Gaussian Mode Research Articles

Size-invariant twisted optical modes for the efficient generation of higher-dimensional quantum states

Optical vortex beams are profiled as helical wavefronts with a phase singularity carrying an orbital angular momentum (OAM) associated with their spatial distribution. The transverse intensity distribution of a conventional optical vortex has a strong dependence on the carried topological charge. However, perfect optical vortex (POV) beams have their transverse intensity distribution independent of their charge. Such “size-invariant” POV beams have found exciting applications in optical manipulation, imaging, and communication. In this paper, we investigate the use of POV modes in the efficient generation of high-dimensional quantum states of light. We generate heralded single photons carrying OAM using spontaneous parametric downconversion (SPDC) of POV beams. We show that the heralding efficiency of the SPDC single photons generated with a POV pump is greater than that with normal optical vortex beams. The dimensionality of the two-photon OAM states is increased with POV modes in the pump and projective measurements using Bessel–Gaussian vortex modes that give POV, instead of Laguerre–Gaussian modes.

Engineering Entangled Photons for Transmission in Ring-Core Optical Fibers

The capacity of optical communication channels can be increased by space division multiplexing in structured optical fibers. Radial core optical fibers allows for the propagation of twisted light–eigenmodes of orbital angular momentum, which have attracted considerable attention for high-dimensional quantum information. Here we study the generation of entangled photons that are tailor-made for coupling into ring core optical fibers. We show that the coupling of photon pairs produced by parametric down-conversion can be increased by close to a factor of three by pumping the non-linear crystal with a perfect vortex mode with orbital angular momentum ℓ, rather than a gaussian mode. Moreover, the two-photon orbital angular momentum spectrum has a nearly constant shape. This provides an interesting scenario for quantum state engineering, as pumping the crystal with a superposition of perfect vortex modes can be used in conjunction with the mode filtering properties of the ring core fiber to produce simple and interesting quantum states.

Generation and conditional switching of isolated C-points in optical beam output of few-mode fiber

We demonstrate here an experimental observation on generation and conditional switching between π-symmetric isolated C-points such as lemon and star in a few mode optical fiber. This scheme is of potential advantage in switching between lemon and star by controlling either polarization or phase helicities of the vortex modes involved in the formation of singular pattern. A half wave plate and a cylindrical lens are used at the fiber output end for this purpose. These singular patterns can be generated from the fiber through the combination of orthogonally polarized Gaussian and vortex modes co-excited simultaneously by controlling the coupling conditions at the launching end.

Performance Evaluation of a 4 × 20-Gbps OFDM-Based FSO Link Incorporating Hybrid W-MDM Techniques

Free space optics (FSO) has been recognized as a crucial technique to meet the high-bandwidth requirements in future wireless information transmission links. It provides a feasible solution to the last-mile bottleneck problem due to its merits that include high-speed data transportation and secure and low-latency networks. Due to these merits, FSO is a reliable technology for future health-care and biomedical services like the transmission of biomedical sensor signals. But the main limiting factor in the data transmission employing FSO links is adverse atmospheric weather conditions. This research work reports the designing and simulative evaluation of the performance of a high-speed orthogonal frequency division multiplexing–based free space optics link by incorporating wavelength division multiplexing of two independent frequency channels (193.1 THz and 193.2 THz) along with mode division multiplexing of distinct spatial laser Hermite–Gaussian modes (HG01 and HG03). Four independent 20-Gbps quadrature amplitude-modulated data signals are transported simultaneously under different atmospheric weather conditions using the proposed link. Also, the link performance has been investigated for an increasing beam divergence angle.

Investigation on reduction of dross height by analyzing beam intensity distribution in fiber laser cutting

Nowadays, fiber lasers have become a main energy source in laser cutting because of their highly electro-optical conversion efficiency and high beam quality. However, the amount of dross produced by fiber laser cutting is larger than that by CO2 laser cutting, and postprocessing is required to obtain a flat surface without dross, which leads to increasing the processing cost. If fiber laser achieves dross-free cutting of a steel plate, further expansion of cutting applications can be expected. Therefore, in order to achieve further reduction of dross, the influence of beam intensity distribution on dross height was investigated by fiber laser cutting experiments and ray tracing analysis. The laser cutting experiment of steel plate cold commercial with 3.2 mm thickness was carried out by a 3 kW fiber laser with nitrogen assist gas, and a round Gaussian mode of 114 μm spot diameter and a square top-hat mode of 132 μm were used. The square top-hat mode can achieve smaller dross height below 12 μm, which is approximately half of the round Gaussian mode. Ray tracing analysis revealed that the square top-hat mode increased the uniformity of absorbed energy on the cutting front surface, and the more uniform intensity distribution contributed to a small ellipticity of the cutting front shape of the kerf. It was clarified that the shape of the cutting front with a small ellipticity reduced the amount of molten metal ejected from the side of the kerf, which resulted in the reduction of dross height by the fiber laser cutting.

