Fundamental Gaussian Beam Research Articles

Flattop axial Bessel beam propagation with analytical form of the phase retardation function

This work focuses on a novel, to the best of our knowledge, analytical form of the phase retardation function for achieving a uniform axial intensity of Bessel beams. Traditional methods of generating Bessel beams often result in significant oscillations in the intensity along the beam’s axial path, which limits their practical applications. However, the proposed phase retardation function in this study overcomes these limitations by ensuring consistent beam creation regardless of factors such as the beam waist size, wavelength, or axicon angle. By implementing the proposed spatial phase function, a fundamental Gaussian laser beam, thereby generating a Bessel beam with an elongated and constant axial intensity profile, supports our theoretical predictions. The functionality of this new phase retardation function was further scrutinized using different wavelengths and beam waist sizes to confirm that the axial intensity remained uniform profile. Additionally, when contrasting our phase function with those from earlier researches, it was observed that our findings are consistent with both theoretical models and experimental outcomes.

Utilizing an aspheric lens and compound ellipsoidal cavity for a laser uniform illumination system

To achieve uniform laser illumination of an active imaging system with a small aperture diameter and large field angle, we have developed what we believe to be a novel structure for achieving uniform beam shaping that integrates a laser source, an aspheric lens, and a composite ellipsoidal cavity to enable active laser illumination. Through an aspheric lens, the fundamental mode Gaussian beam is transformed into double Gaussian and flat-top radiation at the target plane. The double Gaussian radiation is further reflected by a complex ellipsoidal cavity, where it is evenly distributed into equal radiation flux. This flux combines with the flat-top radiation, resulting in a uniform distribution at the target plane. The parameters of the complex ellipsoidal cavity are determined using an equalization algorithm. After combining the transmission for flat-top shaping by the aspheric lens and secondary reflection shaping by the composite ellipsoidal cavity, we achieved an aperture measuring 29.7 mm with an aperture angle of 84.0°, at a distance of 2 m from the target plane, with a diameter of 3.6 m, resulting in uniformity reaching 92.7%. RMS and MT/R determine the effectiveness of the compound ellipsoidal cavity design, depending on the maximum reflection angle and transmission angle. MT/R is inversely proportional to the maximum reflection angle, while RMS is directly proportional to the transmission angle. By setting the maximum reflection angle to 32.0° and the transmission angle to 8.0°, we were able to achieve a minimum root-mean-square focusing radius of 108.6 µm along with a minimum effective MT/R ratio of 1.07. The overlap degree between transmission and reflection directly impacts the target plane’s uniformity, adjusted through a defined adjustment factor. Optimizing this factor to 0.9 maximizes the uniformity of the target plane.

Experimental Verification of the Gouy Phase for Higher-Order Hermite-Gaussian Beams

The Gouy phase is related to the axial phase shift experienced by any focused light beam with respect to a reference plane wave when passing through its focus. Generally, the Gouy phase ΦG for a higher-order Hermite-Gaussian (HG) beam is this for the fundamental Gaussian beam multiplied by a factor, which is the sum of the mode indices of the HG beam plus unity. Although this result is a paradigm in optics, we are not aware of its experimental verification. In this paper, we present experimental results obtained with a single-lens interferometer for higher-order HG modes generated using spatial light modulator. The retrieved Gouy phase ΦG is found in a very good quantitative agreement with the mentioned theoretical result.

Scintillation analysis of gaussian beams in anisotropic and uniaxial media

Scintillation of Gaussian beams both in anisotropic and uniaxial media is examined numerically utilizing the split step approach. Both the point-like and the power scintillation indices of Gaussian beams that propagate for a 5 Km in anisotropic and uniaxial media are investigated. The effect of turbulence strength on the scintillation level is also studied. In this regard, the scintillation level of the three components of Gaussian beam both the anisotropic and the uniaxial are analysed and compared with the scintillation of the fundamental Gaussian beam. The provided results show that the x-component of the Gaussian beam as propagate in both the anisotropic and the uniaxial media has the lowest scintillation. In addition, in uniaxial medium, the three components of the Gaussian beam have a power scintillation level less than the fundamental Gaussian.

Analysis of finite energy fresnel bessel beams scintillation level in turbulent communication links

Scintillation indices of Finite Energy Fresnel-Bessel Beams (FEFBBs) propagating for 6 Km in a turbulent atmosphere are analyzed. In this context, the effects of beam order and Gaussian beam waist on the reduction of scintillation level are evaluated. Both the point-like scintillation and the power scintillation indices are examined. The obtained results show that beam order does not have a significant impact on the scintillation levels. FEFBBs are able to reduce the power scintillation levels, then improve the system performance better than fundamental Gaussian beams. Thus, the provided results are significant for not only the performance improvement of the free-space optical (FSO) communication systems but also for the applications that require line of sight alignment namely directed infrared countermeasure (DIRCM).

