Gaussian Beam Propagation Research Articles

Optical properties of molybdenum disulfide based photonic crystal

In this paper, the transmission properties of a one-dimensional photonic crystal containing molybdenum disulfide ( $$MoS_2$$ ) monolayers are studied theoretically using the transfer matrix method. The considered photonic crystal structure contains $$MoS_2$$ monolayers, which are embedded between dielectric layers. It is found that the presence of $$MoS_2$$ causes to creation of a new photonic band gap which is almost omnidirectional and also polarization insensitive. Besides, the spatial distribution of the tangential component of the electric field for a TE-polarized plane wave has been shown for some wavelengths. It is found that the behaviour of the waves from the $$MoS_2$$ induced band gap is different from that of Bragg gaps. Finally, the Gaussian beam propagation inside and outside of the photonic crystal have been simulated using the finite element method for critical wavelengths and different incident angles which verify the behavior of field profiles.

Degenerate optical resonator for the enhancement of large laser beams.

There are several applications for enhancement cavities where a beam of large size (several millimeters) resonates, in particular in atomic physics. However, reaching large beam waists in a compact geometry (less than a meter long) typically brings the resonator close to the degeneracy limit. Here we experimentally study a degenerate optical cavity, 44-cm long and consisting of two flat mirrors placed in the focal planes of a lens, in a regime of intermediate finesse (∼150). We study the impact of the longitudinal misalignement on the optical gain, for different input beam waists up to 5.6 mm, and find data consistent with the prediction of a model based on ABCD propagation of Gaussian beams. We reach an optical gain of 26 for a waist of 1.4 mm, which can have an impact on several applications, in particular atom interferometry. We numerically investigate the optical gain reduction for large beam waists using the angular spectrum method to consider the effects of optical aberrations, which play an important role in such a degenerate cavity. Our calculations quantitatively reproduce the experimental data and will provide a key tool for designing enhancement cavities close to the degeneracy limit. As an illustration, we discuss the application of this resonator geometry to the enhancement of laser beams with top-hat intensity profiles.

3-D Terahertz Imaging Based on Piecewise Constant Doppler Algorithm and Step- Frequency Continuous-Wave Signaling

A novel 3-D time-domain terahertz (THz) imaging system based on piecewise constant Doppler (PCD) algorithm and step-frequency continuous-wave (SFCW) signaling is proposed in this article. First, the SFCW THz imaging system configuration and the Gaussian beam propagation model are introduced. Then, the conventional time-domain correlation imaging algorithm is reviewed, and the closed-form expression of its point spread function (PSF) is derived to quantify the range and lateral resolutions. To reduce the computational complexity, a 2-D recursive imaging process based on the plane approximation of the range surface is proposed, by which the original PCD algorithm is extended for 3-D imaging with 2-D aperture synthesis. The 3-D PCD imaging principle, implementation, and complexity analysis are discussed afterward. Finally, simulation and experimental results are provided to validate the theoretical analysis of the 3-D time-domain THz imaging and demonstrate the high quality of the proposed imaging algorithm at a low computational cost.

Propagation of Gaussian beam based on two-dimensional fractional Schrödinger equation

In this paper, the dynamic evolution of Gaussian beam governed by the two-dimensional fractional Schrödinger equation with variable coefficient is studied. The influences of the longitudinal modulation, the Lévy index and the chirp parameters on the evolution of the Gaussian beam are discussed in detail. The results show that in the absence of the beam chirp, the unchirped Gaussian beam is axisymmetric and exhibits a ring-shaped structure, but due to the longitudinal modulation, the size of the ring will change. In the presence of the beam chirp, the axisymmetry is broken and optical beam in propagation exhibits a crescent structure. In the longitudinal periodic modulation, the chirped Gaussian beam oscillates periodically along a certain direction. The influence of the Lévy index on the evolution of the Gaussian beam is also studied, and the result shows that the increasing of the Lévy index will enhance the diffraction of the optical beam in propagation.