OAM mode-excited surface plasmon resonance for refractive index sensing based on a photonic quasi-crystal fiber

In this paper, a novel, to the best of our knowledge, surface plasmon resonance (SPR) fiber biosensor is theoretically proposed to detect the surrounding refractive index based on a Stampfli-type photonic quasi-crystal fiber with one air hole coated gold thin film. Surface plasmon polaritons (SPPs) at the metal/dielectric interface are excited by the orbital angular momentum (OAM) mode (other than Gaussian mode) that propagates very robustly along the fiber with helical phase, facilitating the energy transformation of OAM mode to SPP mode and then realization of the typical resonant loss peak. The proposed OAM-SPR fiber sensor exhibits a refractive index sensitivity of 4466.5 nm/RIU and a resolution of 2.3 × 1 0 − 5 RIU in a broad refractive index range from 1.36 to 1.435. Numeric results show that both structure parameters of the fiber and thickness of the gold layer influence sensing performance as the phase matching condition varies. This work offers theoretical guidance for the design of an OAM-SPR fiber biosensor and has great potential applications in sensing bio-molecular and bio-chemical liquids.

Properties of spin and orbital angular momenta of light

This paper analyses the algebraic and physical properties of the spin and orbital angular momenta of light in the quantum mechanical framework. The consequences of the fact that these are not angular momenta in the quantum mechanical sense are worked out in mathematical detail. It turns out that the spin part of the angular momentum has continuous eigenvalues. Particular attention is given to the paraxial limit, and to the definition of Laguerre–Gaussian modes for photons as well as classical light fields taking full account of the polarization degree of freedom.

Entangled ripples and twists of light: radial and azimuthal Laguerre–Gaussian mode entanglement

It is well known that photons can carry a spatial structure akin to a ‘twisted’ or ‘rippled’ wavefront. Such structured light fields have sparked significant interest in both classical and quantum physics, with applications ranging from dense communications to light–matter interaction. Harnessing the full advantage of transverse spatial photonic encoding using the Laguerre–Gaussian (LG) basis in the quantum domain requires control over both the azimuthal (twisted) and radial (rippled) components of photons. However, precise measurement of the radial photonic degree-of-freedom has proven to be experimentally challenging primarily due to its transverse amplitude structure. Here we demonstrate the generation and certification of full-field LG entanglement between photons pairs generated by spontaneous parametric down conversion in the telecom regime. By precisely tuning the optical system parameters for state generation and collection, and adopting recently developed techniques for precise spatial mode measurement, we are able to certify fidelities up to 85% and entanglement dimensionalities up to 26 in a 43-dimensional radial and azimuthal LG mode space. Furthermore, we study two-photon quantum correlations between nine LG mode groups, demonstrating a correlation structure related to mode group order and inter-modal cross-talk. In addition, we show how the noise-robustness of high-dimensional entanglement certification can be significantly increased by using measurements in multiple LG mutually unbiased bases. Our work demonstrates the potential offered by the full spatial structure of the two-photon field for enhancing technologies for quantum information processing and communication.

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.

Generation and detection of optical vortices superposition by using interferometer setups

A simple free-space optics recipe for the generation and detection of the optical vortices superposition is demonstrated. For the purpose a doughnut laser beam is produced by the cracked glass plate. To control the vorticity of produced doughnut light, one can deform the cracked plate. For the generation of the optical vortices superposition and determination the vorticity of the produced doughnut light, two simple interferometry setups are employed. The experimental Sagnac interferometry setup for preparing and analysing superpositions of an optical vortex and Gaussian modes is presented. Furthermore, the superpositions of two twisted beam with the opposite topological charge numbers by an experimental Michelson–Sagnac interferometry is proposed. These simple free-space experiments are useful to the application of orbital angular momenta superpositions in the quantum cryptography and the undergraduate educations

High-order femtosecond vortices converted from a tunable high-order Hermite–Gaussian Yb:CALGO laser

