Higher-order Laguerre-Gauss Modes Research Articles

Stimulated Raman-induced beam focusing

Stimulated Raman scattering, employing a pump and a Stokes beam, exhibits itself through both the Raman loss observed in the pump beam and the Raman gain in the Stokes beam. This phenomenon finds application in spectroscopy for chemical analyses and microscopy for label-free bioimaging studies. Recent efforts have been made to implement super-resolution Raman microscopy using a doughnut-shaped pump, Stokes, or depletion beam. In this study, it is shown that the amplitude and phase of the pump or Stokes beam undergo significant modulation through the stimulated Raman process when they are configured as one of the higher-order Laguerre-Gauss modes, achieved using appropriate spiral phase plates or spatial light modulators. The resulting intensity distributions of the pump and Stokes beams are determined by a superposition of multiple Laguerre-Gauss modes that are coupled through nonlinear Raman gain and loss processes. Calculation results are used to elucidate the limitations associated with super-resolution coherent Raman imaging with a toroidal pump or Stokes beam. This stands in contrast with the stimulated emission depletion fluorescence microscopy technique, which has no fundamental limit in the spatial resolution enhancement.

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.

ℓ 00 ℓ entanglement and the twisted quantum eraser

We demonstrate the generation of unbalanced two-photon entanglement in the Laguerre–Gaussian (LG) transverse-spatial degree-of-freedom, where one photon carries a fundamental (Gauss) mode and the other a higher-order LG mode with a non-zero azimuthal (ℓ) or radial (p) component. Taking a cue from the N00N state nomenclature, we call these types of states ℓ00ℓ-entangled. They are generated by shifting one photon in the LG mode space and combining it with a second (initially uncorrelated) photon at a beamsplitter, followed by coincidence detection. In order to verify two-photon coherence, we demonstrate a two-photon “twisted” quantum eraser, where Hong–Ou–Mandel interference is recovered between two distinguishable photons by projecting them into a rotated LG superposition basis. Using an entanglement witness, we find that our generated states have fidelities of 95.31% and 89.80% to their respective ideal maximally entangled states. In addition to being of fundamental interest, this type of entanglement will likely have a significant impact on tickling the average quantum physicist's funny bone.

Controllable experimental modulation of high-order Laguerre-Gaussian laser modes.

High-order helical and sinusoidal Laguerre-Gaussian (LG) laser modes have uneven energy distribution among their multiple concentric vortex core rings and lobes, respectively. Here, we explore an experimental method to reshuffle the optical energy among their multiple concentric vortex core rings and lobes of high-order LG modes in a controllable manner. We numerically designed a diffractive optical element displayed over a spatial light modulator to rearrange optical energy among multiple concentric vortex core rings. This changes outer low-intensity concentric vortex core rings into high-intensity vortex core rings of high-order helical LG modes at the Fourier plane. The precise generation of a high-order modulated helical LG laser mode has a maximum number of highly intense concentric vortex core rings compared to known standard helical LG modes. Further, this method is extended to high-order sinusoidal LG modes consisting of both low- and high-intensity lobes to realize modulated sinusoidal LG modes with a maximum number of highly intense lobes in a controllable manner. We envisage that the modulated helical and sinusoidal high-order LG modes may surpass standard LG modes in many applications where highly intense rings and lobes are crucial, as in particle manipulation of micro- and nanoparticles, and optical lithography.

Amplification of higher-order Laguerre-Gaussian modes using a dual-pass MOPA system.

Structured light beams that are tailored for purpose have found a myriad of applications, from improved efficiency of laser-based industrial manufacturing processes to enhanced bandwidth in optical communication. While the selection of such modes is readily achievable at low powers (<100 mW) with external shaping devices, creating and controlling structured light at higher powers (>1 W) has proven to be a non-trivial task, particularly if dynamic control is required. Here we demonstrate the power amplification of low-power higher-order Laguerre-Gaussian modes using a novel in-line dual-pass master oscillator power amplifier (MOPA). The amplifier, operating at a wavelength of 1064 nm, consists of a polarization-based interferometer that alleviates parasitic lasing effects. Through our approach we demonstrate a gain factor of up to 17×, corresponding to an overall enhancement of 300% in amplification compared to a single-pass output configuration while preserving the beam quality of the input mode. These findings are confirmed computationally using a three-dimensional split-step model and show excellent agreement with the experimental data.

