Search Results (13)

In this paper, the evolution of the beam from the double Hermite–Gaussian beam superposition state to the double Laguerre–Gaussian beam superposition state is realized based on the astigmatism conversion. Firstly, the tunable output of the double Hermite–Gaussian mode superposition state is realized by adjusting the off-axis pumping distance of the crystal. On this basis, an astigmatic mode converter is added to the back end of the resonant cavity output mirror. By utilizing it, the evolution from the double Hermite–Gaussian mode superposition state to the specific double Laguerre–Gaussian mode superposition state is realized. The evolution process of the double mode superposition state based on the astigmatic mode is analyzed theoretically. The light field change of the evolution process is demonstrated experimentally. Full article

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. Full article

In this paper, the Laguerre–Gaussian (LG) mode superposition is obtained by using the technology of double-end off-axis pumping Tm:YLF crystal, and the LG mode superposition is achieved by combining the extra-cavity conversion method. The impact of changing the off-axis distance on the order of Hermite–Gaussian (HG) mode and the topological charge of LG mode is studied. The results show that when the off-axis distance of the pump source at both ends is tuned, when the off-axis distance is in the range of 260 μm~845 μm, the single-ended 0~10 order HG mode can be obtained. Subsequently, the mode converter is placed to obtain the LG mode beam, and the double-end simultaneously pumps the crystal to obtain the superimposed LG mode. The tuning off-axis quantity changes the topological charge number. When P = 0, $l_1=l_2$, the superimposed LG mode is a single-ring spot, and the vortex beam center’s dark hollow area increases with the topological charge number. When P = 0, $l_1=-l_2$, the superimposed LG mode is a petal-like spot. The number of petals differs from the topological charges of two opposite numbers. Finally, in the case of changing the topological charge number of the double-ended LG mode, the output of the vortex array structured beams of the tuning mode order 1.9 μm Tm:YLF is completed in the case of conversion and superposition. Full article

Paraxial beam modes, which propagate in space and focus without changing their transverse intensity pattern, are of great value for multiplexing transmitted data in optical communications, both in waveguides and in free space. The best-known paraxial modes are the Hermite-Gaussian and Laguerre-Gaussian beams. Here, we derive explicit analytical expressions for Ince-Gaussian (IG) beams for several first values of the indices p = 3, 4, 5, and 6. In total, we obtain expressions for the amplitudes of 24 IG beams. These formulae are written as superpositions of the Laguerre-Gaussian (LG) or Hermite-Gaussian (HG) beams, with the superposition coefficients explicitly depending on the ellipticity parameter. Due to simultaneous representation of the IG modes via the LG and HG modes, it is easy to obtain the IG modes in the limiting cases wherein the ellipticity parameter is zero or approaches infinity. The explicit dependence of the obtained expressions for the IG modes on the ellipticity parameter makes it possible to change the intensity pattern at the beam cross-section by continuously varying the parameter values. For the first time, the intensity distributions of the IG beams are obtained for negative values of the ellipticity parameter. The obtained expressions could facilitate a theoretical analysis of properties of the IG modes and could find practical applications in the numerical simulation or generation of such beams with a liquid-crystal spatial light modulator. Full article

We studied theoretically and experimentally the propagation of structured Laguerre–Gaussian (sLG) beams through an optical system with general astigmatism based on symplectic ABCD transforms involving geometry of the second-order intensity moments symplectic matrices. The evolution of the coordinate submatrix ellipses accompanying the transformation of intensity patterns at different orientations of the cylindrical lens was studied. It was found that the coordinate submatrix W and the twistedness submatrix M of the symplectic matrix P degenerate in the astigmatic $\mathrm{sLG}$ beam with simple astigmatism, which sharply reduces the number of degrees of freedom, while general astigmatism removes the degeneracy. Nevertheless, degeneracy entails a simple relationship between the coordinate element $W_{xy}$ and the twistedness elements $M_{xy}$ and $M_{yx}$ of the submatrix M, which greatly simplifies the measurement of the total orbital angular momentum (OAM), reducing the full cycle of measurements of the Hermite–Gaussian (HG) mode spectrum (amplitudes and phases) of the structured beam to the only measurement of the intensity moment. Moreover, we have shown that Fourier transform by a spherical lens enables us to suppress the astigmatic OAM component and restore the original free-astigmatic $\mathrm{sLG}$ beam structure. However, with further propagation, the $\mathrm{sLG}$ beam restores its astigmatic structure while maintaining the maximum OAM. Full article

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. Full article

If a vortex propagation-invariant beam is given by all its intensity nulls, then its topological charge (TC) can be defined easily: its TC is equal to the sum of topological charges of all optical vortices in these intensity nulls. If, however, a propagation-invariant beam is given as a superposition of several light fields, then determining its TC is a complicated task. Here, we derive the topological charges of four different types of propagation-invariant beams, represented as axial superpositions of Hermite–Gaussian beams with different amplitudes and different phase delays. In particular, topological charges are obtained for such beam families as the Hermite–Laguerre–Gaussian (HLG) beams and two-parametric vortex Hermite beams. We show that the TC is a quantity resistant to changing certain beam parameters. For instance, when the parameters θ and α of the HLG beams are altered, the beam intensity also changes significantly, but the TC remains unchanged. Full article

