Gaussian Laser Modes Research Articles

Conical refraction output from a Nd:YVO4 laser with an intracavity conerefringent element.

A conical refraction (CR) laser based on an a-cut Nd:YVO4 laser was demonstrated. By using a KGW crystal as a CR element, a typical laser with a Gaussian intensity output profile was transformed into a laser with conically refracted output. The CR laser delivered 220mW of output power for 500mW of pump power. The separation of the laser gain medium and the CR element reduced the complexity of the pumping scheme, and resulted in the generation of well-behaved CR laser beams with outstanding quality. The presented approach is power scalable and offers a unique possibility of studying the transformation of a Gaussian laser mode into a conically refracted one in a laser cavity.

Effects of Cr4+ ions on forming Ince–Gaussian modes in passively Q-switched microchip solid-state lasers

The effects of Cr4+ ions on forming Ince–Gaussian (IG) laser modes in a tilted pumped Cr4+:YAG passively Q-switched (PQS) Nd:YAG microchip lasers has been studied experimentally and theoretically. The formation of Cr4+-ion domains in Cr4+:YAG crystal has been proposed based on the spatial distribution of Cr4+ ions in Cr4+:YAG crystal. The spatial modulation effect of Cr4+-ion domains on selecting a transverse mode has been investigated based on their periodic distribution and nonlinear absorption of the Cr4+ saturable absorber. The formation of IG modes in the Nd:YAG/Cr4+:YAG PQS microchip laser under tilted pumping has been demonstrated theoretically with the spatial modulation of the Cr4+-ion domains in Cr4+:YAG crystal and the inversion population distribution, by taking account of the thermal lens effect. The IG modes selected theoretically in the Nd:YAG/Cr4+:YAG PQS microchip laser are in good agreement with experimentally obtained IG modes. This work provides a theoretical model of the selection of IG modes with Cr4+-ion domains in a tilted beam pumped Nd:YAG/Cr4+:YAG PQS microchip laser to produce efficient, stable and controllable IG laser modes.

Generating laser transverse modes analogous to quantum Green’s functions of two-dimensional harmonic oscillators

We theoretically analyzed the relationship between quantum Green’s functions of two-dimensional harmonic oscillators and radial-order Laguerre–Gaussian laser modes of spherical resonators. By using a nearly hemispherical resonator and a tight focusing in the end-pumped solid-state laser, we successfully generated various laser transverse modes analogous to quantum Green’s functions. We further experimentally and numerically verified that the transverse order associated with quantum Green’s functions is noticeably raised with increasing the pump power induced by the thermal effect. More importantly, the high lasing efficiency and the salient structure enable the present laser source to be used in exploring the light–matter interaction.

Optimization of electromagnetically induced transparency by changing the radial size of Laguerre–Gaussian laser modes

We demonstrate electromagnetically induced transparency (EIT) in ultracold Rb87 with the control laser in a Laguerre–Gaussian mode and the probe laser in a Gaussian mode. The effects on EIT transmission spectra due to varying control mode sizes are explored and optimized. The narrowest EIT features that still exhibit large signal contrast occur when the control and probe laser have equivalent waists, despite the differences in the radial intensity profiles of the probe and control beams.

Development of optical grade (TbxY1−x)3Al5O12 ceramics as Faraday rotator material

AbstractSuper full dense (TbxY1−x)3Al5O12 (x=0.5‐1.0) ceramics with optical grade (pore‐free) were successfully produced by solid‐state reaction between Tb4O7 and Al2O3 raw powders. Transparent sintered bodies were obtained by sintering at 1720°C for 5 hours in vacuum furnace. By additional HIP treatment, optical scattering centers were effectively removed, and finally the optical quality of the sintered bodies was improved to optical grade. Optical loss of the obtained samples at 1064 nm was approximately 0.1%/cm, and optically inhomogeneous parts were not observed inside the materials. Gaussian mode laser beam quality was not deteriorated after passing through the sample. Transmitted wavefront distortion inspected by interferometry was as excellent as λ/12. Verdet constant increased with an increase of Tb content in the garnet composition. When x=1.0, the Verdet constant was 307, 196, and 60 rad T−1 m−1 for 532, 633, and 1064 nm, respectively, at each measuring wavelength. These values were about 1.5 times higher than that of the commercially available TGG (Tb3Ga3O12) crystal. Insertion loss of the produced (Tb0.6Y0.4)3Al5O12 and TAG ceramics at 1064 nm was 0.01 and 0.05 dB, respectively, and extinction ratio was 39.5 and 40.3 dB, respectively. These properties were superior to that of the commercial high‐quality TGG single crystal (insertion loss: 0.05 dB, extinction ratio: 35.0 dB).

