LG Modes Research Articles

Chirped LG modes interference formed chiral beams

Non-Gaussian spatial intensity distribution beams used in laser micro- and nano-machining find many applications. For instance, Bessel beams, having a small diameter and a very long focal zone, allow the fabrication of high aspect ratio modifications in transparent materials. Higher-order Laguerre–Gauss modes are used in particle manipulation and even for multiplexing in optical communication. The temporal intensity distribution of a pulse is mostly overlooked or fixed to Gaussian shape distribution. However, pulse-shaped beams could improve the same fields of particle manipulation as optical traps, or the laser manufacturing. In this paper, we demonstrate a method of constructing a helical spatiotemporal intensity distribution beam the rotation of which in time can be varied. We demonstrate the analytical and numerical results and show an experimental realization of such a structure.

A full duplex LG modes enabled millimeter-wave based FSO communication system for disaster zone

A full duplex LG modes enabled millimeter-wave based FSO communication system for disaster zone

Study on the effect of pump beam on the purity of high-order HG mode in off-axis pumped Tm:YLF laser

In this paper, the effect of the pump beam radius on the purity of the HG modes is investigated based on the off-axis pumped Tm:YLF laser, and LG mode vortex laser of 1.9 μm is realized. The multi-mode rate equations are established to reveal that a smaller pump beam radius leads to higher purity of the HG mode beam. At the same time, it is experimentally found that each HG mode alternated with increasing off-axis displacement at a pump beam radius of 200 μm, with a purity of 87.9 % for the HG8,0 mode. However, at the pump beam is 400 μm, the phenomenon of multiple HG modes output increases in the process of adjusting the off-axis displacement. The consistency between the experimental and theoretical results proves the effect of the size of the pump beam on the purity of the high-order HG mode laser. The 1.9 μm LG vortex beam within the 8th order is achieved with a pump beam radius of 200 μm, and the slope efficiency of the LG1,0 mode could reach 34.51 %.

Intra-Cavity Cascaded Pumped 946/1030 nm Dual-Wavelength Vortex Laser Using a Spot-Defect Mirror

Due to their unique properties, vortex lasers have high application value in frontier fields such as optical micromanipulation, super-resolution imaging, quantum entanglement, and optical communication. In this study, we demonstrated a 946/1030 nm Laguerre-Gaussian (LG01) mode dual-wavelength vortex laser by using an intracavity cascade pumped structure and a spot-defect output mirror. Using a coaxial linear cavity structure, the 808 nm laser diode (LD) was used to end-pump the Nd:YAG crystal to generate a 946 nm laser and then use it to directly pump the Yb:YAG crystal in the cavity to generate a 1030 nm laser, and finally a 946/1030 nm dual-wavelength laser came out. By making a spot defect in the center of the output mirror to suppress the oscillation of the fundamental Gaussian mode laser and carefully adjusting the position of the laser crystals, the LG01 mode dual-wavelength vortex laser was output in single handedness. When the pump power was 40 W, the total output was 664 mW (356 and 308 mW at 946 and 1030 nm LG01 mode vortex lasers), and the total optical-optical conversion efficiency was 1.7%; the output power fluctuations of 946 and 1030 nm LG01 mode vortex lasers within 1 h were 3.43% and 3.13%, respectively; the beam quality factors M2 of 946 and 1030 nm LG01 mode vortex lasers were 2.35 and 2.40, respectively. It was proved that the generated dual-wavelength vortex laser had the wavefront phase expiϕ by the self-interference method.

946/1030 nm Dual-Wavelength Laguerre-Gaussian (LG01) Mode Vortex Laser Based on Intracavity Cascade Pumped Resonator

In this paper, the 946/1030 nm dual-wavelength LG01 mode vortex laser is obtained by applying the intracavity cascade pumped structure and annular-beam end-pumped method, an innovative and pioneering exploration of the transverse mode of the dual-wavelength laser. First, we demonstrate the oscillation characteristic theoretical model of the dual-wavelength LG01 mode laser, considering the reabsorption effect. Then the length of the laser crystal and the transmittance of the output mirror are simulated and analyzed, respectively, related to the oscillation characteristics of the 946 and 1030 nm LG01 mode vortex lasers. Finally, a 946/1030 nm LG01 mode vortex laser with the same handedness is successfully achieved in our experiment. With 20 W of annular-beam pump power, the output power of 946 and 1030 nm LG01 mode vortex lasers is 0.404 and 0.510 W, the slope efficiency is 3.6% and 6.2%, and the total optical-optical conversion efficiency is 4.6%. At the maximum output power, the fluctuations of output power within 1 h are 4.02% and 4.23%, and the beam quality factors M2 are 2.32 and 2.27, respectively, for 946 and 1030 nm LG01 mode vortex lasers. The wavefront phase exp(iϕ) of the 946/1030 nm dual-wavelength is also proved by the self-interference method.

