Hermite-Gaussian Beams Research Articles

Orbital angular momentum coherent state beams

Paraxial propagation through isotropic, homogeneous, linear media exhibits invariance under rotations around the propagation axis, a symmetry described by the su(2) Lie algebra. We explore a family of paraxial beams that exploit this symmetry, constructed as linear superpositions of Laguerre–Gaussian beams (LGBs), serving as optical analogs of generalized SU(2) Lie group coherent states. A single complex parameter controls a smooth transition between Laguerre–Gaussian and Hermite–Gaussian beams (HGBs), producing intermediate beams that blend the characteristics of both families. Our beams exhibit propagation-invariant properties, up to a scaling factor, a highly desirable feature for optical applications. Experimental validation via digital holography demonstrates the practical feasibility of our approach.

Dihedral beams

Abstract In this work, a group theory-based formulation that introduces new classes of dihedral-symmetric beams is presented. Our framework leverages the algebraic properties of the dihedral group of rotations and reflections to transform input beams into closed-form families of dihedral-invariant wavefields, which will be referred to as dihedral beams. Each transformation is associated with a specific dihedral group in such a way that each family of dihedral beams exhibits the symmetries of its corresponding group. Our approach is inspired by one of the outcomes of this work: elegant Hermite–Gauss beams can be described as a dihedral interference pattern of elegant traveling waves, a new set of solutions to the paraxial equation also developed in this paper. Particularly, when taking elegant traveling waves as input beams, they transform into elegant dihedral beams possessing quasi-crystalline properties and including features like phase singularities, self-healing, and pseudo-nondiffracting propagation, as well as containing elegant Hermite and Laguerre–Gauss beams as special cases. Our approach can be applied to arbitrary scalar and vector input beams and constitutes a general group-theory formulation that can be extended beyond the dihedral group.

Biaxial Gaussian Beams, Hermite–Gaussian Beams, and Laguerre–Gaussian Vortex Beams in Isotropy-Broken Materials

We have developed the paraxial approximation for electromagnetic fields in arbitrary isotropy-broken media in terms of the ray–wave tilt and the curvature of materials’ Fresnel wave surfaces. We have obtained solutions of the paraxial equation in the form of biaxial Gaussian beams, which is a novel class of electromagnetic field distributions in generic isotropy-broken materials. Such beams have been previously observed experimentally and numerically in hyperbolic metamaterials but have evaded theoretical analysis in the literature up to now. Biaxial Gaussian beams have two axes: one in the direction of the Abraham momentum, corresponding to the ray propagation, and another in the direction of the Minkowski momentum, corresponding to the wave propagation, in agreement with the recent theory of refraction, ray–wave tilt, and hidden momentum [Durach, 2024]. We show that the curvature of the wavefronts in the biaxial Gaussian beams correspond to the curvature of the Fresnel wave surface at the central wave vector of the beam. We obtain the higher-order modes of the biaxial beams, including the biaxial Hermite–Gaussian and Laguerre–Gaussian vortex beams, which opens avenues toward studies of the optical angular momentum (OAM) in isotropy-broken media, including generic anisotropic and bianisotropic materials.

Optical trapping forces exerted by a pulsed Hermite–Gaussian beam on a dielectric nanosphere

Optical trapping forces exerted by a pulsed Hermite–Gaussian beam on a dielectric nanosphere

The control for multiple kinds of solitons generated in the nonlinear fractional Schrödinger optical system based on Hermite-Gaussian beams

The control for multiple kinds of solitons generated in the nonlinear fractional Schrödinger optical system based on Hermite-Gaussian beams

Generalized fractional one-dimensional Hermite-Gaussian beams

Generalized fractional one-dimensional Hermite-Gaussian beams

Experimental confirmation of phase profile of Hermite-Gauss beams.