Femtosecond optical vortices open a variety of applications, ranging from femtosecond micro-processing to vortex strong-field physics. Thus far, the generation of high-order femtosecond vortices remains a challenge. The 1st to 4th order tunable femtosecond vortices generated by a z-type cavity semiconductor saturable absorber mirror mode-locked Yb:CALGO laser are reported in this study. The anti-reflection coated Yb:CALGO crystal is used as the gain material and is positioned perpendicular to the laser beam to avoid an angle dispersion, which results in multi-transverse-mode running. The astigmatism caused by the tilted curved mirrors is compensated by elevating the folding mirrors adjacent to the curved mirrors. The 1st to 5th order tunable femtosecond Hermite–Gaussian (HGn0) modes are realized by employing the off-axis pumping technique. The mode-locked pulse width is in the range of 220–580 fs for various HG modes. The mode-locked HG modes are converted into femtosecond vortices using a cylindrical-lens mode converter. The work provides a reliable way to generate high-order femtosecond vortex beams.

Rotational Doppler shift from a rotating rod.

This Letter reports on a rotational Doppler effect obtained from a rotating rod illuminated by a fundamental Gaussian laser beam. More specifically, we decompose the transmitted light behind the rotating rod into Laguerre-Gaussian modes and investigate the associated frequency shifts. The main contributing modes correspond to modes having the same rotational symmetry as the rotating object. Furthermore, their shifts equal the topological charge of the beam times the rotational frequency of the object. Potential applications in pattern recognition and rotation identification are then considered.

Enhanced detection techniques of orbital angular momentum states in the classical and quantum regimes

The orbital angular momentum (OAM) of light has been at the center of several classical and quantum applications for imaging, information processing and communication. However, the complex structure inherent in OAM states makes their detection and classification nontrivial in many circumstances. Most of the current detection schemes are based on models of the OAM states built upon the use of Laguerre–Gauss (LG) modes. However, this may not in general be sufficient to capture full information on the generated states. In this paper, we go beyond the LG assumption, and employ hypergeometric-Gaussian (HyGG) modes as the basis states of a refined model that can be used—in certain scenarios—to better tailor OAM detection techniques. We show that enhanced performances in OAM detection are obtained for holographic projection via spatial light modulators in combination with single-mode fibers (SMFs), and for classification techniques based on a machine learning approach. Furthermore, a three-fold enhancement in the SMF coupling efficiency is obtained for the holographic technique, when using the HyGG model with respect to the LG one. This improvement provides a significant boost in the overall efficiency of OAM-encoded single-photon detection systems. Given that most of the experimental works using OAM states are effectively based on the generation of HyGG modes, our findings thus represent a relevant addition to experimental toolboxes for OAM-based protocols in quantum communication, cryptography and simulation.

Transverse mode locking of different frequency-degenerate families based on annular beam pumping.

Optical vortex arrays have been achieved in an end-pumped Nd:YVO4 laser pumped by an annular beam. Spontaneous transverse mode locking of Laguerre-Gaussian modes in different frequency-degenerate families has been obtained by merely adjusting the pump power. A maximum output power of 0.88 W and optical conversion efficiency of 13.6% are achieved for optical vortex arrays. Optical vortex arrays formed in different frequency-degenerate families of Laguerre-Gaussian modes can be actively controlled by the position of the axicon. This work provides a way to research transverse mode locking of Laguerre-Gaussian modes in different frequency-degenerate families based on annular beam pumping.

Modal decomposition of fiber modes based on direct far-field measurements at two different distances with a multi-variable optimization algorithm.

We present a novel method for modal decomposition of a composite beam guided by a large-mode-area fiber by means of direct far-field pattern measurements with a multi-variable optimization algorithm. For reconstructing far-field patterns, we use finite-number bases of Hermite Gaussian modes that can be converted from all the guided modes in the given fiber and exploit a stochastic parallel gradient descent (SPGD)-based multi-variable optimization algorithm equipped with the D4σ technique in order for completing the modal decomposition with compensating the centroid mismatch between the measured and reconstructed beams. We measure the beam intensity profiles at two different distances, which justifies the uniqueness of the solution obtained by the SPGD algorithm. We verify the feasibility and effectiveness of the proposed method both numerically and experimentally. We have found that the fractional error tolerance in terms of the beam intensity overlap could be maintained below 1 × 10-7 and 3.5 × 10-3 in the numerical and experimental demonstrations, respectively. As the modal decomposition is made uniquely and reliably, such a level of the error tolerance could be maintained even for a beam intensity profile measured at a farther distance.

