High-order Hermite-Gaussian Modes Research Articles

Experimental Verification of the Gouy Phase for Higher-Order Hermite-Gaussian Beams

The Gouy phase is related to the axial phase shift experienced by any focused light beam with respect to a reference plane wave when passing through its focus. Generally, the Gouy phase ΦG for a higher-order Hermite-Gaussian (HG) beam is this for the fundamental Gaussian beam multiplied by a factor, which is the sum of the mode indices of the HG beam plus unity. Although this result is a paradigm in optics, we are not aware of its experimental verification. In this paper, we present experimental results obtained with a single-lens interferometer for higher-order HG modes generated using spatial light modulator. The retrieved Gouy phase ΦG is found in a very good quantitative agreement with the mentioned theoretical result.

High-power vortex beams generated from a Yb:YAG thin-disk laser with spot-defect mirrors

We report the generation of high-power and high-order vortex beams based on a Yb:YAG thin-disk laser oscillator with a spot-defect mirror. High-quality vortex beams were directly emitted by the oscillator with an output power of 80 W, which is the highest output power of any vortex laser oscillator. Tunable high-order Hermite-Gaussian modes from HG1,1 to HG5,1 were also generated, and subsequently converted to Laguerre-Gaussian beams by a cylindrical-lens mode converter. The vortex characteristics of the output were confirmed with a Mach-Zehnder interferometer. This work demonstrates an effective way to generate high-quality, high-power and high-order optical vortex beams.

High-power laser beam in higher-order Hermite–Gaussian modes

The sensitivities of current gravitational-wave detectors are limited around signal frequencies of 100 Hz by mirror thermal noise. One proposed option to reduce this thermal noise is to operate the detectors in a higher-order spatial laser mode. This operation would require a high-power laser input beam in such a spatial mode. Here, we discuss the generation of the Hermite–Gaussian modes HG2,2, HG3,3, and HG4,4 using one water-cooled spatial light modulator (SLM) at a continuous-wave optical input power of up to 85 W. We report unprecedented conversion efficiencies for a single SLM of about 43%, 42%, and 41%, respectively, and demonstrate that the SLM operation is robust against the high laser power. This is an important step toward the implementation of higher-order laser modes in future gravitational-wave detectors.

10dB Quantum-Enhanced Michelson Interferometer with Balanced Homodyne Detection.

Future generations of gravitational-wave detectors (GWD) are targeting an effective quantum noise reduction of 10dB via the application of squeezed states of light. In the last joint observation run O3, the advanced large-scale GWDs LIGO and Virgo already used the squeezing technology, albeit with a moderate efficiency. Here, we report on the first successful 10dB sensitivity enhancement of a shot-noise limited tabletop Michelson interferometer via squeezed light in the fundamental Gaussian laser mode, where we also implement the balanced homodyne detection scheme that is planned for the third GWD generation. In addition, we achieved a similarly strong quantum noise reduction when the interferometer was operated in higher-order Hermite-Gaussian modes, which are discussed for the GWD thermal noise mitigation. Our results are an important step toward the targeted quantum noise level in future GWDs and, moreover, represent significant progress in the application of nonclassical states in higher-order modes for interferometry, increased spatial resolution, and multichannel sensing.

Generation of Higher-Order Hermite–Gaussian Modes via Cascaded Phase-Only Spatial Light Modulators

The spatial distribution of higher-order Hermite–Gaussian (HG) modes is more complicated than the fundamental mode, and the characteristics of different modes and their orthogonal characteristics have essential applications in the fields of measurement, imaging, and large-capacity communications. The main issue in future applications is how to efficiently generate higher-order HG modes. The spatial light modulator has high spatial resolution and excellent maneuverability, so it is a simple and effective way to generate higher-order HG modes. Here, the efficient generation of higher-order HG modes via cascaded spatial light modulators was experimentally investigated. For the HG90 mode, the conversion efficiency is 61%. The method with high conversion efficiency has promising application potentials in biophotonics, laser physics, and quantum information.

Observation of Squeezed States of Light in Higher-Order Hermite-Gaussian Modes with a Quantum Noise Reduction of up to 10dB.

