Gaussian Beam In Free Space Research Articles

Integrated optical phased array with on-chip amplification enabling programmable beam shaping

We present an integrated optical phased array (OPA) which embeds in-line optical amplifiers and phase modulators to provide beam-forming capability with gain and beam steering in the 1465–1590 nm wavelength range. We demonstrate up to 21.5 dB net on-chip gain and up to 35.5 mW optical output power. The OPA circuit is based on an InP photonic integration platform and features the highest measured on-chip gain and output power level recorded in an active OPA (i.e., with amplification), to the best of our knowledge. Furthermore, the OPA enables the independent control of both amplitude and phase in its arms and through this we demonstrate programmable beam shaping for two cases. First, we carried out a Gaussian apodization of the power distribution profile in the OPA emitter waveguides, leading to 19.8 dB sidelobe suppression in the far-field beam, which is the highest value recorded for active OPAs, and then we demonstrated beam forming of 0th, 1st, and 2nd order 1D Hermite–Gaussian beams in free-space.

Modeling of Finite Beams in Periodic FDTD Methods

This article presents a finite-difference time-domain (FDTD) framework that accelerates the modeling of the interaction of infinite periodic structures with practical sources (such as Gaussian or Bessel beams) by exploiting periodic boundary conditions (PBCs). The technique involves the introduction of arbitrary beam-generating sources in periodic simulations via the array-scanning method (ASM). The proposed method is both efficient and practical, being naturally broadband and highly parallelizable. We present examples of Gaussian beams in free space and interacting with grating geometries, efficiently replicating the results of multi-period brute-force simulations.

Limits of Coupling Efficiency Into Hollow-Core Antiresonant Fibres

We theoretically explore the fundamental limits on the efficiency of coupling light into hollow-core antiresonant fibres. We study in particular the coupling of a free-space Gaussian beam to the guided modes of one of the most successful antiresonant fibre (ARF) geometries, the the nested antiresonant nodeless fibre (NANF). Through finite element simulations, we study the effect of the geometrical parameters of the fibre on the coupling efficiency, showing that coupling into the fundamental LP <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</sub> -like mode is typically maximized around 96-98 % when the incident beam waist is about 70 % of the core diameter. We find that due to the nature of antiresonance guidance, higher coupling efficiencies are achieved for fibres operating in the second antiresonant window (or generally even-numbered windows) than in those operating in the fundamental antiresonant window (or generally odd numbered windows), although the difference between even and odd decreases with the order of the window. We verify this theoretical finding experimentally with precise measurements of coupling efficiency into two NANFs operating in first and second windows, respectively. Our results which consistently show a steady 1.4 percentage point higher coupling efficiency for the second window fibre imply that such fibers may be the most suitable candidates for applications such as laser delivery which require up to a few hundred meters of fiber.

Paraxial Propagation Properties of Symmetric Dual Pearcey Gaussian Beams in Free Space

AbstractIn this article, a new kind of symmetric dual Pearcey Gaussian beam (SDPGB) is introduced and their properties of auto‐focusing, self‐similarity, inversion, and self‐healing are discussed. The self‐similarity, the auto‐focusing, and the inversion properties of the propagating SDPGBs are turned out by analytical derivation and experimental observation. Additonally, a second‐order chirp factor for SDPGBs is introduced to investigate their secondary auto‐focusing and abrupt auto‐focusing properties in further detail. Finally, the effects of the obstacle diameter and the obstacle placement plane on the self‐healing of the SDPGBs are discussed.

Paraxial Propagation Properties of Radially Polarized Odd‐Pearcey Gaussian Beams in Free Space

AbstractA new type of radially polarized odd‐Pearcey Gaussian beam (RPOPGB) whose paraxial propagation in free space is studied analytically and numerically, is introduced. Intriguingly, the energy of RPOPGBs is found to auto‐focus several times with the Gaussian beam waist radius increasing to some certain extents. Furthermore, RPOPGBs exhibit a special transversal intensity distribution that has an optical trap in the center. During the propagation, at first the RPOPGBs' two main lobes auto‐focus toward the center with side lobes, and then the two main lobes separate after the end of auto‐focusing. The Poynting vectors prove that the energy variation of the lobes maintains excellent central symmetry throughout the propagation. In addition, the fractional vortices are observed from the angular momentum and phase. These findings will be of potential use to particle capture.

