LG Modes Research Articles

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).

Intra-Cavity Generation of Linearly Distributed and Continuously Varied Optical Vortices

Linearly distributed and continuously varied optical vortices are experimentally obtained from a dual-polarization microchip laser. The number of the linearly distributed optical vortices can increase from 1 to 4. It’s the results of intra-cavity generated coherent superposition of different Laguerre-Gaussian Modes (LGMs). For the generation of linearly distributed optical vortices with multi LGMs, the principle is given by theoretical analyzation and simulations. It shows that the relative intensity weights and the same initial phase of the LGMs are the reason for the linear distribution of the intra-cavity generated optical vortices. For the generation of linearly distributed optical vortices, the weight should be higher if the LG mode is closer to the center of the LGMs row.

Transfer of orbital angular momentum superposition from asymmetric Laguerre–Gaussian beam to Bose–Einstein Condensate

In this paper, we have formulated a theory for the microscopic interaction of the asymmetric Laguerre–Gaussian (aLG) beam with the atomic Bose–Einstein condensate (BEC) in a harmonic trap. Here the asymmetry is introduced to an LG beam considering a complex-valued shift in the Cartesian plane keeping the axis of the beam and its vortex states co-axial to the trap axis of the BEC. Due to the inclusion of the asymmetric nature, multiple quantized circulations are generated in the beam. We show how these quantized circulations are transferred to the BEC, resulting in a superposition of matter vortex states. The calculated Rabi frequencies for the dipole as well as quadrupole transitions during the transfer process show distinct variability with the shift parameters of the beam. A significant enhancement of the quadrupole Rabi frequency for higher vorticity states is observed compared to the symmetric single orbital angular momentum (OAM) mode beam at a particular range of the shift parameters. We also demonstrate the variation of superposition of matter vortex states and observe its distinct feature compared to the superposition of the LG modes for different shift parameters. The first order spatial correlation of the superposed states supports this feature and highlights asymmetry in the degree of transverse coherence along orthogonal directions on the surface.

Direct generation of orthogonally polarized dual-wavelength continuous-wave and passively Q-switched vortex beam in diode-pumped Pr:YLF lasers.

We report on direct generation of an orthogonally polarized dual-wavelength vortex laser, for the first time to our knowledge, by means of a diode-pumped V-shaped Pr:YLF laser platform. A method of misaligning the folded mirror is proposed to realize the simultaneous orthogonally polarized dual-wavelength laser, while a method of orthogonally rotating the laser gain medium is proposed to generate an intracavity vortex beam (LG01 mode). With the two methods, in continuous-wave (CW) mode, we have achieved simultaneous lasing of an orthogonally polarized dual-wavelength vortex laser at 604 and 607nm with maximum output power of 237.7mW. Moreover, based on this operation, a simultaneous orthogonally polarized dual-wavelength passively Q-switched vortex laser is also realized by inserting a Co:ASL crystal into the laser resonator as a saturable absorber. This work provides the simplest way for direct generation of an orthogonally polarized dual-wavelength vortex laser for potential applications.

Optical mode conversion through nonlinear two-wave mixing

Hermite\penalty1000-\hskip0ptGaussian (HG), Laguerre\penalty1000-\hskip0ptGaussian (LG), and Ince-Gaussian (IG) modes have been of considerable importance for photonics. They have revealed a unique way to optical manipulation and are particularly promising for optical communications. This paper combines HG modes, as a basis, inside the nonlinear crystal and the generated second harmonic field turns to LG and IG modes. Here we present a way to use second order nonlinear media to convert optical beam modes as we wish.

Direct Generation of a Laguerre-Gaussian-Mode Optical Vortex Beam in a Single-Frequency Nd:YVO4 Unidirectional Ring Laser

A single-frequency, unidirectional ring laser with a first order Laguerre-Gaussian (LG01) mode output end-pumped by using a ring-shaped pump beam is reported. This approach has been applied to a diode-pumped Nd:YVO4 laser in a traveling wave resonator configuration yielding 2.1 W and 1.5 W of single-frequency LG01 mode outputs with helical wavefronts of left- and right-handedness, respectively. Moreover, we show that its wavefront helicity can be switched by changing the lasing direction and frequency. The selection mechanism of the wavefront helicity and the prospects of this approach are discussed.

