Looking into the future of interferometry using free-space beam propagation

In this paper, an integral solutions for the transverse and longitudinal components of the laser field for ultrashort pulsed-beam propagation in free space are derived, applying Fourier transform and the paraxial approximation in frequency domain. Furthermore, using the complex analytical signal (CAS) theory, the solutions for the components of a pulsed Gaussian-like beam in rectangular coordinate are derived and contrasted with those derived with slowly-varying-envelop-approximations (SVEA). Meanwhile, the results show that if the pulses as short as sub-cycle, SVEA will cause the spatial singularity for both transverse and longitudinal components of the laser field and CAS must be applied to eliminate the singularity.

We report on a numerical investigation of propagation property of high-power broadband laser beam in free space. We use Hankel transformation to solve Helmholtz equation numerically in the frequency domain. The modulation property of the broadband laser beam propagating in the Fresnel diffraction region is disclosed. It is found that the number of diffractive modulation rings equals to half the Fresnel number corresponding to the central wavelength of the broadband laser beam. The intensity modulation contrast of the broadband laser beam is smaller than that of monochromatic laser beam, suggesting that the broadband laser beam can suppress the harmful effect of near-field diffraction to some extent. Furthermore, it is demonstrated that the uniformity of near-field diffraction profile is determined by Fresnel number and bandwidth of the broadband beam.

We demonstrate that the presence of a twist phase in a random light beam leads to classical entanglement between phase space degrees of freedom of the beam. We find analytically the bi-orthogonal decomposition of the Wigner function of a twisted Gaussian Schell-model (TGSM) source and quantify its entanglement by evaluating the Schmidt number of the decomposition. We show that (i) classical entanglement of a TGSM source vanishes concurrently with the twist in the fully coherent limit and (ii) entanglement dramatically increases as the source coherence level decreases. We also show that the discovered type of classical entanglement of a Gaussian Wigner function does not degrade on beam propagation in free space.

Diffraction-free beam propagation in free space can keep the light intensity distribution constant, but the complex system and bulky devices bring inconvenience to the experiment. In this paper, we propose an effective approach to generate a terahertz diffraction-free beam from diffractive transmitted deformed axicon. The main research methods are phase folding technique and three-dimensional (3D)-printing technique. Based on the existing research, the refractive transmitted axicon is compressed into a lighter diffractive element to implement a 0.1THz beam with 344.75mm diffraction-free length. The effect of element thickness on the phase folding efficiency is investigated, and the results of the refractive axicon and diffractive deformed axicon are compared to demonstrate the advantages of diffractive optical elements in generating diffraction-free beams.

The complex geometrical optics (CGO) was applied for the spatiotemporal evolution of arbitrary number of 3D mutually incoherent (with different carrier frequencies) Gaussian wave packets (GWPs) interacting and propagating in a nonlinear medium of Kerr type. The CGO reduced description of the propagation of the beam, the pulse and the wave packet to complex ordinary differential equations (ODE) This leads to exceptionally fast numerical algorithms. We observed high efficiency of the CGO method to compute interactions of arbitrary number of 3D Gaussian wave packets propagating in a nonlinear (anomalous) dispersive medium of the Kerr type. The derived CGO equations were compared with equations obtained by the variational method. CGO described the Gaussian beam propagation in free space as well as the Gaussian pulse spreading in the linear anomalous dispersive medium more illustratively than both the Fourier transform method and the Fresnel diffraction integral method. The spatiotemporal CGO has been proven to be a method more practical than the spectral analysis, the variational method, the method of moments and the method of the generalized eikonal approximation. Complementary to the presented results, an on-line CGO solver, implemented in Javascript, is freely available at the authors' website: http://slawek.ps.pl/odelia.html.

Propagation of a fundamental laser mode and its numerical simulation by the angular spectrum technique

An optical system consisting of a laser source and two independent consecutive phase-only spatial light modulators (SLMs) is shown to accurately simulate a generated random beam (first SLM) after interaction with a stationary random medium (second SLM). To illustrate the range of possibilities, a recently introduced class of random optical frames is examined on propagation in free space and several weak turbulent channels with Kolmogorov and non-Kolmogorov statistics.

