Higher-order Laguerre-Gauss Modes Research Articles

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.

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.

Transcoder for the spatial and temporal modes of a photon.

Encoding information in light with orbital angular momentum (OAM) enables networks to increase channel capacity significantly. However, light in only the fundamental Gaussian mode is suitable for fibre transmission, and not higher order Laguerre Gaussian modes, which carry OAM. Therefore, building a bridge to interface light with OAM and Gaussian mode time-binning is crucially important. Here, we report the realization of a photonic transcoder, by which light with an arbitrary OAM superposition is experimentally converted into a time-bin Gaussian pulse, and vice versa. Furthermore, we clearly demonstrate that coherence is well conserved and there is no cross-talk between orthogonal modes. This photonic device is simple and can be built with scalable architecture. Our experimental demonstration paves the way towards a mixed optical communication in free-space and optical fibre.

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.

Spatial multimode structure of atom-generated squeezed light

We investigated the spatial distribution of quantum fluctuations in a squeezed vacuum field, generated via polarization self-rotation (PSR) interaction of an ensemble of Rb atoms and a strong near-resonant linearly polarized laser field. We found that the noise suppression is greatly effected by the transverse profile of a spatial mask, placed in both the squeezed field and the local oscillator, as well as its position along the focused beam near the focal point. These observations indicate the spatial multi-mode structure of the squeezed vacuum field. We have developed a theoretical model that describes the generation of higher-order Laguerre-Gauss modes as a result of PSR light-atom interaction. The prediction of this model are in a good qualitative agreement with the experimental measurements.

Higher-order Laguerre-Gauss interferometry for gravitational-wave detectors within situmirror defects compensation

The use of higher-order Laguerre-Gauss modes has been proposed to decrease the influence of thermal noise in future generation gravitational-wave interferometric detectors. The main obstacle for their implementation is the degeneracy of modes with same order, which highly increases the requirements on the mirror defects, beyond the state-of-the-art polishing and coating techniques. In order to increase the mirror surface quality, it is also possible to act in situ, using a thermal source, sent on the mirrors after a proper shaping. In this paper we present the results obtained on a tabletop Fabry-Perot Michelson interferometer illuminated with a LG_(3,3) mode. We show how an incoherent light source can reduce the astigmatism of one of the mirrors, increasing the quality of the beam in one of the Fabry-Perot cavities and then the contrast of the interferometer. The system has the potential to reduce more complex defects and also to be used in future gravitational-wave detectors using conventional Gaussian beams.

Cascade Raman sideband generation and orbital angular momentum relations for paraxial beam modes

In this work, the nonlinear parametric interaction of optical radiation in various transverse modes in a Raman-active medium is investigated both experimentally and theoretically. Verification of the orbital angular momentum algebra (OAM-algebra) [Strohaber et al.,Opt. Lett.37,3411 (2012)] was performed for high-order Laguerre Gaussian modes ℓ>1. It was found that this same algebra also describes the coherent transfer of OAM when Ince-Gaussian modes were used. New theoretical considerations extend the OAM-algebra to even and odd Laguerre Gaussian, and Hermite Gaussian beam modes through a change of basis. The results of this work provide details in the spatiotemporal synthesis of custom broadband pulses of radiation from Raman sideband generation.

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.

Observation and analysis of single and multiple high-order Laguerre-Gaussian beams generated from a hemi-cylindrical cavity with general astigmatism

We experimentally verified that anisotropic Hermite-Gaussian modes can be generated from a hemi-cylindrical laser cavity and can be transformed into high-order Laguerre-Gaussian modes using an extra-cavity cylindrical lens. We further combined the Huygens integral and the ABCD law to clearly demonstrate the transformation along the propagation direction. By controlling the pump offset and the pump size in hemi-cylindrical cavities, we experimentally observed the unique laser patterns that displayed the optical waves related to the coherent superposition of Laguerre-Gaussian modes.

New class of optical beams for large baseline interferometric gravitational wave detectors

A folded resonant Fabry-Perot cavity has the potential to significantly reduce the impact of coating thermal noise on the performance of kilometer scale gravitational wave detectors. When constructed using only spherical mirror surfaces it is possible to utilize the extremely robust $TEM_{00}$ mode optical mode. In this paper we investigate the potential thermal noise improvements that can be achieved for third generation gravitational wave detectors using realistic constraints. Comparing the previously proposed beam configurations such as e.g. higher order Laguerre-Gauss modes, we find that similar or better thermal noise improvement factors can be achieved, while avoiding degeneracy issues associated with those 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.

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.

