Higher-order Laguerre-Gauss mode generation and interferometry for gravitational wave detectors

Cascaded metasurfaces for high-purity vortex generation

We introduce a new paradigm for generating high-purity vortex beams with metasurfaces. By applying optical neural networks to a system of cascaded phase-only metasurfaces, we demonstrate the efficient generation of high-quality Laguerre-Gaussian (LG) vortex modes. Our approach is based on two metasurfaces where one metasurface redistributes the intensity profile of light in accord with Rayleigh-Sommerfeld diffraction rules, and then the second metasurface matches the required phases for the vortex beams. Consequently, we generate high-purity LGp,l optical modes with record-high Laguerre polynomial orders p = 10 and l = 200, and with the purity in p, l and relative conversion efficiency as 96.71%, 85.47%, and 70.48%, respectively. Our engineered cascaded metasurfaces suppress greatly the backward reflection with a ratio exceeding -17 dB. Such higher-order optical vortices with multiple orthogonal states can revolutionize next-generation optical information processing.

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.

Versatile all-digital transport-of-intensity based wavefront sensor and adaptive optics using a DMD

Measuring and correcting wavefront aberrations is an important process in a wide variety of disciplines, from ophthalmology, laser cutting, and astronomy to free-space communication and microscopy, and always relies on measuring intensities to infer phase. One approach is to use the transport-of-intensity as a means for phase retrieval, exploiting the connection between observed energy flow in optical fields and their wavefronts. Here we present a simple scheme, using a digital micro-mirror device (DMD), to perform angular spectrum propagation and extract the wavefront of optical fields at various wavelengths, dynamically, with high resolution and tuneable sensitivity. We verify the capability of our approach by extracting common Zernike aberrations, turbulent phase screens, and lens phases under static and dynamic conditions at multiple wavelengths and polarizations. We use this setup for adaptive optics, correcting distortion using a second DMD to apply conjugate phase modulation. We observed effective wavefront recovery under a variety of conditions which allowed for convenient real-time adaptive correction in a compact arrangement. Our approach provides an all-digital system that is versatile, cheap, fast, accurate, broadband and polarization invariant.

1645-nm single-frequency vortex laser from an Er:YAG nonplanar ring oscillator

A 1645-nm single-frequency vortex beam with narrow linewidth from an Er:YAG nonplanar ring oscillator (NPRO) using an annular pump beam is demonstrated. The pump beam from a 1532-nm fiber laser is shaped to an annular beam by an axicon. The Er:YAG NPRO generates a 1.96-W single-frequency vortex beam under a pump power of 13 W. The linewidth of the 1645-nm vortex laser is measured as 6 kHz. This work provides a convenient way of single-frequency vortex beam generation.

Mode analyzer for known optical vortices from a spatial light modulator with collinear holography

The optical vortex has already found lots of applications in various domains. Among such applications, the precise and quantitative mode analysis of optical vortices is of great significance. In this work, we experimentally validate a simple method to analyze the mode of an already known optical field with collinear holography based on the phase-shifting technology. Further, we propose a ring interference strategy to improve the accuracy of mode analysis. In the proof-of-concept experiment, the complex amplitude is characterized, and the mode purity is well analyzed. This method has excellent accuracy and rapidity, which can be implemented in micro-manipulation, optical communication, and rotation speed measurement based on the rotating Doppler effect.

Experimentally measuring the mode indices of Laguerre-Gaussian beams by weak measurement

As a special experimental technique, weak measurements extract very little information from the measured system and does not cause the measured state to collapse. When coupling the Laguerre-Gaussian (LG) state with a well-defined pre- and post-selected system of a weak measurement process, there will be an indirect interconnection between the expected value of coordinate operators of the final state and the mode indices of the measured LG state. The mode of the light is impacted very slightly after the weak measurement. Based on this we propose an experiment scheme and have managed to experimentally measure the mode indices of LG beams spanning from l = -6 to l = +6, p = 0 to p = +8 accurately with the final intensity distributions approximatly at their origin.

Interaction of Tungsten tips with Laguerre-Gaussian beams

Interaction of femtosecond laser pulses with metallic tips have been studied extensively and they have proved to be a very good source of ultrashort electron pulses. We present our study of interaction of Laguerre-Gaussian (LG) laser modes with Tungsten tips. We report a change in the order of the interaction for LG beams and the difference in the order of interaction is attributed to ponderomotive shifts in the energy levels corresponding to the enhanced near field intensity supported by numerical simulations.

