Free-space Propagation Research Articles

Changes in the statistical properties of electromagnetic double multi-Gaussian Schell-model beams on propagation in free space.

A class of electromagnetic random sources with a multi-Gaussian functional form in the spectral density and in the correlations part of the cross-spectral density matrix is introduced based on the genuine cross-spectral density-matrix theory. The analytic propagation formulas of the cross-spectral density matrix of such beams propagating in free space are derived by use of Collins' diffraction integral. With the help of analytic formulas, the evolution of statistical characteristics, i.e.,the spectraldensity, the spectral degree of polarization, and the spectral degree of coherence for such beams in free space are analyzed numerically. Employing the multi-Gaussian functional form in the cross-spectral density matrix introduces one more freedom in the modeling of Gaussian Schell-model sources.

Direct Position Determination Using Compressive Sensing Measurements Without Reconstruction

This paper proposes a direct position determination (DPD) method for stationary emitters with compressed signal measurements. Employing Hadamard matrix properties, the method estimates the source location directly in the compressing measurement domain, without the step of signal reconstruction and time-differences-of-arrival (TDOA) parameter extraction. In case of free space propagation, an augmented DPD method is proposed to further utilize the position related received signal strength (RSS) information. In addition, the Cramér-Rao lower bounds (CRLBs) for emitter position of both DPD methods are derived for performance evaluation.

Theoretical Analysis of the Time Transient of the THz Self-Mixing Rectification Voltage in a Semiconductor Barrier

THz detection in a silicon structure can be an effective instrument not only for image detection, and material and gas sensing, but also for communications. Next-generation 6G communications assume the possibility of achieving a large-band transmission, using free space propagation with THz carriers. This possibility relies on the availability of an effective, low-cost detector technology. THz detection by self-mixing can provide an effective amplitude demodulation of the incoming carrier, with antennas directly fabricated on the chip. In this case, the speed of the detectors represents a crucial point in the definition of the bandwidth whereby several GHz are indeed required by the communication systems. The self-mixing process is intrinsically very fast, since it depends on the non-linear interaction of the radiation with the majority carriers inside the semiconductor structure. In this paper, we evaluate analytically the time dependence of the onset of the rectified voltage. A potential propagation along the detector channel follows the self-mixing rectification, accompanied by the charging of the parasitic capacitances of the structure. A numerical simulator can easily evaluate the delay due to this propagation along the structure, but the transient of the true origin of the signal, i.e., the establishment of the self-mixing voltage, at the current time, can be only inferred by analytical approach. In this work, we use the model developed for the THz rectification in the depletion region of an MOS capacitance to develop a transient model of the formation of the characteristic self-mixing charge dipole, and of the generation of the rectified potential. Subsequently, we show by TCAD simulations the propagation of the effect on the semiconductor structure, which surrounds the rectifying barrier, and evaluate the overall time response of a detector.

Multiscale Phase-Contrast Tomography at BM18

Synchrotron phase-contrast micro-tomography is considered the gold standard in non-destructive volumetric imaging of millimeter and centimeter-sized objects. Micro-tomography beamlines are operating at many synchrotron radiation facilities, including the Extremely Brilliant Source (EBS) at the European Synchrotron Radiation Facility (ESRF). Applications favor objects which cannot be sufficiently resolved by state-of-the-art industrial micro-CT scanners. Synchrotron tomography features much superior time resolution, e.g., for in situ micro-CT, as well as superior photon flux, thus making this method suitable for Region of Interest scanning (i.e., multiresolution tomography). This report presents first results from the EBS' latest industrial beamline BM18, which was built for hierarchical propagation phase-contrast tomography. BM18 makes use of the exceptionally high coherence of the new ESRF-EBS lattice. Thanks to the wide polychromatic high-energy beam, one can scan and zoom into larger parts, e.g., from additive manufacturing or battery packs. In particular, BM18 allows for recording multiple scans at different resolutions ranging from 42 μm down to 0.6 μm, without the need to remove the object or manually change detectors. Free space propagation of up to 36 m yields excellent phase-contrast which in turn enhances the resolving power of the system. BM18 is generating an unprecedented amount of very large datasets. Consequently, novel strategies for data processing, storage and visualization are under development for this particular instrument.

Switchable optical ring lattice in free space.

Optical lattices with spatially regular structures have recently attracted considerable attention across physics and optics communities. In particular, due to the increasing emergence of new structured light fields, diverse lattices with rich topology are being generated via multi-beam interference. Here, we report a specific ring lattice with radial lobe structures generated via superposition of two ring Airy vortex beams (RAVBs). We show that the lattice morphology evolves upon propagation in free space, switching from a bright-ring lattice to dark-ring lattice and even to fascinating multilayer texture. This underlying physical mechanism is related to the variation of the unique intermodal phase between the RAVBs as well as topological energy flow with symmetry breaking. Our finds provide an approach for engineering customized ring lattices to inspire a wide variety of new applications.