Linearly polarized pumped passively Q-switched Nd:YVO4 microchip laser for Ince–Gaussian laser modes with controllable orientations

A tilted, linearly polarized laser diode end-pumped Cr4+:YAG passively Q-switched a-cut Nd:YVO4 microchip laser for generating numerous Ince–Gaussian (IG) laser modes with controllable orientations has been demonstrated by selecting the crystalline orientation of an a-cut Nd:YVO4 crystal. The same IG laser mode with different orientations has been achieved with the same absorbed pump power in a passively Q-switched Nd:YVO4 microchip laser under linearly polarized pumping when the incident pump power and the crystalline orientation of an a-cut Nd:YVO4 crystal are both properly selected. The significant improvement of pulsed laser performance of controllable IG modes has been achieved by selecting the crystalline orientation of an a-cut Nd:YVO4 crystal. The maximum pulse energy is obtained along the a-axis of an a-cut Nd:YVO4 crystal and the highest peak power is achieved along the c-axis of an a-cut Nd:YVO4 crystal, respectively, which has potential applications on quantum computation and optical manipulation. The generation of controllable IG laser modes in microchip lasers under linearly polarized pumping provides a convenient and universal way to control IG laser mode numbers with anisotropic crystal as a gain medium.

Creation of twisted terahertz waves carrying orbital angular momentum via a plasma vortex

In this paper a new method for generating twisted terahertz radiation is proposed. The generation of twisted terahertz radiation in a plasma vortex, where the plasma density profile has helical structure, is investigated. The method is described on the basis of angular momentum exchange between plasma vortex and laser beam. The interaction of the vortex plasma and photons causes the laser angular momentum to change. Twisted terahertz radiation is produced at the beat frequency of laser and electron plasma waves. In this process, for Gaussian laser modes, the angular momentum of terahertz wave derives from the plasma vortex, while for the Laguerre–Gaussian it originates in the difference in topological charge of the laser and electron plasma vortex.

Tunable beam shaping with a phased array acousto-optic modulator.

We demonstrate the generation of Bessel beams using an acousto-optic array based on a liquid filled cavity surrounded by a cylindrical multi-element ultrasound transducer array. Conversion of a Gaussian laser mode into a Bessel beam with tunable order and position is shown. Also higher-order Bessel beams up to the fourth order are successfully generated with experimental results very closely matching simulations.

Confinement of ultracold atoms in a Laguerre–Gaussian laser beam created with diffractive optics

We report 2D confinement of 87Rb atoms in a Laguerre–Gaussian laser beam. Changing of the sign of the detuning from the atomic resonance dramatically alters the geometry of the confinement. With the laser detuned to the blue, the atoms are confined to the dark, central node of the Laguerre–Gaussian laser mode. This trapping method leads to low ac Stark shifts to the atomic levels. Alternatively, by detuning the laser to the red of the resonance, we confine atoms to the high intensity outer ring in a multiply-connected, toroidal configuration. We model the confined atoms to determine azimuthal intensity variations of the trapping laser, caused by slight misalignments of the Laguerre–Gaussian mode generating optics.