Generation of OAM-carrying space-time wave packets with time-dependent beam radii using a coherent combination of multiple LG modes on multiple frequencies.

Space-time (ST) wave packets, in which spatial and temporal characteristics are coupled, have gained attention due to their unique propagation characteristics, such as propagation invariance and tunable group velocity in addition to their potential ability to carry orbital angular momentum (OAM). Through experiment and simulation, we explore the generation of OAM-carrying ST wave packets, with the unique property of a time-dependent beam radius at various ranges of propagation distances. To achieve this, we synthesize multiple frequency comb lines, each assigned to a coherent combination of multiple Laguerre-Gaussian (LGℓ,p) modes with the same azimuthal index but different radial indices. The time-dependent interference among the spatial modes at the different frequencies leads to the generation of the desired OAM-carrying ST wave packet with dynamically varying radii. The simulation results indicate that the dynamic range of beam radius oscillations increases with the number of modes and frequency lines. The simulated ST wave packet for OAM of orders +1 or +3 has an OAM purity of >95%. In addition, we experimentally generate and measure the OAM-carrying ST wave packets with time-dependent beam radii. In the experiment, several lines of a Kerr frequency comb are spatially modulated with the superposition of multiple LG modes and combined to generate such an ST wave packet. In the experiment, ST wave packets for OAM of orders +1 or +3 have an OAM purity of >64%. In simulation and experiment, OAM purity decreases and beam radius becomes larger over the propagation.

Research on 946 nm LG01 mode laser considering thermal effect

Laguerre–Gaussian (LG) beams have important application prospects in Frontier Fields such as optical micromanipulation, optical communication, and super-resolution microscopy. In this letter, the thermal effect generated by Nd:YAG crystal that is end-pumped by the annular-beam is taken into account in the analysis of the LG01 mode beam generation. The 946 nm LG01 mode laser is obtained by using annular-beam end-pumped Nd:YAG crystal shaped by custom mirror M01. When the incident pump power is 19.9 W, the maximum output power is 1.35 W, the optical-optical conversion efficiency is 6.8%, the slope efficiency is 10.9%, and the beam quality factor M2 in X and Y directions is 2.22 and 2.28 respectively. The handedness of LG01 mode laser remains stable in the whole pump range. The theoretical model established considering thermal effects can guide the design of LG mode lasers, and the 946 nm LG01 mode laser obtained expands the new wavelength of vortex light and increases its potential new application direction.

Fast oscillations of orbital angular momentum and Shannon entropy caused by radial numbers of structured vortex beams.

We address theoretical and experimental considerations of two-parameter excitation of each Hermite-Gaussian (HG) mode in composition of a structured Laguerre-Gaussian (sLG) beam. The complex amplitude of the sLG beam is shaped in such a way that the radial and azimuthal numbers of eigenmodes are entangled with each other. As a result, variations in the amplitude and phase parameters of mode excitation, although dramatically changing the intensity and phase patterns, do not change the structural stability of the beam. We reveal that the radial number of the sLG beam can cause fast oscillations of the orbital angular momentum and Shannon entropy, dramatically increasing the uncertainty of detecting the beam in some particular state. We found that despite the fast oscillations, the sLG beam has an invariant in the form of a module of the total topological charge (TC), with the exception of narrow intervals of the phase parameter, where the measurement error does not allow us to accurately measure the sign of the TC. The difference between the interpretation of informational entropy as a measure of uncertainty and a measure of information capacity is considered on the example of the measurement of Shannon entropy in the bases of LG and HG modes.

High order modes of intense second harmonic light produced from a plasma aperture

Because of their ability to sustain extremely high-amplitude electromagnetic fields and transient density and field profiles, plasma optical components are being developed to amplify, compress, and condition high-power laser pulses. We recently demonstrated the potential to use a relativistic plasma aperture—produced during the interaction of a high-power laser pulse with an ultrathin foil target—to tailor the spatiotemporal properties of the intense fundamental and second-harmonic light generated [Duff et al., Sci. Rep. 10, 105 (2020)]. Herein, we explore numerically the interaction of an intense laser pulse with a preformed aperture target to generate second-harmonic laser light with higher-order spatial modes. The maximum generation efficiency is found for an aperture diameter close to the full width at half maximum of the laser focus and for a micrometer-scale target thickness. The spatial mode generated is shown to depend strongly on the polarization of the drive laser pulse, which enables changing between a linearly polarized TEM01 mode and a circularly polarized Laguerre–Gaussian LG01 mode. This demonstrates the use of a plasma aperture to generate intense higher-frequency light with selectable spatial mode structure.