Coherence singularity and evolution of partially coherent Bessel-Gaussian vortex beams.

For a partially coherent Bessel-Gaussian (PCBG) vortex beam, information regarding the topological charge (TC) is hidden in the phase of the cross-spectral density (CSD) function. We theoretically and experimentally confirmed that during free-space propagation, the number of coherence singularities is equal to the magnitude of the TC. In contrast to the Laguerre-Gaussian vortex beam, this quantitative relationship only holds for the case with an off-axis reference point for the PCBG vortex beam. The phase winding direction is determined by the sign of the TC. We developed a scheme for CSD phase measurement of PCBG vortex beams and verified the aforementioned quantitative relationship at different propagation distances and coherence widths. The findings of this study may be useful for optical communications.

Rotated chirped volume Bragg gratings for compact spectral analysis.

We introduce a new, to the best of our knowledge, optical component-a rotated chirped volume Bragg grating (r-CBG)-that spatially resolves the spectrum of a normally incident light beam in a compact footprint and without the need for subsequent free-space propagation or collimation. Unlike conventional chirped volume Bragg gratings in which both the length and width of the device must be increased to increase the bandwidth, by rotating the Bragg structure we sever the link between the length and width of a r-CBG, leading to a significantly reduced device footprint for the same bandwidth. We fabricate and characterize such a device in multiple spectral windows, we study its spectral resolution, and confirm that a pair of cascaded r-CBGs can resolve and then recombine the spectrum. Such a device can lead to ultracompact spectrometers and pulse modulators.

Spiral fractional vortex beams.

A new type of spatially structured light field carrying orbital angular momentum (OAM) mode with any non-integer topological order, referred to as the spiral fractional vortex beam, is demonstrated using the spiral transformation. Such beams have a spiral intensity distribution and a phase discontinuity in the radial direction, which is completely different from an opening ring of the intensity pattern and an azimuthal phase jump, common features that all previously reported non-integer OAM modes (referred to as the conventional fractional vortex beams) shared. The intriguing properties of a spiral fractional vortex beam are studied both in simulations and experiments in this work. The results show that the spiral intensity distribution will evolve into a focusing annular pattern during its propagation in free space. Furthermore, we propose a novel scheme by superimposing a spiral phase piecewise function on spiral transformation to convert the radial phase jump to the azimuthal phase jump, revealing the connection between the spiral fractional vortex beam and its conventional counterpart, of which OAM modes both share the same non-integer order. Thus this work is expected to inspire opening more paths for leading fractional vortex beams to potential applications in optical information processing and particle manipulation.

Partially coherent sources whose coherent modes are spatiotemporal optical vortex beams

We analyze three non-stationary partially coherent sources whose coherent modes are spatiotemporal optical vortex (STOV) beams. Using spatiotemporal (ST) Bessel–Gauss and Laguerre–Gauss beams (STOV-carrying solutions to the space-time paraxial wave equation) as eigenfunctions in the coherent-modes representation of the mutual coherence function, we derive the ST versions of J 0-Bessel-correlated, I n -Bessel-correlated, and twisted Gaussian Schell-model beams. We model, in simulation, these ST random beams via their coherent-modes expansions, compare and contrast the simulated results to theory, and analyze/discuss their free-space propagation characteristics. The work presented in this paper will be useful for simulating or physically generating these ST beams for use in applications or future studies.

Modified Huygens-Fresnel method for the propagation of partially coherent beams through turbulence.

Partially coherent beams (PCBs) have been extensively studied as a method to mitigate the deleterious effects of atmospheric turbulence for applications such as free-space optical communication. However, it can be difficult to study and assess the performance of PCBs in turbulence due to the complicated physics of the atmosphere and the wide variety of PCBs possible. Here, we introduce a modified approach to study the propagation of second-order field moments of PCBs analytically in turbulence, reformulating the problem in terms of free-space propagation of the beam. We illustrate the method by studying a Gaussian Schell-model beam in turbulence.