Gaussian beam propagation through a biaxial anisotropic circular cylinder

Based on the electromagnetic field expansions over appropriate cylindrical vector wave functions, the scattering features of a Gaussian beam by a biaxial anisotropic circular cylinder are analyzed. The unknown expansion coefficients are determined from a system of linear equations derived by using continuous boundary conditions. For a TE and TM polarized Gaussian beam with different propagation directions, the normalized near-surface and internal field intensity distributions are evaluated. The propagation properties are compared and discussed briefly.

Shape-preserving beam transmission through non-Hermitian disordered lattices

We investigate the propagation of Gaussian beams through optical waveguide lattices characterized by correlated non-Hermitian disorder. In the framework of coupled mode theory, we demonstrate how the imaginary part of the refractive index needs to be adjusted to achieve perfect beam transmission, despite the presence of disorder. Remarkably, the effects of both diagonal and off-diagonal disorder in the waveguides and their couplings can be efficiently eliminated by our non-Hermitian design. Waveguide arrays thus provide an ideal platform for the experimental realization of non-Hermitian phenomena in the context of discrete photonics.

Propagation of the first order annular Bessel Gaussian beams in a uniaxial crystal along the optical axis governed by the Pockels effect.

We investigate the first order annular Bessel Gaussian beams propagating in a strontium barium niobate (SBN) crystal governed by the Pockels effect. The left-hand circularly polarized incident waves propagating along the optical axis in the crystal give rise to the right-hand circularly polarized vortex fields with a topological charge of 2. If an external dc field is applied along the optical axis of the SBN crystal, the anisotropy strength can be controlled rapidly, and the rotational invariance around the optical axis is still maintained. In this case, the normalized intensity in the focal region, the power exchange between left-hand and right-hand components, and the exchange between the spin and orbit contributions of the angular momentum flux can be manipulated. We also consider the case where the incident waves are linearly polarized along the x axis. The cylindrical symmetry of two Cartesian components is broken during propagation due to the anisotropy, and the intensity distribution as well as the polarization state of the beams can be regulated electrically.

Impact of atmospheric turbulence on coherent beam combining for laser weapon systems

The performance of a laser weapon system based on coherent beam combining (CBC) depends on its propagation properties in the atmosphere. In this study, an analytical model based on partial coherent beam combining (PCBC) for assumed coherence coefficients between beams in a CBC lattice was developed. The Kolmogorov model of atmospheric turbulence and the Hufnagel-Valley model of Cn2 dependence on atmospheric parameters were implemented. Novel simplified metrics were proposed to assess the CBC performance. Several beam profiles (super-Gaussian, truncated Gaussian, etc.) and geometries were analyzed in terms of maximal intensity in the far field. An approximate formula for PCBC efficiency dependent on the Fried radius was proposed. The results of CBC modeling were compared to those of the Gaussian beam propagation model in a turbulent atmosphere. The dependence of CBC performance on the Cn2 parameter, range, and elevation angle was analyzed. It could be concluded that the application of CBC for medium and long range propagation is impractical without an effective adaptive optics system.

Gravitational light deflection in Earth-based laser cavity experiments

As known from Einstein's theory of general relativity, the propagation of light in the presence of a massive object is affected by gravity. In this work, we discuss whether the effect of gravitational light bending can be observed in Earth-based experiments, using high-finesse optical cavities. In order to do this, we theoretically investigate the dynamics of electromagnetic waves in the spacetime of a homogeneous gravitational field and give an analytical expression for the resulting modifications to Gaussian beam propagation. This theoretical framework is used to calculate the intensity profile at the output of a Fabry-P\'erot cavity and to estimate the imprints of Earth's gravity on the cavity output signal. In particular, we found that gravity causes an asymmetry of the output intensity profile. Based on that, we discuss a measurement scheme, that could be realized in facilities like the GEO600 gravitational wave detector and the AEI 10 m detector prototype.