Coherent optical vortices from relativistic electron beams

The interaction between light and a relativistic electron beam can be used to generate optical vortices in a free electron laser, providing a way to engineer bright orbital angular momentum light at shorter X-ray wavelengths. Recent advances in the production and control of high-brightness electron beams (e-beams) have enabled a new class of intense light sources based on the free electron laser (FEL) that can examine matter at ångstrom length and femtosecond time scales1. The free, or unbound, electrons act as the lasing medium, which provides unique opportunities to exquisitely control the spatial and temporal structure of the emitted light through precision manipulation of the electron distribution. We present an experimental demonstration of light with orbital angular momentum (OAM; ref. 2) generated from a relativistic e-beam rearranged into an optical scale helix by a laser. With this technique, we show that a Gaussian laser mode can be effectively up-converted to an OAM mode in an FEL using only the e-beam as a mode-converter. Results confirm theoretical predictions3,4, and pave the way for the production of coherent OAM light with unprecedented brightness down to hard X-ray wavelengths for wide ranging applications in modern light sources.

Shaping Laguerre–Gaussian laser modes with binary gratings using a digital micromirror device

Laguerre-Gaussian (LG) beams are used in many research fields, including microscopy, laser cavity modes, and optical tweezing. We developed a holographic method to generate pure LG modes (amplitude and phase) with a binary amplitude-only digital micromirror device (DMD) as an alternative to the commonly used phase-only spatial light modulator. The advantages of such a DMD include very high frame rates, low cost, and high damage thresholds. We have shown that the propagating shaped beams are self-similar and their phase fronts are of helical shape as demanded. We estimate the purity of the resultant beams to be above 94%.

Conjugation and transformation of the wave front by stimulated Brillouin scattering of vortex Laguerre — Gaussian laser modes

We study experimentally stimulated Brilluoin scattering (SBS) of vortex laser beams, namely, the LG11 and LG01 Laguerre -Gaussian modes. The wave front transformation is experimentally demonstrated in the case of SBS of the LG11 laser mode, directly focused into the SBS cell, when the fundamentalGaussian mode LG00 rather than the conjugate mode is selectedfrom the Stokes beam. It is shown that optical vortices become phase conjugate by destroying the laser mode structure in the SBS cell. Phase conjugation (PC) of the LG01 and LG11 modes is obtained in the SBS mirror using a regular aberrator (microlens raster) in the system of laser beam focusing into the SBS cell.

Quantum state for the two-variable Hermite polynomial–Gaussian laser modes of the electromagnetic field

AbstractIn Ref. [7] by using the plane-wave representation of the fundamental Gaussian mode as a seed function, Enderlein and Pampaloni derived higher-order beam modes (Laguerre–Gaussian laser beams) of the electromagnetic field by acting with differential operators on this fundamental solution. In this paper we show that their approach can be improved by directly performing the integration with the aid of the two-variable Hermite polynomials, in so doing these modes can exhibit some new good characters. Their relationship to the eigenmodes of light propagation in the quadratic graded-index (GRIN) medium is pointed out. By introducing the two-mode entangled state representation the quantum states corresponding to these modes are also found which turns out to be the Hermite-polynomial excitation on the two-mode squeezed vacuum state.

Bose–Einstein condensation transition studies for atoms confined in Laguerre–Gaussian laser modes

Multiply-connected traps for cold, neutral atoms fix vortex cores of quantum gases. Laguerre–Gaussian laser modes are ideal for such traps due to their phase stability. We report theoretical calculations of the Bose–Einstein condensation transition properties and thermal characteristics of neutral atoms trapped in multiply connected geometries formed by Laguerre–Gaussian (LG p l ) beams. Specifically, we consider atoms confined to the anti-node of a LG 0 1 laser mode detuned to the red of an atomic resonance frequency, and those confined in the node of a blue-detuned LG 1 1 beam. We compare the results of using the full potential to those approximating the potential minimum with a simple harmonic oscillator potential. We find that deviations between calculations of the full potential and the simple harmonic oscillator can be up to 3%–8% for trap parameters consistent with typical experiments.