Experimental test of higher-order Laguerre–Gauss modes in the 10 m Glasgow prototype interferometer

Brownian noise of dielectric mirror coatings is expected to be one of the limiting noise sources, at the peak sensitivity, of next generation ground based interferometric gravitational wave (GW) detectors. The use of higher-order Laguerre–Gauss (LG) beams has been suggested to reduce the effect of coating thermal noise in future generations of gravitational wave detectors. In this paper we describe the first test of interferometry with higher-order LG beams in an environment similar to a full-scale gravitational wave detector. We compare the interferometric performance of higher-order LG modes and the fundamental mode beams, injected into a 10 m long suspended cavity that features a finesse of 612, a value chosen to be typical of future gravitational wave detectors. We found that the expected mode degeneracy of the injected LG3, 3 beam was resolved into a multiple peak structure, and that the cavity length control signal featured several nearby zero crossings. The break up of the mode degeneracy is due to an astigmatism (defined as |Rcy − Rcx|) of 5.25 ± 0.5 cm on one of our cavity mirrors with a radius of curvature (Rc) of 15 m. This observation agrees well with numerical simulations developed with the FINESSE software. We also report on how these higher-order mode beams respond to the misalignment and mode mismatch present in our 10 m cavity. In general we found the LG3, 3 beam to be considerably more susceptible to astigmatism and mode mismatch than a conventional fundamental mode beam. Therefore the potential application of higher-order Laguerre–Gauss beams in future gravitational wave detectors will impose much more stringent requirements on both mode matching and mirror astigmatism.

The effect of mirror surface distortions on higher order Laguerre-Gauss modes

Higher order Laguerre-Gauss (LG) beams have been proposed for use in future generation gravitational wave detectors for their potential to reduce the effects of the thermal noise of the test masses. However, it has been reported that due to the degeneracy of higher order modes using these beams will be extremely challenging. Our aim was to quantify these degeneracy effects. We present a new analytical approximation to compute the coupling between different LG modes, verified with simulation results of realistic arm cavities. This method is applied to Advanced LIGO mirror maps and used to derive requirements for mirrors for the use of the LG33 beam.

Effects of mirror aberrations on Laguerre-Gaussian beams in interferometric gravitational-wave detectors

A fundamental limit to the sensitivity of optical interferometers is imposed by Brownian thermal fluctuations of the mirrors' surfaces. This thermal noise can be reduced by using larger beams which ``average out'' the random fluctuations of the surfaces. It has been proposed previously that wider, higher-order Laguerre-Gaussian modes can be used to exploit this effect. In this paper, we show that susceptibility to spatial imperfections of the mirrors' surfaces limits the effectiveness of this approach in interferometers used for gravitational-wave detection. Possible methods of reducing this susceptibility are also discussed.

High-power Q-switched laser with high-order Laguerre–Gaussian modes: application for extra-cavity harmonic generations

We present a compact efficient scheme for generation of high-order Laguerre–Gaussian TEM p,0 modes in a diode-pumped actively Q-switched Nd:YVO4 laser. The resonator is composed of two plane mirrors with an intracavity concave lens to expand the cavity mode size for generating a high-power Laguerre–Gaussian TEM5,0 mode. We further confirm that the TEM5,0 mode is noticeably superior to the TEM0,0 mode in the processes of second and third harmonic generations.

Field properties and vacuum electron acceleration in a laser beam of high-order Laguerre–Gaussian mode

The electric field intensity distribution and the phase velocity distribution of high-order Laguerre–Gaussian (LG ρℓ) mode laser beams are analyzed. Using three-dimensional test particle simulation, the numerical results of electrons accelerated by LG00, LG40 and LG41 mode laser beams are presented. Compared with the LG00 mode (the fundamental mode) laser beam, low-energy injection electrons can be more favorably accelerated in a high-order LG mode laser beam. Contrary to anticipation, a high-order LG mode laser beam with intense axial electric field distribution is inferior to the LG00 mode in capture acceleration for electrons with high injection energy.

Very high-order pure Laguerre-Gaussian mode selection in a passive Q-switched Nd:YAG laser

An intra-cavity phase element, combined with a passive Q-switch saturable absorber and a suitable intra-cavity aperture, can provide extremely high mode discrimination, so as to obtain laser operation with single, pure, very high order Laguerre-Gaussian mode. With a Nd:YAG laser setup, well controlled and extremely stable Q-switched operation in the degenerate Laguerre-Gaussian TEM04, TEM14, TEM24, TEM34, and TEM44 modes was obtained. The measured output energy per pulse for each of these modes was 5.2mJ, 7.5mJ, 10mJ, 12.5mJ, and 13.7mJ respectively, compared to 2.5mJ for the Gaussian mode without the phase element (more than a five fold increase in output energy). Correcting the phase for these modes, so that all transverse lobes have uniform phase, results in a very bright and narrow central lobe in the far field intensity distribution that can theoretically contain more than 90% of the output energy.