Propagation propertiesof a novel generalized flattened Hermite-cosh-Gaussian light beam

In this paper, we have introduced a general formula of a new laser beam with a nearly Flattened-top profile. The propagation properties of this beam, called Generalized Flattened Hermite-cosh-Gaussian (GFHChG) beam are studied in detail. Based on the Huygens–Fresnel integral, an analytical expression of the intensity distribution for GFHChG passing through a paraxial ABCD optical system is developed. Several particular cases such as the propagation of the flattened Gaussian beam, the cosh-Gaussian beam, the higher and squared cosh-Gaussian beam and the Hermite-cosh-Gaussian beam are deduced from our result. Numerical simulations are also given in free space and through a circular thin lens in a free space to study the comportment of this beam during propagation.

Precision analysis of turbulence phase screens and their influence on the simulation of Gaussian beam propagation in turbulent atmosphere.

The slip-step method is widely used in simulating optical wave propagation in turbulent atmosphere, which treats propagation and phase perturbations caused by turbulence separately and in discrete steps along the propagation axis. The phase perturbations are represented by a series of phase screens, and hence, the precision of the phase screen concerns the accuracy of the simulation. In this paper, we first discuss the precision and computational performance of phase screens generated by the subharmonic complemented discrete Fourier transformation (DFT) (DFT-SH) method, three kinds of randomized spectral sampling techniques (sparse spectrum (SS) technique, sparse spectrum technique with uniform wave vectors (SU), randomized DFT technique), and optimization-based (OB) method; then, the simulations are implemented with the phase screens generated by these methods. Some statistical quantities of the received optical field are calculated, such as beam wander variance, long-term beam radius, short-term beam radius, and on-axis scintillation index. The statistical results show that the undersampling of phase screen in the low-frequency region causes underestimation of the values of beam wander variance, long-term beam radius, and focused beam on-axis scintillation index because these quantities are sensitive to the large-scale inhomogeneities. However, the undersampling does not affect the predicted values of the short-term beam radius and collimated beam on-axis scintillation index because these quantities are insensitive to the large-scale inhomogeneities.

Propagation of Gaussian Schell-model beams through a jet engine exhaust.

Theoretical predictions of light beam interactions with jet engine exhaust are of importance for optimization of various optical systems, including LIDARs, imagers and communication links operating in the vicinity of aircrafts and marine vessels. Here we extend the analysis previously carried out for coherent laser beams propagating in jet engine exhaust, to the broad class of Gaussian Schell-Model (GSM) beams, being capable of treating any degree of coherence in addition to size and radius of curvature. The analytical formulas for the spectral density (SD) and the spectral degree of coherence (DOC) of the GSM beam are obtained and analyzed on passage through a typical jet engine exhaust region. It is shown that for sources with high coherence, the transverse profiles of the SD and the DOC of the GSM beams gradually transition from initially circular to elliptical shape upon propagation at very short ranges. However, such transition is suppressed for sources with lower coherence and disappears in the incoherent source limit, implying that the GSM source with low source coherence is an excellent tool for mitigation of the jet engine exhaust-induced anisotropy of turbulence. The physical interpretation and the illustration are included.

The Focusing Effect of Lens on the Propagation of Intense Femtosecond Annular Gaussian Beam in Atmosphere

The Focusing Effect of Lens on the Propagation of Intense Femtosecond Annular Gaussian Beam in Atmosphere

КОМПЕНСАЦИЯ АСТИГМАТИЗМА В БЛОКЕ ВРЕМЕННОГО РАСШИРЕНИЯ ИМПУЛЬСА КАНАЛА НАКАЧКИ МОЩНОЙ ЛАЗЕРНОЙ СИСТЕМЫ

A high peak and high average power femtosecond laser system based on media doped with Yb3+ ions is being developed at the Institute of Laser Physics of the SB RAS. For efficient laser amplification and to avoid optical damage is actually to compensate wave front distortion caused by grating astigmatism in pump channel. Based on theory of propagation of gaussian beam in space and through optical elements the calculation of optimal parameters of two lenses telescope and comparison with experimental data has been performed. The obtained results can be used for decrease of astigmatic effect on beam profile quality in design of laser systems with elements involving astigmatism.