Having full control of light propagation in free space represents the ultimate goal for an imaging system. Spatial Light Modulators (SLMs), featuring the ability to actively control the spatial distribution of light components, are usually limited either to performing small and continuous adjustments to imaging aberrations or to rapidly shifting discrete segments of the wavefront with severe diffraction artifacts. Here a photothermally modulated optical structure is introduced as a highly responsive SLM capable of producing arbitrarily shaped wavefront patterns with smooth as well as step‐like features. The phase‐shift inducing temperature profile within the plasmonic metamaterial at the core of the SLM structure replicates closely the pattern of illuminating light intensity avoiding the common speed and spatial gradient limitations. As a result, the SLM concept is insensitive to polarization, free of diffraction artifacts, and offers sub‐millisecond response time and high transmittance >80%. The dynamic generation of a set of common optical functions is demonstrated, including low‐order Zernike polynomials patterns, phase grating, or vortex, which build an essential phase modulation toolbox across different imaging applications.

It is shown that a highly spatially incoherent light distribution may be generated from a highly coherent one on propagation in free space. This result essentially demonstrates that there exists an inverse of a classic result of optical coherence theory, namely, the van Cittert-Zernike theorem. The analysis also indicates that the technique of phase conjugation may be used to reverse changes in the coherence properties of light, at least those which are generated on propagation in free space.

In this paper, we present an enhanced model to predict the effect of thermal blooming and atmospheric turbulence, on high energy laser beams free space propagation. We introduce an implementation technique for the proposed mathematical models describing the effect of thermal blooming and atmospheric turbulence including wind blowing, and how it effect high power laser beam power, far field pattern, phase change effect and beam quality . An investigated model of adaptive optics was introduced to study how to improve the wave front and phase distortion caused by thermal blooming and atmospheric turbulence, the adaptive optics model with Actuator influence spacing 3 cm the that shows observed improvement in the Strehl ratio and in wave front and phase of the beam. These models was implemented using cooperative agents relying on GLAD software package. Without taking in consideration the effect of thermal blooming It was deduced that the beam at the source takes the Gaussian shape with uniform intensity distribution, we found that the beam converge on the required distance 4 km using converging optics, comparing to the laser beam under the effect of thermal blooming the far field pattern shows characteristic secondary blip and “sugar scoop effect which is characteristic of thermal blooming. It was found that the thermal blooming causes the beam to steer many centimeters and to diverge beyond about 1.8 km than come to a focus at 4 km where the beam assumed to be focused on the required target. We assume that this target is moving at v = (4,-4) m/sec at distance 4 km and the wind is moving at v = (-10,-10) m/sec, it was found that the effect will be strongest when wind and target movement are at the same velocity. GLAD software is used to calculate the attenuation effects of the atmosphere as well as the phase perturbations due to temperature change in the air and effects caused as the beam crosses through the air due to wind and beam steering.

Background: The problem of radiation propagation of vortex laser beams of a metal waveguide laser is considered. The results of the propagation of such beams have a wide range of potential applications, from imaging and spectroscopy to communication, sensing, biomedicine, and solving problems related to the interaction of electromagnetic waves with matter: diagnostics of thin films, surfaces of materials, various biological objects, as well as astronomy and space research. The aim of the work is to obtain analytical expressions for the description of non-paraxial mode diffraction of the waveguide metal resonator of a terahertz laser during their interaction with a spiral phase plate and to study the physical features of the obtained vortex beams during their propagation in free space by means of numerical modeling. Materials and methods: The Rayleigh-Sommerfeld vector theory was used to study the propagation of vortex laser beams in the Fresnel zone, which were excited by the modes of a metal waveguide quasi-optical resonator. Results: Analytical expressions were obtained to describe the non-paraxial mode diffraction of the metal waveguide resonator of a terahertz laser. Also, with the help of numerical modeling, the physical features of emerging vortex beams during their propagation in free space were investigated. Conclusion: In free space, the spiral phase plate for the excitation of the TE11 mode from the profile with the intensity maximum in the center (n = 0) forms an asymmetric ring with two maxima (n = 1, 2). For the TE01 excitation mode, the initial ring (n = 0) structure of the field strength is transformed into a structure with maximum radiation intensity in the center (n = 1), and then again into a ring (n = 2). The phase front of the beam for the Ey component linearly polarized along the y axis of the TE11 mode changes from spherical to helical with one singularity point on the axis. In the phase profile of the transverse components of the TE01 azimuthally polarized mode, a section with two and three off-axis points of phase singularities appears.