Generation and Thermal Properties of a Dual-Transverse-Mode With Dual-Polarization and Dual-Frequency by a Dual-Medium Microchip Laser

A dual-polarization, dual-frequency and dual-transvers-mode laser beam is generated by a dual-medium microchip laser. The dual-transvers-mode includes a linearly polarized LG01 mode and a perpendicular polarized TEM00 mode, which have different optical frequencies. How is the beat frequency of the dual-mode influenced by the thermal factors, including cooling temperature of birefringent crystal and thermal effect of gain medium, is experimentally investigated and theoretically analyzed. These studies offer an extension and better understanding of the dual-medium based dual-frequency laser, which is of important applications in coherent Lidar detection and optical communications.

Method for Generating High Purity Laguerre–Gaussian Vortex Modes

Generation of a donut-shaped first-order Laguerre–Gaussian (LG01) vortex mode via a method designed to yield high mode purity is reported. Our approach utilizes a novel twin-spot end-pumping scheme to directly excite the first order Hermite–Gaussian (HG01) mode in a solid-state laser, followed by a novel astigmatic mode converter based on spherical (concave) mirrors aligned at oblique incidence. A simple theoretical model for the mode converter is derived and from this the design approach is explained along with the potential benefits compared with conventional schemes-based cylindrical-lens astigmatic mode converters, particularly for power scaling. As a proof-of-principle and to confirm the benefits of this scheme in terms of high mode purity we have applied it to an end-pumped Nd:YVO4 laser to generate a (LG01) beam with a controllable sense of azimuthal phase and hence orbital angular momentum. A method for characterizing the resulting beam-based on analysis of the spiral interference pattern derived with the aid of a Mach–Zehnder interferometer is described and yields a value for the LG01 mode purity of 94%. Common sources of mode impurity are identified and the prospects for scaling to higher power whilst maintaining high mode purity are considered.

Simple intra-cavity beam shaping for generating a shape-invariant flat-top laser beam

For laser users, the usual Gaussian beam (GB) may not always be the best intensity profile. Often, a preferred option is a Flat-Top (FT) beam which is generally obtained by using diffractive optics in a reshaping operation. In this case, the resulting FT profile occurs only in the focal plane of the focusing lens, and its vicinity. We consider here the generation of a shape-invariant FT laser beam resulting from the incoherent weighted (50%-50% in power) mixing of LG00 (GB) and LG01 (doughnut) beams. For that we consider the insertion inside the laser cavity of a diaphragm and an absorbing ring, and optimising their sizes makes possible the simultaneous oscillation on LG00 and LG01 modes allowing the generation of a shape-invariant laser beam.

Direct excitation of chirality controllable LG01 vortex beam in solid-state lasers by intracavity astigmatism manipulation

In this letter, we report a systematic approach to directly generate chirality controllable Laguerre–Gaussian (LG01) mode in solid-state lasers. This approach is based on two concepts. The first is the off-axis pumping technique, which has been exploited to achieve Hermite–Gaussian modes. The second is intracavity astigmatism manipulation, which has been introduced to the laser cavity by tilting curved mirrors to generate LG modes. The control method of chirality has been discussed in detail. The feasibility of this approach is shown in both theoretical model and experimental analysis of the generation process.

Optical parametric amplification of a Laguerre–Gaussian mode

We theoretically study the optical parametric amplification (OPA) process seeded by a Laguerre–Gaussian (LG) mode. Based on the nonlinear coupled-wave equations, we analyze the overlap integral among interacting LG beams, which presents the selection laws for the azimuthal and radial indices of a pure LG mode in the OPA process. In the numerical simulations, we demonstrate the amplification of an LG01 mode as an example with high purity and high gain. Our results provide a potential way to efficiently amplify an LG mode for optical communications.

Spontaneous generation of orbital angular momentum crystals using a monolithic Nd:YAG nonplanar ring laser.

We report the emission of localized orbital angular momentum (OAM) crystals in a millimeter-size monolithic Nd:YAG nonplanar ring laser. Narrow-linewidth single-frequency lasing in the kilohertz level featuring crystal-like vortices is obtained via phase locking of Laguerre-Gaussian modes in the cavity. It is found that the spatially degenerate OAM of high-order LG modes can be easily broken by superimposing a low-order mode, leading to crystal-like vortices. Our theoretical analysis is found to be in agreement with the experimental results for both intensity and interference patterns.

Vortex laser from anti-resonant ring coupled cavities.