Generation of higher-order Laguerre–Gaussian modes from a diode-pumped Pr3+:LiYF4 laser with an intra-cavity spherical aberration

We demonstrate, for the first time to the best of our knowledge, the direct generation of higher-order Laguerre–Gaussian (LG) petal modes, formed of the coherent superposition of positive and negative LG modes with the topological charge of ± ℓ as an eigen mode, from a compact diode end-pumped P r 3 + : L i Y F 4 (YLF) laser with an intra-cavity lens configuration. The on-axis displacement of the intra-cavity lens with spherical aberration allows the selective operation of the desired higher-order LG modes with | ℓ | ≤ 31 from the laser cavity at 640 nm and 607 nm. Such visible higher-order LG modes will offer new applications in optical manipulation, quantum/optical underwater telecommunication, and microfabrication.

High-order Laguerre-Gaussian mode laser generated based on spherical aberration cavity

The high-order Laguerre-Gaussian (LG) mode output from an end-pumped Nd:YVO&lt;sub&gt;4&lt;/sub&gt; laser cavity with strong spherical aberration (SA) induced by short-focal-length lens is studied in this work. A long-focal-length lens L1 is used in the cavity to expand and collimate the beam, so that the beam incident on another short-focal-length lens L2 in the cavity undergoes a strong SA. Since the ring-shaped LG modes with different values of angular index &lt;i&gt;m&lt;/i&gt; have different beam radii, the actual focal points of each order of beam are then spatially displaced. A flat output coupler (OC) is located near the focal point of L2, which is composed of a cat-eye retroreflector together with the lens. Such a retroreflector can provide only ideal retroreflection to the incident beam with a focal point exactly on the OC. Given the focal point displacements of the LG beams with different orders, such a mechanism can be used for implementing the transverse mode selection. The mode which has an actual focal point on the OC has a smaller loss than the other defocused modes. With an &lt;i&gt;a&lt;/i&gt;-cut Nd:YVO&lt;sub&gt;4&lt;/sub&gt; as laser crystal, scalar (linear-polarized) single-mode LG output with radical index &lt;i&gt;p&lt;/i&gt; = 0 and angular index &lt;i&gt;m&lt;/i&gt;&gt;0 is obtained. The laser mode-order is selectable from LG&lt;sub&gt;0, ±10&lt;/sub&gt; to LG&lt;sub&gt;0, ±33&lt;/sub&gt; under 878.6-nm incident diode pump power of 1.03 W, by simply adjusting the distance between the OC and L2 in a range of 0.5 mm, when using lens L1 with &lt;i&gt;f&lt;/i&gt; = 150 mm and lens L2 of &lt;i&gt;f&lt;/i&gt; = 33.9 mm. It is found that sufficient SA which makes the optical paths of the neighboring modes well distinguishable is essential for single-mode operation of a wanted order of LG mode. However, too strong an SA can stop the high-order mode beam from oscillating, since the width and radius of the ring-shaped LG mode are an increasing function of indices &lt;i&gt;p&lt;/i&gt; and &lt;i&gt;m&lt;/i&gt;, which bring a stronger loss to the corresponding mode. Based on this analysis, we turn to a focal-length combination of &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; = 100 mm and &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; = 51.8 mm, to reduce the SA to a level suitable for further higher mode operation. A highest-order LG&lt;sub&gt;0, ±75&lt;/sub&gt; is obtained by such an SA mode-selecting technique under fixed pump power of 1.03 W.

A Low-Divergence Circularly Polarized Dual-Mode OAM Antenna Based on Higher Order Laguerre–Gaussian Modes

An open resonator antenna for orbital angular momentum (OAM) generation and dual-mode application is proposed. The excitation of OAM mode is deduced by the open resonator theory and the circular array theory. In the cavity, eight aperture coupled patch antenna elements are used to excite two higher-order Laguerre-Gaussian HE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> modes with a 90° phase difference. Verifying by simulation and experiment, the proposed low-profile antenna can radiate left-hand or right-hand circularly polarized waves of OAM modes l=±1, which have a relatively low divergence angle of ±9° and high gain of around 13 dBi.

Laguerre-Gaussian beam generation via enhanced intracavity spherical aberration

We demonstrate an end-pumped Laguerre-Gaussian (LG) mode-selectable Nd:YVO4 laser utilizing enhanced intracavity spherical aberration. The cavity was designed to exploit strong spherical aberration generated by an expanded beam, incident on a short-focal-length lens, which enabled oscillation of cavity modes of different order. This compact-cavity laser could operate efficiently with high-order LG mode, with the order of this mode being selectively changed by simply adjusting the distance between the short-focal-length lens and the output coupler. Scalar LG modes from LG0,±10 to up to LG0,±33 were observed in the experiment. The output power of the LG0, ±33 mode was 1.87 W under an absorbed pump power of 6.6 W.

768-ary Laguerre-Gaussian-mode shift keying free-space optical communication based on convolutional neural networks.