Millimeter-Wave Channel Measurements and Path Loss Characterization in a Typical Indoor Office Environment

In this paper, a path loss characterization at millimeter-wave (mmWave) frequencies is performed in a typical indoor office environment. Path loss results were derived from propagation channel measurements collected in the 25–40 GHz frequency band, in both line-of-sight (LOS) and obstructed-LOS (OLOS) propagation conditions. The channel measurements were performed using a frequency-domain channel sounder, which integrates an amplified radio over fiber (RoF) link to avoid the high losses at mmWave. The path loss was analyzed in the 26 GHz, 28 GHz, 33 GHz and 38 GHz frequency bands through the close-in free space reference distance (CI) and the floating-intercept (FI) models. These models take into account the distance dependence of the path loss for a single frequency. Nevertheless, to jointly study the distance and frequency dependence of the path loss, multi-frequency models were considered. The parameters of the ABG (A-alpha, B-beta and G-gamma) and the close-in free space reference distance with frequency path loss exponent (CIF) models were derived from the channel measurements in the whole 25–40 GHz band under the minimum mean square error (MMSE) approach. The results show that, in general, there is some relationship between the model parameters and the frequency. Path loss exponent (PLE) values smaller than the theoretical free space propagation were obtained, showing that there are a waveguide effect and a constructive interference of multipath components (MPCs). Since the measurements were obtained in the same environment and with the same configuration and measurement setup, it is possible to establish realistic comparisons between the model parameters and the propagation behavior at the different frequencies considered. The results provided here allow us to have a better knowledge of the propagation at mmWave frequencies and may be of interest to other researchers in the simulation and performance evaluation of future wireless communication systems in indoor hotspot environments.

Convolution, Correlation and Generalized Shift Operations Based on the Fresnel Transform.

The Fresnel transform (FrT) is commonly used to describe the free-space propagation of optical waves. In this work, we present new definitions for the convolution, correlation and generalized shift operations based on the FrT. The generalized shift operation is defined by using simultaneous space and phase shifts. The generalized shift operation is useful for centred optical systems in the Fresnel domain (FrD) when the data distributions at the input plane of the optical system are shifted. The new convolution and correlation operations defined in terms of the FrT, the wavelength and the propagation distance, can be considered as a generalization of the usual convolution and correlation operations. The sampling theorem for distributions, whose resulting FrT has finite support, is formulated by using the new convolution operation introduced in this work and a new definition of the Dirac comb function. These new definitions and results could be applied to describe, design and implement optical processing systems related to the FrT. Finally, we present a centred optical systems used in holography and optical security systems that can be described or modelled by the new definitions of the operations proposed in this paper.

Free-space creation of a perfect vortex beam with fractional topological charge.

Perfect vortex beams can only propagate stably with integer topological charges. Thus, creating perfect fractional vortex beams capable of stable propagation in free space, as perfect integer vortex beams, is crucial. This study proposed perfect vortex beams carrying fractional topological charge of l + 0.5, which are special solutions of the wave equation, and can maintain stable propagation with physical laws same as integer topological charge. Perfect fractional vortex beams were created in free space, which can break the cognition of traditional fractional perfect vortex beams and promote the development of scientific fields such as optical communication, quantum sensing, and optical imaging.

Laguerre-Gaussian Expansion of Step-Index Multimode Fiber Beams in Free-Space

We show that the complex conjugate of the overlap integrals between the fiber end-facet field and the Laguerre-Gaussian modes provides the expansion coefficients for the step-index multimode fiber beams. We also show that the fractional power in different azimuthal mode orders remains unchanged from fiber to free-space propagation.

Close link between Fabry–Pérot resonance and natural-resonance frequencies

Mathematical and numerical analyses have been performed to examine the close link between Fabry–Pérot resonance and natural-resonance frequencies. For the mathematical analysis, the conditions resulting in minimum magnitudes of reflection coefficients in frequency-domain are derived for air-backed and metal-backed low-loss non-dispersive (or weakly dispersive) dielectric samples with relative complex permittivity and thickness L for free-space wave propagation at normal incidence. The close relation between Fabry–Pérot resonance and natural-resonance frequencies is demonstrated for three different sample scenarios as (i) no-dispersion and lossless case ( and L = 50 mm), (ii) no-dispersion and low-loss case ( and L = 50 mm), and (iii) weak-dispersion and low-loss case ( and L = 50 mm where σ is the conductivity of the sample and ω is the angular frequency). It is noted that operating frequency should be increased to observe late-time natural-resonance frequencies for a sample with smaller length or vice versa.

On z-coherence of Schell-model sources carrying a prescribed astigmatic phase.

A simple expression for the correlations of beams radiated by Schell-model sources carrying a prescribed astigmatic phase (cross phase) in 3D space is derived. The z-coherence of such sources upon free-space propagation is investigated in detail. It is demonstrated that the z-coherence does not decrease to zero with an increasing separation of two axial points. Our results show that the initial cross phase, coherence, and correlation state of such sources affect the distribution of the z-coherence. Furthermore, the cross phase plays a role in maintaining z-coherence, which will be useful in applications where high z-coherence is required.