Direct generation of continuous-wave and passively Q-switched visible vortex beams from a doughnut-shaped diode-pumped Pr: YLF laser.

We demonstrate the direct generation of visible vortex beams (LG01 mode) from a doughnut-shaped diode-pumped Pr:YLF laser. In continuous-wave mode, the maximum vortex output power was 36 mW at 523 nm, 354 mW at 607 nm, 838 mW at 639 nm, 722 mW at 721 nm, respectively. Moreover, based on this operation, the orange and red passively Q-switched vortex lasers were also achieved by inserting a Co:MgAl2O4 crystal into the laser cavity as a saturable absorber. The shortest pulse width of Q-switched vortex laser was 58 ns for 607 nm, and 34 ns for 639 nm, respectively. Our work provides a reliable and efficient method for the direct generation of visible vortex lasers for potential applications.

Experimental Demonstration of Sub-THz Wireless Communications Using Multiplexing of Laguerre-Gaussian Beams When Varying two Different Modal Indices

The ability to multiplex multiple structured beams for sub-terahertz (sub-THz) wireless communications has been recently explored. The spatial orthogonality of structured beams enables mode-division multiplexing (MDM). In an MDM system, multiple data-carrying beams are transmitted and received simultaneously through a single aperture pair with low inherent crosstalk. This can increase data capacity and spectral efficiency of the system. Here, we experimentally demonstrate multiplexing orthogonal sub-THz Laguerre-Gaussian (<inline-formula><tex-math notation="LaTeX">${{\bf L}}{{{\bf G}}_{\ell,{{\bf p}}}}$</tex-math></inline-formula>) beams when varying two different modal indices (i.e., both <inline-formula><tex-math notation="LaTeX">$\ell $</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${{\bf p}}$</tex-math></inline-formula>); this contrasts with prior reports when varying only one index (i.e., <inline-formula><tex-math notation="LaTeX">$\ell $</tex-math></inline-formula>) and could potentially provide a larger set of channels and beams in an MDM system. In our demonstration, specially designed phase patterns are used: (1) at the transmitter, to convert two THz Gaussian beams to two different LG beams, each carrying an independent data channel; and (2) at the receiver, to separate and convert the LG beams back to Gaussian-like THz beams. An 8-Gbit&#x002F;s quadrature-phase-shift-keying (QPSK) link containing two multiplexed LG modes over 40 cm is experimentally demonstrated. For the above link, three different LG modal sets are chosen (i.e., {<inline-formula><tex-math notation="LaTeX">${{\bf L}}{{{\bf G}}_{ - 2,0}}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${{\bf L}}{{{\bf G}}_{1,1}}$</tex-math></inline-formula>} or {<inline-formula><tex-math notation="LaTeX">${{\bf L}}{{{\bf G}}_{3,0}}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${{\bf L}}{{{\bf G}}_{0,1}}$</tex-math></inline-formula>} or {<inline-formula><tex-math notation="LaTeX">${{\bf L}}{{{\bf G}}_{2,1}}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${{\bf L}}{{{\bf G}}_{0,1}}$</tex-math></inline-formula>}). All channels are recovered with bit errorrates (BERs) below the 7&#x0025; forward error correction (FEC) limit. The experimental results indicate that: (a) higher-order LG modes experience more divergence, larger size, and lower conversion efficiency, contributing to higher power loss; and (b) the modal coupling and crosstalk for different LG modes is &lt;&#x2212;12 dB, which could be due to the transmitter&#x002F;receiver misalignments as well as beam truncation by the limited-sized receiver aperture.

Direct generation of ultrafast vortex beam from a Tm:CaYAlO4 oscillator featuring pattern matching of a folded-cavity resonator.