Controlled generation of vortex and vortex dipole from a Gaussian pumped optical parametric oscillator

We report on direct generation of optical vortices from a continuous-wave (cw), Gaussian beam pumped doubly resonating optical parametric oscillator (DRO). Using a 30-mm long MgO doped periodically poled lithium tantalate (MgO:sPPLT) crystal based DRO, pumped in the green by a frequency-doubled Yb-fiber laser in Gaussian spatial profile we have generated signal and idler beams in vortex mode of order, l = 1, tunable across 970-1178 nm. Controlling the overlap between the Gaussian pump beam with the fundamental cavity mode of the resonant signal and idler beams of the DRO through the tilt of the pump beam and/or the cavity mirror in transverse plane, we have generated both signal and idler beams in vortex and vortex dipole spatial profiles. Using the theoretical formalism for the vortex beam generation through the superposition of two Gaussian beams we have numerically calculated the spatial profile of the generated beam in close agreement with our experiment results. The generic experimental scheme can be used to generate optical vortex across the electromagnetic spectrum and in all time scales (cw to ultrafast) using suitable OPO.

Spatially and spectrally resolved orbital angular momentum interactions in plasmonic vortex generators

Understanding the near-field electromagnetic interactions that produce optical orbital angular momentum (OAM) is crucial for integrating twisted light into nanotechnology. Here, we examine the cathodoluminescence (CL) of plasmonic vortices carrying OAM generated in spiral nanostructures. The nanospiral geometry defines a photonic local density of states that is sampled by the electron probe in a scanning transmission electron microscope (STEM), thus accessing the optical response of the plasmonic vortex with high spatial and spectral resolution. We map the full spectral dispersion of the plasmonic vortex in spiral structures designed to yield increasing topological charge. Additionally, we fabricate nested nanospirals and demonstrate that OAM from one nanospiral can be coupled to the nested nanospiral, resulting in enhanced luminescence in concentric spirals of like handedness with respect to concentric spirals of opposite handedness. The results illustrate the potential for generating and coupling plasmonic vortices in chiral nanostructures for sensitive detection and manipulation of optical OAM.

Goos-Hänchen and Imbert-Fedorov shifts of higher-order Laguerre-Gaussian beams reflected from a dielectric slab

We consider reflection of the Laguerre-Gaussian light beams by a dielectric slab. In view of the unified operator approach, the higher-order Laguerre-Gaussian beams represent a parametric family with the transverse beam profile given by an arbitrary generating parameter. Relying on the Fourier expansion in the focal plane of the beam, we compute the Goos-Hänchen and the Imbert-Fedorov shifts for light beams with non-zero order and azimuthal index. It is demonstrated that both shifts exhibit resonant behavior as functions of the angle of incidence due to the interference between the waves reflected from the upper and lower interfaces. The centroid shifts strongly depend on the order and azimuthal index of the beam. Most interestingly, it is found that the generating parameter of the higher-order beam families strongly affects the shifts. Thus, reshaping of the incident wavefront with fixed order and azimuthal index changes the linear Goos-Hänchen shift up to one half of the beam radius, both negative and positive.

Thermal-noise-limited higher-order mode locking of a reference cavity

Higher-order mode locking has been proposed to reduce the thermal noise limit of reference cavities. By locking a laser to the HG₀₂ mode of a 10-cm long all ultra-low expansion (ULE) cavity and measuring its performance with the three-cornered-hat method among three independently stabilized lasers, we demonstrate a thermal-noise-limited performance of a fractional frequency instability of 4.9×10^-16. The results match the theoretical models with higher-order optical modes. The achieved laser instability improves the all ULE short cavity results to a new low level.

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.

Higher-order Laguerre-Gauss modes in (non-) planar four-mirror cavities for future gravitational wave detectors

One of the limiting noise sources in the current generation of gravitational wave detectors, such as the advanced laser interferometer gravitational wave observatory (aLIGO), is the thermal noise in the interferometer's test mass coatings. One proposed method to reduce the coupling of this noise source to the gravitational wave readout is using a laser beam in the higher-order spatial LG₃₃ mode within the interferometer. Here we show that the current four-mirror cavities of aLIGO are not compatible with Laguerre-Gauss modes due to astigmatism. A non-degeneracy of modes of the same order could be observed in experiment and simulation. We demonstrate that a non-planar cavity could be used instead as it compensates for the astigmatism and transmits the LG₃₃ mode undisturbed.

Experimental study of diode pumped rubidium amplifier for single higher-order Laguerre-Gaussian modes

In this paper, we have set up a diode laser pumped rubidium amplifier for higher-order Laguerre-Gauss (LG) modes. We experimentally realized amplification of higher-order LG modes including helical and sinusoidal LG₀₃, LG₁₃, LG₂₃, and LG₃₃ modes with their high purity held. This novel scheme of generating high-purity higher-order LG beams at high laser power is preferred to the second-generation gravitational wave interferometers. To the best of our knowledge, it is the first time this scheme is formulated.