Correction of Complex Permittivity Inversion in Free-Space Gaussian Beam Reflection Model

To determine the complex permittivity of material mounted on the metal surface, the free-space reflection method is a good candidate due to its advantages of being nondestructive and contactless. When using the method, the extraction of the complex reflection coefficient (CRC) of the metal-backed material is the key to realize accurate measurement. Traditionally, the free-space reflection method assumes that the interrogating wave is a single plane wave, and the plane-wave reflection model is used. However, a focused beam is usually used in practice for reducing the edge effect that leads to the difference between the actual test scene and the traditional test model. In this study, a focused-wave reflection model is constructed to invert the complex permittivity, where the focused wave is considered as a Gaussian beam. The CRC of the Gaussian beam is deduced by using the plane-wave spectrum technique and plane-wave scattering-matrix (PWSM) theory. Based on the difference between the CRCs of the focused-wave and plane-wave, inverted complex permittivity corresponding to two reflection models is compared. Numerical results are given to show how the errors introduced by the plane-wave assumption are related to the waist size of the incident beam and the thickness and relative complex permittivity of the material. Measurement of a Teflon slab is given to further demonstrate the capability of the proposed procedure.

High-efficiency gate-defined quantum dot to single mode fiber interface assisted by a photonic crystal cavity

Efficiently interfacing photonic with semiconductor qubits plays an important role in future quantum communication applications. In this paper, we model a photon to exciton interface based on an optically active gate-defined quantum dot (OAQD) embedded in a carefully designed photonic crystal cavity constraining its emission profile via the Purcell effect while maintaining a low enough quality factor to allow for electrical tuning of the emission wavelength. By matching the in-plane k-vector of a cavity mode and the reciprocal lattice constant of the photonic crystal, vertical emission is obtained. A back-reflection mirror located below the cavity and integrated as part of an already predefined process flow allows for not only the increasing of the light extraction efficiency but also the tailoring of the extracted beam profile to match that of a single mode fiber. We numerically show that a photon emitted by the OAQD can be coupled to the targeted free-space Gaussian beam with a probability above 50%, limited by electrode absorption. Further efficiency improvement up to 90% is possible by using indium tin oxide instead of gold as a gate material.

Gaussian beam solutions in a longitudinally varying medium with a transverse quadratic-index profile.

Research in laser-plasma interaction, high harmonic generation, and filamentation involves Gaussian beams propagating through inhomogeneous media, where the refractive index varies spatially in both the transverse and longitudinal directions. However, most analytical Gaussian beam solutions to the paraxial wave equation for inhomogeneous media are limited to media with the refractive index only varying quadratically in the transverse direction. In this paper, we present a new class of Gaussian beam solutions for a longitudinally varying medium with a transverse quadratic-index profile. We also highlight a few examples from this class of solutions, which include features such as a one-parameter generalization of the free-space Gaussian beam, beam "collimation," beam self-focusing, and the existence of multiple beam waists.

An Accurate Method for Designing, Characterizing, and Testing a Multi-Layer Radome for mm-Wave Applications

This paper presents an accurate procedure to design, characterize and test a radome for millimeter-wave applications. In this procedure, an accurate analytical model is presented to design a radome structure that takes into consideration the bandwidth, losses, reflections and depolarization factor as a function of frequency and incident angle. To guarantee a good operational electrical performance, the proposed procedure includes a material characterization and accurate test procedure based on the free-space Gaussian beam method and time gating filtering technique. Four radomes (two-monolithic and two A-sandwich) at 82 GHz and 94 GHz are designed, characterized and tested to validate the proposed technique. Results obtained with this procedure are compared with numerical simulations and experimental results. This method is shown to be accurate and versatile for radomes in mm-Wave applications.

Free-space coupling to symmetric high-Q terahertz whispering-gallery mode resonators.

We report on the coupling of a free-space Gaussian beam to symmetric high-quality (Q) whispering-gallery mode resonators (WGMRs) for terahertz (THz) radiation. We achieve very high excitation efficiencies up to 50% to THz WGMs with a Q-factor of 1.5×104 at 0.7THz. The high coupling efficiencies have been realized by leveraging a Gaussian beam with a nearly diffraction-limited focal spot, as well as readily available low-loss, high-index silicon spheres with diameters comparable to the wavelength. The results convincingly underline the viability of free-space coupling in the THz frequency range.

Propagation properties of autofocusing off-axis hollow vortex Gaussian beams in free space.

