6.5. CONCLUSION 66
success-6.5. CONCLUSION 67 fully demonstrated to produce RP or AP doughnut modes with output power up to 60mW. The output can be easily switched between the radial and azimuthal polarization by horizontal translation of the intra-cavity lens. PER of the output up to 100:1 was observed. Propagation factor, M2 = 2-2.5 confirms mode purity.
Apart from the fundamental RP and AP doughnut modes, various other circular mode structures including AP or RP rings and modes combinations with mixed polarizations (AP and RP) can be produced from the same scheme. Using intra-cavity short focus lenses with spherical aberrations together with the birefringent crystal a sequence of hollow AP or RP modes of high orders have been obtained.
The large variety of beams with axially symmetric polarizations from the output of the proposed laser scheme may find interesting applications in different fields.
7
Conclusion
While researchers have always viewed spherical aberrations in laser cavity as a disadvantage, we have come up with an optimistic approach and demonstrated a method to exploit the same for generation of high-order modes. In the dis-cussions so far, we have reported successful mode selection using a plano-convex lens as the mode selecting element in an Yb:YAG ceramic laser cavity. Mode se-lection in scalar Laguerre-Gaussian (LG) modes, modes with near-diffraction free propagation characteristics and radial and azimuthally polarized modes have been demonstrated.
The varying focal length across the refracting surface of a plano-convex lens in the presence of spherical aberration transforms the point focus of the ideal lens into a line focus. This changes the stability conditions of the intra-cavity lens resonator and changing on the position of the lens inside the resonator, allowed mode selection in various high-order modes. When the initial conditions of the resonator were set such that focal length conditions were satisfied at one of the cavity mirrors for annular rings of increasing diameter along the lens surface, the corresponding increase in mode radius at the other cavity mirror/output coupler resulted in continuous selection of hollow scalar LG modes with increasing az-imuthal orders. The highest possible azaz-imuthal mode order was l = 27 restricted by the diameter of the cavity optics. This is definitely a breakthrough since the 68
7.1. SCALAR LAGUERRE-GAUSSIAN BEAMS 69 proposed methods in literature have not offered practical possibility of generating modes with l ≥5.
Apart from the dominant focusing condition at the cavity mirror, for significant shifts of the lens from its initial position at reference focus, the imaging condition at the mirror was also stable. The cavity modes exhibited coupling because of aperture guiding at the gain element and the narrow stability region that resulted under these conditions generating beams with near-diffraction free properties at their central parts similar to that of Bessel-like beams. The near-diffraction prop-erties unlike the Bessel beams do not have a limited propagation distance. The properties are verified to exist to over tens of meters and no changes have been observed with propagation distance.
Polarization properties are associated with the modes generated from the cavity by introducing a uniaxial crystal and discriminating either the ordinary or extra-ordinary ray at the cavity stability limits generating modes with radial and az-imuthal polarization properties. The doughnut modes generated from this scheme showed excellent polarization contrast ratio as high as 100:1 in certain cases. Apart from the doughnut AP and RP modes, high-order AP and RP modes and rings were also generated from the same laser scheme by mere shift of intra-cavity lens.
Output containing a combination of AP and RP modes were also generated for the first time.
In the following parts of the chapter we shall discuss the applications of the high-order modes that we generated using the proposed scheme. We will also elaborate on the future prospects and points of improvement to the work.
7.1 Scalar Laguerre-Gaussian beams
Hollow LG beams are vastly exploited as optical tweezers for macroscopic particles, where the transfer of orbital angular momentum leads to rotation in a direction determined by the helicity of the beam. The vortex nature of these beams is ex-ploited in the study of optical solitons. These types of laser modes also produce
7.2. BEAMS WITH NEAR-DIFFRACTION FREE CHARACTERISTICS 70 atom traps. Magneto-optical traps have been demonstrated using a combination of LG01 (donut-mode) beams and very weak Gaussian beams. This leads to an increase in the number of trapped atoms due to a decrease in collisions between ground-state and excited-state atoms that lead to trap loss. LG beams are also used for optical dipole traps. While previous experiments confine atoms in the cen-ter of a donut-mode beam, there is recently considerable incen-terest in high-order LG beams as toroidal traps for Bose-Einstein condensates. Confinement of multiple condensates in the concentric, multiply connected traps formed by high-order LG modes allows observation of vortices by matter-wave interference.LG beams are also extensively used to write optical waveguides in atomic vapors. While several methods of generating LG beams have been proposed since the 1960’s, the search for efficient methods has not stopped because of the complications and cost. Our current work, has brought about an efficient, cost-effective and simple scheme to serve the purpose.
High-l LG modes provide deeper potential wells and tighter confinement of cold atoms in optical traps whereas high-p LG modes experience less diffractive spreading and thus offer a more uniform optical dipole potential for atom guid-ing [75–77]. Recently, possible applications of high order hollow and peaked LGpl modes in laser schemes for gravitational waves detection and for particles accelera-tion were discussed [78,79]. LG modes of higher azimuthal index cause significant narrowing of the line shape of Hanle electromagnetically induced transparency and absorption resonances, which may have several important applications such as atomic clocks, magnetometers, in slow light experiments [80].