numerically maximizing a polynomial that is a function of the state of the beam in a finite interval, thus being numerically very efficient. We show with a simple example that this method is particularly efficient against other common methods used in the laboratory when it comes to laser beams composed of a coherent superposition of higher-order Laguerre-Gauss modes, as it is the case for instance for beams traversing optical elements suffering from spherical aberration.

Babinet-bilayered geometric phase optical elements

Geometric phase optical elements based on structured anisotropy are widely used for phase shaping via their orientational degree of freedom. To date, amplitude shaping via space-variant retardance is much less investigated, a practical reason being that the spin-orbit interaction of light couples retardance with the dynamic part of the optical phase. Inspired by the complementary diffractive elements associated with Babinet's principle, a bilayered subwavelength grating design is proposed in order to cancel out the spatial modulation of the dynamic phase usually associated with space-variant birefringent phase retardation. This concept is illustrated in the framework of single-mode Laguerre-Gauss beam shaping.

Fast modal decomposition for optical fibers using digital holography

Eigenmode decomposition of the light field at the output end of optical fibers can provide fundamental insights into the nature of electromagnetic-wave propagation through the fibers. Here we present a fast and complete modal decomposition technique for step-index optical fibers. The proposed technique employs digital holography to measure the light field at the output end of the multimode optical fiber, and utilizes the modal orthonormal property of the basis modes to calculate the modal coefficients of each mode. Optical experiments were carried out to demonstrate the proposed decomposition technique, showing that this approach is fast, accurate and cost-effective.

Tailoring optical orbital angular momentum spectrum with spiral complex field modulation

We report the generation of prescribed optical orbital angular momentum (OAM) spectrum with spiral complex field modulation. Both symmetric and asymmetric OAM spectrums are generated with a vector beam generator and measured with a hybrid conformal mapper. Three methods for OAM spectrum generation ranging from the pure spiral phase modulation, the spiral amplitude and phase modulation, to the spiral phase and polarization modulation are demonstrated. The OAM spectrum generation with spiral complex field modulation may find applications in optical trapping and high-speed data communication.

Revealing the radial modes in vortex beams

Light beams that carry orbital angular momentum are often approximated by modulating an initial beam, usually Gaussian, with an azimuthal phase variation to create a vortex beam. Such vortex beams are well defined azimuthally, but the radial profile is neglected in this generation approach. Here, we show that a consequence of this is that vortex beams carry very little energy in the desired zeroth radial order, as little as only a few percent of the incident power. We demonstrate this experimentally and illustrate how to overcome the problem by complex amplitude modulation of the incident field.

Encoding information using Laguerre Gaussian modes over free space turbulence media

We experimentally demonstrate an efficient information transmission technique using Laguerre Gaussian (LG) modes. This technique is based on multiplexing and demultiplexing multiple LG modes with different azimuthal and radial components. At the reception, the initially sent modes encoding the information are extracted with high fidelity using a complete decomposition allowing to identify a particular mode from a set of modes within a unique iteration. Importantly, we investigate the effects of the atmospheric turbulence on the proposed communication system. We believe that the proposed technique is promising for high-bit-rate spatial division multiplexing in optical fiber and free space communication systems.

Adaptive mode control of a few-mode fiber by real-time mode decomposition

A novel approach to adaptively control the beam profile in a few-mode fiber is experimentally demonstrated. We stress the fiber through an electric-controlled polarization controller, whose driven voltage depends on the current and target modal content difference obtained with the real-time mode decomposition. We have achieved selective excitations of LP01 and LP11 modes, as well as significant improvement of the beam quality factor, which may play crucial roles for high-power fiber lasers, fiber based telecommunication systems and other fundamental researches and applications.

Optical beam and its operation in low dimensional space

This paper proposes the concept of low dimensional optical beam and operator. In low dimensional space, beam (or operator) is decomposed into a limited number of orthogonalized low dimensional beams (or operators) through the singular value decomposition. It is possible to generate an unconventional beam by these low dimensional beams. Low dimensional operator allows independent operation of orthogonal dimensions which may produce greater freedoms. Storage space and computation resource are saved dramatically by using this method. Experimental realization of this scheme is briefly discussed at the end.

Measurement of the orbital angular momentum density of Bessel beams by projection into a Laguerre-Gaussian basis

We present the measurement of the orbital angular momentum (OAM) density of Bessel beams and superpositions thereof by projection into a Laguerre-Gaussian basis. This projection is performed by an all-optical inner product measurement performed by correlation filters, from which the optical field can be retrieved in amplitude and phase. The derived OAM densities are compared to those obtained from previously stated azimuthal decomposition yielding consistent results.

Doughnut laser beam as an incoherent superposition of two petal beams

Laguerre-Gaussian beams with a nonzero azimuthal index are known to carry orbital angular momentum (OAM), and are routinely created external to laser cavities. The few reports of obtaining such beams from laser cavities suffer from inconclusive evidence of the real electromagnetic field. In this Letter we revisit this question and 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 point out the requirements for future analysis of such fields from laser resonators.

Holographic spatial coherence analysis of a laser

We show that the second-order coherent-mode representation of a stationary quasi-monochromatic scalar light beam can be experimentally characterized by dual-mode holographic interference using an arbitrary basis. Analysis of the laser beam emitted from a stable spherical mirror cavity, using a mismatched Hermite-Gaussian basis, recovered the profiles and powers of a set of cavity modes with the expected spot size, including a hybrid of frequency degenerate modes. Observed near- and far-field irradiance transverse profiles and associated M2 parameter measures confirmed the results.

Reconstruction of laser beam wavefronts based on mode analysis

We present the reconstruction of a laser beam wavefront from its mode spectrum and investigate in detail the impact of distinct aberrations on the mode composition. The measurement principle is presented on a Gaussian beam that is intentionally distorted by displaying defined aberrations on a spatial light modulator. The comparison of reconstructed and programmed wavefront aberrations yields excellent agreement, proving the high measurement fidelity.