Phase distribution of Hermite-Gauss (HG) beams generated by a gas laser is investigated experimentally by studying their interference with a plane wave and diffraction by a single slit by selecting pairs of bright lobes with different phases. Experimentally recorded interference and diffraction profiles support HG mode phase profiles expounded on in this paper. We find that the phase difference between one bright lobe and another is not simply zero or π but increases (or decreases) uniformly in steps of π as the number of zeros between them increases, in agreement with analytic function theory. An immediate application of this phase profile is that an HG mode can serve as a phase ruler with bright lobes as markers in steps of π.

Optical phase image encryption using stokes parameters and singular value decomposition

Abstract In this paper, we propose an optical asymmetric phase image encryption method in which the vectorial light field is used to encode the data. In transverse plane, the vectorial light field has spatially varying polarization distributions where we are allowed to have a greater number of degrees of freedom. In this scheme, the input image is first phase encoded and then modulated by a phase encrypting key, synthesized from the speckles obtained by the scattering of Hermite–Gaussian beams. The modulated image is further processed using fractional Fourier transform with a specific order (α). A pixel scrambling operator is utilized to increase the randomness to further enhance the security and singular value decomposition approach is employed to add the nonlinearity in the encryption process. Now, the stokes parameters, i.e. S 1 and S 2 are calculated using the light intensities correspond to different polarizations. S 1 is used as the encrypted image for transmission and S 2 is reserved as one of the private decryption keys. The robustness of the proposed technique is tested against various existing attacks, such as known plaintext attack, chosen plaintext attack, and contamination attacks. Numerically simulated results validate the effectiveness and efficiency of the proposed method.

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.

Ince-Gaussian laser beams as superposition of Hermite-Gaussian or Laguerre-Gaussian beams

Abstract: We obtain explicit analytic expressions for the Ince-Gaussian (IG) beams for several first indices p = 3, 4, 5, 6. Earlier, explicit expressions have been derived for amplitudes of the IG beams with p = 0, 1, 2 and without regard for the ellipticity parameter. Here, we give expressions for the amplitudes of 24 IG beams written as superpositions of the Laguerre-Gaussian (LG) or Hermite-Gaussian (HG) beams, with the superposition coefficients explicitly depending on the ellipticity parameter. Simultaneously expressing the IG modes both via the LG and HG modes allows easily obtaining the IG modes in the extreme cases when the ellipticity parameter is zero or infinite. Explicit dependence of the obtained expressions for the IG modes on the ellipticity allows the intensity pattern at the beam cross-section to be varied by continuously varying the parameter value. For the first time, intensity distributions are obtained for the IG beams with negative ellipticity parameter.

Interaction of Hermite–Gaussian Beams with a Macroscopic Atomic Target

AbstractA theoretical analysis is presented on the photoexcitation of a macroscopic atomic target by a Hermite–Gaussian (HG) beam within the framework of density matrix theory. Special emphasis is paid to the influence of the incoming HG mode on the population of an excited state and the emitted fluorescence radiation. In particular, a general expression for the alignment parameter of the excited state is derived, which depends on the beam parameters of the HG mode. Although the developed theory can be applied to any atomic system, here the electric dipole transition in neutral sodium atoms is investigated when driven by three , and modes. For this optical (valence‐shell) excitation, it is demonstrated that the population of the excited state is sensitive to the beam waist and the mode index of the HG beam. Furthermore, the influence of beam parameters on the angular distribution and linear polarization of the emitted fluorescence radiation is discussed.

