Calculation of fractional orbital angular momentum of superpositions of optical vortices by intensity moments

Estimation of dislocated phases and tunable orbital angular momentum using two cylindrical lenses

A first-order optical system consisting of two cylindrical lenses separated by a distance is considered. It is found to be non-conserving of orbital angular momentum of the incoming paraxial light field. The first-order optical system is effectively demonstrated to estimate phases with dislocations using a Gerchberg-Saxton-type phase retrieval algorithm by making use of measured intensities. Tunable orbital angular momentum in the outgoing light field is experimentally demonstrated using the considered first-order optical system by varying the distance of separation between the two cylindrical lenses.

Design of a dynamic multi-topological charge graphene orbital angular momentum metalens

Traditional OAM generation devices are bulky and can generally only create OAM with one specific topological charge. Although metasurface-based devices have overcome the volume limitations, no tunable metasurface-based OAM generators have been demonstrated to date. Here, a dynamically tunable multi-topological charge OAM generator based on an ultrathin integrable graphene metalens is demonstrated by simulation using the detour phase technique and spatial multiplexing. Different topological charges can be designed on different focal planes. Stretching the OAM graphene metalens allows the focal plane and the topological values to be changed dynamically. This design method paves an innovative route toward miniaturization and integrating OAM beam-type photonic devices for practical applications.

Wavelength-tunable spiral-phase-contrast imaging

Wavelength-tunable spiral-phase-contrast (SPC) imaging was experimentally accomplished in the visible wavelengths spanning a broad bandwidth of ∼200 nm based on a single off-axis spiral phase mirror (OSPM). By the rotation of an OSPM, which was designed with an integer orbital angular momentum (OAM) of l = 1 at a wavelength of 561 nm and incidence angle of 45°, high-quality SPC imaging was obtained at different wavelengths. For the comparison with wavelength-tunable SPC imaging using an OSPM, SPC imaging using a spiral phase plate (manufactured to generate an OAM of l = 1 at 561 nm) was performed at three wavelengths (473, 561, and 660 nm), resulting in clear differences. Theoretically, based on field tracing simulations, high-quality wavelength-tunable SPC imaging could be demonstrated in a very broad bandwidth of ∼400 nm, which is beyond the bandwidth of ∼200 nm obtained experimentally. This technique contribute to developing high-performance wavelength-tunable SPC imaging by simply integrating an OSPM into the current optical imaging technologies.

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.

Optical vortex beams with a symmetric and almost symmetric OAM spectrum

We show both theoretically and numerically that if an optical vortex beam has a symmetric or almost symmetric angular harmonics spectrum [orbital angular momentum (OAM) spectrum], then the order of the central harmonic in the OAM spectrum equals the normalized-to-power OAM of the beam. This means that an optical vortex beam with a symmetric OAM spectrum has the same topological charge and the normalized-to-power OAM has an optical vortex with only one central angular harmonic. For light fields with a symmetric OAM spectrum, we give a general expression in the form of a series. We also study two examples of form-invariant (structurally stable) vortex beams with their topological charges being infinite, while the normalized-to-power OAM is approximately equal to the topological charge of the central angular harmonic, contributing the most to the OAM of the entire beam.

Real-time OAM cross-correlator based on a single-pixel detector HOBBIT system

The creation and detection of spatial modes of light with transient orbital angular momentum (OAM) properties is of critical importance in a number of applications in sensing and light matter interactions. Most methods are limited in their frequency response as a result of their modulation techniques. In this paper, a new method is introduced for the coherent detection of transient properties of OAM using a single pixel detector system for the creation of an OAM spectrogram. This technique is based on the ideas utilized in acousto-optic based optical correlators with log-polar optical elements for the creation and detection of higher order bessel beams integrated in time (HOBBIT) at MHz data rates. Results are provided for beams with time varying OAM, coherent combinations, and transient scattering by phase objects.