Mirror thermal noise will be a main limitation for the sensitivities of the next-generation ground-based gravitational-wave detectors (Einstein Telescope and Cosmic Explorer) at signal frequencies around 100Hz. Using a higher-order spatial laser mode instead of the fundamental mode is one proposed method to further mitigate mirror thermal noise. In the current detectors, quantum noise is successfully reduced by the injection of squeezed vacuum states. The operation in a higher-order mode would then require the efficient generation of squeezed vacuum states in this mode to maintain a high quantum noise reduction. In our setup, we generate continuous-wave squeezed states at a wavelength of 1064nm in the fundamental and three higher-order Hermite-Gaussian modes up to a mode order of 6 using a type-I optical parametric amplifier. We present a significant milestone with a quantum noise reduction of up to 10dB at a measurement frequency of 4MHz in the higher-order modes and pave the way for their usage in future gravitational-wave detectors as well as in other quantum noise limited experiments.

Index-Tunable Structured-Light Beams from a Laser with an Intracavity Astigmatic Mode Converter

Structured-light lasers are highly topical due to not only their ability to tailor customized distribution of intensity, phase, orbital angular momentum (OAM), and other optical properties, but also the compact and simple at-the-source generation scheme. Here we propose a form of structured-light laser, intracavity mode convertor laser, with the ability to generate two-dimensional (2D) tunable high-order Hermite-Gaussian (HG) modes with a large indice range (up to 15). The mode convertor constituted by two cylindrical lenses is always used for external OAM conversion, but here we show that it can be inserted into a laser cavity as an intracavity element for symmetry-breaking control, which we also demonstrate with a complete matrix optics theory. The generated 2D HG modes can also be converted into Laguerre-Gaussian (LG) vortex beams with both tunable OAM and radial momentum. Moreover, we also show the ability to directly generate vortex beam from our laser cavity. Our approach meets the urgent necessity for a practical laser device for more versatile light, providing more alternative parametric space for structure control and fostering extended applications.

Dual-wavelength vortex beam with high stability in a diode-pumped Yb:CaGdAlO4 laser

We present a stable dual-wavelength vortex beam carrying orbital angular momentum (OAM) with two spectral peaks separated by a few terahertz in a diode-pumped Yb:CaGdAlO4 (CALGO) laser. The dual-wavelength spectrum is controlled by the pump power and off-axis loss in a laser resonator, arising from the broad emission bandwidth of Yb:CALGO. The OAM beam is obtained by a pair of cylindrical lenses serving as a convertor for high-order Hermite–Gaussian modes. The stability is verified by the fact that a OAM beam with two spectral peaks at 1046.1 nm and 1057.2 nm (3.01 THz interval) can steadily operate for more than 3 h. It has great potential for scaling the application of OAM beams in terahertz spectroscopy, high-resolution interferometry, and so on.

Wavelength-tunable Hermite-Gaussian modes and an orbital-angular-momentum-tunable vortex beam in a dual-off-axis pumped Yb:CALGO laser.

A dual-off-axis pumping scheme is presented to generate wavelength-tunable high-order Hermite-Gaussian (HG) modes in Yb:CaGdAlO4 lasers. The mode and wavelength can be actively controlled by the off-axis displacements and pump power. The purities of the output HG modes are quantified by intensity distributions and the measured M2 values. The highest order reaches m=15 for stable HGm,0 mode, and wavelength-tunable width is about 10nm. Moreover, through externally converting the HGm,0 modes, the vortex beams carrying orbital angular momentum (OAM) with a large OAM-tunable range from ±1ℏ to ±15ℏ are produced. This work is effective for largely scaling the spectral and OAM tunable ranges of optical vortex beams.

Control of ultrafast plasmon pulses by spatiotemporally phase-shaped laser pulses

We numerically demonstrate that spatially and temporally phase-shaped ultrafast laser pulses can spatiotemporally control ultrafast plasmon pulses generated at metal nanostructures. Excitation laser pulses designed by the superposition of high-order Hermite–Gaussian modes can localize the plasmon excitation at desired areas in nanostructures, and at the same time the temporal plasmon evolution is determined by the excitation pulse shape and the local plasmon response function. We numerically demonstrate this control scheme for local plasmons at the Au nanostructures and a surface plasmon polariton waveguide.