Beyond orbital angular momentum of Laguerre-Gaussian (LG) modes, the radial index can also be exploited as information channel in free-space optical (FSO) communication to extend the communication capacity, resulting in the LG- shift keying (LG-SK) FSO communications. However, the recognition of radial index is critical and tough when the superposed high-order LG modes are disturbed by the atmospheric turbulences (ATs). In this paper, the convolutional neural network (CNN) is utilized to recognize both the azimuthal and radial index of superposed LG modes. We experimentally demonstrate the application of CNN model in a 10-meter 768-ary LG-SK FSO communication system at the AT of Cn2 = 1e-14 m-2/3. Based on the high recognition accuracy of the CNN model (>95%) in the scheme, a colorful image can be transmitted and the peak signal-to-noise ratio of the received image can exceed 35 dB. We anticipate that our results can stimulate further researches on the utilization of the potential applications of LG modes with non-zero radial index based on the artificial-intelligence-enhanced optoelectronic systems.

Laguerre–Gaussian induced temperature and refractive index profiles in thermal lens effect

In this work, we present a theoretical model that describes induced temperature and refractive index profiles generated by the Laguerre–Gaussian (LG) excitation beam. A comparison between LG and conventional fundamental mode T E M 00 is drawn. It indicates that there is a decrease or increase around the optical axis ( z , r = 0 ) in the refractive index by L G 1 0 and L G 0 5 , thus enabling an enhancement of the refractive index gradient along the radius r . The temperature and refractive index profiles produced by the higher-order LG modes are compared with those of a conventional fundamental T E M 00 Gaussian beam. The results indicate that there is an increase along the radius in the refractive index gradient generated by L G 1 0 and L G 0 5 , which could enhance the sensitivity in photothermal lens detection.

Digital laser for on-demand intracavity selective excitation of second harmonic higher-order modes.

In this article, we demonstrate selective excitation of second harmonic higher-order modes inside a diode end-pumped solid-state laser resonator that comprises of a nonlinear potassium titanyl phosphate (KTP) crystal and a digitally addressed holographic end-mirror in a form of a reflective phase-only spatial light modulator (SLM). The emitted second harmonic higher-order modes at 532 nm are generated by an intracavity nonlinear KTP crystal that is pumped by high-order fundamental modes operating at 1064 nm. The fundamental modes are digitally controlled by displaying a computer-generated hologram in the form of a grey-scale image to the SLM screen for on-demand high-order modes. The phase matching of the fundamental mode to the generated frequency-doubled mode is achieved by controlling the phase of the digital hologram to either achieve a high or quasi-degree of orbital angular momentum conservation. We show that we can intracavity generate frequency-doubled high-order Laguerre-Gaussian modes and Hermit-Gaussian modes that are either quasi or fully reproducible in the far-field. To the best of our knowledge, this is the first laser to generate frequency-doubled on-demand higher-order modes inside the cavity at the visible (green) wavelength of 532 nm.

Maximum coupling efficiency to an optical resonator based on the Laguerre-Gauss decomposition of a beam.

We present a new numerical method to calculate the optimum lens transformation to implement on a monochromatic laser beam path, in order to maximize its coupling to the fundamental Gaussian mode of a resonator or to a single-mode optical fiber whose mode can be described as Gaussian to a good approximation. This method relies on a useful mathematical relation on Laguerre-Gauss modes of different waists and reduces in the end to numerically maximizing a polynomial that is a function of the state of the beam in a finite interval, thus being numerically very efficient. We show with a simple example that this method is particularly efficient against other common methods used in the laboratory when it comes to laser beams composed of a coherent superposition of higher-order Laguerre-Gauss modes, as it is the case for instance for beams traversing optical elements suffering from spherical aberration.

Generation of super-high-order petal-like laser beam using Theon-sieve resonator

The Laguerre–Gaussian (LG) mode beam has very important applications in many research fields. Here, the Theon sieve is first introduced into the laser resonator to generate petal-like laser beams by coherently superimposing two high-order LG modes. The effectiveness was verified by GLAD software. The petal-like laser beam is derived from the light field redistribution and coherent superposition caused by the diffraction effect of the Theon sieve. The relationship between the order of the petal-like laser and the cavity structures has also been investigated in detail. Light field operation in the laser cavity greatly simplifies the optical structure and is more beneficial to optical diagnostics and imaging.

Passively Q-switched pulsed fiber laser with higher-order modes

We experimentally demonstrate a passively Q-switched fiber laser that generates higher-order modes pulse beam based on HfSe2 saturable absorber and spatial light modulator. Due to the large modulation depth of the HfSe2 film, a Q-switched pulse with wide repetition rate can be realized based on the saturable absorption effects. Further investigation shows various higher-order Laguerre-Gaussian modes can be achieved by launching the Q-switched fundamental mode pulse onto spatial light modulator. Our studies provide a simple way to obtain a stable Q-switched fiber laser with higher-order modes pulse beam.

