Non-diffracting Modes Research Articles

Nonlinear frequency conversion of nondiffracting modes via nondegenerate four-wave mixing in atomic vapor

Nonlinear frequency conversion of nondiffracting modes via nondegenerate four-wave mixing in atomic vapor

An Intriguing Interpretation of 1D and 2D Non-Diffracting Modes in Cosine Profile

We provide a simple analysis based on ray optics and Dirac notation for 1D (one-dimensional) and 2D (two-dimensional) non-diffracting modes in the cosine profile, which are often called Cosine beams. We explore various kinds of structured modes formed by the superposition of two 1D Cosine beams. We then went on to understand the properties of the Bessel beams in terms of Cosine beams. For the first time, we report on the generation of three-dimensional tunable needle structures based on the interference of 1D Cosine beams. These size-tunable optical needles can have multiple advantages in material processing. Also, we report, for the first time, on the Talbot effect in Cosine beams. Straightforward mathematical calculations are used to derive analytical expressions for Cosine beams. The present method of demonstrating Cosine beams may be utilized to understand other structured modes. The Dirac notation-based interference explanation used here can provide new researchers with an easy way to understand the wave nature of light in a fundamental aspect of interferometric experiments as well as in advanced-level experiments such as beam engineering technology, imaging, particle manipulation, light sheet microscopy, and light–matter interaction. We also provide an in-depth analysis of similarities among Cosine, Bessel, and Hermite–Gaussian beams.

Experimental generation of nondiffracting Mathieu beams using a thin-disk laser configuration

Nondiffracting modes were experimentally generated in an end-pumped thin-disk laser with a new kind of axicon-based stable laser resonator. The eigenvalue and eigenvector of the resonator were investigated based on the geometrical optics view. Ytterbium ions doped in the YAG crystal as an active medium were then utilized in this configuration. The experimental generation of the Mathieu–Gauss and Ince–Gauss modes was performed and also discussed during the thin-disk deformation.

Generating and measuring nondiffracting vector Bessel beams

Nondiffracting vector Bessel beams are of considerable interest due to their nondiffracting nature and unique high-numerical-aperture focusing properties. Here we demonstrate their creation by a simple procedure requiring only a spatial light modulator and an azimuthally varying birefringent plate, known as a q-plate. We extend our control of both the geometric and dynamic phases to perform a polarization and modal decomposition on the vector field. We study both single-charged Bessel beams as well as superpositions and find good agreement with theory. Since we are able to encode nondiffracting modes with circular polarizations possessing different orbital angular momenta, we suggest these modes will be of interest in optical trapping, microscopy, and optical communication.

The generation of an array of nondiffracting beams by a single composite computer generated hologram

Nondiffracting beams have generated great interest recently owing to their potential applications and unique properties. In this paper, we propose and validate a simple and effective method to generate arrays of various nondiffracting modes using a composite computer-generated hologram, which comprises N × N holograms each generating an individual nondiffracting beam. Employing the composite hologram approach, we can modulate individual nondiffracting beam in an array by varying the location, dimension, and phase information coded on each hologram. We experimentally generated regular arrays of Bessel beams, customized-shaped arrays of Bessel beams, and arrays of self-imaged optical bottle beams. The interference among the beams in the arrays was found to be weak within the nondiffracting distance.

Controllable 3D spatial localization of light fields synthesized by non-diffracting modes

the 3d shaping of light fields based on the superposition of coherent non-diffracting modes is proposed and examined. The transverse amplitude profile of the field is composed of non-diffracting spots whose positions can be predetermined and their spatial shape and size controlled. Due to the self-imaging effect the formed transverse amplitude profile appears at the planes placed periodically along the propagation direction. The transverse and longitudinal localization of the light field is improved if the number of superposed non-diffracting modes is increased. The light then can be confined in the volume element whose transverse and longitudinal dimensions are comparable with the wavelength.

Controllable 3D spatial localization of light fields synthesized by non-diffracting modes

Controllable 3D spatial localization of light fields synthesized by non-diffracting modes

Fidelity of the periodical self-reconstruction of wavefield

The periodical self-reconstruction of the wave function is examined for monochromatic wavefields fulfilling the Helmholtz equation. The effect is possible for an arbitrary signal wavefield with the predetermined wave function due to the pseudosampling of its spatial spectrum in cylindrical coordinates. The simplest description of the effect, based on the decomposition of the wave function into the base of ideal non-diffracting modes carrying infinite energy, is replaced by the model dealing with the pseudo non-diffracting modes. It can be closely related to the experimental realization. The fidelity of the self-reconstruction is examined applying the criterion based on the correlation concept.

Self-reconstruction effect in free propagation of wavefield

We investigate conditions of the periodic self-reconstruction of the predetermined object or the transverse amplitude profile of the beam. The effect appears in free propagation of the monofrequency wavefield due to the decomposition of the complex amplitude into the conveniently chosen nondiffracting modes. The beam self-guiding and the self-imaging of the point source are presented as applications of the self-reconstruction effect.