Generating Optical Vortex Array Laser Beams of Superimposing Hermite–Gaussian Beams with a Dual–Phase Modulation Digital Laser System

This study presents an efficient and practical intra-cavity approach for selectively generating vortex array laser beams employing a dual-phase modulation digital laser system, which has not yet been completed in single-phase modulation digital laser. The stable optical vortex array laser beams were formed by superimposing cavity Hermite–Gaussian (HG) eigenmodes. In particular, when the selected cavity HG modes shared the same Gouy phase, the resulting optical vortex beam could preserve its light field pattern, thereby maintaining the optical vortex properties in the near and far fields. Numerical results demonstrated that employing dual-phase modulation could establish optimal boundary conditions for the selection of HG modes within the cavity, successfully generating various vortex array laser beams. The experimental validation of the proposed method confirmed the ability to select optical vortex array lasers solely by controlling the loaded phase of the dual-phase modulation digital laser. These results demonstrate the ability of digital lasers to generate and dynamically control optical vortex array lasers.

Hermite-Gaussian-Talbot carpets.

In this Letter, we demonstrate the generation of Hermite-Gaussian-Talbot carpets (HGTC) based on the interference of a Hermite-Gaussian (HG) beam array with constant successive separation (shift). Despite the acceleration of HG beams during propagation, their symmetric structure ensures that the self-imaged carpets are generated in straight lines perpendicular to the propagation direction, at particular distances, multiples of the famous Talbot distance zT. By considering the separation as a multiple or a fraction of the Hermite-Gaussian beam width, the calculated Talbot distance zT is expressed as a function of the beam parameters, such as the Rayleigh length. The same carpets are also observed in planes situated at different fractions of zT, but with different frequency appearances. An interesting feature of these carpets is that the dimension of one cell of the beam array remains constant in each period (period fraction). We believe that such novel, to our knowledge, carpets will be useful in photonics for creating lattices and optical potentials.

Twisted splitting and propagation factor of superimposed twisted Hermite-Gaussian Schell-model beams in turbulent atmosphere

We believe this to be a new superposition twisted Hermite-Gaussian Schell-model (STHGSM) beam hat is proposed. Analytic formulas for the intensity distribution and propagation factor of the STHGSM beam in non-Kolmogorov turbulence are derived by utilizing the generalized Huygens-Fresnel principle (HFP) and the Wigner function. The evolution characteristics of STHGSM beams propagating are numerically calculated and analyzed. Our findings indicate that the light intensity of the STHGSM beam gradually undergoes splitting and rotation around the axis during propagation through non-Kolmogorov turbulence, eventually evolving into a diagonal lobe shape at a certain distance of transmission. The anti-turbulence capability of the beam strengthens with higher beam order or twist factor values.

Nonlinear absorption with Hermite-Gaussian beams

Nonlinear absorption with Hermite-Gaussian beams

Calculation of trapping optical forces induced by a focused continuous Hermite Gaussian beam on a nano-dielectric spherical particle

An analytical expression for the intensity distribution of a focused continuous Hermite Gaussian beam after passing through a positive lens has been derived. Analytically, this intensity has been used to derive the gradient force acting on a nano-dielectric spherical particle . It is found that, the beam modes (p, l) have a direct influence on the trap stability, the number of trapping regions, the area of trapping zones and the particle size range.

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.

A symmetric optical cryptosystem based on QZ decomposition and Hermite Gaussian beam speckles

A symmetric optical cryptosystem based on QZ decomposition and Hermite Gaussian beam speckles

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.

Mode conversion of various solitons in parabolic and cross-phase potential wells

We numerically establish the controllable conversion between Laguerre–Gaussian and Hermite–Gaussian solitons in nonlinear media featuring parabolic and cross-phase potential wells. The parabolic potential maintains the stability of Laguerre–Gaussian and Hermite–Gaussian beams, while the actual conversion between the two modes is facilitated by the cross-phase potential, which induces an additional phase shift. By flexibly engineering the range of the cross-phase potential well, various higher-mode solitons can be generated at desired distances. Beams carrying orbital angular momentum can also be efficiently controlled by this method. In addition, other types of beams, such as sine complex-various-function Gaussian and hypergeometric-Gaussian vortex beams, can be periodically transformed and manipulated in a similar manner. Our approach allows the intricate internal relationships between different modes of beams to be conveniently revealed.