By solving the (2 + 1) dimensional Schrödinger equation in free space, we find that the autofocusing off-axis hollow vortex Gaussian beams (HVGBs) are analytically derived for the first time. The off-axis HVGBs can be adjusted by changing the off-axis coordinate (x0,y0) and topological charge n2. In particular, by increasing the off-axis coordinate (x0,y0), the self-focusing intensity can be increased. Besides, the self-focusing property can be more obvious. Furthermore, by increasing the hollow order n1, we can deepen the depth of focus, make the focus position further away, and increase the self-focusing intensity too. We also discuss other propagation properties that are used to enrich the autofocusing off-axis HVGBs, such as Poynting vector, angular momentum, gradient force, and maximum scattering force during propagation.

Investigation of electromagnetic mode transition and filtering of an asymptotically single-mode hollow THz Bragg fibre

The mechanism for electromagnetic (EM) mode transition and filtering in an asymptotically single-HE11-mode hollow THz Bragg fibre is investigated. We designed, fabricated, and measured Bragg fibres with an asymptotically single-mode pattern, achieving measured signal propagation loss of better than 3 dB m−1 at 0.265 THz and with an operating frequency range from 0.246 to 0.276 THz. Mode transition and filtering effects are both verified by 3D full-wave simulations using measured material properties, with geometrical parameters extracted from the fabricated Bragg fibre prototypes. By optimizing the coupling efficiency between the free-space Gaussian beam and the guided Bessel function mode, the optimum distance of mode transition from the Gaussian-beam excitation into the guided mode is calculated to be ~13.7 free-space wavelengths in our fibre, to ensure fast EM-field convergence to the desired asymptotically single-mode mode pattern in the Bragg fibre. After this mode transition region, the electric field amplitude ratio between the desired HE11 mode and the main competing HE12 mode is approximately 7 times, with the HE12 mode attenuation being more than 10 dB m−1 larger than the fundamental HE11 mode; the results indicate that our fibre is one of the best candidates for low-loss asymptotically single-mode terahertz signal interconnections.

Chirped Airy collinear Laguerre–Gaussian wave packets in free space

By solving the (3 + 1)-dimensional free-space Schrödinger equation in cylindrical coordinates analytically, we have studied the chirped Airy collinear Laguerre–Gaussian wave packets. The different three-dimensional spatiotemporal profiles can be obtained by selecting a different mode number or relative amplitude, and whether the spatiotemporal profiles rotate or not relies on the mode number during propagation; but the wave packets will accelerate during propagation. Furthermore, we also have done a numerical experiment of the collinear Laguerre–Gaussian beams in free space. In addition, the wave packets will also rotate when varying the relative phase, while they will not only accelerate or decelerate, but reverse when varying the quadratic chirp factor.

Performance Analysis of the ITER Plasma Position Reflectometry (PPR) Ex-vessel Transmission Lines

As the design of the ITER Plasma Position Reflectometry (PPR) diagnostic progresses, some segments of the transmission line have become fully specified and estimations of their performance can already be obtained. This work presents the calculations carried out for the longest section of the PPR, which is in final state of design and will be the main contributor to the total system performance. Considering the 88.9 mm circular corrugated waveguide (CCWG) that was previously chosen, signal degradation calculations have been performed. Different degradation sources have been studied: ohmic attenuation losses for CCWG; mode conversion losses for gaps, mitre bends, waveguide sag and different types of misalignments; reflection and absorption losses due to microwave windows and coupling losses to free space Gaussian beam. Contributions from all these sources have been integrated to give a global estimation of performance in the transmission lines segments under study.

Nonparaxial propagation of a partially coherent four-petal Gaussian beam in free space

Based on the generalized Rayleigh-Sommerfeld diffraction integral, the equations of nonparaxial propagation, far field propagation and paraxial propagation of a partially coherent four-petal Gaussian beam in free space are obtained. The results show that the far field propagation and paraxial propagation can be regarded as special cases of nonparaxial propagation. The normalized intensity and degree of coherence of a nonparaxial partially coherent four-petal Gaussian beam are illustrated and analyzed using numerical example.