Optical vortices, beams with spiral wavefronts and screw phase dislocations have been explored in applications in optical manipulation, quantum optics, and the next generation of optical communications. In traditional methods, optical vortices are generated using space light modulators or spiral phase plates, which would sharply decrease the integration of optical systems. Different from previous transverse mode conversion outside the cavity, here we experimentally demonstrate a direct generation of ultrafast vortex beam from a Tm:CaYAlO4 oscillator by pattern matching of a six-mirror-folded-cavity resonator. By accurately adjusted the angle of the end mirror and the distance L between the M4 and the SESAMs to control the beam diameter of laser incidence on the gain medium in the sagittal and tangential planes, a stable 2 µm ultrafast vortex laser emission of annular Laguerre-Gaussian (LG) mode was obtained with a maximum output power of 327 mW and pulse duration of 2.1 ps. A simple YAG crystal plate was used as handedness selector and a homemade Mach-Zehnder (MZ) interferometer has verified the vortical property of the LG01 mode. By furtherly controlling the cavity mode pattern matching, other stable transverse-mode operations for TEM00, high-order Hermite-Gaussian (HG) transverse mode and doughnut-shaped beams were successfully realized. This work provides a flexible and reliable way to generate mid-infrared ultrafast vortex beams and is of special significance for applications in the areas of molecular spectroscopy and organic material processing amongst others.

Performance analysis of free space optical system incorporating circular polarization shift keying and mode division multiplexing

Abstract In this work, a free-space optical (FSO) communication system with the integration of mode division multiplexing and circular polarization shift keying (CpolSK) is proposed at 2 × 40 Gbps using LG00 and LG01 modes. Effects of diverse weather conditions such as clear weather, light rain, moderate rain, heavy rain, thin fog, thick fog, and heavy fog are studied on system performance. Further, a detailed comparison of CpolSK and polarization shift keying (PolSK) is performed at different FSO lengths in terms of log bit error rate. For implementation, analysis, and comparison, Optiwave Optisystem software is used and results show that CpolSK covers 100 km link distance and PolSK limits to 90 km only. Also, LG00 mode performs better than LG01 mode under all weather instabilities in the proposed system.

ML-Based Identification of Structured Light Schemes under Free Space Jamming Threats for Secure FSO-Based Applications

This paper exploits for the first time the use of machine learning (ML) based techniques to identify complex structured light patterns under free space optics (FSO) jamming attacks for secure FSO-based applications. Five M-ary modulation schemes, construed using Laguerre and Hermite Gaussian (LG and HG) mode families, were used in this investigation. These include 8-ary LG, 8-ary superposition-LG, 16-ary HG, 16-ary LG and superposition-LG, and 32-ary LG and superposition-LG and HG formats. The work was conducted using experimental demonstrations for two different jammer positions. The convolutional neural network (CNN)-based ML method was utilized to differentiate between the stressed mode patterns. The experimental results show a 100% recognition accuracy for 8-ary LG, 8-ary superposition-LG, and 16-ary HG at 1, −2, and −2 dB signal-to-jammer ratios (SJR), respectively. For SJR values &lt; 0 dB, the standard LG modes are the most affected by jamming and are not recommended for data transmission in such an environment. Besides, the accuracy of determining the jammer direction of arrival was investigated using CNN and a simpler classifier based on linear discriminant analysis (LDA). The results show that advanced networks (e.g., CNN) are required to achieve reliable performance of 100% direction determination accuracy, at −5 dB SJR, as opposed to 97%, at 2 dB SJR, for a simple LDA classifier.

Passively Q-switched radially polarized LG01 mode laser using circular Dammann grating

Cylindrical vector-polarized vortex pulses from a passively Q-switched laser are demonstrated. Pump radiation reshaped into a size-controlled annular profile via circular Dammann grating produces an efficient excitation of the LG01 mode. The YAG / Nd : YAG / Cr4 + : YAG composite crystal structure is found to reduce the Q-switching threshold and significantly suppress thermal damage, thus allowing ability to obtain a passively Q-switched pulse. The threshold pumping power is found to be 4.35 W, with a slope efficiency of 23.1%. A maximum peak power of 3.24 kW, maximum pulse energy of 53.46 μJ, pulse width of 17.5 ns, and repetition rate of 2.695 kHz are obtained. Furthermore, a radially polarized output with a polarization degree of 88.9% is confirmed. Finally, mode and polarization tuning are also discussed.

SESAM-based mode-locked vortex Ti:sapphire laser using spot-defect spatial filter for intra-cavity mode selection

In virtue of the significance of ultrashort vortex pulses, a mode-locked LG01-mode vortex Ti:sapphire laser is first realized. In the study, an intra-cavity spot-defect spatial filter was used to suppress the TEM00 mode’s oscillation and a semiconductor saturable absorber mirror was used as the mode-locked device. As a result, the mode-locked laser emitted LG01-mode vortex pulses of 186 ps at 804.4 nm with a repetition rate of 78.95 MHz and a maximum average output power of 176 mW. The phase of the LG01 mode was measured by a Mach–Zehnder interferometer and both right- and left-handed helical wavefronts were obtained.