A Cr4+:YAG passively Q-switched Nd:YVO4 microchip laser for controllable high-order Hermite–Gaussian modes

A nanosecond, high peak power, passively Q-switched laser for controllable Hermite–Gaussian (HG) modes has been achieved by manipulating the saturated inversion population inside the gain medium. The stable HG modes are generated in a Cr4+:YAG passively Q-switched Nd:YVO4 microchip laser by applying a tilted pump beam. The asymmetrical saturated inversion population distribution inside the Nd:YVO4 crystal for desirable HG modes is manipulated by choosing the proper pump beam diameter and varying pump power. A HG9,8 mode passively Q-switched Nd:YVO4 microchip laser with average output power of 265 mW has been obtained. Laser pulses with a pulse width of 7.3 ns and peak power of over 1.7 kW working at 21 kHz have been generated in the passively Q-switched Nd:YVO4 microchip laser.

Exploring transverse pattern formation in a dual-polarization self-mode-locked monolithic Yb: KGW laser and generating a 25-GHz sub-picosecond vortex beam via gain competition.

Formation of transverse modes in a dual-polarization self-mode-locked monolithic Yb: KGW laser under high-power pumping is thoroughly explored. It is experimentally observed that the polarization-resolved transverse patterns are considerably affected by the pump location in the transverse plane of the gain medium. In contrast, the longitudinal self-mode-locking is nearly undisturbed by the pump position, even under the high-power pumping. Under central pumping, a vortex beam of the Laguerre-Gaussian LGp,l mode with p = 1 and l = 1 can be efficiently generated through the process of the gain competition with a sub-picosecond pulse train at 25.3 GHz and the output power can be up to 1.45 W at a pump power of 10.0 W. Under off-center pumping, the symmetry breaking causes the transverse patterns to be dominated by the high-order Hermite-Gaussian modes. Numerical analyses are further performed to manifest the symmetry breaking induced by the off-center pumping.

Shaping of light beams by 3D direct laser writing on facets of nonlinear crystals.

We demonstrate experimentally spatial-mode conversions of light beams generated in a quadratic nonlinear process by micron-scale structures placed on the facets of nonlinear crystals. These structures were printed on the crystal facets using a three-dimensional (3D) direct laser writing system. The functional structures were designed to modify the phase of the beam at specific wavelengths, thereby enabling conversion of a fundamental Gaussian laser beam into different high-order Hermite-Gaussian modes, Laguerre-Gaussian modes, and zeroth-order Bessel beams of the second harmonic. This facet functionalization opens exciting new opportunities for robust and compact beam shaping in a nonlinear interaction without compromising the conversion efficiency.

Generation of Higher Order Vortex Beams From a YVO<sub>4</sub>/Nd:YVO<sub>4</sub> Self-Raman Laser via Off-Axis Pumping With Mode Converter

The generation of high-order Hermite-Gaussian (HG) beams at the Stokes wavelength in a YVO4 /Nd:YVO4 self- Raman laser with off-axis pumping is demonstrated. The high- order vortex beams at the Stokes field are successfully created by transforming these HG modes via an extra-cavity mode converter. The stimulated Raman scattering (SRS) threshold pump power for the diode-end-pumped laser is theoretically analyzed to verify the feasibility of generating high-order HG modes by off-axis pump- ing. At a pump power of 18.6 W, the SRS output powers can be higher than 1.0 W for the HG modes from TEM0 ,0 to TEM3 ,0 . Under the same pump power, the maximum order can be up to TEM 28 ,0 . Index Terms—Optical vortices, Raman scattering, diode pump- ing, Beam transformation.

Anomalous lasing of high-speed 850 nm InGaAlAs oxide-confined vertical-cavity surface-emitting lasers with a large negative gain-to-cavity wavelength detuning

The impact of a large negative quantum well gain-to-cavity etalon wavelength detuning on the static and dynamic characteristics of 850 nm InGaAlAs high-speed oxide-confined vertical-cavity surface-emitting lasers (VCSELs) was investigated. Three distinct lasing regimes were revealed in large square aperture (≥7 μm per side) devices with large detuning including: (1) an anomalous lasing via higher order Hermite–Gaussian modes at low forward bias current; (2) lasing via the lowest order Hermite–Gaussian modes at high bias current; and (3) simultaneous lasing via both types of transverse modes at intermediate bias currents. In contrast to conventional multimode VCSELs a two-resonance modulation response was observed for the case of co-lasing via multiple transverse modes with high spectral separation. The reduction in the oxide aperture area resulted in classical lasing via the lowest order modes with a conventional single-resonance frequency response.