Orbital angular momentum and topological charge of a multi-vortex Gaussian beam

We report on a theoretical and numerical study of a Gaussian beam modulated by several optical vortices (OV) that carry same-sign unity topological charge (TC) and are unevenly arranged on a circle. The TC of such a multi-vortex beam equals the sum of the TCs of all OVs. If the OVs are located evenly along an arbitrary-radius circle, a simple relationship for the normalized orbital angular momentum (OAM) is derived for such a beam. It is shown that in a multi-vortex beam, OAM normalized to power cannot exceed the number of constituent vortices and decreases with increasing distance from the optical axis to the vortex centers. We show that for the OVs to appear at the infinity of such a combined beam, an infinite-energy Gaussian beam is needed. On the contrary, the total TC is independent of said distance, remaining equal to the number of constituent vortices. We show that if TC is evaluated not along the whole circle encompassing the singularity centers, but along any part of this circle, such a quantity is also invariant and conserves on propagation. Besides, a multi-spiral phase plate is studied for the first time to our knowledge, and we obtained the TC and OAM of multi-vortices generated by this plate. When propagated through a random phase screen (diffuser) the TC is unchanged, while the OAM changes by less than 10% if the random phase delay on the diffuser does not exceed half wavelength. Such multi-vortices can be used for data transmission in the turbulent atmosphere.

Estimation of dislocated phases in wavefronts through intensity measurements using a Gerchberg-Saxton type algorithm

Estimation of the phase of a singular paraxial light field from experimentally measured intensities using a Gerchberg-Saxton type algorithm is demonstrated. A combination of cylindrical lenses which does not conserve the orbital angular momentum of the light field is used in obtaining the measured intensities. Consistent extraction of the phases in regard of the orbital angular momentum is demonstrated both at the input and output transverse planes, using the measured intensities.

Topological charge of asymmetric optical vortices

We obtain theoretical relationships to define topological charge (TC) of vortex laser beams devoid of radial symmetry, namely asymmetric Laguerre-Gaussian (LG), asymmetric Bessel-Gaussian (BG), and asymmetric Kummer beams, as well as Hermite-Gaussian (HG) vortex beams. Although they are obtained as superposition of respective conventional LG, BG, and HG beams, these beams have the same TC equal to that of a single mode, n. At the same time, the normalized orbital angular momentum (OAM) that the beams carry is different, differently responding to the variation of the beam's asymmetry degree. However, whatever the asymmetry degree, TC of the beams remains unchanged and equals n. Although separate HG beam does not have OAM and TC, superposition of only two HG modes with adjacent numbers (n, n + 1) and a π/2-phase shift produces a modal beam whose TC is -(2n + 1). Theoretical findings are validated via numerical simulation.

Topological charge of a linear combination of optical vortices: topological competition

We theoretically show that optical vortices conserve the integer topological charge (TC) when passing through an arbitrary aperture or shifted from the optical axis of an arbitrary axisymmetric carrier beam. If the beam contains a finite number of off-axis optical vortices with same-sign different TC, the resulting TC of the beam is shown to equal the sum of all constituent TCs. If the beam is composed of an on-axis superposition of Laguerre-Gauss modes (n, 0), the resulting TC equals that of the mode with the highest TC. If the highest positive and negative TCs of the constituent modes are equal in magnitude, the "winning" TC is the one with the larger absolute value of the weight coefficient. If the constituent modes have the same weight coefficients, the resulting TC equals zero. If the beam is composed of two on-axis different-amplitude Gaussian vortices with different TC, the resulting TC equals that of the constituent vortex with the larger absolute value of the weight coefficient amplitude, irrespective of the correlation between the individual TCs. In the case of equal weight coefficients of both optical vortices, TC of the entire beam equals the greatest TC by absolute value. We have given this effect the name "topological competition of optical vortices".

Second-harmonic generation of asymmetric Bessel-Gaussian beams carrying orbital angular momentum

Nonlinear processes of laser beams carrying orbital angular momentum (OAM) offer a means to generate new wavelengths and to manipulate OAM charge numbers. We demonstrate the second-harmonic generation (SHG) of asymmetric Bessel-Gaussian (BG) beams carrying OAM of both integer and fractional charge numbers. Experimental results show a good one-to-one correspondence of the charge numbers and compliance with the OAM conservation law. The SHG conversion process and efficiency with different combined charge numbers are also discussed.