Quasi-Bessel beam generation by a diffractive axicon with an exponential phase function

A simple phase function for a diffractive axicon to allow generation of a quasi-Bessel beam with a uniform axial intensity profile is reported. By adding the new exponential phase function for the diffractive axicon, we theoretically show that a quasi-Bessel beam with a uniform axial intensity profile can be generated without amplitude oscillation or energy loss. We apply this spatial phase function to a spatial light modulator, illuminated by a fundamental Gaussian laser beam, and produce a quasi-Bessel beam with a long, uniform axial intensity profile, which is in very good agreement with theoretical calculation. Dependence of the phase parameters on the axial intensity profile and their optimization are discussed.

Bottle-shaped second harmonic generation with adjustable locations

Nonlinear photonic crystals (NPCs) have been widely used for studying nonlinear wave behaviors and in many applications requiring generation of light at new frequencies. In particular, the nonlinear photonic structures can be smartly designed to facilitate multiple functions in a single crystal. Here we show how to design a two-dimensional NPC to realize bottle-shaped second harmonic generation from a fundamental Gaussian beam with adjustable converging properties. The influences of structural parameters on the bottle beam generation are also investigated. These results are important for playing full potentials of NPCs and provide a convenient way to generate special beam at new frequencies with controllable properties.

Description and reconstruction of typical structured light beams with vector spherical wave functions.

It is well known that the generalized Lorenz-Mie theory (GLMT) is a rigorous analytical method for dealing with the interaction between light beams and spherical particles, which involves the description and reconstruction of the light beams with vector spherical wave functions (VSWFs). In this paper, a detailed study on the description and reconstruction of the typical structured light beams with VSWFs is reported. We first systematically derive the so-called beam shape coefficients (BSCs) of typical structured light beams, including the fundamental Gaussian beam, Hermite-Gaussian beam, Laguerre-Gaussian beam, Bessel beam, and Airy beam, with the aid of the angular spectrum decomposition method. Then based on the derived BSCs, we reconstruct these structured light beams using VSWFs and compare the results of the reconstructed beams with those of the original beams. Our results will be useful in the study of the interaction of typical structured light beams with spherical particles in the framework of GLMT.

Spin-orbit interaction in quasi-monochromatic singular beams

It is shown that the magnitude of the spin-orbit coupling is the energy efficiency of energy transfer between orthogonally polarized beam components. The energy efficiency changes as the Gaussian beam propagates through the anisotropic crystal. For a fundamental Gaussian beam, the energy efficiency cannot exceed 50%, and for elegant Hermite-Gaussian and Laguerre-Gaussian beams of higher orders, the energy efficiency can reach a value close to 100%. At the same time, for ordinary higher-order Hermite-Gaussian and Laguerre-Gaussian mode beams, the energy efficiency can only slightly exceed 50%. It is shown that zero-order Bessel-Gaussian beams are capable of achieving an energy efficiency close to 100% when an axial optical vortex is generated in the orthogonally polarized beam component when passing through an anisotropic medium, in both monochromatic and polychromatic light. It is shown that for elegant polychromatic Laguerre-Gaussian or Hermite-Gaussian beams, the energy efficiency is reduced to a value not exceeding 50%. The spin moment is compensated by a change in the orbital momentum of the entire beam, which occurs as a result of the difference in topological charge (TC) in the orthogonally polarized components by 2 units.

Generation of Perfect Vortex Beams with Complete Control over the Ring Radius and Ring Width

We have experimentally created perfect vortex beams (PVBs) by Fourier transformation of Bessel–Gaussian vortex beams, which are generated by modulating the fundamental Gaussian beam with the spiral phase plates and the axicons, respectively. Although the method has been used many times by other authors, as far as we know, few people pay attention to the quantitative relationship between the control parameters of the PVB and ring width. The effects of the waist radius of the fundamental Gaussian beam wg, base angle of the axicon γ, and focal length of the lens f on the spot parameters (ring radius ρ, and ring half-width Δ) of PVB are systematically studied. The beam pattern of the generated Bessel–Gaussian beam for different propagation distances behind the axicon and the fundamental Gaussian beam wg is presented. We showed experimentally that the ring radius ρ increases linearly with the increase of the base angle γ and focal length f, while the ring half-width Δ decreases with the increase of the fundamental beam waist radius wg, and increases with enlarging the focal length f. We confirmed the topological charge (TC) of the PVB by the interferogram between the PVB and the reference fundamental Gaussian beam. We also studied experimentally that the size of the generated PVB in the Fourier plane is independent of the TCs. Our approach to generate the PVB has the advantages of high-power tolerance and high efficiency.

Nonlinear generation of an optical bottle beam in domain-engineered ferroelectric crystals.