Quasi-linearly polarized hybrid modes in tapered and metal-coated tips with circular apertures: understanding the functionality of aperture tips

In this study, we investigate analytically and experimentally the roles of quasi-linearly polarized (LP), hybrid, plasmonic and photonic modes in optical detection and excitation with aperture tips in scanning near-field optical microscopy. Aperture tips are tapered and metal-coated optical fibers where small circular apertures are made at the apex. In aperture tips, there exist plasmonic modes that are bound at the interface of the metal cladding to the inner dielectric fiber and photonic modes that are guided in the area of the increased index in the dielectric fiber core. The fundamental photonic mode, although excited by the free-space Gaussian beam, experiences cutoff and turns into an evanescent mode. The photonic mode also becomes lossier than the plasmonic mode toward the tip aperture, and its power decay due to absorption and reflection is expected to be at least 10−9. In contrast, the fundamental plasmonic mode has no cutoff and thus reaches all the way to the tip aperture. Due to the non-adiabaticity of both modes’ propagations through the taper below a core radius of 600 nm, there occurs coupling between the modes. The transmission efficiency of the plasmonic mode, including the coupling efficiency and the propagation loss, is expected to be about 10−6 that is at least 3 orders of magnitude larger than that of the photonic mode. Toward the tip aperture, the longitudinal field of the photonic mode becomes stronger than the transverse ones while the transverse fields always dominate for the plasmonic mode. Experimentally, we obtain polarization resolved images of the near-field at the tip aperture and compare with the x- and y-components of the fundamental quasi-LP plasmonic and photonic modes. The results show that not only the pattern but also the intensity ratios of the x- and y-components of the aperture near-field match with that of the fundamental plasmonic mode. Consequently, we conclude that only the plasmonic mode reaches the tip aperture and thus governs the near-field interaction outside the tip aperture. Our conclusion remains valid for all aperture tips regardless of the cladding metal type that mainly influences the total transmission efficiency of the aperture tip.

Properties of vortex beams formed by an array of fibre lasers and their propagation in a turbulent atmosphere

Using a numerical simulation, we investigate the possibility of synthesising vortex laser beams with a variable orbital angular momentum by a hexagonal array of fibre lasers under a phase control of individual subapertures of the array. We report the requirements to the parameters of the device generating a vortex beam (number and size of subapertures, as well as their mutual arrangement). The propagation dynamics of synthesised vortex beams is compared with that of conventional Laguerre – Gaussian beams in free space and in a turbulent atmosphere. The spectral properties of the synthesised beam, represented as a superposition of different azimuthal modes, are determined during its propagation in free space. The energy and statistical parameters of the synthesised and Laguerre – Gaussian vortex beams are shown to coincide with increasing propagation distance in a turbulent medium.

Surface-normal coupled four-wave mixing in a high contrast gratings resonator.

We demonstrate enhanced four-wave mixing using a silicon high contrast grating (HCG) resonator on a SOI (silicon-on-insulator) wafer directly coupled with free space Gaussian beam in surface-normal direction. The measured quality factor for HCG resonator is ~7330. Peak conversion efficiency of -19.5dB is achieved at low pumping power ~900µW. Surface-normal coupling allows for easily and robust alignment system. The very small footprint and high efficiency of our device provide an effective method for wavelength conversion in chip-scale integrated optics.

Engineering of slow Bloch modes for optical trapping

In the present paper, we propose an approach based on slow Bloch mode microcavity that enables the optical trapping of small nanoparticles over a broad surface. A specific design based on a double-period photonic crystal is presented. It enables an easy coupling using a wide free-space Gaussian beam and the cavity Q factor can be tuned at will. Moreover, the microcavity mode is mainly localized within the photonic crystal holes, meaning that each hole of the microcavity behaves as efficient nanotweezers. Experimental studies have shown that 200 nm and 100 nm particles can be trapped within the microcavity, in a spatial region that corresponds to the size of one hole (200 nm wide). The experimental trap stiffness has been extracted. It shows that this approach is among the most performant ones if we take into account the size of the cavity.

The Far Properties of Nonparaxial Cosine-Squared Gaussian Beams

Based on the Rayleigh-Sommerfeld diffraction integrals, the closed-form expression of nonparaxial cosine-squared Gaussian beams in free space is derived. The power in the bucket (PIB) of nonparaxial regime is introduced to characterize the beam quality of nonparaxial beams in the far field. It is found that the intensity and PIB of nonparaxial cosine-squared Gaussian beams depends onfparameter, decentered parameter, and the PIB is additionally depends on the bucket’s size taken. For a given bucket’s size, the smaller decentered parameter andfparameter result in the better power focusability in the far field and the better beam quality.