A Method for Coupling Monte Carlo Simulations of Photon Transport to Focused Gaussian Beam Propagation

We present a method for modeling focused Gaussian beams in turbid media. Compared to previous methods based on ray tracing, our method is simple and fast. Rather than sampling photon launch positions from the surface of the media, we directly sample launch positions from inside the sample volume using the probability distribution for the position that a ballistic photon will first interact with the tissue. The examples presented illustrate the importance of accounting for Gaussian beam optics when simulating a focused beam. Not doing so will give an artificially large irradiance at the beam waist position. Thermal models used to predict laser damage to tissue will predict temperature rises that are too large for samples containing the beam focus.

Derivation and Experimental Verification of the Near-field 2D and 3D Optical Intensities From a Finite-size Light Emitting Diode (LED)

We derive the near-field light intensity distributions of an inorganic LED on its surface and in volumetric space. Our closed-form solution for 3D intensity distribution for a finite-size LED is consistent with Lambert's Cosine Law, which provides the 3D intensity distribution for an infinitesimal, flat light source. We also derive the formula for the 2D intensity distribution on a diode surface showing its similarity to a Gaussian function, which is typically used to approximate the surface light intensity profile for an LED and a laser diode. Our 2D intensity distribution function produces light propagation similar to the Gaussian beam propagation in space. However, unlike the Gaussian approximation, our formula invariably produces this behavior without assuming the refractive index inside the diode follows a quadratic function of the transverse spatial domains. Our 2D and 3D spatial intensity formulas in near-field for LEDs offer a unique way to calculate the peak intensity that occurs at the center of the flat LED source. We demonstrate, as expected, that the peak intensity increases with the size of the LED source as well as the brightness of each radiative electron-hole pair, which is a function of the drive current and quantum efficiency of the LED.

Dielectric metamaterials with quasicrystal structure

Three types of quasicrystal lattices based on the Penrose tiling are considered. We analyze the maximum filling fraction of these structures and find a design with the filling fraction corresponding to the case of periodic lattices. By using simulations of a Gaussian beam propagation through the quasicrystal structure we obtain a homogeneous field distribution that is a hallmark of near-zero regimes in metamaterials.

Investigation of paraxial and nonparaxial self-focusing of Gaussian beam in chalcogenide glass medium using NLSE

Variational method is used for the investigation of paraxial and nonparaxial self-focusing of Gaussian beam in bulk chalcogenide glass (Kerr media). Stationary self-focusing for paraxial Gaussian beam with distinct singularity and focusing-defocusing cycles for nonparaxial propagation of Gaussian beam is observed. Emphasis is laid on the study of variation in beam width and intensity of the beam with propagation distance.

2-D Propagation Modeling in Inhomogeneous Refractive Atmosphere Based on Gaussian Beams Part I: Propagation Modeling

Gaussian beams as solutions of the parabolic wave equation (PWE) in inhomogeneous 2-D media are studied. Closed-form expressions of the Gaussian beam propagation are derived, based on the assumption that the gradient of the refractive index is locally vertical, constant, and bounded within realistic values observed in the troposphere. The proposed algorithm uses the closed-form expressions of the Gaussian beams along with a multibeam expansion procedure, in order to expand any incident field and to deal with particularly important variations of the atmosphere refractive index. The method is also able to model the propagation in refractivity grids from weather forecast algorithms, such as the Weather Research and Forecasting (WRF) model. Results are accurate up to several hundreds of kilometers when compared to the PWE solved by a split-step Fourier approach in ducting condition.

Generalized Gaussian beams in terms of Jones vectors

Based on the operator formalism that arises from the underlying SU(2) group structure, a formula is derived that provides a description of the generalized Hermite–Laguerre–Gauss modes in terms of a Jones vector, traditionally used to describe polarization. This identity highlights the relation between these generalized Gaussian beams, the elliptical ray families, and the Majorana constellations used to represent structured-Gaussian beams. Moreover, it provides a computational advantage over the standard formula in terms of Wigner d functions.