Generating Controllable Laguerre-Gaussian Laser Modes Through Intracavity Spin-Orbital Angular Momentum Conversion of Light

The rapid developments in orbital-angular-momentum-carrying Laguerre-Gaussian (LG0 l) modes in recent years have facilitated progresses in optical communication, micromanipulation and quantum information. However, it is still challenging to efficiently generate bright, pure and selectable LG0 l laser modes in compact devices. Here, we demonstrate a low-threshold solid-state laser that can directly output selected high-purity LG0 l modes with high efficiency and controllability. Spin-orbital angular momentum conversion of light is used to reversibly convert the transverse modes inside cavity and determine the output mode index. The generated LG0 1 and LG0 2 laser modes have purities of ~97% and ~93% and slope efficiencies of ~11% and ~5.1%, respectively. Moreover, our cavity design can be easily extended to produce higher-order Laguerre-Gaussian modes and cylindrical vector beams. Such compact laser configuration features flexible control, low threshold, and robustness, making it a practical tool for applications in super-resolution imaging, high-precision interferometer and quantum correlations.

Cascade conical refraction for annular pumping of a vortex Nd:YAG laser and selective excitation of low- and high-order Laguerre–Gaussian modes

We proposed an efficient and vortex Nd:YAG laser for selective lasing of low- and high-order vortex modes, in which multiple-ring pump light was originated from cascaded conical refraction of multiple biaxial crystals. In our proof of concept demonstration, we used two-crystal cascade conical refraction to generate two-ring pump light; the mutual intensity ratio and relative separation of the inner ring and outer ring were controlled by rotating the second biaxial crystal and by moving the imaging lens, respectively. As a result, we obtained selective excitation of Laguerre–Gaussian (LG01 and LG03) vortex modes in the end-pump Nd:YAG laser. For LG01-mode output, the laser power reached 439 mW with 52.5% slope efficiency; for LG03-mode output, the laser power reached 160 mW with 41.3% slope efficiency. Our results revealed that the multiple-ring pumping technique based on cascaded conical refraction would pave the way for realization of the efficient and switchable excitation of low- and high-order LG modes in an end-pumped solid-state laser.

Generation of arbitrary axisymmetrically polarized pulses by using the combination of 4-f spatial light modulator and common-path optical system.

We proposed and constructed a system to realize broadband generation of arbitrary axisymmetrically polarized (AP) pulses with spatial complex amplitude modulation. This system employs the combination of a spatial light modulator in the 4-f configuration (4-f SLM), and a space variant wave plate as a common path interferometer. The 4-f SLM and the common path interferometer offer compensation for spatial dispersion with respect to wavelength and stability to perturbation, respectively. We experimentally demonstrated the various AP pulses generation by applying modulations of fundamental and higher-order Laguerre-Gauss modes, whose radial indices were, respectively, p = 0 and 1, with high purity, which showed that we were able to generate arbitral AP pulses with spatial complex amplitude modulation. This technique is expected to be applied in both classical and quantum communications with higher-order modes.

Examining second-harmonic generation of high-order Laguerre-Gaussian modes through a single cylindrical lens.

We experimentally investigate the second-harmonic generation of a high-order Laguerre-Gaussian (LG) mode under the quasi-phase-matching (QPM) configuration. First, we introduce a simple method to observe the azimuthal (l) and radial (p) indices of the high-order LG modes. Based on the astigmatic transformation technique, l and p are revealed in the number of dark stripes of the converted pattern in the focal plane. Then, using this efficient method of measurement, we demonstrate in experiments a second-harmonic LG mode with its radial and azimuthal indices being twice those of the inputted fundamental wave through QPM in a periodically poled KTP crystal. Our results provide a feasible way to obtain simultaneously the LG modes with larger radial and azimuthal indices.

On-chip generation of broadband high-order Laguerre-Gaussian modes in a metasurface.

With experimental results, we demonstrate the generation of high-order Laguerre-Gaussian modes with non-zero radial indices using a metal meta-surface, which is composed of a series of rectangle nanoholes with different orientation angles. The phase shift after transmission through the metasurface is determined by the orientation angle of the nanohole. This device works over a broad wavelength band ranging from 700 to 1000nm. Moreover, we achieve a LG mode with a radial mode index of 10. Our results provide an integrated method to obtain high-order LG modes, which can be used to enhance the capacity in optical communication and manipulation.