Decrease in spatial coherence of light propagating in free space

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.

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.

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.

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.

Parametric characterization of vortex cosine-hyperbolic-Gaussian beams

12 - Radio Frequency Propagation

A TEM cell is a rectangular or square coaxial transmission line tapered at each end to form a closed cell. The one end of the cell can be fed with a signal generator and the other end can be terminated by a resistor load equal to the characteristic impedance of the line (Crawford, IEEE Trans Electromagn Compat 16(4):189–195, 1974) [1]. Between the inner conductor (the septum) and the top and bottom plates, a field propagates from the source to the termination as a planar field in free space. Transverse electromagnetic (TEM) cells are used to generate uniform EM waves in a shielded space. The cell has a tapering section at each end, so that the rectangular coaxial transmission line is able to adapt to standard coaxial connectors (Tippet and Chang, Radiation characteristics of dipole sources located inside a rectangular, coaxial transmission line, 1976) [2]. TEM cells are used for Radiated emission and Radiated immunity testing of small products, for biomedical experiments, and for calibration of RF probes/sensors. The wave propagation inside the cell is similar to far-field plane propagation in free space and the wave has an impedance of free space, i.e., 377 Ω [1]. The cutoff frequency of the cell depends upon its dimensions. This is the limitation of the cell because this constrains the size of a product and we can test within the cell. The TEM cell designed is considered to be of an open type.

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.

In the free space optical communication system with circle polarization shift keying (CPolSK) modulation, the changes of polarization state of light beam have significant influence on the system performance. Keeping the state of polarization (SOP) unchanged on propagation can reduce the bit error rate. Based on the unified theory of coherence and polarization, we derive the sufficient condition for Gaussian Schell-model (GSM) beam to keep the SOP unchanged. We found that when the three spectral correlation widths (delta(xx), delta(yy) and delta(xy)) equal to each other and sigma(x) = sigma(y), the GSM beam maintains the SOP on propagation. This conclusion can be helpful for the design of the transmitter in the CPolSK system.

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.

The principle for constructing physical models (simulators) of extended routes of optical (laser) radiation propagation in free space is substantiated. A version of the construction of the optical system of a simulator, designed to calibrate measures of effective scattering area with minimum errors under laboratory conditions, is proposed.

This chapter contains sections titled: Isotropic and Anisotropic Antennas Antenna Gain Power Flux Density at One Point in Space Effective Radiated Power PERP

The instantaneous cross-spectral density of non-stationary wavefields

Airy beams are solutions to the paraxial Helmholtz equation known for exhibiting shape invariance along their self-accelerated propagation in free space. These two properties are associated with the fact that they are not square integrable, that is, they carry infinite energy. To circumvent this drawback, families of so-called finite-energy Airy-type beams have been proposed in the literature and, in some cases, also implemented in the laboratory. Here an analysis of the propagation of this type of structured light beam is presented from a flux trajectory perspective with the purpose of better understanding the mechanisms that make infinite and finite energy beams exhibit different behaviors. As is shown, while the foremost part of the beam can be clearly and unambiguously associated with the well-known accelerating term, the rear part of the beam corresponds to a nearly homogeneous distribution of flow trajectories, particularly for long propagation distances. This is shown to be related to an effective transfer of trajectories between adjacent lobes (gradually, from the fore part of the beam to its rear part), which leads to smearing out the transverse flow along the rear part of the beam. This is in sharp contrast to the situation found in ideal Airy beams, where trajectories belonging to a given lobe of the intensity distribution remain the same all along the propagation. The analysis is supplemented with an also trajectory-based description of Young's experiment performed with finite-energy Airy beams to provide a dynamical understanding of the autofocusing phenomenon observed with circular Airy beams.

A fast surface reconstruction method for fluorescence molecular tomography based on cross-beam edge back projection