Meta-q-plate for complex beam shaping

Optical beam shaping plays a key role in optics and photonics. In this work, meta-q-plate featured by arbitrarily space-variant optical axes is proposed and demonstrated via liquid crystal photoalignment based on a polarization-sensitive alignment agent and a dynamic micro-lithography system. Meta-q-plates with multiple-, azimuthally/radially variant topological charges and initial azimuthal angles are fabricated. Accordingly, complex beams with elliptical, asymmetrical, multi-ringed and hurricane transverse profiles are generated, making the manipulation of optical vortex up to an unprecedented flexibility. The evolution, handedness and Michelson interferogram of the hurricane one are theoretically analysed and experimentally verified. The design facilitates the manipulation of polarization and spatial degrees of freedom of light in a point-to-point manner. The realization of meta-q-plate drastically enhances the capability of beam shaping and may pave a bright way towards optical manipulations, OAM based informatics, quantum optics and other fields.

Single-mode squeezing in arbitrary spatial modes

As the generation of squeezed states of light has become a standard technique in laboratories, attention is increasingly directed towards adapting the optical parameters of squeezed beams to the specific requirements of individual applications. It is known that imaging, metrology, and quantum information may benefit from using squeezed light with a tailored transverse spatial mode. However, experiments have so far been limited to generating only a few squeezed spatial modes within a given setup. Here, we present the generation of single-mode squeezing in Laguerre-Gauss and Bessel-Gauss modes, as well as an arbitrary intensity pattern, all from a single setup using a spatial light modulator (SLM). The degree of squeezing obtained is limited mainly by the initial squeezing and diffractive losses introduced by the SLM, while no excess noise from the SLM is detectable at the measured sideband. The experiment illustrates the single-mode concept in quantum optics and demonstrates the viability of current SLMs as flexible tools for the spatial reshaping of squeezed light.

Laguerre-Gauss beams versus Bessel beams showdown: peer comparison

We present for the first time a comparison under similar circumstances between Laguerre-Gauss beams (LGBs) and Bessel beams (BB), and show that the former can be a better option for many applications in which BBs are currently used. By solving the Laguerre-Gauss differential equation in the asymptotic limit of a large radial index, we find the parameters to perform a peer comparison, showing that LGBs can propagate quasi-nondiffracting beams within the same region of space where the corresponding BBs do. We also demonstrate that LGBs, which have the property of self-healing, are more robust in the sense that they can propagate further than BBs under similar initial conditions.

Reflective coating optimization for interferometric detectors of gravitational waves

Brownian fluctuations in the highly reflective test-mass coatings are the dominant noise source, in a frequency band from a few tens to a few hundreds Hz, for Earth-bound detectors of Gravitational Waves. Minimizing such noise is mandatory to increase the visibility distance of these instruments, and eventually reach their quantum-limited sensitivity. Several strategies exist to achieve this goal. Layer thickness and material properties optimization have been proposed and effectively implemented, and are reviewed in this paper, together with other, so far less well developed, options. The former is the simplest option, yielding a sensible noise reduction with limited technological challenges; the latter is more technologically demanding, but is needed for future (cryogenic) detectors.

Generation of high-order Laguerre-Gaussian modes by means of spiral phase plates

Spiral phase plates for the generation of Laguerre-Gaussian (LG) beam with non-null radial index were designed and fabricated by electron beam lithography on polymethylmethacrylate over glass substrates. The optical response of these phase optical elements was theoretically considered and experimentally measured, and the purity of the experimental beams was investigated in terms of LG modes contributions. The far-field intensity pattern was compared with theoretical models and numerical simulations, whereas interferometric analyses confirmed the expected phase features of the generated beams. The high quality of the output beams confirms the applicability of these phase plates for the generation of high-order LG beams.

The generation of higher-order Laguerre-Gauss optical beams for high-precision interferometry

Thermal noise in high-reflectivity mirrors is a major impediment for several types of high-precision interferometric experiments that aim to reach the standard quantum limit or to cool mechanical systems to their quantum ground state. This is for example the case of future gravitational wave observatories, whose sensitivity to gravitational wave signals is expected to be limited in the most sensitive frequency band, by atomic vibration of their mirror masses. One promising approach being pursued to overcome this limitation is to employ higher-order Laguerre-Gauss (LG) optical beams in place of the conventionally used fundamental mode. Owing to their more homogeneous light intensity distribution these beams average more effectively over the thermally driven fluctuations of the mirror surface, which in turn reduces the uncertainty in the mirror position sensed by the laser light.

We demonstrate a promising method to generate higher-order LG beams by shaping a fundamental Gaussian beam with the help of diffractive optical elements. We show that with conventional sensing and control techniques that are known for stabilizing fundamental laser beams, higher-order LG modes can be purified and stabilized just as well at a comparably high level. A set of diagnostic tools allows us to control and tailor the properties of generated LG beams. This enabled us to produce an LG beam with the highest purity reported to date. The demonstrated compatibility of higher-order LG modes with standard interferometry techniques and with the use of standard spherical optics makes them an ideal candidate for application in a future generation of high-precision interferometry.