Optical vortex Laguerre-Gaussian (LG0l) modes have wide-ranging applications due to their annular spatial form and orbital angular momentum. Their direct generation from a laser is attractive, due to the pure and high-power modes possible; however, previous demonstrations have had limited ranges of applicability. Here, we propose and implement direct LG0l vortex mode generation with an anti-resonant ring (ARR) coupled laser cavity geometry, where the gain medium inside the ARR is shared between two laser cavities. This generation uses standard wavelength-insensitive optical components, is suitable for high peak and average power levels, and could be applied to any bulk gain medium in pulsed or continuous wave regimes. This work demonstrates the technique with a diode end-pumped Nd:YVO4 gain medium. From 24 W of pump power, 8.9 W LG01 and 4.3 W LG02 modes were generated, all with high mode purity and pure handedness. The LG01 mode handedness was controlled with a new technique.

Direct Generation of Vortex Laser by Rotating Induced Off-Axis Pumping

We propose a simple method for direct generation of vortex laser based on all-solid-state laser technology. Diagonal HG01 mode is first achieved by rotating the Nd:YVO4 gain medium in xz plane. Further rotating the gain medium (in yz plane) leads to mode conversion from diagonal HG 01 to LG01. A simple home-made interference device has been used to verify the vortical property of the LG01 mode with well-determined handedness. The generated LG01 mode has a maximum output power of 2.85 W and slope efficiency of about 41.1%, which indicate that the present method is very efficient. Moreover, this method has good universality and can be used for the generation of other solid state vortex lasers, which paves the way toward simple, reliable, and efficient generation of vortex lasers for various applications.

400-Gbit/s QPSK free-space optical communicationlink based on four-fold multiplexing of Hermite-Gaussian or Laguerre-Gaussian modes by varying both modal indices.

We experimentally demonstrate the four-fold multiplexing of Hermite-Gaussian (HGmn) or Laguerre-Gaussian (LGlp) modes to achieve a 400Gbit/s quadrature-phase-shift-keyed (QPSK) free-space optical communication link. In this experiment, both modal indices for the HG and LG modes are simultaneously utilized to achieve a larger potential orthogonal modal space. Moreover, we also investigate and compare the effects of aperture size, lateral displacement, and rotation on the system. We measure the degree of performance degradation due to the following: (1)a receiver aperture with a limited size causes power loss and crosstalk for both HG and LG modes; (2)a lateral misalignment between the transmitter and receiver which leads to crosstalk for LG modes, but might not affect HG0n or HGm0 modes due to axial symmetry; and (3)a rotational misalignment between the transmitter and receiver which causes crosstalk for the HG modes, but does not tend to affect the LG modes due to azimuthal symmetry.

Optical millimeter wave mode division multiplexing of LG and HG modes for OFDM Ro-FSO system

Abstract The scarcity of RF spectrum at lower frequencies has recently been addressed by millimeter wave transmission in fiber-wireless and radio-over-free-space optics networks for more flexible frequency spectrum allocation. This work focuses on parallel transmission of four independent radio OFDM based channels, each carrying 20Gbps data, by optical millimeter mode division multiplexing of spiral-phased Laguerre–Gaussian modes and Hermite–Gaussian modes using a spatial light modulator to realize 80 Gbps–160 GHz data over 50 km free-space link. The performance of proposed system is evaluated under the influence varying levels of fog.

Direct emission of chirality controllable femtosecond LG01 vortex beam

Direct emission of a chirality controllable ultrafast LG01 mode vortex optical beam from a conventional z-type cavity design SESAM (SEmiconductor Saturable Absorber Mirror) mode locked LD pumped Yb:Phosphate laser has been demonstrated. A clean 360 fs vortex beam of ∼45.7 mW output power has been achieved. A radial shear interferometer has been built to determine the phase singularity and the wavefront helicity of the ultrafast output laser. Theoretically, it is found that the LG01 vortex beam is obtained via the combination effect of diagonal HG10 mode generation by off-axis pumping and the controllable Gouy phase difference between HG10 and HG01 modes in the sagittal and tangential planes. The chirality of the LG01 mode can be manipulated by the pump position to the original point of the laser cavity optical axis.

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.

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.

Mode Division Multiplexing of Helical-Phased LG Modes in Multimode Fiber with Electronic Dispersion Compensation

Mode Division Multiplexing of Helical-Phased LG Modes in Multimode Fiber with Electronic Dispersion Compensation