Nonlinear wavefront shaping in periodically poled ferroelectric crystals has received great attention because it offers a convenient way to generate a structured light beam at new frequencies. In contrast to structurally uniform beams like Laguerre-Gaussian or Hermite-Gaussian modes, here we demonstrate the possibility to generate a spatially varied optical bottle beam via a frequency doubling process in a domain-engineered Sr0.61Ba0.39Nb2O6 (SBN) crystal. The nonlinear holography method was employed to design the modulation pattern of the second-order nonlinear coefficient χ(2), and the femtosecond laser poling was used to imprint the χ(2) pattern into the SBN crystal via ferroelectric domain inversion. The second harmonic bottle beam with zero intensity in its center that is surrounded in all three dimensions by light was observed with the incidence of a fundamental Gaussian beam. These results are useful for nonlinear generation and control of structured light at new frequencies, which has important applications in nonlinear photonics and quantum optics.

A Systematic Summary and Comparison of Scalar Diffraction Theories for Structured Light Beams

Structured light beams have recently attracted enormous research interest for their unique properties and potential applications in optical communications, imaging, sensing, etc. Since most of these applications involve the propagation of structured light beams, which is accompanied by the phenomenon of diffraction, it is very necessary to employ diffraction theories to analyze the obstacle effects on structured light beams during propagation. The aim of this work is to provide a systematic summary and comparison of the scalar diffraction theories for structured light beams. We first present the scalar fields of typical structured light beams in the source plane, including the fundamental Gaussian beams, higher-order Hermite–Gaussian beams, Laguerre–Gaussian vortex beams, non-diffracting Bessel beams, and self-accelerating Airy beams. Then, we summarize and compare the main scalar diffraction theories of structured light beams, including the Fresnel diffraction integral, Collins formula, angular spectrum representation, and Rayleigh–Sommerfeld diffraction integral. Finally, based on these theories, we derive in detail the analytical propagation expressions of typical structured light beams under different conditions. In addition, the propagation of typical structured light beams is simulated. We hope this work can be helpful for the efficient study of the propagation of structured light beams.

Vortex rings in paraxial laser beams.

Interference of a fundamental vortex-free Gaussian beam with a co-propagating plane wave leads to nucleation of a series of vortex rings in the planes transverse to the optical axis; the number of rings grows with vanishing amplitude of the plane wave. In contrast, such interference with a beam carrying on-axis vortex with winding number l results in the formation of |l| rings elongated and gently twisted in propagation direction. The twist handedness of the vortex lines is determined by the interplay between dynamic and geometric phases of the Gaussian beam and the twist angle grows with vanishing amplitude of the plane wave. In the counter-propagating geometry the vortex rings nucleate and twist with half-wavelength period dominated by the interference grating in propagation direction.

Anomalous Interactions of Airy Solitons Modulated by a Fundamental Gaussian Beam and Fourth-Order Diffraction

We investigate the interactions of in-phase Airy beams modulated by a fundamental Gaussian beam and fourth-order diffraction in Kerr nonlinear media. Directly numerical simulations show that normal (anomalous) fourth-order diffraction and an in-phase (out-of-phase) Gaussian beam affect the interactions of solitons generated from Airy beams in unique ways. Different from previous results, suggesting that interactions of in-phase (out-of-phase) conventional beams are always attractive (repulsive), many anomalous interactions of Airy beams are obtained. Stable breathing Airy soliton pairs can be formed with fourth-order diffraction and a fundamental Gaussian beam.

Structuring light beams via nonlinear diffraction in 3D nonlinear photonic crystal

We show that nonlinear diffraction in nonlinear photonic crystal offers a convenient way to generate structured light at new frequencies. To this end we fabricate a 3D nonlinear photonic crystal containing two layers of fork-shaped ferroelectric domain gratings. Illumination of the structure by a fundamental Gaussian beam leads to the generation of two co-propagating second harmonic vortices with opposite topological charges, whose subsequent interference forms Hermite–Gaussian (HG) beams in far field.

Second-Harmonic Generation of the Vortex Beams with Integer and Fractional Topological Charges

The single-pass second-harmonic generation (SHG) of a vortex beam under low fundamental wave depletion is systematically studied. Vortex modes at 1064 nm with integer topological charges from ±1 to ±9 and fractional ones at ±0.75 are generated by modulating the fundamental Gaussian beam with different spiral phase plates. The frequency doubling of these fundamental vortex modes is realized via single-pass SHG through the KTP. A detailed theoretical model is set up in the single-pass SHG of the vortex beams. Theoretical analysis indicates that the higher the order of the vortex beams, the lower the SHG efficiency, when the beam waists and fundamental power are given. The experimentally measured SHG output characteristics verify those obtained via theoretical analysis. Conservation of the orbital angular momentum during the SHG process is also verified, regardless of the fractional or integer vortex beams. SH LG0,2l vortex beams with high mode purity are obtained. The beam waists of fundamental/SH in KTP measured using a 4f system demonstrate that the Rayleigh ranges of the fundamental wave and SH wave are the same. The paper comprehensively presents some basic laws in the single-pass SHG of a vortex beam. In addition, it also indicates that SHG is an effective method to improve the mode purity of vortex beam.