Generation of high-purity higher-order Laguerre-Gauss beams at high laser power

We have investigated the generation of highly pure higher-order Laguerre-Gauss (LG) beams at high laser power of order 100 W, the same regime that will be used by second-generation gravitational wave interferometers such as Advanced LIGO. We report on the generation of a helical-type LG33 mode with a purity of order 97% at a power of 83 W, the highest power ever reported in literature for a higher-order LG mode. This is a fundamental step in proving technical readiness for use of LG beams in gravitational wave interferometers of future generations.

Novel vortex generator and mode converter for electron beams

A mode converter for electron vortex beams is described. Numerical simulations, confirmed by experiment, show that the converter transforms a vortex beam with a topological charge m=±1 into beams closely resembling Hermite-Gaussian HG(10) and HG(01) modes. The converter can be used as a mode discriminator or filter for electron vortex beams. Combining the converter with a phase plate turns a plane wave into modes with topological charge m=±1. This combination serves as a generator of electron vortex beams of high brilliance.

Weak measurements with orbital-angular-momentum pointer states

Weak measurements are a unique tool for accessing information about weakly interacting quantum systems with minimal back action. Joint weak measurements of single-particle operators with pointer states characterized by a two-dimensional Gaussian distribution can provide, in turn, key information about quantum correlations that can be relevant for quantum information applications. Here we demonstrate that by employing two-dimensional pointer states endowed with orbital angular momentum (OAM), it is possible to extract weak values of the higher order moments of single-particle operators, an inaccessible quantity with Gaussian pointer states only. We provide a specific example that illustrates the advantages of our method both in terms of signal enhancement and information retrieval.

Electro-optically generating and controlling right- and left-handed circularly polarized multiring modes of light beams

We propose a simple method for generating and controlling right- and left-handed circularly polarized (RHP and LHP) multiring modes of light beams by means of Pockels effect in a single strontium barium niobate (SBN) crystal. The numerical results show that an LHP Laguerre-Gaussian LG(0l) beam, propagating along the optical axis of the crystal, will partly turn into an RHP vortex light field of order l+2. Moreover, a pair of the LHP and RHP components of the output light field is LG-like modes sharing an identically radial index, which is electro-optically controllable. The power ratio between these two components depends on the applied electric field and the mode of input beam.

Radial mode dependence of optical beam shifts

It is known that orbital angular momentum (OAM) couples the Goos-Hänchen and Imbert-Fedorov shifts. Here, we present the first study of these shifts when the OAM-endowed LG(ℓ,p) beams have higher-order radial mode index (p>0). We show theoretically and experimentally that the angular shifts are enhanced by p while the positional shifts are not.

Fraunhofer diffraction of light with orbital angular momentum by a slit

We study the Fraunhofer diffraction problem while taking into account the orbital angular momentum of light. In this case, the phase singularity of the light beam is incident on the slit in two different cases: in one, it is incident slightly above the slit, and in the other it is centered on the slit. We observed that the symmetry and the fringe formation in the interference pattern strongly depend on the amount of orbital angular momentum and the slit position in relation to the beam.

Analysis and improvement of Laguerre-Gaussian beam position estimation using quadrant detectors

Laguerre-Gaussian beams have become increasingly important in areas like optical manipulation and quantum communications. A good understanding of the accuracy and sensitivity of their displacement measurements are required for these applications. In this Letter, we present a method to analyze and compare the performance of these measurements, and an estimation technique is proposed to improve their measurement accuracies. The effectiveness of our methods is verified by simulation studies.

Nonlinear generation of a neat semi-Gaussian laser beam with a transversely varying periodically-poled LiTaO3 crystal

We experimentally demonstrate a compact, all-solid-state 532 nm semi-Gaussian laser beam (SGB) source based on a 1064 nm laser and a transversely varying periodically-poled LiTaO3 (TPPLT) crystal as the laser beam shaper as well as the nonlinear frequency converter. We have used the designed TPPLT crystal to obtain a neat 532nm SGB with the quality of QSGB=1:17.5 by a single-pass second harmonic generation. The dependence of the generated SGB quality on the designed TPPLT parameter and the potential applications of the neat SGB are also discussed.

Quadrant detector calibration for vortex beams

This Letter reports an experimental and theoretical study of the response of a quadrant detector (QD) to an incident vortex beam, specifically a Laguerre-Gaussian (LG) beam. We have found that the LG beam response depends on the vorticity index ℓ. We compare LG beams with hard-ringed beams and find that at higher ℓ values, the QD response to LG beams can be approximated by its response to hard-ringed beams. Our findings are important in view of the increasing interest in optical vortex beams.