Incoherent beam combination of low order Laguerre–Gaussian beams propagating in turbulent atmosphere

An incoherent beam combination of lower order Laguerre–Gaussian beams is analytically modeled and analyzed in the presence of atmospheric turbulence. For purpose of analysis, 44 individual laser elements are considered and intensity profile of the combined beam is analyzed at regular distances from the source. The resultant intensity is then compared with the similarly combined Gaussian beams. It is found that while combined intensity of LG10 mode is greater than that of Gaussian for lower propagation distance, it becomes less than Gaussian for distances greater than 3 km from the source. LG01 mode, on the other hand, shows considerably higher combined intensity as compared to Gaussian even at a distance of 10 km from the source, thus making them a viable prospect for high power directed energy systems.

Single-pixel identification of 2-dimensional objects by using complex Laguerre–Gaussian spectrum containing both azimuthal and radial modal indices

We simulate and experimentally demonstrate the optical single-pixel identification of two-dimensional (2D) objects by analyzing the corresponding complex-valued (i.e, amplitude and phase) Laguerre–Gaussian​ (LGl,p) spectra containing both the azimuthal (i.e., l) and radial (i.e., p) indices. A sequence of optical beams, each carrying a different superposition of one LG mode and one fundamental Gaussian mode, propagate through the objects. The amplitude and phase contributions of each LG modal component are then obtained by four sequential power measurements using a single-pixel detector. We reconstruct the 2D spatial structures of fan-shaped objects with different orientation angles and an “SC” logo using the measured complex LG spectra that contain 31 different azimuthal and 31 different radial index values. The simulation and experimental results show that (i) the minima positions of the amplitude-only LG sub-spectra (fixed l=0, varying p) are dependent on the object’s spatial information along its radial direction, (ii) the amplitude-only LG spectrum is likely to be insensitive to the object’s orientation angle, and (iii) the slopes of the phase-only LG sub-spectra (fixed p, varying l) are linearly proportional to the object’s orientation angle.

Airy transform of Laguerre-Gaussian beams.

Airy transform of Laguerre-Gaussian (LG) beams is investigated. As typical examples, the analytic expressions for the Airy transform of LG01, LG02, LG11, and LG12 modes are derived, which are special optical beams including the Airy and Airyprime functions. Based on these analytical expressions, the Airy transform of LG01, LG02, LG11, and LG12 modes are numerically and experimentally investigated, respectively. The effects of the control parameters α and β on the normalized intensity distribution of a Laguerre-Gaussian beam passing through Airy transform optical systems are investigated, respectively. It is found that the signs of the control parameters only affect the location of the beam spot, while the sizes of the control parameters will affect the characteristics of the beam spot. When the absolute values of the control parameters α and β decrease, the number of the side lobes in the beam spot, the beam spot size, and the Airy feature decrease, while the Laguerre-Gaussian characteristic is strengthened. By altering the control parameters α and β, the performance of these special optical beams is diversified. The experimental results are consistent with the theoretical simulations. The Airy transform of other Laguerre-Gaussian beams can be investigated in the same way. The properties of the Airy transform of Laguerre-Gaussian beams are well demonstrated. This research provides another approach to obtain special optical beams and expands the application of Laguerre-Gaussian beams.

Digital sorting perturbed Laguerre-Gaussian beams by radial numbers.

We developed a new alterative technique of the digital sorting of Laguerre-Gaussian beams (LG) by radial numbers resorting to algebra of the high-order intensity moments. The term "digital mode sorting" involves sorting the main mode characteristics (in the form of a mode spectrum) by the computer cells. If necessary, the spatial mode spectrum can be reproduced, for example, by means of a spatial light modulator. In the experiment, we investigated both a single LG mode and a composition of LG modes with the same topological charge but different radial numbers subjected to perturbations via a hard-edged circular aperture. The LG beams sorting was accomplished by monitoring the amplitude spectrum of the triggered secondary LG modes then recovering the sorted modes and the perturbed beam as a whole. We have revealed degenerate states of the perturbed LG beam composition when the one kth mode in the amplitude spectrum can be related to a set of LG modes with the same radial numbers. In order to decrypt and to sort beams in such a degenerate state, it is necessary to know several keys, the number of which is equal to the number of LG modes in the initial wave composition. We were also able to analyze and to sort such degenerate mode states. For monitoring the measure of uncertainty arising in the perturbed beam, we measured informational entropy (Shannon entropy).