Free space dynamics of Laguerre-Gaussian-vortex beam

In this paper, we analytically demonstrate the propagation of a useful structured light laser beam;namely, the vortex Laguerre-Gaussian beam, the latter is an eigenmode of free space propagation,which is invariant under propagation in lossless systems. Through some numerical simulations, weshow the main spatial features of such interesting beams.

Terawatt-Class Few-Cycle Short-Wave Infrared Vortex Laser

As a driving source for many nonlinear vortex phenomena, such as the generation of isolated attosecond optical vortices, terahertz vortices, etc., terawatt-class few-cycle short-wave infrared vortex lasers are now attracting widespread attention. However, because the vortex characteristics of optical vortices are difficult to maintain in the amplification and compression stages, the generation of high-intensity few-cycle vortex lasers is still in the exploratory stage. In this article, we report 20-Hz, 18.6-mJ, 60-fs, and 1.45-μm infrared vortex lasers with 1, 2, and 3 topological charges successfully generated in an optical parametric chirped pulse amplification system. A clean intensity node at the beam center is observed and highly stable propagation in free space is demonstrated. Moreover, this high-energy vortex pulse is spectrally broadened in multiple thin plates and temporally compressed to 10.59 fs (2.2 optical cycles) with chirped mirrors, corresponding to a peak power of 1.08 TW, while highly preserving the vortex information. We believe that the generated high-energy few-cycle vortex laser has important applications from vortex optics to strong-field physics.

Rain-Based Attenuation and Dispersion Characteristics of Terahertz Wave in Tropical Climate: Experimentally Verified Reliability Study

In the frontier of next generation communication system, the terahertz spectrum can be treated un-parallel as far as the implementation of wireless link with high data-rate is concerned. Atmospheric condition can affect the electromagnetic/radio signal transmission severely. Since, the presence of seasonal hydrometeors in atmosphere may lead to drastic degradation in the free-space propagation of terahertz signal, therefore thorough and comprehensive investigation is essentially required to optimize the future channel-model for terahertz carrier frequency. The atmospheric attenuation causes power loss and in turn receiver signal amplitude gets attenuated. Rain attenuation has pronounced impact on terahertz signal propagation and attenuation of transmitted wave. In tropical weather scenario, the drop-dimension of seasonal rainfall exceeds the maximum dimension of temperate rain. Through an indigenously developed and experimentally verified Non-Linear Terahertz Rain Attenuation Model simulator, the authors have thoroughly investigated the rain-attenuation characteristics of terahertz signal in tropical climate condition for different hydrometeor properties including rain-rates and drop-size distribution. The effect of tropical thunderstorm has been uniquely incorporated by the authors in the present study along with atmospheric humidity and temperature based fluctuations. The reliability issues that are related with THz communication in tropical rain-fall have also been comprehensively analysed. Besides, a best-fit analysis has also been covered under different drop-size distribution statistics. It has been found that, in Indian Scenario (as a part of tropical climate), the peak attenuation level of THz spectrum under tropical rain-fall can be found in the range of (7THz-9THz). With increase of rain-rate from 2mm/hr to 200mm/hr, the peak attenuation level rises from ~100dB/km to ~1000dB/km. The basic model has been validated through experimental data where close proximity(with ± 10% variation from the mean data) has been observed. The present study on terahertz signal attenuation profile in tropical rainy weather will help the communication engineers to open the new door for the ultra-high speed world of 6G terahertz communication.

Topological charge of superposition of optical vortices described by a geometric sequence

Here, we investigate coaxial superpositions of Gaussian optical vortices that can be described by a geometric sequence. For all superpositions analyzed, a topological charge (TC) is derived. In the initial plane, the TC can be either integer or half-integer, acquiring an integer value upon free-space propagation of the light field. Generally, the geometric sequence of optical vortices (GSOV) has three integer parameters and one real parameter. Values of these four parameters define the TC of the GSOV. Upon free-space propagation, the intensity pattern of the GSOV is not conserved, but can have intensity petals whose number is equal to one of the four beam parameters. If the GSOV has a unit real parameter, all constituent angular harmonics in the superposition have the same weight. In this case, the TC of the superposition is equal to the average index of the constituent angular harmonics. For instance, if the TC of the first and of the last angular harmonics, respectively, equals k and n, then the total TC of the superposition in the initial plane will be (n + k) /2, becoming equal to n upon free-space propagation.