The objective of this study is to propose a heuristic model of energy propagation due to an anomaly; electromagnetic (EM) field penetration into a continuously covered conducting enclosure (Faraday shield) from an external radio frequency source, violating the accepted model in the EM field theory. In this study, at an arbitrarily selected frequency, range of 26.965–1,800 MHz, of an external frequency source, an EM field inside the conducting enclosure was observed, contrary to expectations, which was followed by a systematic examination. Although no induced voltage could be expected inside the enclosure according to the classical theory, the experiment revealed a clear induced voltage inside, an attenuated induced voltage of −18.0 to −1.0 dB (for the range of frequencies 26.965–1,800 MHz) was observed. Hence, these results apparently contradict the established notion that an EM field cannot penetrate a Faraday shield. Rationalizing these observations and the results of the investigation leads to an alternative model to the existing models of energy propagation in free space. In this model, novel quantities named “I-Spin-energy” and “I-Spin-energy field” are defined to replace the concept of electric and magnetic fields in the classical EM theory. The proposed I-Spin-energy model is capable of explaining the unexpected presence of the EM field inside the Faraday shield as well as the induction of an alternating current in a conductor placed inside a Faraday shield along with other existing observations in physics such as those in famous Young’s double-slit experiment on interference of light, which provided the basis for the wave theory.

Parametric characterization of vortex cosine-hyperbolic-Gaussian beams

It was recently shown that the spectrum of partially coherent light can change on propagation.1 So far most of the work has applied to propagation in free space and has been limited to far-zone observation points. In this paper we consider the propagation of partially coherent light through homogeneous and inhomogeneous media. Our formulation is based on the analysis of Agrawal et al.,2 which applies to graded-index fibers whose index of refraction changes quadratically as a function of the radial distance from the core center. With this formulation we derive expressions by using the paraxial approximation for the spectrum of the field for arbitrary propagation distances. This allows us to examine the evolution of spectral changes as a function of the propagation distance and the state of coherence of the source. The results for propagation in free space and in homogeneous media are derived by using the appropriate limits. The effects of chromatic dispersion are also investigated by allowing the refractive index to be frequency-dependent.

**Please read the paper on the following link:** https://ieeexplore.ieee.org/document/9212567 **Abstract:** To pave the way for system-on-chip MEMS confinement up to 50 GHz, the mechanical properties of a CMOS back-end-of-line (BEOL) are studied by analytic and finite element approaches. In particular, the two main directions of vertical and horizontal wave propagation are investigated. With respect to the symmetry of the BEOL, the movement through the nonperiodic horizontal layers is described by the Rayleigh-Lamb equation. It is shown that our finite element method (FEM) approach, preventing Brillouin zone folding, can be employed in simulations of these structures, since the results are in excellent accordance to the corresponding analytical solutions. The vertical propagation through the periodic stack on the other hand is subject to phononic crystal effects resulting in Bragg-like band gaps (BGs) for either a certain or every polarization. Factoring in both types of propagation, it is demonstrated by our FEM simulations how these BGs can be tailored to specific values through variations in the BEOL layers to improve the quality factor of monolithically integrated MEMS devices.