Generation of a mode-tunable optical vortex based on a mirror curvature dynamically controlled Z-shaped resonant cavity.

We report a novel, to the best of our knowledge, mode-tunable optical vortex generation method based on a mirror curvature dynamically controlled Z-shaped resonant cavity, a mode conversion beamline, and a reference laser beamline. By changing the mirror curvature of an intra-cavity deformable mirror (DM) at a certain pumping voltage and current, various Hermite-Gaussian (HG) mode beams were obtained in the Z-shaped resonant cavity of a laser diode pumped Yb:CALGO laser. The vortex beams were realized finally by using an external cavity astigmatism converter. In the experiment, the dynamic tuning of the 1st to 9th order HG mode beams and Laguerre-Gaussian mode vortex beams carrying different orbital angular momenta, ranging from 1ℏ to 9ℏ were achieved by dynamically adjusting the driving voltage of the DM.

Numerical and experimental study of a multimode optical fiber sensor based on Fresnel reflection at the fiber tip for refractive index measurement

This paper presents the numerical and experimental study of a multimode optical fiber (MMF) sensor based on Fresnel reflection at the fiber tip. Considering different modal power distributions (uniform mode distribution, gaussian and equilibrium mode distribution), the effective fraction of the incident light reflected at the interface between the end of the fiber and the surrounding medium is first calculated numerically with a ray model. Even when considering modal power distribution and non-normal incidence influence, simplifying assumptions such as normal incidence hypothesis can be made to facilitate experimental data exploitation, with a maximum error on the deduced medium refractive index of the 10-4 order. A statistical analysis of noise is then made, to study the influence of a random noise between 0.1% and 5% noise level: results show that the approximation error made by using normal incidence formula for a Fresnel sensor based on a MMF is significantly smaller than the repeatability error. These assumptions are then verified experimentally with two experimental setups by measuring the refractive index at 1550 nm of reference solutions (distilled water-isopropanol and distilled water-sodium chloride mixtures) with a Fresnel based on a multimode fiber, and a Fresnel based on single-mode fiber for comparison. Good agreement is found with refractive index values from the literature with a maximum relative difference of only 0.1%, and the maximum experimental uncertainties in this work is 1.1×10-4. Differences between refractive index measured with a Fresnel based on single-mode and multimode fiber are found to be in accordance with values from the statistical study.

Multifunctional All‐Dielectric Metasurfaces for Terahertz Multiplexing

AbstractHermite–Gaussian (HG) beams, corresponding to high‐order transverse modes, reveal a great potential in the space division multiplexing in optical and wireless communications. Higher data rates are made possible by the introduction of multiplexing, which is critical for next‐generation wireless communications working at terahertz frequency. Here, the multifunctional all‐dielectric metasurfaces are studied both theoretically and experimentally to implement terahertz mode and polarization division multiplexing. Terahertz incidence with fundamental Gaussian mode could be converted to high‐order HG modes by the silicon‐based metasurface. More interestingly, phase distributions of the axicons and deflectors are integrated into the mode conversion to reduce the divergence of the output beam and spatially separate each mode. The proposed multifunctional metasurfaces open a new avenue to the potential application of metasurface‐based devices in terahertz communication systems.

Pure modulation and accurate measurement of optical beam's tilt and displacement.

We developed a tilt modulation technique of a laser beam with a wedged crystal. Combined with a phase-compensating crystal, a pure tilt modulation with a wide bandwidth (actually determined by the bandwidth of electro-optic crystals) is realized. By Fourier transformation with a lens, the tilt signal is transformed into displacement. With homodyne detection using a local oscillator of the first-order Hermite-Gauss mode (HG10) and a 4F phase-monitoring system, we measure the displacement and tilt of a laser probe beam. This technique can be used in metrology, such as Newtonian gravitational constant determination and gravitational wave detection, or the calibration of a spatial sensor, such as tilt/displacement sensors.

Relevance of longitudinal fields of paraxial optical vortices

Longitudinal electromagnetic fields generally become comparable with the usually dominant transverse components in strongly focused, non-paraxial beams. For paraxial optical vortex modes it is highlighted here how their angular momentum properties produce longitudinal fields that in general must be accounted for. First-order longitudinal components of quantized Laguerre–Gaussian modes are derived and numerically studied with respect to the paraxial parameter, highlighting light-matter and spin-orbit interactions that stem from the longitudinal fields of paraxial beams in free space. New restrictions are cast on the validity of neglecting longitudinal fields for paraxial optical vortices interacting with atoms, molecules and other nanostructures.