Effect of orbital angular momentum on dust-ion-acoustic waves in a superthermal plasma

Laser or electromagnetic radiation, in general, interacts with plasma in very interesting ways. In most cases, they induce orbital angular momentum (OAM) in such plasmas due to their polarization effects. Dust-ion-acoustic waves (DIAWs) with immovable dust particles are studied with the effect of rotation produced due to laser or electromagnetic interaction. The electrons are considered in the non-Maxwellian limit, with inertial ions and static dust grains possessing negative charges. Fluid theory is employed for obtaining the linear paraxial equation with regard to ion density perturbations. The fundamental Gaussian and Laguerre Gaussian (LG) beam solutions are talked over with the later being proved to be the source for OAM. By calculating the electrostatic potential for such linear waves, the components of the electric field with respect to the LG potential are shown. Finally, the energy density equation is used to calculate the OAM associated with DIAWs. The Laguerre Gauss mode is numerically shown to have greatly changed by varying the values of relevant plasma parameters, such as the electron superthermality parameter, radial and angular mode numbers, beam waist, and azimuthal angle. The present results may be useful in apprehending dust-ion-acoustic wave excitation due to Brillouin backscattering phenomenon of laser light interacting with plasma.

Design and experimental results of a 28 GHz, 400 kW gyrotron for electron cyclotron resonance heating

A high-power 28 GHz gyrotron has been successfully developed at the Institute of Applied Electronics, China Academy of Engineering Physics. This gyrotron was designed for electron cyclotron resonance heating (ECRH) in the spherical tokamak XL-50. A diode magnetron injection gun was designed to produce the required gyrating electron beam. The gyrotron operates in the TE8,3 mode in a cylindrical open cavity. An internal quasi-optical mode converter was designed to convert the operating mode into a fundamental Gaussian wave beam and separate the spent electron beam from the outgoing microwave power. A tube has been built and successfully tested. The operational frequency of the tube is 28.1 GHz. For beam parameters at an accelerating voltage of 71 kV and beam current of 16 A, the gyrotron has delivered an output power of 400 kW, with a pulse length of 5 s. The output efficiency is about 50% with a single-stage depressed collector. The gyrotron has been installed on the XL-50 and has played an important role in the ECRH experiments.

Non-geometric tilt-to-length coupling in precision interferometry: mechanisms and analytical descriptions

This paper is the second in a set of two investigating tilt-to-length (TTL) coupling. TTL describes the cross-coupling of angular or translational jitter into an interferometric phase signal and is an important noise source in precision interferometers, including space gravitational wave detectors like LISA. We discussed in Hartig et al (2022 J. Opt. 24 065601) the TTL coupling effects originating from optical path length changes, i.e. geometric TTL coupling. Within this work, we focus on the wavefront and detector geometry dependent TTL coupling, called non-geometric TTL coupling, in the case of two interfering fundamental Gaussian beams. We characterise the coupling originating from the properties of the interfering beams, i.e. their absolute and relative angle at the detector, their relative offset and the individual beam parameters. Furthermore, we discuss the dependency of the TTL coupling on the geometry of the detecting photodiode. Wherever possible, we provide analytical expressions for the expected TTL coupling effects. We investigate the non-geometric coupling effects originating from beam walk due to the angular or translational jitter of a mirror or a receiving system. These effects are directly compared with the corresponding detected optical path length changes in Hartig et al (2022 J. Opt. 24 065601). Both together provide the total interferometric readout. We discuss in which cases the geometric and non-geometric TTL effects cancel one-another. Additionally, we list linear TTL contributions that can be used to counteract other TTL effects. Altogether, our results provide key knowledge to minimise the total TTL coupling noise in experiments by design or realignment.

Optical Imaging Using Orbital Angular Momentum: Interferometry, Holography and Microscopy

Light with helical phase wavefront carries orbital angular momentum, a unique feature widening the horizon of optical imaging applicability. Here, we take particular interest in the common but important imaging techniques of interferometry, holography and microscopy using orbital angular momentum of light. In contrast to the conventional imaging techniques that rely on the plane-wave or fundamental Gaussian beam, the orbital angular momentum of light introduces a new physical dimension into the play to enrich the applicable imaging mechanism. Indeed, we revisit the milestone achievements that exploit the orbital angular momentum of light as the essential roles of the interference reference, multiplexing channel, spatial-filter, or excitation source. These methods bestow the imaging applications with many new and various benefits.