Dynamic size tuning of multidimensional optically bound matter

We generate and dynamically control one-, two- and three-dimensional optically bound structures of soft matter in the geometry of counter-propagating incoherent laser beams. We report results for the Bessel, Gaussian, and Laguerre-Gaussian laser modes and particularly focus on the influence of the lateral dimensions of the beam profile on the resulting self-arranged optically bound structures. Employing the transfer of the orbital angular momentum of light in the Laguerre-Gaussian beams, we show that optically bound structures can conserve their spatial arrangements even while orbiting along the beam circumference.

Derivation of the Frantz-Nodvik Equation for Diode-Side-Pumped Zigzag Slab Laser Amplifiers With Gaussian Laser Mode and Pump Beam Shapes

The theory for Gaussian beam pulse propagation in a zigzag slab amplifier with a Gaussian pump distribution is detailed. Provisions are made for amplification of an input signal with an elliptical Gaussian spatial mode by modifying the time-dependent photon transport equations as described by Eggleston Frantz, and Injeyan. A comparison is made with experimental results of a diode-side-pumped zigzag slab amplifier element amplifying a near-Gaussian beam.

Analytical solutions for the electromagnetic fields of flattened and annular Gaussian laser modes III Arbitrary length pulses and spot sizes

In the first two parts of this study, the electromagnetic field components were derived for infinitely long, flattened Gaussian laser beams [J. Opt. Soc. Am. B23, 2157 and J. Opt. Soc. Am. B23, 2166 (2006)]. These results are now extended without approximation to allow for finite laser pulses having an arbitrary duration beginning with the standard Gaussian beam profile and then generalizing these results to a flattened Gaussian. The resulting models thus allow for all pulse durations and spot sizes from infinite, paraxial beams to single-cycle, wavelength-size spots, with a savings of more than 2 orders of magnitude in computation time. Pulses having fewer than ten cycles exhibit significant modification from the monochromatic fields as a result of the finite bandwidth. Specifically, the energy in the focus is shown to decrease from the theoretical value of 86.5% to as low as 72.2% for a single-cycle pulse.

Analytical solutions for the electromagnetic fields of flattened and annular Gaussian laser modes I Small F-number laser focusing

Many laser interaction models assume that incident focused laser fields are Gaussian and use either the approximate TEM00 series model or the exact integral Gaussian angular-spectrum solution. Many practical laser systems, however, produce flat-top transverse intensity profiles, and indeed, such profiles are often desired. Here, an exact, integral solution is derived for all of the vector components having a general flattened Gaussian profile using the angular-spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The resulting integrals are solved for tight focusing conditions exactly by making use of a Fourier-Gegenbauer expansion. This technique follows closely that of Sepke and Umstadter [Opt. Lett.31, 1447 (2006)] but, by redefining the expansion coefficients, the simplicity of the model is greatly enhanced and the computation time reduced by roughly a factor of 2 beyond the 2 orders of magnitude improvement obtained previously. This series solution is stable at all points and converges after S∼20w0 terms, where w0 is the 1/e waist normalized to the laser wavelength.

Analytical solutions for the electromagnetic fields of flattened and annular Gaussian laser modes II Large F-number laser focusing

A spherical Hankel function series solution for the vector components of a general flattened Gaussian laser field is derived, based on the angular spectrum of plane waves. This perturbative series is valid for spot sizes greater than ten wavelengths, creating a complete vector solution for a general flattened Gaussian laser profile for all focusing conditions when coupled to the model developed in Part I of this investigation [J. Opt. Soc. Am. B23, 2157 (2006)]. The focusing and propagation properties of these fields are then explored numerically. Finally, the exact solution is compared to the perturbative Hermite-Gaussian (0,0) laser mode by comparing the focal plane boundary conditions imposed in each and is found to be a separate and distinct solution under tight focusing conditions.

Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes

The exact vector integral solution for all the electromagnetic field components of a general flattened Gaussian laser mode is derived by using the angular spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The integrals are of the form of Gegenbauer's finite integral and are computed analytically for each case, yielding fields satisfying the Maxwell equations exactly in the form of quickly converging Fourier-Gegenbauer series.