We derive analytical formulae for the complex amplitudes of variants of generalized Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) beams. We reveal that, at particular values of parameters of the exact solution of the paraxial propagation equation, these generalized beams are converted into conventional elegant HG and LG beams. We also deduce variants of asymmetric HG and LG beams that are described by complex amplitudes in the form of Hermite and Laguerre polynomials whose argument is shifted into the complex plane. The asymmetric HG and LG beams are, respectively, shown to present the finite superposition of the generalized HG and LG beams. We also derive an explicit relationship for the complex amplitude of a generalized vortex HG beam, which is built as the finite superposition of generalized HG beams with phase shifts. Newly introduced asymmetric HG and LG beams show promise for the study of the propagation of beams carrying an orbital angular momentum through the turbulent atmosphere. One may reasonably believe that the asymmetric laser beams are more stable against turbulence when compared with the radially symmetric ones. Full article

We investigate the concept that the value of the spin-orbit coupling is the energy efficiency of energy transfer between orthogonal components. The energy efficiency changes as the beam propagates through the crystal. For a fundamental Gaussian beam, its value cannot exceed 50%, while the energy efficiency for Hermite–Gaussian and Laguerre–Gaussian beams of higher orders of the complex argument can reach a value close to 100%. For Hermite–Gauss and Laguerre–Gauss beams of higher orders of real argument, the maximum energy efficiency can only slightly exceed 50%. It is shown that zero-order Bessel–Gauss beams are able to achieve an energy efficiency close to 100% when generating an axial vortex in the orthogonal component in both monochromatic and polychromatic light, while for a polychromatic Laguerre–Gauss or Hermite–Gauss beam of a complex argument, the energy efficiency reduced to a value not exceeding 50%. The spin angular momentum is compensated by changing the orbital angular momentum of the entire beam, which occurs as a result of the difference in the topological charge of the orthogonally polarized component by 2 units. Full article

In this paper, dual tuning of orbital angular momentum (OAM) and the wavelength of a Tm:YLF vortex laser was realized by off-axis pumping and F-P etalon. The tuning of Hermite–Gaussian (HG) modes by off-axis pumping was theoretically analyzed. In the experiment, the highest 17th order HG_17,0 mode was realized by off-axis pumping. The threshold power increased from 2 to 17.51 W with the increase in off-axis distance, and the curve of threshold power vs. off-axis distance was partially consistent with the theoretical simulation analysis. The Laguerre–Gaussian (LG) modes carrying OAM were produced by mode converter, and the beam quality of LG modes was good. The phase distribution of the LG modes was verified by interference. Subsequently, an F-P etalon was inserted into the resonant cavity to tune the wavelength. Finally, the OAM tuning of the vortex beam from LG_1,0(OAM = $-1\hslash$) to LG_16,0(OAM = $-16\hslash$) was realized, and the corresponding wavelength tuning range was from 1898–1943 nm to 1898–1937 nm. Full article

In this paper, we develop new classification and estimation algorithms in the context of free space optics (FSO) transmission. Firstly, a new classification algorithm is proposed to address efficiently the problem of identifying structured light modes under jamming effect. The proposed method exploits support vector machine (SVM) and the histogram of oriented gradients algorithm for the classification task within a specific range of signal-to-jamming ratio (SJR). The SVM model is trained and tested using experimental data generated using different modes of the structured light beam, including the 8-ary Laguerre Gaussian (LG), 8-ary superposition-LG, and 16-ary Hermite Gaussian (HG) formats. Secondly, a new algorithm is proposed using neural networks for the sake of predicting the value of SJR with promising results within the investigated range of values between −5 dB and 3 dB. Full article

This article demonstrates the crucial importance of the symmetrization method for the formation of autofocusing beams. It is possible to impart autofocusing properties to rather arbitrary distributions, for example, truncated and inverted classical modes (such as Hermite–Gaussian, Laguerre–Gaussian, and Bessel modes) or shift the fundamental Gaussian beam by inserting mirror or circular symmetry. The most convenient for controlling autofocusing characteristics is the truncated sinus function with a power-law argument dependence. In this case, superlinear chirp beams (with power q > 2) exhibit sudden and more abrupt autofocusing than sublinear chirp beams (with power 1 < q < 2). Comparison of the different beams’ propagation is performed using fractional Fourier transform, which allows obtaining the field distribution in any paraxial region (both in the Fresnel and Fraunhofer diffraction regions). The obtained results expand the capabilities of structured beams in various applications in optics and photonics. Full article

The rapid development of high-energy and high-power laser technology provides an important experimental means for the research of extreme physical state in the laboratory and for the design of large laser facilities for realizing inertial confinement fusion. However, when the incident laser field is very strong, the Kerr effect of materials affects the nominal performance of optical elements. In this work, the impact of Kerr effect on the focusing performance of an optical lens is studied by calculating and comparing the filed patterns of focal spots for three different incident laser beams together with three different levels of light intensities. The traditional transfer function of an optical lens is firstly modified according to the theory of nonlinear Kerr effect. We use the two-dimensional fast Fourier transform algorithm and angular spectrum algorithm to numerically calculate the field distributions of focal spots in the nominal focal plane of lens and its adjacent planes based on the Fresnel diffraction integral formula. The obtained results show that the Kerr effect affects the focusing characteristics of lens, especially for the incidence of high-order Gaussian beams, such as Hermite-Gaussian beams and Laguerre-Gaussian beams. At the same time, the focal length and refractive index of lens also change the field patterns of focal spots. The presented methodology is of great value in engineering applications where the practical problem with beam size up to 100 mm can be calculated using a common laptop computer. The work provides an efficient numerical technique for high-intensity incident laser beams focused by lens that takes Kerr effect into consideration, which has potential applications in high energy density physics and large laser facilities for inertial confinement fusion. Full article