Physics of elliptical reflectors at large reflection and divergence angles II: Analysis of optical beam distortions in integrated ultra-large-angle elliptical curved reflectors

In this work, we study the behavior of elliptical reflectors in nanophotonic integrated circuits in the context of two-dimensional multimode Gaussian beam. We show that the transformation of the beam profile at the input/output waveguide mouths, and the transformation of the beam profile at the reflector can be described in terms of 2D Hermite-Gaussian (HG) beam modes under first order approximation (FOA), referred to as HG-FOA. Due to the wavelength-scale waveguides in nanophotonic integrated circuits, the beams incident on the elliptical reflector have large diffraction angle which will result in asymmetric amplitude distortion upon non-normal reflection even for ideal elliptical reflecting surfaces. The amplitude distortion can be illustrated in the oscillation of the peaks of the reflected beam profiles around the propagation axis of the reflected beam. The amplitude distortion can also be shown by the deterioration in the coupling efficiency from the input waveguide to the output waveguide due to the excitation of higher order HG modes during the reflection. These two observations can both be explained by the HG-FOA method and are verified with Finite-Difference Time-Domain (FDTD) method. Moreover, we show that the coupling loss from the input waveguide to the output waveguide due to the higher order modes excited can be eliminated via insertion of a second reflector. Two specific arrangement of the second reflector are discussed and verified by the FDTD simulation.

Generation of high-order Hermite-Gaussian modes in end-pumped solid-state lasers for square vortex array laser beam generation

This study reports the first systematic approach to the excitation of all high-order Hermite-Gaussian modes (HGMs) in end-pumped solid-state lasers. This study uses a metal-wire-inserted laser resonator accompanied with the "off axis pumping" approach. This study presents numerical analysis of the excitation of HGMs in end-pumped solid-state lasers and experimentally generated HGM patterns. This study also experimentally demonstrates the generation of an square vortex array laser beams by passing specific high-order HGMs (HGn,n + 1 or HGn + 1,n modes) through a Dove prism-embedded unbalanced Mach-Zehnder interferometer [Optics Express 16, 19934-19949]. The resulting square vortex array laser beams with embedded vortexes aligned in a square array can be applied to multi-spot dark optical traps in the future.

Comment on “Field structure and electron acceleration in a laser beam of a high-order Hermite–Gaussian mode” [J. Appl. Phys. 101, 083113 (2007)

Wang et al. [J. Appl. Phys. 101, 083113 (2007)] investigated vacuum electron acceleration by high-order Hermite–Gaussian laser beams. However, we reveal that some of their explanations for their simulation results are not reasonable. We investigate their simulation in detail and discover that the injection momentum distributions in the longitudinal and transverse directions play an important role in inducing the valley that appears in the plot of the ejection energy as a function of the injection angle.

Simple annular-beam generator with a laser-diode-pumped axially off-set power build-up cavity

We have developed a novel, compact-mode selective annular-beam generator that employs a laser-diode (LD)-pumped, passively locked power build-up cavity (PBC). The PBC functions as a flexible and compact light source that is capable of producing TEM 0n high-order Hermite-Gaussian (HG) beams. The generated HG beams can then be converted to LG modes, particularly to annular-beams, using two cylindrical lenses. The system was theoretically studied and a mode-matching condition was derived. The tailoring position of the active semiconductor laser medium relative to the external cavity of the PBC enabled the production of single high-order HG modes. The optimum position was calculated by model calculations of the mode-coupling efficiency. The desired TEM 0n modes of HG beams were generated by translating the axial position of the external cavity of the PBC in increments of ∼100 μm relative to the LD emission surface. High quality TEM 01 to TEM 015 of the HG beams and their conversion to the desired LG modes having powers of the order of 1 mW was successfully demonstrated. This system is suitable for optical tweezers.

Field structure and electron acceleration in a laser beam of a high-order Hermite-Gaussian mode

We analyze the axial electric field intensity distribution and the phase velocity distribution of high-order Hermite-Gaussian (HG) mode laser beams. Using a three-dimensional test particle simulation, the numerical results of electrons accelerated by Hermite-Gaussian (0,0), and (3,0) mode laser beams are presented. It is established that electrons can be more favorably captured and accelerated in an odd high-order Hermite-Gaussian mode laser beam.