Higher-order Laguerre-Gauss Modes Research Articles

Spectrally resolved spontaneous emission patterns of oxide-confined vertical-cavity surface-emitting lasers

Spectrally resolved spontaneous emission patterns of oxide-confined vertical-cavity surface-emitting lasers under the subthreshold condition were investigated. The spontaneous emission mode patterns show clear and stable Hermite–Gaussian modes and high-order Laguerre–Gaussian modes associated with a distinct spectrum. The coexistence of two sets of identical low-order Hermite–Gaussian modes with different spot sizes reveals the presence of two cavity configurations. The data on mode evolution and spot size variation reveal that the modes with larger spots are supported by the cavity with the carrier-induced aperture, and become the dominant modes above the laser threshold; the modes associated with smaller spots are considered to have been formed by the cavity with the oxidized aperture and are suppressed above the threshold.

Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser

Intra-cavity binary phase elements are incorporated into a Q-switched Nd:YAG laser resonator to obtain efficient high-order transverse mode selection. The resonator configuration is analyzed using the propagation-matrix diagonalization method and the Fox-Li algorithm, and a simple model for predicting the relative output powers of the selected modes is developed. The predicted results are verified experimentally with binary phase elements for selecting the TEM/sub 01/, TEM/sub 02/ and TEM/sub 03/, degenerate Laguerre-Gaussian modes. The output energy per pulse was 15 mJ for the TEM/sub 01/, 16.5 mJ for TEM/sub 02/ and 18.3 mJ for TEM/sub 03/, all higher than the 10 mJ for the TEM/sub 00/. The performance in Q-switched operation was found to be similar to that in free-running operation. The numerical calculations, experimental procedure and experimental results are presented.

Transverse modes in oxide confined VCSELs: Influence of pump profile, spatial hole burning, and thermal effects

We present experimental studies on the transverse mode emission behaviour of oxide-confined Vertical Cavity Surface Emitting Lasers (VCSELs). VCSELs with aperture diameters of 6um and 11um exhibit a wide variety of emission patterns from low order Hermite- Gaussian modes to high order Laguerre-Gaussian modes. We obtain detailed information about the spatial gain distribution by recording spontaneous emission intensity profiles during lasing operation. We conclude from these profiles, that the spatial carrier distribution is primarily governed by the in uence of pump induced current spreading and is only secondarily in uenced by further effects such as spatial hole burning, and thermal gradients in the laser. The combination of these mechanisms causes a strong tendency towards the emission of high order transverse modes.

Creation of vortices in a Bose-Einstein condensate by a Raman technique

We propose a method for taking a Bose-Einstein condensate in the ground trap state simultaneously to a different atomic hyperfine state and to a vortex trap state. This can be accomplished through a Raman scheme in which one of the two copropagating laser beams has a higher-order Laguerre-Gaussian mode profile. Coefficients relating the beam waist, pulse area, and trap potentials for a complete transfer to the m = 1 vortex are calculated for a condensate in the non-interacting and strongly interacting regimes.

Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes

Laguerre-Gaussian modes of various order are frequency doubled. The azimuthal phase structure of the second-harmonic light is measured directly by interfering the beam with its mirror image. We show that the orbital angular momentum per photon is doubled, so conserving the orbital angular momentum in the light beam. The frequency-doubled output beam is shown to have a Gegenbauer-Gaussian amplitude distribution at the beam waist. The beam can be described as a summation of Laguerre-Gaussian modes that interfere so that it changes form with propagation, but the distribution at the beam waist is reproduced in the far field.

Far-field diffraction of truncated higher-order Laguerre-Gaussian beams

A simple analytic expression for the far-field diffraction pattern of a general high-order Laguerre-Gaussian mode from a circular aperture is derived. Aperturing of the fundamental Gaussian beam is shown as a special case, where in the limit of waist size much larger than the aperture the Airy pattern is recovered and in the opposite limit we get a Gaussian intensity pattern. The diffraction pattern is shown to be an infinite series of Bessel functions and is strongly dependent on the ratio of the aperture area to the beam waist area (also known as the truncation parameter). This formulation leads to a more intuitive understanding of the far field of these modes, and the effect of the aperture as a spatial filter is discussed.

Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes.

Laser light with a Laguerre-Gaussian amplitude distribution is found to have a well-defined orbital angular momentum. An astigmatic optical system may be used to transform a high-order Laguerre-Gaussian mode into a high-order Hermite-Gaussian mode reversibly. An experiment is proposed to measure the mechanical torque induced by the transfer of orbital angular momentum associated with such a transformation.